CHAPTER 5 - Portfolio Theory

7/22/2019 CHAPTER 5 - Portfolio Theory

1/58

CHAPTER 5CHAPTER 5VALUATION CONCEPTS PART IIIVALUATION CONCEPTS PART IIIPORTFOLIO THEORYPORTFOLIO THEORY

Learning outcome

After studying this chapter, you should be able to understand the following:

Introduction to risk management

Portfolios and portfolio theory

Portfolio risk and diversification

Determination of an optimum portfolio

International Portfolio Diversification

Limitations of Portfolio Analysis

Investors preferences Investors indifference curve!

"orrelation of Investments

#fficient frontier of risky investments

"apital $arket Line

Information and the efficiency of capital markets

5.0 INTRODUCTION TO RISK MANAGEMENT

The reality of life is that Businesses do not operate in a perfect world wherethere is no risk. Risk in business, or any activity of life for that matter, issomething everyone who undertakes to do business must be ready toencounter. Risk is a concept that denotes a potential negative impact to anasset or some characteristic of value that may arise from some presentprocess or future event. In everyday usage, "risk" is often used synonymouslywith the probability of a loss or threat. Risk is defined in Websters dictionaryas a !haard# a peril# e$posure to loss or in%ury.& Thus risk refers to thechance that some unfavourable event will occur. In professional riskassessments, risk combines the probability of an event occurring with theimpact that event would have and with its different circumstances.

Risk does not always only refer to the avoidance of negative outcomes. Infinance, risk is only a measure of the variance of possible outcomes.Insurance is a classic e$ample of an investment that reduces risk ' the buyerpays a guaranteed amount, and is protected from a potential large loss.(ambling is a risk increasing investment, wherein money on hand is riskedfor a possible large return, but also the possibility of losing it all. By this

Chapter 5Portfolio Theory

112


2/58

definition, purchasing a lottery ticket such as )ick * lot, is an e$tremely riskyinvestment +a high chance of no return, but a small chance of a huge return,while putting money in a bank at a defined rate of interest is a risk'aversecourse of action +a guaranteed return of a small gain.

(enerally speaking, %isk $anagement is the process of measuring, or

assessing risk and developing strategies to manage it. -trategies includetransferring the risk to another party, avoiding the risk, reducing the negativeeffect of the risk, and accepting some or all of the conseuences of aparticular risk. Traditional risk management focuses on risks stemming fromphysical or legal causes +e.g. natural disasters or fires, accidents, death, andlawsuits. /inancial risk management, on the other hand, focuses on risksthat can be managed using traded financial instruments.

In ideal risk management, a prioritiation process is followed whereby therisks with the greatest loss and the greatest probability of occurring arehandled first, and risks with lower probability of occurrence and lower lossare handled later. In practice the process can be very difficult, and balancingbetween risks with a high probability of occurrence but lower loss versus arisk with high loss but lower probability of occurrence can often bemishandled.

Intangible risk management identifies a new type of risk ' a risk that has a0112 probability of occurring but is ignored by the organiation due to a lackof identification ability. /or e$ample, knowledge risk occurs when deficientknowledge is applied. Relationship risk occurs when collaborationineffectiveness occurs. )rocess'engagement risk occurs when operationalineffectiveness occurs. These risks directly reduce the productivity ofknowledge workers, decrease cost effectiveness, profitability, service, uality,

reputation, brand value, and earnings uality. Intangible risk managementallows risk management to create immediate value from the identificationand reduction of risks that reduce productivity.

Risk management also faces difficulties allocating resources. This is the ideaof opportunity cost. Resources spent on risk management could have beenspent on more profitable activities. *gain, ideal risk management minimiesspending while ma$imiing the reduction of the negative effects of risks.

5.0.1 THE DIFFERENCE BETWEEN RISK AND UNCERTAINTY

In his seminal work "Risk, 3ncertainty, and )rofit", /rank 4night +0560established the distinction between risk and uncertainty.


113


3/58

7 &ncertainty must be taken in a sense radically distinctfrom the familiar notion of %isk, from which it has neverbeen properly separated' ( )he essential fact is that*risk* means in some cases a +uantity susceptible ofmeasurement, while at other times it is something

distinctly not of this character and there are far-reachingand crucial differences in the bearings of the phenomenadepending on which of the two is really present andoperating' ( It will appear that a measurable uncertainty,or *risk* proper, as we shall use the term, is so fardifferent from an un-measurable one that it is not ineffect an uncertainty at all'


114
http://en.wikipedia.org/wiki/Image:Cquote2.pnghttp://en.wikipedia.org/wiki/Image:Cquote1.png


4/58

5.0.2 Ris F!"" I#$"s%&"#%s

(overnment bonds are certainly low risk, but they are not risk'free. There hasto be a government there willing to repay them on maturity. If the revolutioncomes, or the national debt has to be repaid and deposited funds arereuisitioned, or a period of hyper'inflation occur, they will have little value.

8conomies do collapse and governments do fall. 9o country is immune.

5.0.'E("&"#%s )* T)%+( Ris

Whether it is investing, driving, or %ust walking down the street, everyonee$poses themselves to risk. :our personality and lifestyle play a big deal onhow much risk you are comfortably able to take on. If you invest in stocksand have trouble sleeping at nights because of your investments you areprobably taking on too much risk. The chance of financial loss, i.e. assetshaving greater chances of loss are viewed as more risky than those withlesser chances of loss. Investors are risk averse. This means that given two

assets that offer the same return, investors will prefer the less risky one.Thus, an investor will take on increased risk only if compensated by highere$pected returns. ;onversely, an investor who wants higher returns mustaccept more risk. The e$act trade'off will differ by investor. The implication isthat a rational investor will not invest in a portfolio if a second portfolio e$istswith a more favourable risk'return profile ' i.e. if for that level of risk analternative portfolio e$ists which has better e$pected returns.

B,si#"ss Ris

Business risk arises from the nature of the environment in which a companyoperates. It is primarily determined by the general economic conditions to whichthe firm is e$posed and the type of industry in which a company is involved.

(eneral economic conditions refer to variables such as inflation, politicalstability and government regulations. These factors affect all companies withina country. Industry factors are variables that affect specific sectors of theeconomy, for e$ample, the price of copper has a ma%or impact on the coppermining sector, but relatively little influence on the sugar producing industry. It isimportant to note that the management of the firm has very little control over thebusiness risk of a firm.

O-"!+%i# Ris


5/58

use methods such as ;ost'>olume')rofit +;>) analysis to assess the operatingrisk of the firm. ?owever, a comparison between companies in the sameindustry on the basis of ;>) analysis shows that differences e$ist. Thisindicates that management has some degree of control over the cost structure ofthe company.

Fi#+#/i+( Ris

/inancial risk arises from the e$tent to which a firm relies on debt to finance itsoperations. When a firm borrows, it is liable for the interest payments of debt.Whilst operating risk refers to the proportions of the firm@s fi$ed total productioncosts, financial risk is essentially illustrated by the proportion of debt capital tothe total capital of the firm. Interest payments can be thought of as the firm@sfi$ed cost of finance. /inancial risk is entirely under the control of the firm@smanagement.

C!"i% )! D"*+,(% Ris

This is the risk that a company or individual will be unable to pay thecontractual interest or principal on its debt obligations. This type of risk is ofparticular concern to investors who hold bond@s within their portfolio.(overnment bonds, especially those issued by the /ederal government, havethe least amount of default risk and least amount of returns while corporatebonds tend to have the highest amount of default risk but also the higherinterest rates. Bonds with lower chances of default are considered to be!investment grade,& and bonds with higher chances are considered to be

%unk bonds.

C),#%! Ris

This refers to the risk that a country won@t be able to honor its financialcommitments. When a country defaults it can harm the performance of allother financial instruments in that country as well as other countries it hasrelations with. ;ountry risk applies to stocks, bonds, mutual funds, optionsand futures that are issued within a particular country. This type of risk ismost often seen in emerging markets or countries that have a severe deficit.

