ACTL5303Week6_2015

Business School

ACTL4303 AND ACTL5303 ASSET LIABILITY MANAGEMENT

Week 6 Fixed Income Securities

Greg Vaughan

Review of Equity Pricing and Revision

b is earnings retention (1 – payout ratio) E is next year’s earnings k is the equity discount rate eg Rf + B(Rm-Rf) ROE is return on newly invested equity

2

Given b, E and ROE you can determine P if you have k, or determine k if you have P (market implied returns, consistent with assumptions)

Review of Equity Pricing (2)

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§  If the price accurately reflects stock characteristics (eg ROE) then investment return equals discount rate

§  High PE and high growth do not mean high return

Disequilibrium Example

E(r)

15%

SML

β1.0

Rm=11%

rf=3%

1.25

4

The security characteristic line

( ) ( ) ( )tetRtR HPPSHPHPHP ++= 500&βα5

Portfolio Construction and the Single-Index Model

•  Managers are assessed on their information ratios: •  These relate to their active portfolios. A stocks weight in the active

portfolio is the difference between its portfolio weight and its weight in the index

iAw = i

Pw − iIw

•  Key result: If not for the long only constraint ( ) the single-index model implies

iAw ∝ iα

2σ ie( )

•  ‘..we are concerned only with the aggregate beta of the active portfolio, rather than the beta of each individual security’. Normally this is zero by design, so that portfolio beta is one.

•  Active weights are scaled based on target tracking error

Aασ Ae( )

iPw > 0

6

Arithmetic and geometric returns E(Geometric Average) = E(Arithmetic average) – IF we were observing a stationary return distribution: •  The sample arithmetic average (eg over 55 years) is an unbiased

estimate of the true mean •  However compounding at this rate results in an upwardly biased

forecast for a given horizon (eg over ten years) •  The unbiased estimator for a projection of H years, based on a data

sample of T years is (H/T) x Geometric + (1-H/T) x Arithmetic •  For a short projection horizon, the Arithmetic mean is appropriate, but

where the horizon is longer, or the data span is shorter, the geometric mean becomes increasingly relevant

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2σ

7

Australian Equity Log Returns 1980-2012

Frequency Skewness Excess Kurtosis

Probability of Normality

Monthly -3.1 30.3 0% Quarterly -1.8 8.8 0% Annual -0.5 0.8 56%

8

Random Walk and the EMH

•  Volatility of log returns can be calculated at different data frequencies (eg annual, quarterly, monthly)

•  If there is true independence from one period to the next the results should be consistent (ie variance ratios of 1)

•  There is some mild statistical contradiction of the random walk in Australia (1980-2012)

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Dividend Imputation (2) •  A company makes a profit of $100, and pays

company tax at 30% leaving $70 for distribution as dividend

•  A $30 imputation credit is attached to the $70 dividend in respect of the company tax paid

•  The superannuation fund pays 15% tax on the aggregate of the dividend ($70) and the franking credit ($30). Tax = 15%x($70 + $30) =$15

•  The superannuation fund receives a credit from the tax office of $30 against that tax liability, with the net effect that the superannuation fund receives $15

•  The dividend is worth $85 to the superannuation fund

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This week’s coverage Bodie et al Chapter 14 Bond Prices and Yields Chapter 15 The Term Structure of Interest Rates Chapter 16 Managing Bond Portfolios

INVESTMENTS | BODIE, KANE, MARCUS 12 INVESTMENTS | BODIE, KANE, MARCUS

•  Investors require a risk premium to hold a longer-‐term bond

•  This liquidity premium compensates short-‐term investors for the uncertainty about future prices

Interest Rate Uncertainty and Forward Rates


•  The Expecta=ons Hypothesis Theory •  Observed long-‐term rate is a func=on of today’s short-‐term rate and expected future short-‐term rates

•  fn = E(rn) and liquidity premiums are zero

Theories of Term Structure


•  Liquidity Preference Theory •  Long-‐term bonds are more risky; therefore, fn generally exceeds E(rn)

•  The excess of fn over E(rn) is the liquidity premium •  The yield curve has an upward bias built into the long-‐term rates because of the liquidity premium

Theories of Term Structure


•  The yield curve reflects expecta=ons of future interest rates

•  The forecasts of future rates are clouded by other factors, such as liquidity premiums

•  An upward sloping curve could indicate: •  Rates are expected to rise and/or •  Investors require large liquidity premiums to hold long term bonds

Interpreting the Term Structure

INVESTMENTS | BODIE, KANE, MARCUS 16

Bond Pricing: Two Types of Yield Curves

Pure Yield Curve •  Uses stripped or zero coupon Treasuries

•  May differ significantly from the on-‐the-‐run yield curve

On-‐the-‐Run Yield Curve •  Uses recently-‐issued coupon bonds selling at or near par

