23 Investment Management

Investment managementN. Instefjord2790023

2005

Undergraduate study in Economics, Management, Finance and the Social Sciences

This guide was prepared for the University of London External Programme by:

Dr Norvald Instefjord, Reader in Finance, Department of Accounting, Finance andManagement, University of Essex.

This is one of a series of subject guides published by the University. We regret that dueto pressure of work the author is unable to enter into any correspondence relating to,or arising from, the guide. If you have any comments on this subject guide, favourableor unfavourable, please use the form at the back of this guide.

This subject guide is for the use of University of London External students registered forprogrammes in the fields of Economics, Management, Finance and the Social Sciences(as applicable). The programmes currently available in these subject areas are:

Access route

Diploma in Economics

BSc Accounting and Finance

BSc Accounting with Law/Law with Accounting

BSc Banking and Finance

BSc Business

BSc Development and Economics

BSc Economics

BSc (Economics) in Geography, Politics and International Relations, and Sociology

BSc Economics and Management

BSc Information Systems and Management

BSc Management

BSc Management with Law/Law with Management

BSc Mathematics and Economics

BSc Politics and International Relations

BSc Sociology.

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Published by: University of London Press

© University of London 2005

Printed by: Central Printing Service, University of London, England

Contents

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ContentsIntroduction 1

Subject guide structure and use 1Aims and objectives 1Learning outcomes 2Essential reading 2Further reading 3Examination structure 3Syllabus 4

Chapter 1: Financial markets and instruments 5Essential reading 5Further reading 5Introduction 5Learning outcomes 13Sample examination questions 14

Chapter 2: The history of financial markets 15Essential reading 15Further reading 15Introduction 15A history of financial innovation 15Learning outcomes 20Sample examination questions 20

Chapter 3: Active fund management and investment strategies 21Essential reading 21Further reading 21Introduction 21Learning outcomes 27Sample examination questions 27

Chapter 4: Market microstructure 29Essential reading 29Further reading 29Introduction 29Learning outcomes 35Sample examination questions 36

Chapter 5: Diversification 37Essential reading 37Further reading 37Introduction 37Learning outcomes 48Sample examination questions 48

Chapter 6: Portfolio immunisation 49Essential reading 49Further reading 49Introduction 49Learning outcomes 56Sample examination questions 56

Chapter 7: Risk and performance measurement 57Essential reading 57Further reading 57Introduction 57Learning outcomes 63Sample examination questions 63

Chapter 8: Risk management and VaR based portfolio insurance 65Essential reading 65Further reading 65Introduction 65Put option protection 65Put-call parity 66Volatility hedging 67Learning outcomes 70Sample examination questions 70

Appendix 1: Technical terms 71

Appendix 2: Sample examination paper 77

Investment management

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Introduction

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IntroductionFinance is essentially about pricing financial assets but this subject guidefocuses more on what we use pricing theory for from an investmentperspective. We seek to apply pricing theory (among other things) to tell ussomething about how to invest our money optimally in financial assets ratherthan for pricing itself.

For those who want a more thorough overview of pricing theory, see thesubject guide for unit 92 Corporate Finance.

Subject guide structure and useThe guide has eight chapters.

• Chapter 1 introduces the reader to financial markets and instruments.

• Chapter 2 surveys some of the history behind the innovation of newfinancial instruments and the return that investors have historicallyachieved from holding various classes of financial assets.

• Chapter 3 surveys some of the empirical findings regarding active fundmanagement and investment strategies. We look at the performance ofmutual funds, the performance of certain popular contrarian andmomentum investment strategies, and finally we look at the investmentstrategies of hedge funds.

• Chapter 4 surveys some of the literature on market microstructure, withthe emphasis on how the bid-ask spread is formed in financial marketsand on how speculators seek to optimally benefit from their informationadvantage.

• Chapter 5 discusses optimal investment for investors using optimaldiversification strategies.

• Chapter 6 discusses risk immunisation strategies to remove some or allrisk factors from the investor’s portfolio.

• Chapter 7 discusses risk and performance measurement.

• Chapter 8 looks at portfolio insurance strategies and value-at-risk basedrisk management strategies.

Aims and objectivesThis subject guide is designed to introduce you to the investmentenvironment in the role of a private or professional investor. This moduledoes not cover pricing theory, which is a major part of unit 92 CorporateFinance. Instead it emphasises the use of pricing theory in investmentmanagement. It aims to:

• provide an overview of institutional details linked to financial marketsand the trading process

• provide an overview of historical trends and innovations in financialinstruments and trading processes

• provide an overview of various financial instruments

• provide insight into the use of finance theory in investmentmanagement

• provide a guide to the measurement and analysis of risk of financialinvestments

• provide a guide to the measurement of performance of fundmanagement

• address key issues in risk management.

Learning outcomesOn completion of this subject, you should be able to:

• list the key types of financial instruments and their characteristics

• list key historical trends in markets, interest rates, financial instrumentsand trading

• describe the effects of diversification in stock portfolios

• explain how to immunize bond portfolios from interest rate risk

• design portfolio insurance strategies using option pricing theory

• outline the effects of risk aversion

• apply key financial risk measures

• describe important problems associated with measuring the risk takenby and the performance of professional fund managers.

Essential readingAt the start of each chapter in this subject guide we recommend your readingin two categories, essential reading and further reading, each containingboth textbooks and journal articles.

BooksThere are a number of good textbooks available. The following text is inmany ways the most comprehensive and will form the main bulk of yourrequired readings:

Bodie, Z., A. Kane and A.J. Marcus Investments. (Boston, Mass.; London:McGraw-Hill Irwin, 2005) Sixth International Edition [007123824;0072861789 (pbk)].

Another excellent text with emphasis on portfolio theory and investments,perhaps a bit more technical than Bodie, Kane and Marcus, is:

Elton, E.J., M.J. Gruber, S.J. Brown and W.N. Goetzmann Modern PortfolioTheory and Investment Analysis. (New York; Chichester: John Wiley & Sons,2003) sixth edition [ISBN 0471428566].

Finally, a text with more focus on corporate finance and risk management, is:

Grinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,Mass.; London: McGraw Hill Irwin, 2002) second edition [ISBN 0071123415].

JournalsIt is essential that you support your learning by reading as widely as possibleand by thinking about how these principles apply in the real world. To helpyou read extensively, all external students have free access to the Universityof London online library where you will find either the full text or an abstractof many of the journal articles listed in this subject guide. You will need tohave a username and password to access this resource. Details can be foundin your handbook or online at: www.external.shl.lon.ac.uk/index.asp?id=lse

Barclay, M.J. and J.B. Warner ‘Stealth Trading and Volatility: Which TradesMove Prices?’, Journal of Financial Economics 34: 281–305, 1993.

Glosten, L.R. and P.R. Milgrom ‘Bid, Ask, and Transaction Prices in a SpecialistMarket with Heterogeneously Informed Agents’, Journal of FinancialEconomics 14: 71–100, 1985.


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Further reading

BooksAssness, C., R. Krail and J. Liew Do Hedge Funds Hedge? 2001.Brown, S.J. and W.N. Goetzmann Hedge Funds with Style. (National Bureau of

Economic Research, 2001) [ASIN B0006RM8G6]Duffie, D. and K.J. Singleton Credit Risk: Pricing, Measurement and Management.

(Princeton University Press: 2003) [ISBN 0691090467], chapter 1.

JournalsBasak, S. and A. Shapiro ‘Value-at-Risk-Based Risk Management: Optimal Policies

and Asset Prices’, Review of Financial Studies, 2001.Chan, K., A. Hameed and W. Tong ‘Profitability of Momentum Strategies in the

International Equity Markets’, Journal of Financial and Quantitative Analysis,35: 153–172, 2000.

Grinblatt, M., S. Titman and Wermers ‘Momentum Investment Strategies,Portfolio Performance, and Herding: A Study of Mutual Fund Behavior’,American Economic Review 85: 1088–1105, 1995.

Grinblatt, M. and S. Titman ‘Mutual Fund Performance: An Analysis ofQuarterly Portfolio Holdings’, Journal of Business 62: 393–416, 1989.

Kyle, A.S. ‘Continuous Auctions and Insider Trading’ Econometrica 53:1315–1335, 1985.

Madhavan, A. ‘Market Microstructure: A Survey’, Journal of Financial Markets 3:205–258, 2000.

Mehra, R. and E.C. Prescott ‘The Equity Premium: A Puzzle’, Journal ofMonetary Economics, 15: 145–162, 1985.

Siegel, J.J. and R.H. Thaler ‘Anomalies: The Equity Premium Puzzle’, Journal ofEconomic Perspectives, 11, 1997.

Examination structureImportant: the information and advice given in the following section arebased on the examination structure used at the time this guide was written.Please note that subject guides may be used for several years. Because of thiswe strongly advise you to always check both the current Regulations forrelevant information about the examination, and the current Examiners’reports where you should be advised of any forthcoming changes. Youshould also carefully check the rubric/instructions on the paper you actuallysit and follow those instructions.

The Investment management examination paper is three hours in durationand you are expected to answer four questions, from a choice of eight.

A full sample examination paper appears as an appendix to this guide. Thisunit will be examined for the first time in 2006. After that, if the ChiefExaminer wishes to make any change(s) to the format, style or number ofquestions for this examination paper, you will be notified about this in thelast paragraph of the Examiners’ Report, available on the web (a printedversion will also be sent to you).

You should ensure that four questions are answered, allowing anapproximately equal amount of time for each question, and attempting allparts or aspects of a question. Remember to devote some time prior toanswering each question to planning your answer.

Introduction

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SyllabusExclusions: This unit has replaced unit 121 International financial marketsand may not be taken if you are taking or have passed unit 121 Internationalfinancial markets. If you have failed unit 121 and wish to transfer to unit 23,your fail on unit 121 will count as one of the three chances you have to passthe new unit.

Prerequisites: You must have already taken unit 24 Principles of Bankingand Finance (or unit 94 Principles of Banking for students registeredbefore 1 September 2005). Unit 23 must also be taken with or after unit 92 Corporate Finance.

The syllabus comprises the following topics:

1. Financial markets and instruments: money and bond markets; equitymarkets; derivative markets; managed funds; exchange traded funds;exchange trading and OTC trading; clearing; settlement, margin trading,short sales and contingent orders; regulation of financial markets

2. History of financial markets: history of financial innovation; case studiesin innovation; historical investment returns; equity premium puzzle.