F)!"i# E/3+#" Ris

When investing in foreign countries you must consider the fact that currency

e$change rates can change the price of the asset as well. /oreign e$changerisk applies to all financial instruments that are in a currency other than yourdomestic currency. *s an e$ample, if you are a resident of Aambia and investin some ;anadian stock in ;anadian dollars, even if the share valueappreciates, you may lose money if the ;anadian dollar depreciates inrelation to the 4wachas.


116


6/58

I#%"!"s% R+%" Ris

* rise in interest rates during the term of your debt securities hurts theperformance of stocks and bonds.

P)(i%i/+( RisThis represents the financial risk that a country@s government will suddenlychange its policies. This is a ma%or reason that second and third worldcountries lack foreign investment.


117


7/58

M+!"% Ris

This is the most familiar of all risks. It@s the day to day fluctuations in a stocksprice. *lso referred to as volatility. arket risk applies mainly to stocks andoptions. *s a whole, stocks tend to perform well during a bull market andpoorly during a bear marketCvolatility is not so much a cause but an effect ofcertain market forces. >olatility is a measure of risk because it refers to thebehavior, or !temperament,& of your investment rather than the reason forthis behavior. Because market movement is the reason why people can makemoney from stocks, volatility is essential for returns, and the more unstablethe investment the more chance it can go dramatically either way.

T)%+( Ris

The total risk of a company is a combination of business, operating andfinancial risks. ;ontrolling the degree of total risk is an important corporate

function. The financial risk is the one variable that a firm can influence.?owever, business risk is determined by the economic environment and is notsub%ect to corporate control whilst operating risk is determined by the natureof the firm@s business activities# hence it is hard to control. )racticale$perience shows that companies with a high degree of business and operatingrisks usually have a low degree of financial risk, while companies with a lowdegree of business and operating risk have more scope for using debt capital.


8/58

non'diversifiable risk. The measurement of non'diversifiable risk is thus ofprimary importance in selecting assets with the most desired risk'returncharacteristics.


119


9/58

5.1 PORTFOLIOS AND PORTFOLIO THEORY

8very financial manager of a business will consider the total risk of the businesscarefully and attempt to manage the risk in such a way that shareholdersreceive the best advantage. /rom an investment analysis point of view,investors consider the most effective way of investing funds. It is well knownthat placing all one@s funds in one investment only is more risky than spreadingthe funds. This is known as diversificationand the different investments, intowhich one diversifies is known as a portfolio of investments.

In the early 05D1@s there was considerable interest in portfolio theory as aninvestment strategy. This theory has been developed further in recent years.

The theory holds that rational investors all hold a portfolio rather than investingin a single investment. The effect of this is that risk is reduced through holdinga portfolio. )ortfolio theory identifies two types of riskE systematic andunsystematic risk. -ystematic +market, non diversifiable, non specific riskrelates to the economy and the stock market as a whole. -hare pricesgenerally are sub%ect to fluctuations. *ny investor who invests in these marketsmust thus be sub%ect to this risk as it cannot be eliminated throughdiversification. 3nsystematic +specific, diversifiable risk relates to specificinvestments. This risk can be eliminated through investing in a portfolio. Fuitesimply, it is based on the principle that some companies will perform well whenothers do badly and vice versa. The differences between company risks can beeliminated but the overall market risk cannot and everyone has to dance to itstune, at least in the short run period.

Get us consider what happens to the risk of a portfolio consisting of a singlesecurity +asset, to which we add securities randomly selected from, say thepopulation of all actively traded securities.

3sing the standard deviation of return, to measure the total portfolio risk, thediagram depicts the behaviour of the total portfolio risk . - A$is as moresecurities are added /- A$is. With theaddition of securities, the total portfoliorisk declines, as a result of the effects of diversification, and tends toapproach a lower limit. Research has shown that, on average, most of therisk'reduction benefits of diversification can be gained by forming portfolioscontaining 0H to 61 randomly selected securities. )he total risk of a security can beviewed as consisting of two parts: )otal security risk 0 1on diversifiable risk 2Diversifiable risk

5.1.1 P)!%*)(i) Ris +# M"+s,!"&"#%

The risk in an investment, or in a portfolio of investment, is that the actual returnwill not be the same as the e$pected return. The actual return may be higher, butit may be lower as well. * prudent investor will want to avoid too much risk, andwill hope that the actual returns from his portfolio are much the same as what hee$pected them to be.


120


10/58

The risk of a security, and the risk of a portfolio, can be measured as the standarddeviation of e$pected of returns, given estimated probabilities of actual returns.

The standard deviation of returns. The standard deviation measures thedispersion around the e$pected value. The larger the standard deviation, thehigher the risk of an investment is considered to be, as a higher standarddeviation infers that there is a greater probability of returns below the

e$pected return. ;onsider the normal distributions for the returns of twodifferent assets * and B illustrated in the figure. Both have been constructedusing 011 data readings of past returns. It is apparent from the summarystatistics and from the graphical representation that asset * carries more risk asthere is a higher chance of earning below the e$pected return of 0H2. *sset Bhas much tighter distribution, with a standard deviation of only 2 and a muchlower chance of earning below 062. *sset * has a greater risk because it has ahigher standard deviation.

What is also apparent is that asset * offers an average return of 0H2 while asset Bonly offers an average return of 062. This is not by chance. Investors demand a

higher return on an asset, which carries risk. This accord with intuition andmarket forces ensures that this relationship is maintained. *ssume fore$ample that both assets had the same e$pected return, but that asset * hasgreater risk as measured by the standard deviation. Rational investors will sellshares in asset * in preference for shares in asset B. This will result in a declinein the share price of asset * +and resultant higher returns for investors whopurchase at the lower price and an increase in the share price of asset B +andresultant lower returns for investors who purchase at the higher price.

TRESPHORD CHAMA

EXAMPLE !

)resphord e3pects that the return from an investment has the followingprobability distribution'

%eturn Probability #3pected %eturn/ 4 P P/

5 6'7 8'986 6'7 7'687 6' 9'68; 6'8 8';

-----88'6

000Re"uire#$


121


11/58

"alculate the


12/58

ANSWER4

The e$pected return is 002, and the standard deviation of the e$pected return iscalculated as followsE the symbol : refers to the e$pected value of the return,002.

Return

6 Y P P7 Y82

J ' 1.6 0.J01 '0 1.6 1.606 0 1.H 1.H0K 1.0 1.5

>ariance .K

-tandard deviation L M .K L 0.JK2

%&%'SA ( CHA%&SHA

EXAMPLE )


13/58

ANSWER

Bi9,s+ S%)/s

R"%,!# P!)9+9i(i% E-"/%" R"%,!# P P

'K 1.6H '0.11 J 1.K1 .1161 1.H D.11

:.20

-tandard NeviationE

Return ;Y P P7;Y82

'K '0.6 1.6H 01.J5 J '0.61 1.K1 1.661 01.J 1.H 0K.65

25.


14/58

E>,+(( W"i3%" P)!%*)(i)

8$pected return L +1.H $ 5.62 P +1.H $ 6.KH2 L H.J2

>ariance L 1.6H +'K2 P 52 $ H Q H.J26P 1.K +J2 P K2 $ H Q H.J26P1 .H +612 ' K2 $ H Q H.J26L 6.DD P .10 P 0.OH L K.K

-tandard deviation L +K.K6L 6.02

,OTE$

)hat the standard deviation of the portfolio is considerably less than that ofeither =ibusa


15/58


126


16/58

EXAMPLE

S'SA, 9'M3E,DA PLC


17/58

ANSWER4

M)s% "**i/i"#% -)!%*)(i)

The method that should be used is to measure risk, as represented by

standard deviation, and e$pected return of each of the possible two assetportfolios. The formula to be used to calculate the standard deviation is theone indicated above for two asset portfolios.

The e$pected return of each portfolio can be calculated usingE

R- @ R+ R9 71;8

WhereE

Rp L 8$pected return of the portfolio

Ra L 8$pected return from investment *

Rb L 8$pected return from investment B

L The proportion of investment * in the portfolio.