•  The one typically published by the financial press


•  Yield to Maturity •  Bond’s internal rate of return •  The interest rate that makes the PV of a bond’s payments equal to its price; assumes that all bond coupons can be reinvested at the YTM

•  Current Yield •  Bond’s annual coupon payment divided by the bond price

•  For premium bonds Coupon rate > Current yield > YTM

•  For discount bonds, rela=onships are reversed

Bond Yields: YTM vs. Current Yield


•  If interest rates fall, price of straight bond can rise considerably

•  The price of the callable bond is flat over a range of low interest rates because the risk of repurchase or call is high

•  When interest rates are high, the risk of call is negligible and the values of the straight and the callable bond converge

Bond Yields: Yield to Call


Figure 14.4 Bond Prices: Callable and Straight Debt


•  Reinvestment Assump=ons •  Holding Period Return

•  Changes in rates affect returns •  Reinvestment of coupon payments •  Change in price of the bond

Bond Yields: Realized Yield versus YTM

INVESTMENTS | BODIE, KANE, MARCUS 21

Bond Prices Over Time: YTM vs. HPR

YTM •  It is the average return if the bond is held to maturity

•  Depends on coupon rate, maturity, and par value

•  All of these are readily observable

HPR •  It is the rate of return over a par=cular investment period

•  Depends on the bond’s price at the end of the holding period, an unknown future value

•  Can only be forecasted

Yield components

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Real risk-free interest rate + Expected inflation rate + Maturity Premium =Sovereign Bond Yield Liquidity Premium + Credit spread = Corporate Bond Spread Corporate Bond Yield = Sovereign Yield + Corporate Spread Corporate Bond Spreads increase with maturity.

Yields spreads and economic sensitivity

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Post-GFC era

Conventional soft economy •  Credit spreads deteriorate

•  Investors require wider risk premium because of rising default risk

•  Issuance drives spreads wider when investors are reluctant holders

•  Secondary market liquidity deteriorates so liquidity premiums expand

•  Credit spreads have narrowed with ‘reach for yield’

•  Relaxed investors because default rates have been low

•  Significant issuance has had little effect on spreads

•  Secondary market has been reasonable healthy

P = the price per $100 face value (rounded to 3 decimal places) v = 1/(1+i) where i is half yearly yield = y/200 where y is %pa f = number of days from settlement to next interest payment date d = number of days in the half year ending on the next interest payment data (181-184) g = the half-yearly rate of coupon payment per 100 n = the term in half years from the next interest-payment date to maturity

Australian bond pricing

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•  Accrued interest = gx(1-f/d) Bond prices may be quoted including accrued interest (Australian practice ) or net of accrued interest (‘clean’ – US practice) The Australian formula naturally calculates the price including accrued interest US based software (excel, financial calculators) are based around the ‘clean’ price convention

Bond pricing and accrued interest

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Table 14.1 Principal and Interest Payments for a Treasury Inflation Protected Security

There are only $5b Australian Government Indexed Bonds on issue compared to $350b conventional Australian Government Bonds

Bank bills

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Bond pricing and yield sensitivity

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•  Bond pricing is based on yields convertible half yearly

•  If we measure time in years then the pricing formula is effectively:

P = Ct∑ ⋅ 1+ y2

#

$%

&

'(−2t

dPdy

= Ct ⋅ −2t( )∑ ⋅ 1+ y2

$

%&

'

()−2t−1

⋅12$

%&'

()= −

11+ y / 2$

%&

'

()⋅ Ct∑ ⋅ t ⋅ 1+ y

2$

%&

'

()−2t

dPdy

!

"#

$

%&

P= −

11+ y / 2!

"#

$

%&× t ⋅wt∑ where wt =Ct ⋅ 1+

y2

"

#$

%

&'−2t

/ P


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•  The duration is the weighted average term of cash flows with weights determined as the proportion of valuation at that point in time

•  This is commonly referred to as Macaulay duration (1938)

•  Modified Duration is the first derivative relative to price :

MacaulayDuration = t ⋅wt∑ where wt =Ct ⋅ 1+y2

"

#$

%

&'−2t

/ P

ModifiedDuration = −

dPdy

"

#$

%

&'

P=

11+ y / 2( )

×MacaulayDuration


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•  Because this is a first derivative we can estimate modified duration by pricing the bond at yields either side of the current yield and estimating by difference

•  Consider a ten year 4% coupon bond with the market yield at 3%.