3. Active fund management and investment strategies: historical mutualfund performance; market efficiency and behavioural finance; returnbased trading strategies; hedge funds.

4. Market microstructure: bid-ask spread; inventory risk; adverse selection;optimal insider trading; stealth trading hypothesis; why microstructurematters to investment analysis.

5. Diversification: expected portfolio return and variance; risk premium;risky/risk free capital allocation; minimum-variance portfolio frontier;market portfolio; expected return relationships; Treynor-Black model;factor models.

6. Portfolio immunisation: term structure of interest rates; duration;immunisation of equity portfolios.

7. Risk and performance management: types of risk; regresssion methodsfor measuring risk; value-at-risk; risk adjusted performance measures; m-squared measure; performance measurement with changing portfolios.

8. Risk management and VaR based portfolio insurance: put optionprotection; put-call parity; volatility hedging; Basak-Shapiro model.


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Chapter 1: Financial markets and instruments

Essential readingBodie, Z., A. Kane, and A.J. Marcus. Investments. (Boston, Mass; London:

McGraw-Hill Irwin, 2005) sixth international edition [ISBN 007123824;0072861789 (pbk)], chapters 1, 2, 3, 4, 14, 20, 22, 23.

Further readingGrinblatt, M. and S. Titman Financial Markets and Corporate Strategy. (Boston,

Mass.; London: McGraw Hill Irwin, 2002) second edition [ISBN 0071123415], chapters 1, 2, 3.

Elton, E.J., M.J. Gruber, S.J. Brown and W. N. Goetzmann Modern PortfolioTheory and Investment Analysis. (New York; Chichester: John Wiley & Sons,2003) sixth edition [ISBN 0471428566], chapters 2 and 3.

IntroductionFinancial assets are distinct from real assets in that they do not generate aproductive cash flow – that is what real assets do. Examples of real assets are:a block of flats that can be let to provide the owner with future rentalincome; the rights to manufacture and sell a particular product generatingfuture sales revenue; or a particular piece of computer software thatgenerates future sales and registration income. Examples of financial assetsare: a loan that is used to fund the acquisition of the block of flats and whosepayments are financed by the rental income; or equity capital used to fundthe research and development costs for the consumer software productsmentioned above. The equity holders benefit in terms of future dividends orcapital gains that are generated from the future sales income of the products.From the point of view of cash flow generation, therefore, financial assets donot have much of a role to play. Financial assets are not neutral in the sensethat they transform the cash flow of real assets for the holder. For instance,the loan generates a relatively stable income even though the underlyingcash flow is risky. Also, the loan might have enabled the investor to raisesufficient funds for investment in the first place. We trade financial assets,therefore, to ‘repackage’ or transform the cash flow of real assets – eitherthrough time or across states of nature.

There is also another important job that financial assets do – they enable usto separate the functions of ownership and control of real assets. As a rule,real assets do not just passively generate a cash flow – they need to bemanaged. A company owns a collection of real assets. The job of managingthese is highly specialised and it is necessary that it is done by a professional.This individual may or may not be the owner of the real assets, so it makessense for the company to keep the ownership and control functions separate.This can be done by issuing equity with claims on the real assets of thecompany – the owners of the company’s equity then become the owners ofthe company – so that the company can hire a professional manager tomanage its pool of real assets.

Who uses financial markets? There are three key sectors:

1. The household sector – you and me – who need to invest for retirementincome or mortgages for house acquisitions and various insuranceproducts, for instance.


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2. The business sector, which consists of firms that need to issue financialclaims on their future cash flow to finance current investments, who needto manage the risk of their business through derivatives trading andinsurance products.

3. The government sector, that has a need to finance public expenditure.This sector is special as it sometimes also intervenes in financial marketsto provide a public policy objective – for instance, influence the interestrate to manage inflation – and additionally by acting as a regulator of theactivity in financial market.

On the other hand, financial markets are not the only way these sectors areserved by financial instrument. Financial intermediaries also provideservices. These are companies such as banks and investment houses who canlend money to, and help companies issue securities, and collect deposits orlend to households, or manage households’ and companies’ funds.

In this chapter, we shall go through a relatively broad range of financialassets (also known as financial instruments), and their key definingcharacteristics.

Money and bond marketsThe simplest form of claim is a bond. A bond is a fixed claim – meaning thatit promises a particular cash flow – normally a coupon payment that is anannual or semi-annual payment measured as a percentage of the principalamount, and then ultimately at maturity the principal repayment. Forinstance, a 10-year 5% bond with principal 100, will pay a coupon paymentof 5% of 100 each year until maturity, or 5, and additionally at maturity, inyear 10, it pays the principal of 100.

The cash flow promised to bond holders comes from the cash flow generatedby real assets. Since the cash flow of real assets is often risky, it may be thatthere is not enough to pay the promised amount at all times. If this happens,the bond may default. In the example above, for instance, the couponpromises a cash flow of 100 to be paid to the bond holders, but if thecorporate cash flow available in year 10, after coupon repayments are made,is only 70 the bond holders stand little chance of receiving their promisedrepayment of 100. The bond defaults, therefore, and the bond holders canexpect to receive at most only 70. Some bonds are, however, practicallydefault-free – for instance, bonds issued by the government (governmentbonds - they are often called treasury bonds in the US and gilts in the UK).

Bond instruments are traded in the money market or the bond market. Thedistinction between these markets is essentially that of the original maturityof the instrument. If a bond was issued with very short maturity – normallyless than six months – it will be traded in the money market. If a bond haslonger maturity it is traded in the bond market. Another distinction is thedenomination of the claim. Normally, money market instruments are tradedin large denominations so as to be out of reach of normal households. Theyare used by banks and corporations to lend and borrow in the short term.Bonds, on the other hand, can be held by households.

Money market instrumentsThe money market consists of fixed-income instruments of relatively shortmaturity. This market also tends to be highly liquid, and instruments can bein very high denominations making it impractical for ordinary people totrade. The players who operated in this market are normally private banks,the central bank, and corporations. There are a number of risk freeinstruments traded, which are issued by the government, such as US treasurybills, certificates of deposits, and commercial papers.


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Treasury bills (T-bills) initially have a maturity of 28, 91, or 182 days (approxone, three, and six months). Treasury bills have two atypical characteristicsthat set them apart from many of the other money market instruments. Theynormally sell in low denominations of US$ 10,000, making them tradeableby individuals.

A certificate of deposit (CD) is a deposit with a bank that has a clearlydefined time limit, so cannot be withdrawn on demand. These are, therefore,very similar to T-bills only they are issued by a private bank instead of thegovernment. CDs are in denominations of US$100,000 or greater, and inmaturities of 3 months or shorter. Although there is a theoretical default riskon CDs, they are treated as normal bank deposits, so will be subject togovernmental deposit insurance schemes.

A commercial paper is another short term fixed income security that issimilar to the ones we have looked at above but is issued by corporations.There is a default risk associated with these instruments, but often they arebacked up by a bank line of credit so the borrower can access funds to pay offthe commercial paper at maturity. These instruments are also often rolledover at maturity, such that the old commercial paper is paid off by issuing anew one. The denominations are in multiples of US$100,000 so commercialpapers are rarely traded by individuals.

An important source of very short term financing used to trade governmentbonds is the repo market (and the mirror Reverse market). A repo (RP) is arepurchase agreement where a dealer sells government securities overnightto an investor and promises to buy the security back the next day at a given(and slightly higher) price. The transaction is, therefore, equivalent to a 1-day loan agreement, since the agreement provides a cash inflow today to theseller (as will be the case of a loan) against a specified cash outflowtomorrow (as will be the case when repaying a loan). These agreements arealso very secure to the buyer in the agreement (in this case he plays the roleof a lender), who holds the government bond overnight which serves ascollateral in the case the borrower cannot raise sufficient funds to buy backthe bond as promised. A reverse repo is the mirror image, a buy transactionheld overnight under the promise of selling the securities the next day.Longer agreements are called term repos, and are used for loans up to 30days or more.

Another important short term financing market is the LIBOR market (theLondon Interbank Offered Rate) which is the rate at which large banks inLondon are willing to borrow and lend money. Access to this market is ofcourse restricted but the LIBOR rate has become very important as areference rate, and many short-term fixed income instruments with a floatingrate tie their rates to the LIBOR (i.e. the rate is LIBOR plus a margin).

Bond market instrumentsThe bond market also offers fixed income securities, only at longer maturitiesthan the money market instruments. A very large part of this market consistsof government bonds – these are debt instruments with paymentsguaranteed by the government. These bonds are important because theyoffer investors claims that are in effect risk free, and they are important tothe government because they provide an important source of borrowing.Common bonds are Treasury bonds and bills (issued by the US government)and Gilts (issued by the UK government). The UK government bond marketalso trades two very unique types of bonds: consol bonds (bonds with noredemption date, they are in effect a perpetual loan that pays a coupon rateforever); and index linked bonds (bonds where the repayments - coupons


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and capital repayments - are index linked to the inflation rate). The yield ofindex linked bonds is the closest we get to a direct estimate of the realinterest rate.

Zero-coupon bonds are bonds that have no coupon payments. These bondsalways trade below par value (the nominal value of the loan) because of thetime value of money. If the interest rate is 5%, the value of a 5-year zero-coupon bond equals the discounted capital repayment. If the par value is100, the current price of the bond is 78.35:

100

Price = 78.35 =

(1.05)5

The convention in quoting bond prices is to adjust for accrued interest. Thismeans that the bond price you actually pay is in general not equal to thebond price that is quoted in the financial pages. The price you pay is thequoted price plus the accrued interest. The adjustment for accrued interestinvolves stripping the bond price of the first coupon payment. Consider twobonds – one bond has maturity 11 years less one day and the other maturity10 years plus one day. Both bonds have an annual coupon with rate of 5% -the holders of the first bond has just received a coupon payment 1 day ago,and the holders of the second bond is due a coupon payment shortly in 1day’s time. Suppose the discount rate is also 5%. The actual prices of the twobonds are

100 + 5Price first bond = = 100.013

(1.05) 364

365

100 + 5Price second bond = = 104.986

(1.05) 1

365

At the time of the next coupon payment, the bonds trade at exactly par valuesince the coupon rate equals the discount rate. But because of the differencein the timing of the coupon the actual prices are different. The accruedinterest for the two bonds is given by the formula

days since last coupon paymentAccrued interest = coupon payments x

days separating coupon payments

We find, therefore, the following quoted prices for the two bonds

1Quoted price first bond = 100.013 - 5 = 100.00

365

364Quoted price second bond = 104.986 - 5 = 100.00

365

The adjustment for accrued interest makes the prices comparable.