The Risk and return for each portfolio can now be calculatedE

B?+(+ F))s +# M,("#+ C)&&,#i/+%i)#s4

Fp L M +0D6 S 1.H6 P +656S 1.H6 P +6S 1.HS1.HS1.1S0DS65

Fp L 0O.J0

Rp L +1.HS00 P +1.HS61 L 0H.H2

B?+(+ F))s +# K)i(" P!i#%"!s

M(172*0.52) + (212*0.52) + (2*0.5*0.5*0.62*17*21)

FpL 0D.06

Rp L +1.HS00 P +1.HS0K L 06.H2

M,("#+ C)&&,#i/+%i)#s +# K)i(" P!i#%"!s

FpL M +656S1.H6 P +606S1.H6 P +6S1.HS1.H S1.K S65 S60

FpL 60.1


128


18/58

Rp L +1.HS61 P +1.HS0K L 0D2.

It is clear that the portfolio containing Bwalya foods and 4oile )rinters is lessefficient than that containing of Bwalya and ulenga since it has both a lowere$pected return of 06.H2 and a higher level of risk of 0D.06. ?owever, it is

not possible to say which of the other two portfolios is the most efficient sincethe Bwalya and 4oile has both a lower risk and a lower return than theulenga and 4oile portfolio. The differences between the levels of risk andreturn for the two portfolios are broadly similar, and hence it is not possibleeven to guess at which may be the most efficient.

5.1.2 P)!%*)(i) Ris +#0 Di$"!si*i/+%i)#

?ow many times have you heard someone say, "Non@t put all your eggs inone basket" When it comes to investing, that@s very good advice. -uccessfulinvestors know that diversifyingtheir investments can help reduce the impactthat a single, poorly performing investment can make on their overallportfolio, or mi$ of investments.

Niversification means having different kinds of investments, such as stocks,bonds, and mutual funds. It also means having a mi$ of investments indifferent sectors or industries. * well'diversified portfolio might includebonds, money market funds, and stocks of small, medium, and largecompanies in a variety of industries and countries. International stocks, fore$ample, may rise at the same time domestic stocks are falling, softening theblow to your overall portfolio. 8ven if your risk tolerance is low, you can stillconsider diversifying into riskier investments as long as you keep the overallrisk of your portfolio low.

*n important first step in building a well'diversified investment portfolio isdeciding how to divide your money among various investments ' a processcalled asset allocation. These types of investments can include individualstocks and bonds, mutual funds that invest in stocks or bonds, or bankaccounts or money market mutual funds.

/inancial professionals such as stockbrokers, financial planners, or insuranceagents can help you analye your financial needs and ob%ectives andrecommend a mi$ of appropriate investments. To help an investor determinethe mi$ of investment options that may be appropriate for his investmentgoals, he should probably be asking the following uestionsE

What are my investment goals ?ow much time do I have to reach these goals ?ow much can I afford to invest regularly ?ow much do my assets need to grow to reach my goals

?ow much investment risk am I willing to take to reach my goals


129


19/58

Niversification is essential for successful investors who have multiple goalswith different time horions. /or e$ample, a 1'year'old unmarried investor islikely to need a different investment mi$ than a H1'year'old with two childrenheading off to college in the ne$t few years. If you are retired, protecting yourprincipal becomes increasingly important as opposed to growing yourinvestments.

Niversification is akin to *not putting all your eggs in one basket'* /ore$ample, if an investors portfolio only consisted of stocks of technologycompanies, it would likely face a substantial loss in value if a ma%or eventadversely affected the technology industry. There are different ways todiversify a portfolio whose holdings are concentrated in one industry. ?emight invest in the stocks of companies belonging to other industry groups.?e might want to allocate his portfolio among different categories of stocks,such as growth, value, or income stock.

Niversification reuires an investor to invest in securities whose investmentreturns do not move together. In other words, their investment returns have

a low correlation. The correlation coefficient is used to measure the degree towhich returns of two securities are related. /or e$ample, two stocks whosereturns move in lockstep have a coefficient of P0.1. Two stocks whosereturns move in e$actly the opposite direction have a correlation of '0.1. Toeffectively diversify, an investor should aim to find investments that have alow or negative correlation.

S+&-(" A!"ssi$" Ass"% A(()/+%i)#

*n aggressive asset allocation is most suitable for investors with a long'terminvestment horion +for e$ample, 61 years or longer, who tolerate risk well,and whose primary goal is growing their investments.

S+&-(" M)"!+%" Ass"% A(()/+%i)#


130


20/58

* moderate asset allocation is most suitable for investors with a medium'term investment horion +for e$ample, 01 years or longer, who tolerate riskmoderately well, and whose primary investment goal is a moderate level ofgrowth.

S+&-(" C)#s"!$+%i$" Ass"% A(()/+%i)#

* conservative asset allocation is most suitable for investors with a short'term investment horion +for e$ample, less than 01 years, whose risktolerance is low, and whose primary investment goals are generating incomeand protecting against inflation.

It@s a good idea for an investor to periodically review his investment plan.Because different investments grow at different rates, his original allocationof money among stocks, bonds, and mutual funds will change over time. Ifthis happens with his investments, the investor will probably need toredistribute some money to bring his investment mi$ back into line with hisoriginal plan. In addition to the annual review, whenever he makes a ma%orlife change, it@s time to reassess his overall financial situation. -ome commone$amples of such changes include switching careers, retiring, getting marriedor divorced, having a child, starting his own business, taking care of anelderly parent, and returning to school or paying tuition for a child. ost ofthese events are likely to affect his ability to invest, his time horion, and hisinvestment goals, both short'term and long'term. It@s never easy to find thetime to review his investment plan when he is in the midst of any of these lifechanges. But it@s worth making the effort. ?e would not want to enter a newphase of his life with a financial plan that was designed for differentcircumstances. In the end, staying on course with a diversified investmentmi$ will help make sure that the performance and risk levels of his overallportfolio reflect his goals and e$pectations.

The benefits of diversification are indisputable. Niversification is essential foreconomic survival and prosperityU )articularly in today@s volatile stock marketenvironment, an investor@s greatest risk is not having a properly balanced,diversified portfolio. If an investors portfolio primarily consist of stocks,


131


21/58

bonds, mutual funds, and other correlated investments that generally movein the same direction, it is advisable to diversify.


132


22/58

5.2 DETERMINATION OF OPTIMUM PORTFOLIOS

*n investor might choose to invest a proportion of his or her wealth in aportfolio of risky assets with the remainder in cash ' earning interest at therisk free rate +or indeed may borrow money to fund his or her purchase ofrisky assets in which case there is negative cash weighting. ?ere, the ratio ofrisky assets to risk free asset determines overall return ' this relationship isclearly linear. It is thus possible to achieve a particular return in one of twowaysE

By investing all of ones wealth in a risky portfolio# and


23/58

R*to some optimal mi$ on the efficient frontier. We@re specifically assumingwhat -harpe said, that high risk investors can and will buy on margin, withmoney borrowed at the low rate R*.That@s why there is %ust one straight linein the picture and one uniue optimal mi$ on the efficient frontier# so theproblem of building an optimal portfolio is "separated" into somehow findingthe optimal mi$ and then combining it with cash to give you your desired risk

tolerance.

9ow for the part that@s really interesting. *ssume that everybody is facing thesame efficient frontier that you are, and that the market is efficient in thespecific sense that it behaves in the aggregate as if everybody is trying tobuild an efficient portfolio this way. That means it behaves as if everybody ison your straight line, with the same optimal mi$ as you. -o the mi$ that themarket is holding ' the inde3' is guaranteed to be your own personal optimalmi$.

5.' INTERNATIONAL PORTFOLIO DIVERSIFICATION

It has been estimated that about D2 of total world euities has beenestimated to comprise cross'border holdings. 8ven so, it is arguable thatthere remains a domestic bias among many types of investor, which can beattributed to a number of barriers to international investment, including thefollowingE

Gegal restrictions e$ist in some markets, limiting ownership of securitiesby foreign investors.

/oreign e$change regulation may prohibit international investment ormay make it more e$pensive.