•  P at 3% = 108.584, P at 3.2%=106.800, P at 2.8% = 110.403

•  Modified Duration = (110.403 – 106.800)/(2x108.584x0.002) = 8.30 years

•  Because of the relation to Macaulay duration it is quoted in years rather than as a percentage (which would be more logical)

•  For every 1% change in yields, price changes inversely by 8.30%

•  The corresponding Macaulay duration is 8.42 years

ModifiedDuration ≅ P− −P+2×P×Δy


•  What Determines Dura=on? •  Rule 1

•  The dura=on of a zero-‐coupon bond equals its =me to maturity

•  Rule 2 •  Holding maturity constant, a bond’s dura=on is higher when the coupon rate is lower

•  Rule 3 •  Holding the coupon rate constant, a bond’s dura=on generally increases with its =me to maturity

Interest Rate Risk


•  What Determines Dura=on? •  Rule 4

•  Holding other factors constant, the dura=on of a coupon bond is higher when the bond’s yield to maturity is lower

•  Rules 5 •  The dura=on of a level perpetuity is equal to:

(1 + y) / y

Interest Rate Risk


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•  The relationship between price and yield is non-linear

•  Recall Taylor’s theorem

•  Estimating change in price is improved by taking account of the second derivative, referred to as Convexity

•  Convexity is related to the spread of cash flows around the duration

•  Convexity = (106.800+110.403-2x108.584)/(2 x 108.584 x 0.002^2) = 40.3 using previous example

f (x + h) = f (x)+ h ⋅ "f (x)+ h2

2!""f (x)+....

Convexity ≅ P+ +P− − 2×P2×P× (Δy)2


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•  If we wanted to estimate the change in price for an increase in yield from 3% to 3.50%, based on our example

•  The actual price is 104.188 at 3.5% yield, a change of -4.05%

•  In practice portfolios can be priced directly without any approximation formula

•  However these concepts are relevant in risk management (eg what is the duration of the fixed interest portfolio)

ΔPP

≅ −ModDur×Δy+ 12( )×Convexity× Δy( )2

ΔPP

= −8.30×0.0050+ 0.5× 40.3×0.00502 = −4.10%

Redington’s 1952 paper on immunization •  Set duration of assets equal to duration of liabilities •  Have convexity of assets greater than convexity of liabilities

If assets and liabilities have the same duration, the the asset-liability hedge can be improved by increasing the convexity of the assets. The convexity contribution will always be positive, and the duration contribution will be zero

Frank Redington (greatest British actuary ever)

Δ A− L( )L

= −(DurA −DurL )×Δy+ 12( )× (ConvA −ConvL )× Δy( )2

•  To achieve greater convexity than liabilities, the asset portfolio will have a wider spread of maturities eg maturity barbell

•  This is OK if the yield curve experiences a parallel shift

•  However if the yield curve steepens for example at the same time as shifting, the high convexity portfolio will underperform a matched convexity portfolio

•  Need to model the risks of asset/liability mismatch more thoroughly

Immunization issues


•  Credit Default Swaps (CDS) •  Acts like an insurance policy on the default risk of a corporate bond or loan

•  Buyer pays annual premiums •  Issuer agrees to buy the bond in a default or pay the difference between par and market values to the CDS buyer

Default Risk and Bond Pricing


•  Credit Default Swaps •  Ins=tu=onal bondholders, e.g. banks, used CDS to enhance creditworthiness of their loan por_olios, to manufacture AAA debt

•  Can also be used to speculate that bond prices will fall •  This means there can be more CDS outstanding than there are bonds to insure

Default Risk and Bond Pricing


Figure 14.12 Prices of Credit Default Swaps

•  The risk of loss resulting from the borrower (issuer of debt) failing to make full and timely payments of interest and/or principal

•  Expected loss=Default Probability x Loss given default

•  For investment grade credits the focus is on default probability, which is very low

•  For speculative grade credit, loss given default becomes very important

•  Recovery rates vary widely by industry

•  They also depend on the credit cycle

Credit Risk (1)

•  Corporate yield spreads depend on credit worthiness and market liquidity

•  Credit rating can migrate with atendency for speculative grade credits to become even lower rated

Credit Risk (2)

Recovery Rating

Average 3 Year Corporate Transition Rates (1981-2014)

Source: Standard & Poor’s 2015

Note for speculative grade the tendency is for ratings to deteriorate rather than improve

•  Investment grade is rated BBB- and above •  Risk of default is very low for investment grade (circa 2%

over 5 years) so covenants and collateral matter much less

•  However for speculative grade (BB+ and below) default risk is significantly higher and lending tends to be ‘secured’

•  ‘Secured’ needs to be interpreted carefully •  A significant number of ‘secured’ loans ultimately realise

losses on default •  For speculative grade the investor needs to consider

both risk of default and loss in the event of default

Investment Grade and Speculative Grade

•  Lien refers to the security of loan •  First lien ranks ahead of second lien in regard to specific

collateral •  Ideally collateral is enough to satisfy both first and

second lien with some left over for general unsecured creditors

•  If collateral is not enough to satisfy claim of first lien, they both rank equally from there on