Bonds are fixed securities but they often feature call provisions. Gilts oftenhave call provisions determining the redemption date so that the UKgovernment may retain flexibility to redeem the bond within given timeintervals. It is common in these circumstances to treat the redemption dateas the first date in the redemption interval if the coupon rate is greater thanthe current market rate (so that the loan is relatively expensive compared to


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the current rate for the UK government) and conversely as the last date inthe redemption interval if the coupon rate is less than the current marketrate.

Equity marketsEquity is, as opposed to a fixed claim like a bond, a residual claim. Thismeans that it has a cash flow that is in the form of the residual cash flow ofthe real asset after all fixed claim with promised payments are paid off. Forinstance, if a business is financed by a 10-year bond in addition to its equity,the equity holders have a claim on the business net of the cash flow that ispromised to the bond holders. The equity claim is the means by whichownership and control for corporations are separated. When we refer to theowners of a corporation we mean the owners of the corporate equity and notthe owners of the corporate debt, although both have claims of the cash flowof the firm. The owners of the equity are, however, normally not directlyinvolved in the running of the corporation – this is the job of the executivemanager who is hired to do precisely this job. Therefore, the ownership isseparated from the control function in corporations. The manager is hired ona long-term basis (although he may be fired at short notice) whereas theowners of the equity can decide for themselves whether they wish to investlong-term or short-term in the corporation. The separation of ownership andcontrol is, therefore, a simple way to achieve a long-term stable managementstructure even if the owners of equity are all short-term investors. Inpartnerships (such as many accounting and legal practices) it would create agreat deal of operational upheaval to have ongoing ownership changestaking place.

We can say, however, that the equity holders have more influence on therunning of the company than the debt holders. The direct influence of anindividual equity holder is nonetheless limited. An equity holder normallygets the right to vote in general meetings. This means in practice that he getsthe chance to influence a few very important decisions such as largeinvestment projects or decisions related to corporate mergers and takeoverthrough his vote, and also to influence the choice of who sits on the non-executive board of directors (NED). The NED has a direct oversight on theexecutive management team of the corporation, and it is essentially throughrepresentation on the NED that shareholders get their main influence in therunning of the firm. A lot of measures aimed at strengthening corporategovernance are aimed at making the NED more effective in overseeing theexecutive management team.

Initially, companies issue equity that is owned privately (i.e. it is not listed ona stock exchange) by an entrepreneur, a family, or by venture capitalists. Theprocess of making private equity public normally involves the corporationseeking listing of its equity on a stock exchange. The equity can thereafter betraded freely by all investors. The first time a company seeks a listing is calledan Initial Public Offering (IPO). Subsequent equity issues are called seasonedissues, and these are much less involved than the IPO since the equity hasbeen traded for a while before the issue. If the company sells existing equity(for instance if the government sells equity that is already issued but fullystate owned) in the IPO or during a seasoned issue, we call it a secondaryissue. If new equity is issued, we call it a primary issue. Sometimes thecompany needs to raise additional capital when it goes public, and in thiscase it is necessary to make some of the issued equity a primary issue.Otherwise, the issue is primarily a process of transferring equity from theinitial owners to the new investors.


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Equity instrumentsEquity instruments consist of stocks – common stocks or preferred stocks – inpublicly traded companies. The two most distinctive features are that theyare residual claims and that an owner can exercise the right to limitedliability (i.e. the owner can decide to relinquish his claim on the realunderlying assets and instead hand these over to the other claimholders). Aresidual claim is a claim that is unspecified, it will be determined as theresidual of the total corporate cash flow net of all fixed claims. Therefore, ifthe corporate cash flow is £100m, on which the debt holders have a fixedclaim of £75m, the residual cash flow due to the equity holders is the residual£100m - £75m = £25m. The implication of the fact that equity is a residualclaim is that its value can never exceed the value of the total real assets of thefirm. The implication of the fact that the equity holders can exercise the rightto limited liability is that the value of the equity can never become negative.

Common stock and preferred stock differ in two respects. First, commonstock holders normally have voting power in general meetings whereaspreferred stock holders have not. Second, the claim of preferred stockholders has seniority over that of common stock holders. Thus, if thecompany wishes to pay dividends to its common stock holders it must alsopay a dividend to its preferred stock holders first.

Common stock is often split into two classes (dual-class shares), usuallycalled A and B shares. These classes differ in their voting power, where oneclass (normally A shares) have superior voting power relative to the otherclass. The reason dual-class share structures are introduced is that acontrolling family may wish to retain the majority of the voting power whilstat the same time may diversify by selling B shares to outside investors. Dual-class share structures are relatively rare in the US and the UK but canfrequently be found on the continent and in Japan.

Derivatives marketsBonds and equity claims are claims that perform a dual role. For the issuer(businesses, banks, or governments), these claims are a means of raisingcapital used for investment or expenditure. For the investors, these claims aremeans of smoothing real cash flows across time and states. Derivatives areinstruments that do not really play a direct role as a means of raising capital– that is, these instruments are in zero net supply. If no buyer exists for aparticular derivative instrument, then also no seller exists. Derivatives are,therefore, almost exclusively used for risk management purposes.

Derivatives are also sometimes called contingent claims. The cash flow ofderivatives is almost always linked to the price of a primary asset such as abond or an equity claim – the underlying asset. In this sense, therefore, thecash flow is a function of, or contingent on, what happens to the price of theunderlying asset. However, recently we also observed derivatives that had acash flow contingent on other events, such as the event that a bond defaults(credit derivatives), or the event that the weather is bad (weatherderivatives).

There are three broad types of derivative claims – futures (forwards), swaps,and options. If you enter into a futures or forward agreement, you effectivelyundertake the obligation to buy or sell an asset at a specified price in thefuture. An option is like a futures agreement, except that you have the rightto buy or sell rather than an obligation. This implies that you have the right


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to opt out of the transaction if you own an option but must always carry thetransaction out if you own a futures contract. A swap is an undertaking toswap one cash flow for another cash flow.

Managed fundsManaged funds represent, in essence, a delegation of the investment decisionfrom the individual investor to a professional fund manager. We distinguishbetween active and passive funds, fixed income and equity funds, and open-end and closed-end funds.

An active fund is one where the fund manager typically makes investmentdecisions that are in the form of bets – the manager might think that certainsectors or certain stocks are better bets than others and influences the fund’sinvestments to these sectors or stocks. A passive fund is one where the fundmanager typically attempts to mimic a broad stock market index (like theFTSE 100 in London and the Standard&Poor 500 in New York). Thisnormally amounts to physically holding the index or a large number of stocksin the index. Open-end funds are funds where the investors clear theirholding directly with the fund. Therefore, if a new investor comes in to buyunits of the fund the fund simply issues new units. The price the investorpays is the Net Asset Value (NAV) less charges. The NAV is calculated as thetotal net value of the fund divided by the number of units issued to investors.Closed-end funds are funds which have a fixed number of units issued. If aninvestor wishes to buy units in the fund he needs to trade with existinginvestors. Units in closed-end funds have, therefore, a value which isindependent of the value of the assets held by the fund. There havehistorically been price discrepancies between the total value of outstandingunits, and the total net value of assets held by the fund, where units havetraded at a considerable discount relative to their theoretical value.

Exchange traded fundsA fairly new innovation for private investors is the so called exchange tradedfunds. These are typically index tracker style funds, but they are exchangetraded like a stock. This makes it possible for small investors to hold an indexcheaply and efficiently without having to physically diversify by trading alarge number of stocks in small quantities. Examples of exchange tradedfunds are the DIAMONDS fund on the NYSE which delivers the Dow JonesIndustrial Average Stock Index, and the iFTSE100 fund on the London StockExchange which delivers the FTSE 100 Index.

Exchange trading and over-the-counter (OTC) tradingThe process by which financial assets are traded can be divided broadlyspeaking into exchange trading and over-the-counter (OTC) trading.Exchange trading involves investors submitting buy-and-sell orders that areaggregated into some system that allows buyers and sellers to be matcheddirectly. OTC trading involves investors submitting buy-and-sell orders to adealer who acts as an intermediary in the trade. The dealer will normallytake proprietary positions in the stock and thereby expose himself toinventory risk, but over time these inventories cancel out as investors executetrades at both the buy and sell side of the dealer’s inventory. Large stockmarkets such as the NYSE (New York Stock Exchange) and the LSE (LondonStock Exchange) are executing exchange trading of securities, whereas theNASDAQ stock market is an OTC market with a panel of dealers offering bidand ask prices for the listed stocks. In a ‘perfect’ world in which each trader isable to trade at the competitive prices at all times the difference in market


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structure does not translate into any real differences in the execution of thetrade. However, the OTC market structure has been criticised for allowingtrading at the bid and ask prices when there exist limit orders inside thespread that could trade at a better price (so called ‘trading through’), andlarge markets such as the NASDAQ market are working to improve theirsystem. In 1997, the LSE carried out a conversion from OTC trading (muchlike the NASDAQ market structure) to exchange trading using a fullycomputerized limit order system (the SETS system). There is nointermediary at all in this market. The NYSE operates a system in which alimit order book executes most trades but that also a significant portion ofthe trading volume is executed by an intermediary (the so called ‘specialist’)who might improve on the quotes implied by waiting limit orders. Thebenefit of having such an intermediary is that relatively competitive quotesare offered also in stocks that are thinly traded. Chapter 3 of Bodie, Kane andMarcus describes in more detail the securities trading process.

Clearing, settlement, margin trading, short sales and contingentorders

The trading process of stocks has become increasingly sophisticated. Alltransactions taking place on a stock exchange are cleared once a day, wherethe net positions are to be settled. If, for instance, you both buy and sell thesame security over the course of a single day, it is only the net trading thatneeds to be settled. Settlement takes place within 3 working days on theNYSE, so that if you have bought net stock on Monday, you will receive yourshare certificates and pay the outstanding amount on Thursday. You can alsotrade stock on margin, which means that you only pay for a part of thepurchase price and you borrow the rest from your broker. The brokernormally has a working relationship with a bank or a financing house tofinance loans made through margin trading. A margin needs to bemaintained over time. For instance, if you purchase shares initially worth£10,000 on a 60% percentage margin, you need to pay only £6,000 and youborrow the remaining £4,000 from your broker. Suppose your accountstipulates a 50% maintenance margin. If the shares decline in value, supposethey drop to £7,000, your margin would have decreased below 60% also. Themargin is now (£7,000-£4,000)/£7,000 = 43%, so you need to inject moremoney into your account to maintain a margin of 50%. After the repayment,your margin is worth £3,500 and the loan is £3,500.