Nouble ta$ation of income from foreign investment may deter investors

There are likely to be higher information and transaction costs associatedwith investing in foreign securities

-ome types of investor may have a parochial home bias for domesticinvestment.

There are a number of arguments in favour of international portfoliodiversification.

Di$"!si*i/+%i)# )* !is

* portfolio which is diversified internationally should in theory be less riskythan a purely domestic portfolio. This is of advantage to any risk' averseinvestor. *s with a purely domestic portfolio, the e$tent to which risk isreduced by international diversification will depend upon the degree ofcorrelation between individual securities in the portfolio. The lower the


134


24/58

degree of correlation between returns on the securities, the more risk can beavoided by diversification.

* few years ago, few investors uestioned the value of investinginternationally. *llocating some portion of one@s portfolio to non ' Aambianeuities had clearly delivered on the promise of providing better risk'ad%usted

returns than a portfolio of Aambian assets alone. In fact, the case forinternational investing was so compelling that most of the research duringthe last decade focused not on whether to invest internationally, but howmuch to invest.


135


25/58

H+s I#%"!#+%i)#+( Di$"!si*i/+%i)# W)!"

The idea behind international diversification is that by adding non' Aambianassets to a Aambian portfolio, investors reduce portfolio'level volatility and,thereby, generate better risk'ad%usted returns. In any given period, portfolioreturns in international markets may be higher or lower than returnsgenerated in an investor@s domestic market. ?owever, over long holdingperiods international diversification has delivered on the promise of reducingportfolio volatility and enhancing risk'ad%usted returns.

/or instance, in the 3-*, from 05D1'6110, an internationally diversifiedportfolio realied both of these benefits. While higher returns and lower riskneed not occur simultaneously for successful international diversification,many investors have come to e$pect both. This is perhaps one source offrustration for investors whose portfolio returns had fallen short of 3.- onlyportfolios, even as portfolio risk levels declined.


1:0 2001

S%!+%" US USEAFE7=0208

6 C3+#"

*nnual Return 00.O2 06.12 P2

Risk +-td.deviation

0H.H2 0K.H2 'D2

-harpe ratio 6.12 D.12 P0H2

Source$:actSet

136


26/58

Wi(( Hi3"! L"$"(s )* C)!!"(+%i)# P"!sis%

While long'term data confirm the benefits of investing internationally,investors are wary of the recent upward trend in correlations between globalmarkets. Noes this trend diminish the benefits of international investing orperhaps signal the demise of international diversification all together Boththe magnitude and duration of any increase in correlation will determine theanswer.


27/58

8ric Brandhorst, a Nirector of Research for (lobal -tructured )roducts in a

3-* firm, observes that while correlations between 3.-. and non'3.-. marketshave moved higher in recent years, this is not the first time they havereached high levels. )revious spikes came in the early and mid D1s, as wellas in the late J1s. * significant drop has followed each spike in correlation. *srecently as the mid'51s, the correlation between 8*/8 e$'Vapan and the 3.-.was as low as 1.H, dropping from a high of 1.J in 05J5. -imilarly, thecorrelation between Vapan and the 3.-. has varied over time with a long'termaverage of %ust 1..


28/58

averages offer a more appropriate measure of the e$tent to which marketsare becoming more connected.


139


29/58

-ome investors argue that the recent increase in correlations reflects a neweconomic environment where firms are more global and economies are moreintegrated. They suggest that these correlation levels will persist andconseuently reduce the effectiveness of international diversification. Ifcorrelations reflect these trends, one would e$pect the correlation of

fundamental measures, such as earnings growth, to have increased.

In our view, an increase in the correlation of underlying cash flow growthsignals that, in fact, economies are becoming more integrated and firmsmore global. ?owever, while changes in )=8 ratios across markets havebecome more correlated in recent years +what we call "valuationcorrelation", the same cannot be said for the correlation between cash'flowgrowth rates across countries. This suggests that the recent increase in thecorrelation of returns is a more temporary reflection of changing views ofglobal risk, rather than a permanent increase in correlation reflecting higherlevels of economic integration. )ut another way, we do not believe that anincrease in "valuation correlation" can persist if there is little evidence of"fundamental correlation". ?ow can markets that are e$periencing trulydifferent cash flow growth have such consistently similar views of changingrisks

Fi,!" 2

/igure 6 illustrates that the correlation between cash earnings'per'sharegrowth for ma%or markets does not appear to be particularly correlated.9either does the correlation appear to be trending upward. )=8 changes arereflecting much higher levels of correlation than underlying fundamentals


140


30/58

would suggest. Gong'term correlations may be on the rise, but a moresustainable level is probably between 1.O and 1.OH. /urthermore, even atincreased correlation levels, diversification benefits still e$ist whichsignificantly improve the risk=return profile of a global portfolio.

H)? D)"s +# I#/!"+s" i# C)!!"(+%i)# I#*(,"#/" %3" RisR"%,!#C3+!+/%"!is%i/s )* + G()9+( P)!%*)(i)

/igure illustrates the percentage improvement in the -harpe ratio of aportfolio comprising J12 3.-. euities and 612 non'3.-. euities for differentlevels of correlation.

Fi,!" '

*dding non'3.-. assets to a 3.-. portfolio improves the risk=return trade'off ofthe portfolio across all different levels of correlation. *s one might e$pect, thelower the correlation between assets, the bigger the improvement in theportfolio@s -harpe ratio. /or e$ample, a portfolio comprised of assets with acorrelation of 1.H offers a 5.02 improvement in the -harpe ratio while only a.K2 improvement e$ists in the portfolio with a correlation level of 1.J. 8venif long'term correlations are creeping upward, say to a new level of 1.OH,significant improvements +O2'D2 in the risk=return tradeoff of the portfolio

can still be achieved by adding non'3.-. assets to the mi$.

It is also important to put the diversification benefit of international euityinto perspective relative to other potential portfolio diversifiers. 8ven if oneassumes a permanent decrease in diversification benefit of internationaleuity as a reflection of a more integrated global economy, the benefits arestill significant relative to many other asset classes.


31/58

that for a 3.-. large'cap euity investor, the benefits of internationaldiversification lie somewhere between the benefits offered by diversifyinginto small'cap euities and bonds.


142


32/58

D)"s I#%"!#+%i)#+( Di$"!si*i/+%i)# M"+# S"%%(i# *)! L"ss

;orrelations aside, many investors simply feel more comfortable investing in3.-. assets due to the return advantage the 3.-. market has en%oyed versusother developed markets over the last 0H years. -ome argue that thefle$ibility and entrepreneurial mindset of 3.-. corporations, sound monetaryand fiscal policy, and the level of regulation in the 3.-. combine to create amore fertile ground for earnings growth and euity return. The e$traordinarymarket gains e$perienced by 3.-. euities over the past decade have onlyreinforced that idea. Those who were invested internationally during the0551s were left feeling as though they had "diversified away" opportunitiesfor e$ceptional returns. ?owever, it is nave and potentially very harmful toe$trapolate historical returns, particularly following a long period of superiorperformance by one asset. /orecasting relative returns between markets isnotoriously difficult, and runs counter to the fundamental idea ofdiversification. *ccepting diversification as an important ob%ective means that

investors believe that over time, markets will price assets to reflect the returnand risk associated with the investment opportunity ' even if the realiationof return can differ uite significantly from e$pectations.

While we believe in the pure benefits of diversification, some historicalperspective on the valuation, capitaliation, and return characteristics ofinternational investments relative to the 3.-. is helpful to investors whouestion the role of international euity in portfolios.

Fi,!"


33/58

The increase in wealth over time for the 3.-., Vapan and 8*/8 e$'Vapanmarkets has essentially been the same for the 0'year period beginning in05D1 and ending in 6110. While the end'point was the same for each asset,the paths to that end'point diverged significantly along the way, as illustratedin /igure K. 9onetheless, historically the 3.-. market has not out'shined otherdeveloped markets, and in fact the superior 3.-. performance since 05JJ is

largely a reversal of superior performance by international markets from05D1 to 05JJ, as seen in /igure H.