•  Subordinated debt ranks after senior creditors which may be secured and unsecured (eg general obligation bonds)

•  Investment grade borrowers typically don’t need to offer security via specific collateral

First Lien, Second Lien, subordination

•  The common credit rating refers to risk of default •  A separate rating addresses loss severity •  Ratings agencies were guilty of over-rating structured

credit leading up to GFC •  Standard corporate credit ratings have been reliable •  The market will usually anticipate downgrades so beware

discrepancies between yield and rating •  Issuer rating refers usually to senior unsecured debt •  Specific issues may be notched (eg subordinate debt will

be rated lower)

Ratings Agencies and Credit Ratings

Credit Rating (S&P)

Credit Rating (S&P)

US Industrial companies – 3 year average

Source: Standard & Poor’s 2011

Ratings and default by time horizon

Ratings and default by time horizon

Default rates and investment grade (2)

Default rates and investment grade (1)

Default rates are cyclical, especially for speculative grade

Default rates vary significantly by industry

Surges in speculative grade issuance have tended to lead the default cycle

Recovery Rating Distribution

•  Two types – incurrence (light) and maintenance(restrictive) covenants

•  At the investment grade level (bonds) where default risk is remote incurrence covenants are common

•  Incurrence covenants are triggered where the issuer takes an action (paying a dividend, making an acquisition, issuing more debt)

•  For example more debt may not be able to be issued if the multiple of debt to cash flow falls below a threshold (eg 5 times)

Loan covenants (1)

•  Maintenance covenants (high yield credit) require the issuer to have ongoing satisfactory financial health, even if there is no intention to issue more debt

•  For example if cash flow declines and debt to cash flow increases a maintenance covenant might be breached

•  Maintenance covenants allow lenders to take action earlier with the onset of financial distress

•  They may increase the spread or seek additional collateral •  Covenants on new issues tend to be stronger during weak

economic conditions

Loan covenants (2)

Maintenance covenants are typically more detailed and may include: •  Coverage – minimum level of cash flow or earnings relative

to interest, debt service (interest plus repayments), fixed charges (debt service plus capex and rent)

•  Leverage – debt to equity or cash flow (eg total debt to EBITDA)

•  Current-ratio – current assets (cash, securities, receivables, inventories) to current liabilities (accounts apyable, short term debt). Quick ratio excludes inventories.

•  Tangible-net-worth – minimum level of book value less intangibles)

•  Maximum-capital-expenditures

Loan covenants (3)

•  High yield companies can have fragile liquidity

•  They may have a slow cash conversion cycle (eg high inventory and receivables)

•  No access to commercial paper market so rely on banks which may impose tight restrictions

•  Private companies cannot easily issue equity

•  Rollover risk - new loans or bond issues are required to pay maturing debt

•  Secured loans in a debt structure make unsecured loans less attractive

High Yield Credit and Liquidity Risk

•  Profitability of companies with high operational leverage is

adversely affected by an economic downturn

•  Liquidity can tighten as banks become more cautious with short-term funding, further crimping profitability

•  Debt becomes difficult to roll over – investors are reluctant

•  The default cycle awakens and spreads widen, reducing the market value of these loans

•  Companies that can only afford cheap debt are in trouble even if they can roll over loans

•  Collateral is worth less so loss given default increases

•  Investors get stuck as the secondary market dries up, and there bonds/loans fall in value

High yield credit is susceptible to a perfect storm

There are a range of interest bearing securities traded on the ASX: •  Australian Government Bonds (for retail investors •  Unsecured notes – sometimes issued by insurers as

regulatory capital •  Convertible notes – debt with an option over equity •  Corporate preference shares – conversion or redemption

may be at company’s option, with risk of security becoming perpetual

•  Bank capital notes – similar to a converting preference shares

The Australian corporate bond market is largely traded ‘over-the-counter’ (ie not through an exchange)

Floating rate mischief on the ASX (1)

•  Floating rate securities are of no standard form and need to be analysed thoroughly

•  Typically pay a margin above Bank Bill Swap Rate •  Although they have zero yield curve duration they still have

spread duration because of term to maturity •  Bank capital notes are every bit as vulnerable as equity in

the event of financial stress (that’s why they’re Tier 1 capital)

•  Where an issuer has options (eg to redeem early), the investor should be compensated by a yield premium

•  Interest is not always cumulative, and may be deferred (eg if APRA says so!)

Floating rate mischief on the ASX (2)

ACTL5303Week6_2015

Documents

company tax

arithmetic mean

tax liability

portfolio weight

superannuation fund

portfolio beta

years earnings

geometric mean