You can sell a stock you do not own to take advantage of price drops.Technically, it is illegal to sell a stock you do not own but you can circumventthese rules by borrowing share certificates from somebody who already ownsthe stock, which are then short sold. The owner of the share certificates willnormally demand a fee. Fund managers who manage large funds (such aspension funds) are often lending their certificates to investors who wish to goshort in the stock, since these funds do not normally plan to sell the stockanyway. Short selling is used particularly by hedge funds as an integral partof the investment strategy.

You can also instruct your broker to execute contingent buy-and-sell orders.The most common of these are called limit orders, where you instruct yourbroker to buy a certain amount of stock as long as the purchasing price isbelow a certain limit, or to sell a certain amount of stock as long as theselling price is above a certain limit. You can also use so called stop loss andstop buy orders. A stop loss order is an instruction to sell a quantity of a stockas long as the price remains below a certain limit, and a stop buy order is aninstruction to buy a quantity of a stock as long as the price remains above acertain limit. These are used to limit the loss potential of long and short


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positions. For instance, if you own a large quantity of a stock that has alreadyappreciated in value, you may wish to protect your profit by giving a stop lossorder. The sell order comes into effect if the stock price goes below a certainlimit. Similarly, if you have a large short position and you wish to protect theexisting profit you may be giving a stop buy order.

Regulation of financial marketsFinancial markets are heavily regulated – laying down rules to the way tradecan be conducted. Because we often speak of the ‘free market’ it is easy toforget how strict the rules are that govern financial trading. Regulation isboth in the form of self-regulation (where the organisers of the market setthe rules) and government regulation (where a regulator appointed by thegovernment sets the rules). The reason for regulation is primarily to provideprotection to market participants, particularly those who are relativelyvulnerable to abuse or fraud by other investors, brokers, or exchanges.

What are the main objectives of regulation? The first is to stop companiesreleasing information to investors that is inaccurate or misleading, orreleased in a way that it gives some investors an advantage over others. Thesecond is to make sure ‘unsophisticated’ investors are not taken advantage ofby more professional or sophisticated investors or by advisers or institutionsinvolved in the trading process.

Activity

1. Discuss why we need regulation of markets.

2. If you buy an asset on a 50% margin, how much would you have to pay initiallyif the price is 126p per share and you buy 1000 shares? How much more do youneed to pay if the price went down to 115p per share?

Learning outcomesAfter reading this chapter and the relevant readings you should be able to:

• describe the distinction between residual (equity) claims and fixed(bond) claims

• explain the difference between primary (debt and equity) claims andsecondary (derivative) claims

• describe the difference between IPOs (initial public offerings) andseasoned offerings

• explain the difference between primary offerings of equity and secondaryofferings of equity

• explain the distinction between exchange trading of securities and OTC(over-the-counter) trading of securities

• describe the differences between money market instruments and bondmarket instruments

• describe the way in which an owner of common stock of a company caninfluence how it is run

• describe the difference between open-end and closed-end managedfunds.


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Sample examination questions1. Explain the difference between exchange trading and over-the-counter

(OTC) trading of an asset.

2. Explain the typical characteristics of, and the differences between, debtclaims, equity claims, and derivative securities.


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Chapter 2: The history of financial markets

Essential readingBodie, Z., A. Kane, and A.J. Marcus Investments. (Boston, Mass.; London:

McGraw-Hill Irwin, 2005) sixth international edition [ISBN 007123824;0072861789 (pbk)], chapter 5.

Siegel, J.J. and R.H. Thaler ‘Anomalies: The Equity Premium Puzzle’, Journal ofEconomic Perspectives, 11, 1997.

Further readingAllen, F. and D. Gale Financial Innovation and Risk Sharing. (Cambridge, Mass.;

London: MIT Press) 1994, chapter 2.Mehra, R. and E.C. Prescott ‘The Equity Premium: A Puzzle’, Journal of

Monetary Economics, 15: 145–162, 1985.

IntroductionHere we look at the historical and empirical evidence surrounding financialmarkets and assets. The first part surveys the innovations regarding financialinstruments and the trading process in financial markets. The second partsurveys the history of investment returns on financial assets. Three questionsare addressed in particular:

• what return can investors expect to earn when investing in various typesof financial assets?

• what are the risk characteristics of these returns?

• are returns and risk characteristics linked?

An interesting issue is the historic relationship between the risk and returnon various instruments. If investors are risk averse we expect to find theydemand compensation for holding risky portfolios. This will be discussed inrelation to the so called ‘equity premium puzzle’.

A history of financial innovationMany early civilisations made use of loan agreements between individuals,and in the old Babylonia and Assyria there were at least two banking firms inexistence several thousand years BC Equities and bonds were developedduring the sixteenth century. Convertible securities also have a long history.In continental Europe in the sixteenth century there existed equity issuesthat could be converted into debt if certain regulations were broken.Similarly, preferred stock has been in use for a long time. Exchange tradingof financial securities also has a surprisingly long history. Equity was tradedin Antwerp and Amsterdam in the 1600s. Moreover, options and futures(called time bargains at the time) were traded on the Amsterdam Bourseafter it was opened in 1611.

Many of the European stock markets experienced major stock market bubblesin the eighteenth century. A famous example is the South Sea Bubble (1720)where the price of the South Sea Company rose from 131% of par inFebruary to 950% by June 23, then fell back to 200% by December. Thisbubble led to the so called Bubble Act which made it illegal to form acompany without a charter or to pursue any line of business other than theone specified in the charter.


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Recent financial innovationsThe 1960s witnessed a number of innovations driven by regulatoryconstraints. The Eurobond market emerged where non-US companies couldborrow in US $. At the time foreign borrowers were excluded from the USmarkets. Similarly, currency swaps were developed during this period tocircumvent UK exchange controls. The 1970s witnessed the introduction offloating-rate instruments (bonds with coupons tied to a floating rate such asthe LIBOR rate in London), and the trading of financial futures, such asfutures on foreign currency, futures on interest rates, and futures on stockmarket indicies.

Often, the innovation of new securities is initially driven to circumventregulatory constraints or to exploit market demand for new types of claims.Once they become established, however, the investors find they have other,broader, advantages that make them a useful addition to the financialsystem. Below you can find a few case studies of new innovations.

Case study 1: Floating rate debtFloating-rate notes were first issued in 1970, and it was an instrument thatwas linked to a floating reference rate – the London Interbank Offered Rate(LIBOR). These instruments came in during a period where inflation riskbecame a serious threat, so the nominal rate would fluctuate dramatically.Allowing loan rates to vary in accordance with these fluctuations was anatural response. In the mid-1970s the market for floating rate debt startedgrowing significantly, and these instruments were fairly widely used in theearly 1980s. Most floating-rate debt is issued in the European market, andthese instruments have never been particularly popular in the US. A spin-offinnovation is floating-rate preferred stock – a preferred stock in which thedividend yield is linked to the variations in the reference rate.

Case study 2: Zero-coupon bondsThese bonds were first issued in the 1960s, but they did not become popularuntil the 1980s. The use of these instruments was aided by an anomaly in theUS tax system, which allowed for deduction of the discount on bonds relativeto their par value. This rule ignored the compounding of interest, and leadsto significant tax-savings when the interest rates are high or the security haslong maturity. Although the tax-loophole was closed fairly quickly, the bondswere desirable to investors because they were very simple investment tools.For a bond that has interim coupon payments the investor would have toreinvest these coupon payments – and there may be considerable risk tied tothese reinvestment strategies. A zero-coupon bond has no reinvestment risk.

Case study 3: Poison pill securitiesThe popularity of corporate acquisitions and mergers has promoted theemergence of a number of anti-takeover techniques. Some of these havetaken the form of financial innovations. One of the earliest was the so calledpreferred stock plans. With these, the target company (the one that thebidding company seeks to acquire) issues a dividend of convertible preferredstock to its shareholders which grants certain rights if the bidding companybuys a large position in the target firm. These rights might be in the form thatthe stockholders can require the acquiring firm to redeem the preferred stockat the highest price paid for common stock in the past year. If the takeoveractually goes through, the highest price will almost certainly be the takeoverprice, and the acquiring company must, therefore, issue a number of new


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stock at the takeover price in exchange for the old preferred stock alreadyissued. This will, obviously, dilute the gains of the takeover to the acquiringparty and reduce the likelihood of a takeover.

Another poison pill security is the so called flip-over plan. This consists of theissue of a common stock dividend consisting of a special right. This rightenables the holder to purchase common stock at an exercise price well abovethe current market price. Normally, nobody would exercise these rights asthe exercise price is high compared to the current market price. However, inthe event of a merger, they ‘flip-over’ and give the right to purchase commonstock at an exercise price well below the current market price. Again, thismakes takeovers costly as the bidder’s profits from the takeover are heavilydiluted by the exercise of the flip-over plans.

Case study 4: SwapsThe first swaps emerged in the 1960s and were currency swaps, and theyemerged like many other innovations on the back of regulation. In this case,a UK based multinational company might have a surplus of funds in the UKthat it wished to invest in a US subsidiary but was prevented due to UKexchange controls. A counterparty in the US with the opposite problem, asurplus of US funds but a need to invest in a UK subsidiary, could often beidentified. Since regulation prevented a straight transfer within eachcompany, the companies could circumvent the rules by simply using parallelloans – the US firm promised to lend dollars to the UK subsidiary against theUK firm promising to lend pounds to the US subsidiary. A major problemwith these arrangements soon emerged, however, which was that there wasa considerable amount of counterparty risk involved. A company might haveentered into the agreement fully solvent but might experience problems inthe interim period before expiry. If one party defaulted, would the otherparty still be obliged to fulfil their part of the arrangement? This deficiencycould be overcome by the swap agreement, where in principle the companiesdeposited money with each other and paid the interim interest payments toeach other according to the prevailing interest rates in the two currencies,and finally the principal amount is cleared at the end of the agreement. Theinterim payments are normally netted out using the prevailing exchange rate,so there is only one payment made.