Fi,!" 5

While the three asset classes e$perienced nearly identical annualied returnssince 05D1, many investors didn@t make their first foray into internationaleuities until the late J1s or early 51s, the e$act period during which Vapanbegan its precipitous fall from grace. This unfortunate timing may be thecause for much of the current an$iety over international investing. Thoseinvestors who eagerly anticipated the rewards of international investing 01 or0H years ago are in some cases considering %umping ship today. * long'termobserver might remark that the timing of this potential e$odus couldn@t beworse. 9ot only do the returns indicate that international assets may bepoised for improved relative performance, but various valuation measuresalso suggest that the 3.-. euity market may be e$pensive relative to othereuity markets.

In summary, we can safely say that International diversification works.


34/58

internationally and if you are still struggling to grasp this concept, %ust thinkabout why most *frican )residents consider investing abroad rather thantheir home countries. *nd the simple reason is that the risk of holding onlydomestic portfolios is so high that they risk being stripped of those portfoliosafter leaving office.

While the realied correlation of returns between countries has risen in recentyears, there is little evidence that changes in underlying cash'flows havebecome more correlated across countries. While the changes in valuationratios across countries have become more correlated, it is possible touestion the e$tent to which elevated @valuation correlation@ can persist inthe face of fundamental cash'flow growth diversification. *lthough it isprudent to be hesitant to endorse international euities from a relative returnstandpoint, it is true that capitaliation, realied return and valuation datasuggest that international euities are at least as attractive as one countryseuities ' if not more so.

5.< LIMITATIONS OF PORTFOLIO ANALYSIS

)ortfolio analysis is useful for diversifying through the firms investmentdecisions. *pplied to selection of investment proposals, portfolio theory has anumber of limitations.

)robabilities of different outcomes must be estimatedE fairly easy for+e.g. machine replacement# more difficult for +e.g. new productdevelopment.

-hareholder preferences between risk and return may be difficult to knowand personal ta$es may impact.

)ortfolio theory is based on the idea of managers assessing the relevant

probabilities and deciding the combination of activities for the business.anagers have their %ob security to consider, while the shareholder caneasily buy and sell securities. anagers may therefore be more riskaverse than shareholders, and this may distort managers investmentdecisions.

)ro%ects may be of such a sie that they are not easy to divide inaccordance with recommended diversification principles.

The theory assumes that there are constant returns to scale, in otherwords that the percentage returns provided by a pro%ect are the samehowever much is invested in it. In practice, there are may be economiesof scale gained from making a larger investment in a single pro%ect.


35/58

The e$pected returns from a portfolio# and The risk that actual returns from the portfolio will be higher or lower than

e$pected. -ome portfolios will be more risky than others.

Traditional investment theory suggests that rational investors wish toma$imie return and minimie risk. Thus, if two portfolios have the sameelement of risk, the investor will choose the one yielding the higher return.-imilarly, if two portfolios offer the same return the investor will select theportfolio with the lesser risk.


146


36/58

I#i**"!"#/" C,!$"s

ean'variance theory provides a neat separation between Investorpreferences and capital market opportunities. The latter are summaried inthe feasible mean'variance opportunity set and its efficient frontier. The

former can be shown with a set of Investor indifference curves

The diagram below shows portions of a map of the preferences of a specificInvestor

?ere are some answers obtained when this Investor was asked to choosebetween various pairs of mean'variance combinationsE

C3))s" 9"%?""# A#s?"! W and : W > and : : and : Non@t care W and A W > and A and : Non@t care

These responses can be written using algebraic notation, with X meaning "ispreferred to" +more properlyE "would be chosen over", Y the converse, and Lmeaning "is eually desirable as" +more properly, "would let someone elsechoose" or "flip a coin". ThusE

W X : : X >


147


37/58

L : W X A X > A L :

If the Investor has transitive preferences, we can combine all these

responses, using the rules of algebraE

W X L : L A X >

Thus if we know that W is preferred to : and : is preferred to >, we assumethat if asked to choose between W and >, the Investor would pick W. Thismay seem obvious, but people often fail to make choices that are "rational"in this sense. Worse yet, when the preferences represent the results ofchoices made by a committee voting by ma%ority rule, instances ofintransitivity are common. In such cases the order in which votes arepresented can easily affect the outcome. Thus W might win over : in a first

vote, and : over > in a second vote, even though in an initial contestbetween W and >, the victory might have gone to >.

The *nalyst who works with Investment ;ommittees must be aware of suchpossibilitiesE a difficult task indeed. -uch is the world of practice. In the worldof theory no such dangers lurk. The Investor is assumed to have transitivepreferences which can, in principle, be graphed as a series of indifferencecurves of the type shown in the figure. The Investor is indifferent among allcombinations of e$pected return and risk plotting on a single indifferencecurve +for e$ample, ,: and A. ?e or she prefers any combination on a curvethat cuts the e$pected return a$is at a higher point to any combination thatcuts it at a lower point. Thus W is preferred to +or : or A or >, and +or :

or A is preferred to >. The %oint task of the Investor and the *nalyst is to putthe former on the highest possible indifference curve. This is shown below,with the red curve plotting the risk and return combinations available with

efficient portfolios.


148


38/58

In this case, point : is optimal. 9ote that point 80 is inferior. 8ven though itrepresents an efficient mean'variance combination, it puts the Investor onthe lowest curve shown, points on which are inferior to points on the middlecurve, given his or her preferences.


39/58

The "AP$, which we will e$plore in more detail in the ne$t chapter, assumesthat the risk'return profile of a portfolio can be optimied ' an optimalportfolio displays the lowest possible level of risk for its level of return.*dditionally, since each additional asset introduced into a portfolio furtherdiversifies the portfolio, the optimal portfolio must comprise every asset,+assuming no trading costs with each asset value'weighted to achieve theabove +assuming that any asset is infinitely divisible. *ll such optimalportfolios, i.e., one for each level of return, comprise the efficient frontier.

*n important property of the efficient frontier is that it@s curved, not straight.This is actually significant ' in fact, it@s the key to how diversification lets youimprove your reward'to'risk ratio. To see why, imagine a H1=H1 allocationbetween %ust two securities. *ssuming that the year'to'year performance ofthese two securities is not perfectly in sync ' that is, assuming that the greatyears and the lousy years for -ecurity 0 don@t correspond perfectly to thegreat years and lousy years for -ecurity 6, but that their cycles are at least alittle off ' then the standard deviation of the H1=H1 allocation will be lessthanthe average of the standard deviations of the two securities separately.(raphically, this stretches the possible allocations to the leftof the straightline %oining the two securities.

In statistical terms, this effect is due to lack of covariance. The smaller thecovariance between the two securities ' the more out of sync they are ' thesmaller the standard deviation of a portfolio that combines them. Theultimate would be to find two securities with negativecovariance +very out of

syncE the best years of one happen during the worst years of the other, andvice versa.

5. CORRELATION AND COVARIANCE OF INVESTMENTS

There is little doubt that the correlation coefficient in its many forms hasbecome the workhorse of uantitative research and analysis. *nd well it


150
http://en.wikipedia.org/wiki/Image:Markowitz_frontier.jpg


40/58

should be, for our empirical knowledge is fundamentally of co'varying things.We come to discern relationships among things in terms of whether theychange together or separately# we come to impute causes on the basis ofphenomena co'occurring# and we come to classify as a result of independent

variation.

When we perceive two things that covary, what do we see When we see onething vary, we perceive it changing in some regard, as the sun setting, theprice of goods increasing, or the alternation of green and red lights at anintersection in ;airo Road. Therefore, when two things covary there are twopossibilities.


41/58

1Source$ Rummel 1!;


42/58

T+9(" 2

8 :rom ta*le ! = High an# lo are #i4i#e# at the a4erage

/rom the table, we can now clearly see that the correlation between the twovariables is positive, since with only one e$ception +in the upper right cellhigh magnitudes are observed together, as are low magnitudes.

If the correlation were negative, then most cases would be counted in thelower left and upper right cells. What if there were about an eual number ofcases in all the cells of the fourfold table Then, there would be littlecorrelationE the two variables would not covary. In other words, sometimeshigh magnitudes on one variable would occur as often with low as with highmagnitudes on the other.

But all this is still imprecise. The four'fold table gives us a way of looking atcorrelation, but %ust considering correlation as covarying high or lowmagnitudes is uite a loss of information, since we are not measuring howhigh or low the figures are. oreover, if we are at all going to be precise

about a correlation, we should determine some coefficient of correlation 'some one number that in itself e$presses the correlation between variables.To be a useful coefficient, however, this must be more than a number uniueto a pair of variables. It must be a number comparable between pairs ofvariables. We must be able to compare correlations, so that we candetermine, for e$ample, which variables are more or less correlated, orwhether variables change correlation with change in cases. /inally, we want acorrelation that indicates whether the correlation is positive or negative.

Investment *dvisers often repeat this line ' always diversify yourinvestments. This is also the common wisdom repeated by the financete$tbooks, including this one. -o how do we construct an investment portfolio

and what does the above really mean

-ome have attempted to put it simply, going back to historical guidance ofnot putting all your eggs in one basket# conventional wisdom states that ifyou were to buy a variety of investments, then the failure of one would notcause your entire portfolio to collapse. ?owever, the reverse is also true, that


5 0

1 K

153

Gow

Gow

?igh

?igh

GNP P"! C+-i%+

Tr

ad

e


43/58

the stellar performance of any one investment would not reap you amaingreturns.

The construction of a diversified portfolio builds on the above, but on slightlymore technical aspects. /irstly, one should diversify amongst the differentasset classes# investors commonly select euities, bonds, cash and some

alternative investments such as hedge funds, property or commodities. Theseasset classes are chosen, as their returns have historically not beencorrelated to one another. What this means for e$ample is that when euitiesmake positive returns, it has been shown that bonds make neutral ornegative returns. *sset classes with low correlation to each other are goodchoices for the diversified portfolio as each can perform independently of oneanother. In recent years, the performance of the metals, energy and softcommodities markets have shown themselves to be able to provideformidable returns, independently of the returns of e$isting asset classes.

The proportion of each asset class in the portfolio is determined by the risktolerance of the investor ' an investor with a higher risk tolerance can acceptgreater volatility and hence can incorporate a larger proportion of the assetclass with a higher volatility. The significance of volatility in this case is thefluctuation of the asset class@ returns about its mean ' an asset with highervolatility can rise higher, but can also suffer sharper falls.

?aving decided the proportion of different asset classes in the portfolio, theinvestor now has to select the components of each asset class. In euities,the famed efficient portfolio model and ;apital *sset )ricing odel describetheoretically how to construct an investment portfolio.

In the hedge fund world, funds of hedge funds attempt to take advantage of

the neutral correlations of the various strategies to build a diversified hedgefund portfolio. *n e$ample of the composition of a fund of hedge funds wouldbe buying into a global macro fund, managed futures, a convertible arbitragefund and a long'short manager.

The investment community sells the concept of diversification as a way tominimie risk and ma$imie returns. ?owever, the devil is in the details andin some cases over'diversification has shown to provide the opposite result 'giving the investor mediocre returns when the general market has given farbetter returns, as can easily happen in an euities bull market. What thismeans is, that the investor has to form an understanding of his or her riskappetite in deciding the level of diversification and the composition of the

investment portfolio.

When you put together a grouping of investments through the term assetallocation, you attempt to use those investments that are slightly dissimilar incharacter and therefore don@t always move the same amount at the sametime for the same reasons. This is the key reason for the use of foreigninvestments. ?owever, as the world has gotten smaller due to the ability to


154


44/58

communicate almost instantaneously. *ccording to a /inancial World article,-outh 4orea, India and Taiwan had e$tremely low correlations of '1.16, 1.1Kand 1.1D between 0550 to 055K as compared to the 3.-. market. +)erfectcorrelation is 0.1. )ortugal was 1.K0 as was Brail. 9ow that doesn@t meanthe markets will go up as is evidenced by some *sian countries that have notdone that well recently. But, along with growth records, correlation is a ma%or

focal point for investing.

W3+% is %3" C)!!"(+%i)# C)"**i/i"#%

The correlation coefficient, a concept from statistics, is a measure of how welltrends in the predicted values follow trends in past actual values. It is ameasure of how well the predicted values from a forecast model "fit" with the

real'life data.

The correlation coefficient is a number between 1 and 0. If there is norelationship between the predicted values and the actual values thecorrelation coefficient is 1 or very low +the predicted values are no betterthan random numbers. *s the strength of the relationship between thepredicted values and actual values increases, so does the correlationcoefficient. * perfect fit gives a coefficient of 0.1. Thus the higher thecorrelation coefficient the better.

T3" /)!!"(+%i)# /)"**i/i"#%

This is a relatively "simple" concept but absolutely mandatory in the use ofinvestments. It basically refers to whether or not "different" investments willmove at the same time for the same reason and in the same direction. If true,they have a correlation of plus 0. If, on the other hand, they were to move ine$actly opposite direction they would have a negative correlation of minus 0.Rarely do portfolios have e$actly either' most of the investments havecorrelations greater than 1 but less than 0.1. In another words, there is somemovement of one investment based on the movement of the other+s.

* more specific note is the use of stocks and bonds. (oing back 61P yearsago, stocks and bonds were effectively negatively correlated. That@s whymost investors were told to use some of each ' or one instead of the otherdepending on economic conditions ' mostly the movement of interest rates.But as the inflation rate and the interest rates have dropped, the correlationsbetween these two is now maybe 1.J. That@s a pretty strong positivecorrelation. Therefore the old O1 2 stocks and K1 2 bonds'used in a numberof supposedly low'risk portfolios' effectively will not provide thediversification that one might e$pect. /oreign stocks might provide some of


155


45/58

this reduced correlation, but even here one needs to be careful since, if aforeign investment has a negative correlation and also a negative return,there has been little gained. :ou also have the increased risk of currencydevaluation.

* correlation coefficient is, therefore, %ust a number between '0 and 0 which

measures the degree to which two variables are linearly related. If there isperfect linear relationship with positive slope between the two variables, wehave a correlation coefficient of 0# if there is positive correlation, wheneverone variable has a high +low value, so does the other. If there is a perfectlinear relationship with negative slope between the two variables, we have acorrelation coefficient of '0# if there is negative correlation, whenever onevariable has a high +low value# the other has a low +high value. * correlationcoefficient of 1 means that there is no linear relationship between thevariables.

I#%"!#+%i)#+( /)!!"(+%i)# )* i#$"s%&"#%s

We find that international euity correlations change dramatically throughtime, with peaks in the late 05th century, the (reat Nepression and the late61th ;entury. Thus, the diversification benefits to global investing are notconstant. )erhaps most important to the investor of the early 60st ;entury isthat the international diversification potential today is very low compared to

the rest of capital market history.


46/58

Intuitively, covariance is the measure of how much two variables varytogether. That is to say, the covariance becomes more positive for each pairof values which differ from their mean in the same direction, and becomesmore negative with each pair of values which differ from their mean inopposite directions. In this way, the more often they differ in the same

direction, the more positive the covariance, and the more often they differ inopposite directions, the more negative the covariance.

P)!%*)(i) S"("/%i)#

8very investor knows that there is a tradeoff between risk and rewardE Toobtain greater e$pected returns on investments, one must be willing to takeon greater risk. In solving the )ortfolio selection problem, we aim to useuantitative measures of risk and reward to obtain a balance between thesetwo factors that suits the individual investor. 9o one combination of securitiesis optimal for all investors. The best portfolio for any one investor depends on

their own tolerance for risk.

8ach investment instrument has its own e$pected monthly return, and itsown propensity for these returns to fluctuate from month to month. ?owever,the returns from different instruments are not in general independent. Insome cases they tend to move "in sync#" for instance the stocks of goldmining companies tend to follow the price of gold. In other cases they tend tomove in opposite directions from each other. These %oint tendencies areuantified by covariances.