The swap agreement has also been modified to agreements involvingswapping cash flows of adjustable (floating) rate loans and cash flows offixed rate loans. Principal payments are in this case not made in the sameway as currency swaps – these are also netted out so that the swapagreement effectively consists of a series of single payments.

Case study 5: Futures tradingThe standardised financial futures contracts are a relatively recentinnovation, in contrast to the older, forward style agreements that haveexisted since the emergence of a financial system. An important feature ofthis contract is the way it is traded, which makes it easy for investors to enterand exit existing futures agreements in between the start of the contract andthe maturity date of the contract. More importantly, however, is that futurestrading allows investors to shift large amounts of risk with very littleinvestment. Futures trades are, therefore, highly levered. For example,margin trading of equity typically involves a margin of 50%, so even if theinvestor can borrow he still needs to finance half the investment cost (andfurther margin calls if the stock price goes down). With futures positions,investors normally maintain margins less than 10% of the face value of the


17

futures contract. The futures contract is marked to market each day, so theinvestor can unwind his position (sell if the original transaction was a buyand vice versa) and his account is settled with no further cash flows takingplace.

Investment returns in equity and bond marketsWhat returns have investors historically made in the bond and equity marketsaround the world? We have about a hundred years of data on stock marketreturns, and the brief answer globally is that the countries most devastatedby World War II had the lowest long-run cumulative returns - Italy, Belgium,Germany and Japan. The countries that experienced the least damage, incontrast, have the highest long run cumulative returns - Australia, Canada,and the US. However, the real returns (corrected for inflation) are prettymuch similar across all countries.

A major theoretical prediction from pricing models is that the expected oraverage return on assets is linked to the risk of holding these assets. Again,the overall empirical evidence supports this prediction. Looking, for instance,to the US experience from 1926 to 2002, we find the following.

Asset type Geometric average Arithmetic average return return

Small-company 11.64% 17.74%stocks

Large-company 10.01% 12.04%stocks

Long-term 5.38% 5.68%treasury bonds

US T-bills 3.78% 3.82%

Inflation 3.05% 3.14%

Table 2.1

For a review of geometric and arithmetic averages, see Appendix 1. If wecompare the numbers in Table 2.1 against the variance of returns, we findthe following.

Asset type Arithmetic average Standard deviation return return

Small-company 17.74% 39.30%stocks

Large-company 12.04% 20.55%stocks

Long-term 5.68% 8.24%treasury bonds

US T-bills 3.82% 3.18%

Inflation 3.14% 4.37%

Table 2.2

Among asset classes, therefore, there is a clear relationship between risk andreturn (inflation is not an asset). The more risk the investor takes on, thegreater is the compensation in terms of expected or average return. This canbe explained by risk aversion – that investors are unwilling to take(actuarially) fair risk.


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The equity premium puzzleThe return on equity is greater than the return on bonds because the risk issmaller. What has been found, however, is that the difference (the so calledequity premium) appears to be bigger than should be expected. Thefollowing example from US stock and bond markets is compelling. A personwho invested $1000 in Treasury bills on December 31, 1925 and kept it insafe US Treasury bills until December 31, 1995 would have an investment in1995 worth $12,720. If the money were invested in the stock market thecorresponding number is $842,000 (66 times the amount for T-bills).Considering that the equity investment would have survived two large stockmarket crashes (one in 1929 and another one in 1987), the difference isstrikingly large.

How should we compare a risky investment with a risk free one? One way todo this is by assuming a risk averse investor holds both risk free T-bills andrisky equities in his portfolio (for a review of utility theory and risk aversion,see Appendix 1). The premium on the equity is then compensation for hisrisk aversion. The greater the premium is, the greater the risk aversion of theinvestor must be. Using historical data, we can therefore make inferencesabout the risk aversion of investors. Risk aversion is measured by the riskaversion coefficient, formally derived from the utility function by therelationship

u’’ (x)Risk aversion coefficient = -

u’ (x)If the investor has CARA (constant absolute risk aversion) utility the utilityfunction takes the form

u (x) = - exp (- x)

The risk aversion coefficient is in this case (as the CARA name suggests), aconstant

If asset returns are, moreover, normally distributed, we can write theexpected utility function as

Suppose a CARA investor is indifferent between holding large-companystocks and long-term US Treasury bills over a long period of time. Then thefollowing expression must hold

which is solved for a risk aversion coefficient of 4. This is a fairly reasonablenumber, but asset returns are not normal so we cannot use this simple modelto estimate the implied risk aversion coefficient. This is the motivation forMehra and Prescott’s study. They fit a rigorous theoretical model to data onthe return on stock market investments and government bonds. The modelgenerates the risk aversion coefficient of a representative investor (seeAppendix 1 for a review of risk aversion and the risk aversion coefficient).They found that a reasonable estimate for the risk aversion coefficient isbetween 30 and 40. This is way too high, as a risk aversion coefficient of 30


19

)var(2

)())(( xxExuE =

22 )0318.0(2

0382.0)2055.0(2

1204.0 =

implies, for instance, that if the investor is facing a gamble where he has a50% chance of doubling his wealth and a 50% chance of halving his wealth,he would be willing to pay up to 49% of his current wealth to avoid thegamble, i.e, if his current wealth is 100, he would be indifferent betweenpaying 49 and keeping 51 for sure, and a gamble where there is half chanceof receiving 50 and half chance of receiving 200. In practice, it would bedifficult to find anybody not preferring the gamble in this case.

Can the equity premium puzzle be resolved? Mehra and Prescott might havesampled data that were special in two senses. First, it might have been tooshort so there is a possibility that the period was in some sense too ‘special’ tomake safe inferences about the implied risk aversion coefficient. Their workhas been extended to include data all the way back to 1802. The mainfinding of this exercise is that the real returns of short-term fixed incomehave fallen dramatically over time. The real excess return on equity would,therefore, on average be about one percentage point lower than thatreported by Mehra and Prescott. This will of course reduce the magnitude ofthe risk aversion coefficient but it is doubtful that the puzzle would becompletely resolved.

The second way the data might have been special is that the time series aretoo long. This might lead to survivorship bias in the data. When collectingmasses of data we inevitably sample those data-series that have survived fora long time. The long-surviving data series would also tend to be ‘healthier’and show average returns that are higher than the perceived expectedreturns at historical points in time. Investors might reasonably worry aboutthe risk of a crisis or catastrophe that can wipe out the entire marketovernight. And indeed, of the 36 stock exchanges that operated at the early1900s, more than one-half experienced significant interruptions or wereabolished outright up to the current time. Hence, the equity premium mightinclude some bias if estimated by long time series of data. Again,survivorship bias might be a source of some errors in the estimation of therisk aversion coefficient but it is unclear how much it contributes.

Activity

1. Explain the role of poison pill securities and discuss whether this is a helpfulinnovation of financial securities.

2. The historical evidences point to the fact that riskier securities have a greateraverage return. Explain why.

Learning outcomesAfter reading this chapter, you should be able to:

• describe some examples of innovations of financial securities

• describe in rough detail the historical evidence relating to the return onequity and the return on bonds

• describe the so called ‘equity premium puzzle’.

Sample examination questions1. What is a zero-coupon bond? What makes a zero-coupon bond often a

more attractive investment vehicle for investors than a coupon bond?

2. Explain, in words, the ‘equity premium puzzle’.


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Chapter 3: Active fund management and investment strategies

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Chapter 3: Active fund management andinvestment strategies

Essential readingBodie, Z., A. Kane, and A.J. Marcus Investments. (Boston, Mass.; London:

McGraw-Hill Irwin, 2005) sixth international edition [ISBN 007123824;0072861789 (pbk)], chapters 4 and 12.

Further readingAssness, C., R. Krail, and J. Liew ‘Do Hedge Funds Hedge?’ Journal of Portfolio

Management. 2001.Brown, S.J. and W.N. Goetzmann Hege Funds with Style. 2001Grinblatt, M. and S. Titman, ‘Mutual Fund Performance: An Analysis of

Quarterly Portfolio Holdings’, Journal of Business 62: 393–416, 1989.Grinblatt, M. and S. Titman ‘Wermers: Momentum Investment Strategies,

Portfolio Performance; Herding: A Study of Mutual Fund Behavior’,American Economic Review 85: 1088–1105, 1995.

Chan, K., A. Hameed and W. Tong ‘Profitability of Momentum Strategies in theInternational Equity Markets’, Journal of Financial and Quantitative Analysis,35: 153–172, 2000.

IntroductionInvestors do not always invest directly in financial assets. Sometimes they useportfolio or fund managers to invest on their behalf. Professional investors orfund managers now control the bulk of private investment in financial assets,and its sheer size has made this sector a subject of a lot of research.

This chapter will provide an overview of the empirical evidence of fundmanagement and investment strategies. In particular, we will discusswhether there is empirical foundation for the notion that fund managersprovide value for money, and whether various types of investment strategies(e.g. technical trading strategies, or the so called contrarian or momentumstrategies) yield abnormal returns.

Among all the evidence surrounding investment strategies to gain long termsustainable trading profits we find a long list of anecdotal stories ofindividuals making huge trading profits in inventive, ad hoc, ways. They areof course interesting in their own right, but it should be noted that they dealnormally with trading opportunities that can be exploited only once. TheEconomist 2004 Christmas Special surveys some cases of exceptionallyprofitable single trades. An interesting observation is that the cases fall intoone of two categories – a normal trader spotting an unexpected arbitrageopportunity, or a large trader using a window of opportunity to exploit hismarket power. An example of the former is the case of the Italian nationalLudovico Filotti who worked for Barings Bank in London. While on holiday inItaly in 1993 Mr Filotti discovered a new savings scheme (guaranteed by theItalian government) issued by Italy’s Post Office offering a very high returnrelative to the Italian government bonds. Although aimed at ordinaryinvestors, the Post Office had not barred institutions from investing in suchbonds. Having borrowed by selling Italian government bonds, Mr Filotti flewpersonally to Italy with a bankers’ draft of $50m into a post office to invest inthe Post Office bonds. The trade made a huge profit and is a classic exampleof an arbitrage transaction – where a trader buys an asset cheaply in one


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market and sell it expensively in another. An example of a large traderexploiting market power is the case of George Soros who in 1992 bettedagainst the UK Pound Sterling staying in the European Exchange RateMechanism (ERM). He borrowed heavily in pounds to invest in othercurrencies, forcing the Bank of England to use its reserves to buy pounds toprop up the exchange rate. Eventually, the pressure on the Bank of Englandreserves became so huge the government decided to withdraw the poundfrom the ERM, netting Soros a profit of around $1bn after unwinding hisposition.