8very investor knows that there is a risk'return tradeoff. In order to obtaingreater returns on investments, the investor must be willing to take on

greater risk. The only investments that are considered to be risk'free are (RATreasury bills, notes, and bonds. These investments yield a risk'free rate ofreturn, r. +9ote that rdepends on the time to maturity of the investment.*ssuming riskless arbitrage opportunities do not e$ist, one cannot e$pect tohave a return greater than the risk'free rate without taking on some risk.

)ortfolio theory assumes that for a given level of risk, investors prefer higherreturns to lower returns. -imilarly, for a given level of e$pected return,investors prefer less risk to more risk. It is standard to measure risk in termsof the variance, or standard deviation of return. We measure return as theaverage annual continuously compounded rate. Therefore, we can assumethat investors would like to invest in an efficient portfolio, that is, one in

which there is no other portfolio that offers a greater return with the same orless risk, or less risk with the same or greater e$pected return.

E**i/i"#% P)!%*)(i)s

*n Investor must choose between two portfolios. The end'of'period value ofeach one is normally distributed. )ortfolio * has an e$pected value of


157


47/58

401,111 and a standard deviation of 40H,111. )ortfolio B has an e$pectedreturn of 40K,111 and a standard deviation of 40H,111. Which will provide thegreatest e$pected utility

The answer is not difficult to obtain. *s long as the Investor@s utility increaseswith wealth and does not depend on the state of the world in which the

wealth is obtained, portfolio B is better. This can be seen in the plot of thecumulative distributions, shown belowE

Take any possibleoutcome, for e$ample,4H,111. This is +H,111'01,111=0H,111 standarddeviations from the

e$pected value of portfolio*. The probability that theactual outcome will fallshort of this amount is+H,111 '01,111=0H,111 or1.O5K.


48/58

;onsider the portfolios shown by the black circles in the figure that plot oncurve :A. 8ach provides the ma$imum e$pected value for a given level ofstandard deviation. If all the portfolio returns are normally distributed, thenany Investor for whom more wealth is better than less and for whom onlywealth matters should choose from among the portfolios on this curve.

What about the portfolios on the section of the curve from : to A The oneplotting at point : provides a greater e$pected value and a smaller standarddeviation than any of the portfolios between : and A. oreover, for everyportfolio on the section between : and A there are alternatives with the samee$pected return but lower standard deviations. /or e$ample, portfolio offers the same e$pected return as A but a lower standard deviation +indeed,the lowest possible, in this case. The figure below plots the cumulative

distributions for these two portfolios.

)ortfolio dominates A over the lower half of the range of possibleoutcomes, but A provides larger chances of obtaining higher values. To dealwith such a case, arkowit proposed that Investors be assumed to be risk-averse' more precisely, each Investor@s marginal utility of wealthis assumedto decline with wealth.

In this case, an Investor with decreasing marginal utility of wealth will prefer to A, since moving from A to will improve bad outcomes symmetricallywith reductions in good outcomes, and the gain in utility from each of theformer reductions will e$ceed the loss in utility from the corresponding latterreduction. /ormally, this is a case of second-degree stochastic dominance.ean'variance theory assumes that Investors prefer +0 higher e$pected


159


49/58

returns for a given level of standard deviation and +6 lower standarddeviations for a given a level of e$pected return. )ortfolios that provide thema$imum e$pected return for a given standard deviation and the minimumstandard deviation for a given e$pected return are termed efficient portfolios.*ll others are inefficient. In practice the curve plotting the ma$imume$pected value for each level of risk will usually be upward'sloping

throughout the range of feasible values. -ections such as :A are rare. Thus itgenerally suffices to assume only that Investors prefer greater e$pectedreturn for given risk, placing a considerably smaller burden on the *nalystwho advocates a focus on only efficient portfolios. The figure below providesan illustration, with e$pected returns e$pressed in terms of e$cess returnsover and above a riskless rate of interest.

In this figure each point represents a portfolio. (iven the Investor@s budgetand the %oint distribution of security and portfolio values, there are manysuch points, only a few of which are shown in the figure. The set of all suchpoints make up a feasible region of mean'variance +or mean'standarddeviation combinations. 8fficient portfolios plot on the upper left'handborder of this region, shown as a red curved line in this case. /or obviousreasons this border is often termed the efficient frontier.

5. CAPITAL MARKET LINE

The capital market line is the tangent line to the efficient frontier that passesthrough the risk'free rate on the e$pected return a$is. * tangent line, called

the capital mar>et lineis drawn to the efficient frontier passing through therisk'free rate. The point of tangency corresponds to a portfolio on the efficientfrontier. That portfolio is called the +uper efficient portfolio'

3sing the risk'free asset, investors who hold the super'efficient portfolio mayE


160


50/58

leverage their position by shorting the risk'free asset and investing theproceeds in additional holdings in the super'efficient portfolio, or

Ne'leverage their position by selling some of their holdings in the super'efficient portfolio and investing the proceeds in the risk'free asset.

The resulting portfolios have risk'reward profiles which all fall on the capitalmarket line. *ccordingly, portfolios which combine the risk free asset with thesuper'efficient portfolio are superior from a risk'reward standpoint to theportfolios on the efficient frontier.

The Capital Mar>et Line

The ;G is derived by drawing a tangent line from the intercept point on theefficient frontier to the point where the e$pected return euals the risk'freerate of return. The ;G is considered to be superior to the efficient frontiersince it takes into account the inclusion of a risk'free asset in the portfolio.

The capital asset pricing model +;*) demonstrates that the marketportfolio is essentially the efficient frontier. This is achieved visually throughthe security market line +-G.

)ortfolio is the efficient portfolio which will appeal to the investor most, ignoringrisk free investments. )ortfolios along the ;G are a mi$ture of the investments in

portfolio and risk free investments. Investors will prefer portfolios along the ;Gto portfolios along the efficient frontier because a higher return is obtained for thesame level of risk. It therefore, goes without saying, that the only portfolioconsisting entirely of risky investments a rational investor should want to hold isportfolio . *ll other risky portfolios are inefficient because they are below the;G.


161


51/58


52/58

favour of efficient capital markets areE +0 the market price will not stray toofar from the true economic price if you allow arbitrageurs to e$ploitdeviations. This will avoid sudden, nasty crashes in the future. +6 *n efficientmarket increases liuidity, because people believe the price incorporates allpublic information, and thus they are less concerned about paying way toomuch. If only the market for television sets were as efficient as the market for

stocksU * lot less comparison shopping would be needed. + *rbitrageursprovideliuidity to investors who need to sell or buy securities for purposesother than "betting" on changes in e$pected returns. /or instance, ;hina hasbeen seeking to limit access to global financial information in -hanghai +siteof its ma%or stock e$change. The government wishes to keep certain kinds ofinformation from market participants. Is this desirable Will this be possible

M+!"% E**i/i"#/ C)!-)!+%" M+#+"!s

arket efficiency has implications for corporate managers as well as forinvestors. This takes a lot of the "gamesmanship" out of corporate

management. If a market is efficient, it is difficult to fool the public for longand by very much. /or instance, only genuine "news" can move the stockprice. It is hard to pump'up the stock price by claims that are not verifiableby investors. "/ake" news will not move the price or if it does, the price willuickly revert to the pre'announcement value when the news proves hollow.)ublicly available information is probably impounded in the price already.

This is hard for some managers to believe. *n e$ample is -ears@ attempt tosell the -ears Tower in ;hicago in the late 05J1@s. The company believedthat, since it carried the property on its balance sheet at greatly depreciatedvalues, the public did not credit the company with the full market price of thebuilding and thus -ears stock was under priced. This proved to be false, infact, it seems that -ears was overestimating the value of the building and the

stock price was relatively efficientU

T3!"" D"!""s )* E**i/i"#/

What kind of information is impounded in the stock price It turns out thatthere are lots of different levels of market efficiency, depending upon thesource or the information being impounded. The best way to illustrate this isby e$ample. -uppose you had a hyper'efficient market that impounded all

private information. This means that even a personal note passed betweenthe ;8< and the ;/< regarding a ma%or financial decision would suddenlyimpact the stock priceU If so, this is called Strong:orm Efficiency. /ewpeople believe that the market is strong'form efficient, but it is nice to have

this benchmarkU

?ow about allpublic information That is, all information available in annualreports, news clippings, gossip columns and so on If the market priceimpounds all of this information the market is called SemiStrong :ormEfficient. ost people believe that the Aambian euity markets by and largereflect publicly available information. But consider this, is information one


163


53/58

puts on the Internet pu*licE *re government files available under thefreedom of information *ct public There must be subtle shades of semi'strong market efficiency, but they are not typically differentiated. 8ach newpiece of information an analyst gathers should be carefully considered withregard to whether it is already impounded in the stock price. The easier itwas to get, the more likely it is to have already been traded upon.