These cases are atypical and one view is that they are also likely to becomeless frequent as the financial system becomes more integrated and global,and as the capital markets become more efficient. This view is supported bythe evidence of active portfolio management.

Historical mutual fund performanceThere is a long-standing academic literature that has analysed theperformance of fund managers. We discuss the measurement problemsassociated with this task later on in this subject guide, but note already herethat it is in general very hard to obtain accurate assessments of fundmanagers despite the fact that the outcome of their decisions (the return onthe portfolio) is normally very easy to obtain. The difficulties are linked totwo factors. First, it is difficult to lay out exactly what the benchmark for‘normal’ or ‘expected’ performance should be. We know that in financialmarkets, expected returns depend on the risk of the asset. A good way toboost the average return is, therefore, simply to take more risk. This is ofcourse not necessarily a good decision. Second, there is an awful lot of ‘noise’in financial markets that make investment returns very uncertain regardlessof whether the investment decision was a good one. A good decision may,therefore, easily end up losing money over a given time period, and a baddecision might easily yield a profit. To sift the good investment decisionsfrom the bad ones in such an environment is, therefore, very difficult.

Nonetheless, the broad picture from the US is the following. Measuringmutual fund performance against a broad stock market index shows thatmore often than not the broad stock market index outperforms the medianfund manager. In addition, of course, investors investing in a mutual fundwill pay management fees which they are not liable to when holding theindex. Since 1971 the compound return on a broad stock market index hasbeen 12.2% versus 11.11% for the average fund. Over such a long period,and excluding management fees, this difference is very large.

Although the average fund might not provide much value for money for theinvestor, it may be that the best funds can. Several studies have examinedwhether funds which perform better than the average over a two-year periodis also likely to perform better than the average in the subsequent two-yearperiod.

Study Initial period Successive period

Top half Bottom half

Goetzmann/Ibbotson Top half 62.0% 38.0%Bottom half 36.6% 63.4%

Malkiel 1970s Top half 65.1% 34.9%

Bottom half 35.5% 64.5%

Malkiel 1980s Top half 51.7% 48.3%

Bottom half 47.5% 52.5%

Table 3.1


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These results demonstrate that whereas winners and losers among fundmanagers have a tendency to remain within their group over time, the effectseems to be vanishing over time. The study based on the 1980s data setshows that past winners are almost equally likely to become future winnersas future losers. Similarly, past losers are almost equally likely to be futurewinners as future losers. Fund management performance appears, therefore,to have become more and more associated with luck than with skill.

Market efficiency and behavioral financeThe results need to be evaluated against our view of the market. So far, wehave implicitly been thinking about the market as a rational price settingmechanism (somewhat similar to the market maker in the Glosten/Milgrommodel outlined in Chapter 4). This view of the market is formalised in theefficient market hypothesis, which stipulates that the prices are so called‘random walks’ relative to the current information set embedded in theprices. The random walk hypothesis is very easy to understand – if themarket ‘thinks’ the price should go up in the future, it will adjust immediatelyto reflect this information. The future price becomes, therefore, equally likelyto go up as to go down from the current level. There is no predictabilityabout the price movements any more. It is also easy to see where the efficientmarket hypothesis should come from. If there were predictability in pricemovements, investors would immediately compete against each other to buyassets that they predict will go up in price and sell assets they predict will godown. Consequently, competition drives prices towards the efficient pricelevels.

This notion has been formalized into the so called ‘efficient markethypothesis’, which comes in three different versions, the weak-form, the semistrong-form, and the strong-form:

• the weak-form efficient market hypothesis states that stock prices reflectall information in past and current prices and transaction volumes. Futureprice movements are, therefore, unpredictable on the basis of informationabout these. This rules out, among other things, making consistenttrading profits on the basis of so called ‘technical analysis’. We know thattechnical trading is very popular among practitioners, but of course theefficient market hypothesis does not predict that profits cannot be madeat all, only that you make roughly the same number of profitable trades asyou make losing trades

• the semi strong-form efficient market hypothesis states that stock pricesreflect all publicly available information, which includes, in addition topast and current prices and volumes, company and industry data such asaccounting and market data as well as broad economic indicators such asinterest rates, currency rates, inflation, and unemployment. Semi strongefficiency rules out making consistent trading profits on the basis of socalled ‘fundamental analysis’

• finally, the strong-form efficient market hypothesis states that allinformation, public and private, is reflected in the current prices. Thereare both practical and theoretical reasons why we should not expectmarkets to be strong-form efficient. On the practical side, there are manyrestrictions on insider trading making it difficult for those who haveprivate information to benefit from speculation. Thus, there are barriersin place preventing private information to reach the market. On thetheoretical side, if we assume prices are strong-form efficient, there is noincentive to spend resources acquiring private information. There isreason to believe, therefore, that prices can never reach strong-formefficiency (this is the so called Grossman-Stiglitz paradox).


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What are the implications of the efficient market hypothesis on fundmanagement performance? Only if professional fund managers have betterinformation (or a finer information set) than is currently embedded in theprices, should they reasonably expect to make trading profits. A trader inpossession of superior information who trades against an uninformed marketexpects to make superior trading profits. Of course there will be someinformation leakage due to the fact that trading activity is detectable by theuninformed market participants but this process is not perfect so someprivate information remains hidden, and this is the basis for the superiortrading profits. An assessment of the performance of mutual funds withinthis framework is, therefore, essentially an assessment of whether the fundmanager is in possession of sufficient amount of hidden private informationto make substantial trading profits. The private information needs to comefrom somewhere, however, and fund managers spend enormous resourceson acquiring such information (through research, fundamental, andtechnical analysis) each year. It is, therefore, perhaps unreasonable to expectthat fund managers should easily be able to make trading profits over andabove the holding profits of a broad index.

The efficient market hypothesis is itself subject to criticism, however.Empirical evidence demonstrate certain patterns of predictability in assetprices, the most prominent being momentum (prices that have gone up tendto increase further and prices that have gone down tend to decrease further)and overreaction to news and events. For instance, a study found thatportfolios of the best-performing stocks in the recent past (3- or 12-monthholding period) tend to outperform other stocks. The performance ofindividual stocks remains highly unpredictable. The ‘fads hypothesis’ assertsthat the stock market overreacts to news, leading to positive autocorrelationover shorter time horizons while the stock market and a reversal or negativeautocorrelation over longer time horizons. Whilst there is empirical evidenceto support short run momentum effects, the long run reversal effect has lessconclusive empirical support. Studies have found, nonetheless, that whenranking stocks into groups based on their 5-year past performance, the loserportfolio (the bottom 35 stocks) outperformed the winner portfolio (the top35 stocks) by an average of 25% over the subsequent 3-year period.

Where do these patterns come from? The growing field of behavioral financehas built a systematic foundation for the momentum and reversal effectsbased on ‘imperfections’ in the human ability to process new informationrationally. There is substantial evidence to suggest that we tend to add toomuch weight to recent evidence, that we tend to be overconfident (a famousstudy of drivers in Sweden found that 90% of those asked ranked themselvesbetter-than-average), that we are also sometimes too slow to react to news,and finally that our choices are affected by a phenomenon called framing. Anindividual might reject a bet when it is posed in terms of the risk surroundingthe potential gains, but may accept the same bet when it is similarly posed interms of the potential losses. In this case, his decision is affected by framing –i.e. the framework within which the prospect is outlined.

Return based trading strategiesThere is now a rapidly growing literature to assess the profitability ofcontrarian and momentum trading strategies. Jagadeesh and Titman find ina study that stock prices react with a delay to common factors, but overreactto firm-specific information. In chapter 7 we discuss factor models of stockreturns, and the decomposition of the variance of stock returns intosystematic factor-driven risk and idiosyncratic firm-specific risk. This studyincorporates, therefore, both the overreaction element in the stock market’s


25

response to firm-specific news, as well as the conservatism in incorporatingnew information about factor risk. This study finds that most of the short-term profits that can be made by following contrarian trading strategies aredue to the tendency of stock prices to overreact to firm-specific news. Thecontrarian strategy tested was based on buying and selling stocks over onemonth, based on the previous months return. Losers were bought andwinners were sold.

In another study, Conrad and Kaul, analyze a wide spectrum of tradingstrategies that are based on past return patterns, and they find that amomentum strategy is usually profitable at the 3 to 12 month holdinghorizon, whereas a contrarian strategy would generate substantial profitsover long horizons prior to 1947 but not after.

The return based trading strategies can be represented by the following‘weighting’ of individual stocks. Consider investing over the holding period[t-1, t] based on the return over the time interval [t-2, t-1]. Portfolios areconstructed at time t-1 on the basis of a ‘weighting’ scheme using an equallyweighted market index. The weights are constructed on the basis of thefollowing formula

where wi,t-1 is the dollar amount to be invested in stock i, N is the totalnumber of stocks considered, Ri,t-1 is the return of stock i over the timeinterval [t-2, t-1], and Rm,t-1 is the corresponding return of the equallyweighted index. The sign is chosen to reflect the strategy used (plus formomentum strategies and minus for contrarian strategies). By construction,the investment cost of the portfolio following this weighting scheme is zero:

Since the weights are proportional to the deviation of the asset’sperformance relative to the equally weighted market index, they capture theidea that the more extreme deviations lead also to more extreme reversaland momentum effects.

In a study of momentum strategies, Chan, Jegadeesh and Lakonishok findthat that underreaction to information might lead to momentum tradingprofits. In particular, they find that past returns and past earnings surpriseseach can predict large drifts in future returns after controlling for the other.The drifts cannot be explained by market risk, size effects, or book-to-marketeffects. Interestingly, they also find little evidence of a future reversal of thereturns process. They conclude, therefore, that the market reacts slowly tonew information about the earnings flow.

Hedge fundsHedge funds have become increasingly popular investment vehicles, despitethe high profile collapse of the Long Term Capital Management hedge fund(LTCM) in 1998. Hedge funds have no specific definition, but their activity ischaracterised by very flexible investment strategies involving both long andshort positions, often in complex securities. They are, moreover, verydifferent from banks and mutual funds in that they are essentiallyunregulated institutions. Originally they invested mainly in fixed incomesecurities, such as the ‘on-the-run/off-the-run’ strategy employed by LTCM,but increasingly they are heavily involved in equity markets also. The ‘on-the-run/off-the-run’ strategy employed by LTCM is based on the institutional

][1

1,1,1, ±= tmtiti RRN

w

===n

tmtmn

tmtii

ti RRRN

RN

w 011

1,1,1,1,1,

feature of the US government bond market which issues new bonds every sixmonths. Every new auction brings, say, a new 30-year government bond tothe market which investors compete to buy (the bond goes ‘on-the-run’).When the bond is six months old, it becomes a 29.5-year bond and a new 30-year bond is issued. The old bond goes ‘off-the-run’. LTCM observed that thedifference between a 30-year bond and a 29.5-year bond is almostimperceptible, so they should have the same yield. In practice, however,there was a spread that was caused by the fact that when the new bond went‘on-the-run’ and its price was bid up. Therefore, LTCM sold short the new 30-year bond and bought the old 29.5-year bond, to unwind its position sixmonths later when the spread was expected to tighten (the short positionwould now be in a 29.5-year bond that is ‘off-the-run’ and the long positionin a 29-year bond, also ‘off-the-run’). We have also seen hedge funds active inequity positions. An example is the recent Deutsche Börse’s attempt at atakeover of the London Stock Exchange. A bid tabled in early 2005 was laterwithdrawn under pressure from some of Deutsche’s shareholders who werehedge funds. These had allegedly taken long positions in Deutsche and shortpositions in the London Stock Exchange, since they figured that theannouncement of a withdrawal of Deutsche’s bid would cause the LondonStock Exchange’s stock price to fall and the Deutsche’s stock price toincrease. Their long-short position in Deutsche and LSE would, therefore,generate considerable short term trading gains.

Do all hedge funds ‘hedge’? The investment strategy involving market neutrallong-short positions (similar to LTCM’s ‘on-the-run/off-the-run’ strategyabove) is relatively safe and profitable. As long as the spread between thecheap asset held long and the expensive asset held short tends to narrowover time, the position makes money regardless of other market movements.This is a position, moreover, with little net investment of wealth (there arenormally margin requirements so it is impossible to have a zero netinvestment) and little exposure to outside risk factors. Research into hedgefund returns shows, however, that the idea that hedge funds on the wholeengage in long-short market neutral arbitrage trading is misleading. Hedgefunds are a surprisingly heterogeneous group of funds adopting a number ofdifferent ‘styles’. They are, in fact, difficult to define in terms of their tradingstrategies. Brown and Goetzmann find, for instance, that differences ininvestment styles alone account for about 20% of the variability ofperformance across hedge funds. Hedge funds also take in practiceconsiderably risky positions. Asness, Krail and Liew, for instance, find thatreporting practices in hedge funds make them appear less risky and moreprofitable than they actually are. Correcting for misleading reporting, theyfind that hedge fund investments in the aggregate contain a considerableamount of market risk.

Activity

1. Describe, in your own words, the efficient market hypothesis.

2. If markets are efficient, how can we nonetheless expect to make abnormalreturns from trading?


26


27

Learning outcomesAfter reading this chapter, you should be able to:

• describe the historical evidence on mutual fund performance, both interms of average performance and in terms of the expected performanceof past winners and losers

• describe the efficient market hypothesis

• describe the way in which irrationality and bias in the way humansprocess new information leads to momentum and reversal effects in stockprices.

Sample examination question1. Momentum and contrarian trading strategies are so called ‘returns based

trading strategies’. Describe what this means in words, and also design aweighting scheme to determine how much to invest in assets based onsuch strategies.

Notes


28

Chapter 4: Market microstructure

29


Essential readingBarclay, M.J. and J.B. Warner ‘Stealth Trading and Volatility: Which Trades

Move Prices?’ Journal of Financial Economics, 34: 281–305, 1993.Glosten, L.R. and P.R. Milgrom ‘Bid, Ask, and Transaction Prices in a Specialist

Market with Heterogeneous’ly Informed Agents’, Journal of FinancialEconomics 14: 71–100, 1985.

Further readingMadhavan, A. ‘Market Microstructure: A Survey’, Journal of Financial Markets 3:

205–258, 2000.Kyle, A.S. ‘Continuous Auctions and Insider Trading’, Econometrica 53,

1315–1335, 1985.

IntroductionThis chapter looks more closely at market microstructure, which is definedbroadly as the process by which latent demand for trading of a securitytransforms into actual transaction prices and volumes. This means that theliterature is interested in how traders who can benefit from participating inthe market, actually behaves in a given market environment, and how thisbehaviour leads to actual transactions. There is a considerable interest in thisarea as there is increasing evidence that the way in which we design marketshas a huge impact on the way transactions are carried out. Participating intrading has, moreover, become increasingly popular among ordinary people.It is currently possible to trade actively in stocks and bonds from your ownhome computer. Your order will be collected and executed (often completelyelectronically) against other orders that arrive around the same time. Atransaction is then carried out and settled automatically against your bankaccount.

What sort of issues does the market microstructure literature look at? Ofparticular importance are two areas. The first is the way in which so calledinformed traders interact with so called uninformed traders. The second isthe way in which the market structure can be designed such as to minimizethe adverse effects of the conflict between informed and uninformed traders.In this chapter, we will not go very deeply into these issues however, butrather provide an introduction to this field.

Market microstructure effects on transaction pricesAn early observation is that buy transactions tend to be transacted at slightlyhigher prices than bid transactions, that is, buy orders are executed near theask price and sell orders near the bid price. The bid-ask spread, therefore,induces a price process that has negative autocovariance (negativeautocovariance implies that high returns tend to be followed by low returnsand vice versa) even if no new information arrives that causes the traders torevise their price expectations. To see this, consider the case that eachincoming order is equally likely to be a buy order as a sell order. The buyorder is executed at the ask price p

A, and the sell order is executed at the bid

price pB, and the ‘fundamental’ price lies between these prices. The bid-ask

spread is S = pA

– pB. Conditional on a current transaction being at the ask

price, the return between the current price and the price of the nexttransaction is either 0 or –S/p

Aand the corresponding return for the previous

transaction was either 0 or +S/pB. Conditional on a current transaction

being at the bid price, the return between the current price and the price ofthe next transaction is either 0 or +S/p

B, and the corresponding return for

the previous transaction was either 0 or –S/pA

. If we think of all outcomes asequally likely, we get the following table of ‘transition’ probabilities from thereturn of the price process as new transactions are made. The last threeentries in the top row represent the returns between the current price andthat of the next transaction, and the last three entries in the left column, thereturn between the previous transaction price and the current transactionprice.

Transition: -S/pA

0 +S/pB

probabilities

-S/pA

0 0.125 0.125

0 0.125 0.25 0.125

S/pB

0.125 0.125 0

The autocovariance is

Autocovariance = E(Future Return)(Past Return) – E(Future Return) E(Past Return)

S2

= 0.25 – – 0p

Ap

BS2

= – 4p

Ap

B

The price process of stocks contains, therefore, negative autocovariance thatis increasing in the bid-ask spread of the stock.

The bid-ask spreadThe next problem is to explain why there is a bid-ask spread in the market inthe first place. Why doesn’t competition between traders push the transactionsprices of both buy and sell order towards the same level? There are twoanswers to this question, both of which are based on the market makerframework which underpins much of the market microstructure literature. Amarket maker market is one in which there is a trader who is ‘special’ in thathis role is primarily to provide liquidity to incoming traders when there aretemporarily too many buyers or sellers in the market. Traders who arrive dealdirectly or indirectly with the market maker, and the market maker’s primaryrole is to set prices at which the job of clearing the market is done asefficiently as possible. The market maker is normally assumed to operate in acompetitive framework so is not able to capture monopoly profits.

Inventory riskThe first story in explaining the bid-ask spread relates to inventory costsassociated with the excess inventory (positive or negative) of risky stocknecessary to be carried by the market maker in order to clear the market. Forinstance, a buyer might wish to sell 50,000 shares in a stock when there is nobuyer present. The market maker makes the transaction in the hope that abuyer comes around soon, but there is a risk that this will not happen. If itdoes not, the market maker is sitting on a non-diversified holding of a stockwith uncertain value. The market maker, consequently, demands a pricediscount from the seller as compensation for this risk. In practice, this means


30

that when you buy from the market maker, you expect to pay the fair priceplus a premium which gives you the price you pay - the ask price. Similarly,when you sell, you expect to receive the fair price minus a discount whichgives you the price you receive - the bid price. In some markets where there isa panel of dealers active for a broad range of stocks (such as the NASDAQmarket and the London market prior to 1997), variations in inventory acrossdealers lead to variations in their quotes of bid and ask prices. In thesemarkets we might observe that the dealer who has the most competitivequote on the bid side might not have the most competitive quote on the askside. The reason is that the one who has the most attractive bid price isattempting to attract sellers who can fill a temporary short position of thedealer, and the one who has the most attractive ask price is attempting toattract buyers who can offload a temporary long position of the dealer.

Adverse selection – the Glosten-Milgrom modelIf traders have different information there is scope for adverse selectionwhich we will illustrate in the following example. Suppose you want to tradea stock with payoff x. You think there is equal chance the payoff x is 1 or 0, soyou are in principle willing to trade at a price p between 0 and 1 (if you arerisk averse and buying the stock you’d like to trade at a price less than onehalf, and if you are selling you’d like to trade at a price greater than one half).If your trading partner knows for sure whether x equals 1 or 0 you would,however, be better off not trading at all. The reason is as follows. If the truepayoff is 1, you know that your trading partner would always turn down asell transaction at any price strictly lower than 1. The only time he trades is ifhe’s buying, in which case he makes a trading gain and you make acorresponding trading loss of 1-p per unit. Similarly, if the true payoff is 0,your trading partner would turn down any buy transaction at a price strictlygreater than 0. The only time he trades is if he’s selling, in which case hemakes a trading gain and you make a corresponding trading loss of p-0 perunit traded. Consequently, if you trade you make an expected loss regardlessof what the transaction price p is. You would be better off not trading at all.This is called adverse selection – referring to the fact that you would tend toselect a trading counterparty with adverse information.

The market maker faces the same problem if there are informed traders (socalled insiders) among the buyers and sellers who approach the market. Ifinsiders operate, they tend to bunch together on the same side of the market– if they have more optimistic information than the average investors theybunch together on the buy side, and if they have more pessimisticinformation they bunch together on the sell side. This poses a dilemma forthe market maker, who is to clear the incoming order imbalance, as on theone side he provides uninformed traders who trade for liquidity reasons, andon the other he is vulnerable to the activity of insiders. The Glosten-Milgrommodel attempts to take this effect into account when the market maker setsthe bid-ask spread.