The final form of market efficiency is 3ea> :orm Efficiency? * weak'formefficient market is one in which past security prices are impounded intocurrent prices. -ince past prices are deemed public information, weak formefficiency implies semi'strong form efficiency and semi'strong form efficiencyimplies strong form efficiency.

Weak form efficiency implies that you can@t make e$cess profits by trading onpast trends. /unny, a lot of people do %ust that. They are called technicalanalysts, or chartists. What would you do if you noticed that every time themarket went up by 02, the ne$t day on average, it went up again by 0=6 2What would you do if you noticed that every time the market went down by02, the ne$t day on average, it went down again by 0=6 2 If your answer isthat you would buy on an up day and sell on a down day, you have themakings of an active T8;?9I;*G TR*N8RU *cademics have been testingtrading rules like this for over forty years, and traders have been e$ploitingthem for even longer.

E$i"#/" F)! M+!"% E**i/i"#/

* simple test for Strong :orm Efficiencyis based upon price changes closeto an event. *cts of nature may move prices, but if private informationreleasedoes not, then we know that the information is already in the stock

price. /or e$ample, consider a merger between two firms. 9ormally, a mergeror an acuisition is known about by an "inner circle" of lawyers andinvestment bankers and firm managers before the public release of theinformation. When these insiders violate the G*W by trading on this privateinformation, they may make money.


164


54/58

3nfortunately, stock prices typically move up before a merger, indicating thatsomeone is acting dishonestly. The early move indicates that the market hasa tendencytowards strong'form efficiency, i.e. even private information isincorporated into prices. ?owever, the public announcement of a merger istypically met with a large price response, suggesting that the market is notstrong'form efficient. Geakage, even if illegal, does occur, but it is not fullyimpounded in stock price. By the way, insider trading is surprisingly legal insome countries.Is %3" s%)/ &+!"% s"&i;s%!)# *)!& "**i/i"#%

The most obvious indication that the market is not always and everywheresemi'strong form efficient is that money managers freuently use publicinformation to take positions in stocks. While there is no evidence that theybeat the market on a risk'ad%usted basis, it is hard to believe that an entireindustry of information production and analysis is for naught. It seems likelythat there is value to publicly available information# however there areprobably degrees to which information really is public knowledge. What issurprising is that recent studies have shown some evidence that e$cessreturns can be made by trading upon $"!public information. These testsusually take the form of *back testing*trading strategies. The assumption ofsemi'strong form efficiency is a good first appro$imation for a market with as

many sharp traders and with as much publicly available information as theAambian euity market.Is %3" s%)/ &+!"% ?"+ *)!& "**i/i"#%

Weak form efficiency should be the simplest type of efficiency to prove, andfor a time it was widely accepted that the Aambian stock market was at least


165


55/58


56/58

model +;*). *t a meeting, 9alukuis anaging Nirector suggests thatportfolio theory would provide the most appropriate and useful measure ofrisk for evaluating the performance of the two portfolios. The ;hairman saysthat she does not understand what the argument is about since both ;*),and the portfolio theory on which it is based, provide the same measure ofrisk.

The Bank of Aambia treasury bills rate of return is H.H2 and the market riskpremium in the financial market is currently estimated at J2.

Re"uire#$

+a 8$plain the principle of portfolio diversification, and its relevance indeveloping the capital asset pricing model. What does the Zbeta of a sharerepresent, and how is it determined

+b Niscuss the ;hairmans view that ;*) and portfolio theory provide thesame measure of risk.

+c 3sing the capital asset pricing model identify which of the two portfolioshas performed better, and comment briefly on the validity of yourconclusions.

ANSWER

7+8 R",/%i)# )* -)!%*)(i) !is

;ombining stocks in a portfolio results in reduction of portfolio risk. *fter theaddition of about 0H to 61 stocks to a portfolio, the risk reduction effectbegins to taper off. The degree of correlation between the returns on thedifferent investments in the portfolio affects the amount of risk reduction.

The greatest risk reduction occurs when correlation is negative. ostsecurities tend to be positively correlated, limiting the scope for riskreduction.

The total risk of a security held in isolation is more than that of the samesecurity held as part of a portfolio ' the risk that is removed through portfoliodiversification is the securitys specific risk, caused by random eventsaffecting the company. The effects of such random events are reduced oreliminated by diversification, so specific risk is also called diversifiable risk.

The technical term for this risk is unsystematic risk.

-ystematic risk affects all the securities in the market, and is associated withfactors such as economic conditions, political events and general marketsentiment. -ystematic risk is also called market risk or undiversifiable risk.Niversified investors are concerned about the systematic risk of a security Qnot the specific risk, which can be diversified away.


167


57/58

The Zmarket portfolio refers to a hypothetical portfolio of all the shares in themarket, weighted according to market capitalisation This is the most efficientportfolio, containing only systematic risk Q all unsystematic risk has beendiversified away.

The beta of a share is the slope of a regression line of the historical returns

on the share against the returns on the market portfolio. It thereforemeasures the change in the shares return that is Ze$plained by change inthe return on the market portfolio, and thus provides a measure of theshares systematic risk. (iven the return on the market portfolio and the risk'free return, the e$pected return on any share can be estimated withreference to the shares beta.

798 M"+s,!"s )* !is

)ortfolio theory uses the standard deviation of a portfolios return to providea measure of the total risk of the portfolio Q both systematic andunsystematic risk. ;*) uses the beta to provide a measure of thesystematic risk only. )ortfolio theory and ;*) would only give the sameportfolio risk measure if the portfolio were so well diversified that allunsystematic risk has been eliminated.

7/8 CAPM

3sing ;*) to assess portfolio performance the weighted average systematicrisk of each portfolio can be calculated and, using ;*), the e$pected returnof each portfolio can be estimated.


168


58/58

P)!%*)(i) 14

)ortfolio beta L +0.6 $ 1.KJ P +1 $ 1.6D6 P +1.J $ 1.0DO P +0.H $ 1.61KL 1.JOKK8$pected return L H.H P +J $ 1.JOKKL 06.K62

The actual return of the portfolio over the last year wasE+0K $ J.D=6H P +O $ O.J=6H P +00 $ K.K=6H P +0H $ H.0=6HL 00.H12)ortfolio 0 has therefore under'performed.

P)!%*)(i) 24

)ortfolio beta L +1.5 $ 1.6J1 P +1. $ 1.0KK P +0.D $ 1.K1 P +1.0 $ 1.6OL 1.J5OJ8$pected return L H.H P +J $ 1.J5OJL 06.OD2

The actual return of the portfolio over the last year wasE+06 $ D=6H P +5 $ .O=6H P +05 $ J.H=6H P +J $ H.5=6HL 0.112

Therefore )ortfolio 6 has over'performed. 3sing ;*), it is possible torecommend )ortfolio 6, which has a positive abnormal return. ?owever, aportfolio of only four investments cannot be said to be well diversified, soa$ima would be e$posed to unsystematic risk as well. *lternative portfolioswith a greater degree of diversification should be considered.

The perfect market assumptions on which the ;*) is based are limitationsthat should also be kept in mind when drawing conclusions. >ariousresearchers have uestioned other aspects of ;*), notablyE

Betas calculated on the basis of historical returns do not necessarilyremain stable.

;*) oversimplifies reality by relating e$pected return to a single factor,i.e. the return on the market portfolio# and

Indices used as market pro$ies in ;*) calculations do not e$actlyrepresent the whole market.

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

CHAPTER 5 - Portfolio Theory

Documents