The model assumes a sequential arrival sequence, where each trader is eithera liquidity trader who is equally likely to buy or sell or an insider who willbuy or sell depending on his information set. The amount traded is fixed. Themarket maker figures out that whereas the liquidity traders are spreadequally on both sides of the market, the insiders tend to go to one side only.The market maker will, therefore, become worried if consecutive buy or sellorders arrive, and will change his quotes accordingly. The Glosten-Milgrommodel shows the optimal quote-setting strategy for a competitive marketmaker. Suppose the market maker thinks there is a probability p that the nexttrader is an insider and 1-p that the next trader is a liquidity trader. If the


31

next trader is a liquidity trader, he is equally likely to buy or sell. If the nexttrader is an insider, he buys for sure if the asset value is high and sells forsure if the asset value is low. Suppose the asset has a high value of 1 withprobability one half and low value of 0 with probability also one half. Whatare the market maker’s bid and ask prices in this situation?

The answer is given by revising the market maker’s beliefs contingent onselling at the ask or buying at the bid. If a buy order arrives so that themarket maker sells at the ask, he knows that this might have happenedthrough uninformed liquidity trading (with probability (1-p)/2) or it mighthave happened through insider trading (with probability p/2). By Bayes’ rulethe probability that the asset value is low contingent on selling at the ask is

Therefore, the market maker thinks the expected value of the asset,contingent on selling at the ask, equals

If the market maker acts competitively and is risk neutral (zero inventoryrisk), he quotes an ask price that is greater than the (unconditional) expectedasset value of one half. The optimal ask price is (1+p)/2. Similarly, theoptimal bid price is (1-p)/2.

The whole Glosten-Milgrom model is essentially an exercise in revisingbeliefs using Bayes rule. This rule assumes that we have a prior probabilitydistribution of events, then we make some observation that causes us torevise our beliefs, and we end up with a posterior probability distribution ofevents. In the Glosten-Milgrom model, the ‘observation’ is that a traderattempts to trade at the bid or the ask side. Given this observation, themarket maker revises his beliefs about the probability distribution over theasset’s values, and the bid and the ask prices are determined according to theposterior probabilities rather than the prior probabilities. In effect, themarket maker sets the bid and the ask prices in a ‘regret-free’ manner – i.e.the market maker does not regret making the first trade at the ask or the bidas long as these prices are determined by the posterior probabilities.

Bayes rule is given in general by the relationship

and this relationship is the key driving force in the formation of bid and askprices in the Glosten-Milgrom model.

Optimal insider trading – the Kyle modelWe know from the Glosten-Milgrom framework that the bid and the askquotes respond to the relative arrival rates of buy and sell orders. In periodswhere these are fairly balanced, the market maker keeps his bid-ask spreadtight to reflect the fact that insider trading is unlikely. In periods where thereis an imbalance, the market maker responds by making the quotes biasedupwards if there is a buy bias and downwards if there is a sell bias. This poses


32

2p1

p)/4-(1p)/2p)/2-((1

p)/2p)/2-((1

)Low)Pr(Low|AskatPr(Sellgh)High)Pr(Hi|AskatSellPr(

gh)High)Pr(Hi|AskatPr(SellAsk)atSell|Pr(High

+=

++

+=

+=

2p1

02p1

12p1

Ask)atSell|(ValueExpected+

=++

=

Pr(B)

A)Pr(A)|Pr(BB)|Pr(A =

a dilemma for insiders. If an insider trades in small quantities he makes alarge profit per trade as prices remain fairly uninformative, but foregoesquantity-related profits. If he trades in large quantities he makes a biggerimpact on price which reveals more accurately the information of the insider,so he foregoes price-related profits. The obvious question is how to balancethe two. This question is posed in the Kyle model, which we sketch below.This model is much more complicated than the Glosten-Milgrom model as itinvolves more than the process of revising beliefs. It also contains the conceptof equilibrium as there are two players – the insider who trades against themarket maker, and the market maker who seeks to infer from the tradingquantities the information of the insider. The insider’s trading strategy needsto be the optimal one given the market maker’s inference, and the marketmaker’s inference needs to reflect correctly the trading strategy of the insider.

The original Kyle model assumes a normally distributed asset price x, which(irrational) noise traders trade in a quantity y which is also normallydistributed. The assumption that asset prices are normal is of courseunrealistic in the case of equities, as limited liability ensures that the value ofequity can be at least zero. This assumption is, however, convenient in termsof algebra. The assumptions are

where N denotes the normal distribution with the first argument denotingthe expectation and the second argument the variance.

The insider trader trades a quantity z, so that the aggregate market order isthe sum q = y + z, which is observable to the market maker. The marketmaker cannot observe y and z separately, so if he observes a large aggregateof buy orders he does not know whether this is caused by an unexpectedlarge number of noisy buy orders, or by an unexpected large number ofinsider trades. The market maker observes the aggregate market order anddetermines the market clearing price

which equals the expected asset price conditional on the market order q.

A linear equilibrium consists of two functions

where b and d are constants, such that z maximizes the insider’s profits giventhe price function p = dq, and the price function p = E(x|q) given the profitmaximising trading strategy z = bx. We work out the price function first.Suppose the insider uses a linear strategy bx. Then the aggregate order flowis equal to bx plus a normally distributed error term (the demand by noisetraders) which is independent of x. If we regress the asset value x on theaggregate order flow q, therefore, we would obtain the relationship

where the insider’s strategy b is simply the coefficient in this regression.When forecasting x based on observations of q, the market maker finds theoptimal forecast


33

),0(~

),0(~2

2

Ny

Nx

)|( qxEp =

dqp

bxz

=

=

ybqx +=

dqqxE =)|(

where the regression coefficient is given by the covariance between q and xover the variance of q. This can be found in basic econometrics books, but wealso recall the beta-factor in the CAPM model which is defined similarly asthe covariance between the return on the asset and the return on the marketover the variance of the return on the market. The beta-factor is also thecoefficient in a regression of asset returns on the index return (see Appendix 1for a review of regression methods). Using this result, we find that

where the first equality gives us the expression of the coefficient of theregression, the second equality follows by the definition of q = bx + y, thethird equality follows from the fact that x and y are independent, so Cov(y,x)= 0, and the fact that Cov(x,x) = Var(x), and finally the last equality followsfrom our initial assumptions of the distributions of x and y. Therefore, themarket maker’s response to aggregate demand is given by the function

Now we turn to the insider’s problem. The insider observes x first, then hedecides his optimal trading quantity z. For each unit traded, the insidermakes profits

which depend on the asset value (x), the amount the insider decides to trade(z), and the amount the noise traders trade (y). The insider cannot observethe noise traders’ demand y, so he takes an expectation over all outcomes ofy:

where y now disappears as it has zero expectation. The insider is obviouslyinterested in maximizing the expected profit on his trading, so he seeks tomaximize z(x-dz) with respect to the trading quantity z. This yields the firstorder conditions

or equivalently,

where we have substituted for d from the expression above. The constant bis, therefore, give by

where the first equality follows directly from the expression above, and thesecond equality follows from the first by multiplying both sides by thedenominator (2b 2) to get 2b2 2 = b2 2 + r2. Subtracting b2 2 from bothsides of this equation, we find b2 2 = r2. Taking square roots on both sides, wefind b as the ratio of the standard deviation of noise trade (r) over the standarddeviation of the asset value ( ). The full equilibrium is, therefore, given by


34

222

2

2 )()(

)(

)(

),(

)(

),(

+=

+=

+

+==

b

b

yVarxVarb

xbVar

ybxVar

xybxCov

qVar

xqCovd

qbb

qxE+

=222

2

)|(

))(()( zydxzx +=

)()( dzxzxE =

dzx 20 =

bxxb

b

d

xz =

+==

2

222

22

=+

=2

222

2b

bb

qp

xz

2=

=

The greater the ratio of the variance of noise trade to that of the asset value,therefore, the more aggressively the insider trades on the basis of hisinformation. A greater ratio leads to a deeper market however, as the marketmaker’s prices respond less to the volume of demand.

The stealth trading hypothesisThe Kyle model demonstrates that insiders do not necessarily trade veryaggressively to exploit their informational advantage. This is to some extentsupported by empirical evidence. Barclay and Werner look at transactiondata to explore the characteristics of the trades that tend to move prices themost. They find that the very small trades and the very large trades do notmove prices a lot. It is, in contrast, the average sized trades that tend to moveprices. This suggests that insiders attempt to ‘hide’ their information whensubmitting their orders. This is called the ‘stealth trading hypothesis’.

Why market microstructure matters to investment analysisThe market microstructure area suggests that the prices of financial assetsmay not only reflect the underlying ‘fundamental’ value of the asset, theymay also contain components that are specific to the environment in whichthey are traded. We have discussed two such factors, one is that prices tendto become depressed when there is temporarily a lack of buyers in the marketand that prices tend to become inflated when there is temporarily a lack ofsellers. The other is that the bid-ask spread between buy and sell transactionsmay become large when there is a possibility that traders with superiorinformation operate.

Second, if you are a relatively unsophisticated trader with poor information,you are likely to incur specific costs of trading against more sophisticatedtraders, the so called adverse selection costs of trading. There is no obviousway to detect and protect yourself from sophisticated, well-informed traders,as these are likely to adopt techniques to hide their trading activity from theother market participants. This is, however, not necessarily an argumentagainst participating in financial market but it is an argument against tradingvery often. A strategy involving buying and holding a portfolio long term is,therefore, likely to be of benefit unsophisticated traders.

Activity

1. Explain the ‘stealth trading’ hypothesis.

2. Explain, in words, why the bid-ask spread tends to be greater when thelikelihood of insider trading is greater.

Learning outcomesAfter reading this chapter you should be able to:

• describe how the bid-ask spread leads to negative autocorrelation intransaction prices

• work out bid and ask quotes in the Glosten-Milgrom model

• derive the optimal trading strategies of an insider, and the optimal pricesetting strategy of the market maker, in the Kyle model.


35

Sample examination questions1. Suppose the ask price is 1% greater than the current price of 100p per

share, and the bid price is 1% lower. If each transaction is equally likely tobe a buy order as a sell order, what is the autocovariance of transactionprices?


36

23 Investment Management

Documents

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