Risk and Return Review Lecture

8/10/2019 Risk and Return Review Lecture

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1

Risk and Return

Professor Allaudeen Hameed

National University of Singapore

Reference:RWJ, Chapters 10, 11, 12, and 13


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Objectives

Basic tool in corporate finance is thediscounted cash flows models

Discounting risky cash flows requiressome way of measuring the discount rate

(cost of capital) How do we measure cost of equity and

cost of capital?


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3

Rates of Return

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Common Stocks

Long T-Bonds

T-Bills

Source: Stocks , Bon ds, Bi l ls, and Inf lat ion2000 Yearbook, Ibbotson Associates, Inc., Chicago (annually updates work by

Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.


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Historical Returns, 1926-2007

Source: Stocks, Bon ds, Bi l ls, and Inf lat ion2008 Yearbook, Ibbotson Associates, Inc., Chicago (annually updates work by


90% + 90%0%

Average Standard

Series Annual Return Deviation Distribution

Large Company Stocks 12.3% 20.0%

Small Company Stocks 17.1 32.6

Long-Term Corporate Bonds 6.2 8.4

Long-Term Government Bonds 5.8 9.2

U.S. Treasury Bills 3.8 3.1

Inflation 3.1 4.2


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The Risk-Return Tradeoff

2%

4%

6%

8%

10%

12%

14%

16%

18%

0% 5% 10% 15% 20% 25% 30% 35%

Annual Return Standard Deviation

AnnualReturn

Average

T-Bonds

T-Bills

Large-Company Stocks

Small-Company Stocks


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6

Normal Distribution

S&P 500 Return Frequencies

0

2

5

11

16

9

1212

1

2

110

0

2

4

6

8

10

12

14

16

62%52%42%32%22%12%2%-8%-18%-28%-38%-48%-58%

Annual returns

Returnfr

equency

Normal

approximation

Mean = 12.8%

Std. Dev. = 20.4%

Source: Stocks , Bon ds, Bi l ls, and Inf lat ion2000 Yearbook, Ibbotson Associates, Inc., Chicago (annually updates work by



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Portfolio Returns: Summary

Distribution of returns are characterized bytwo measures: expected return and risk.

No universal measure of risk

One measure of portfolio risk is thespread/dispersion of returns

Variance and standard deviation

If returns are normally distributed, the

distribution is fully described by mean andstandard deviation


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8

Expected Return:

Variance

Covariance

Correlation Coefficient

K

ssRspRE

1)(

K

s

REs

Rs

p

1

2))((2

K

sBREBsRAREAsRspAB

1

))(,))((,(

BA

ABAB

Review of Statistics


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9

Sample Statistics

The historical returns on asset classes (likestocks) can be summarized by describing the

average return

the standard deviation of those returns

.

TRRR T)( 1

1

)()()( 22221

T

RRRRRRVARSD T


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Diversification of risk

Intuition: two sources of risk are1.firm specific actions that directly affects

the asset price

Firm specific risks: in a portfolio these

risks can average out to zero diversifiable/non-systematic risk

2. marketwide movements that affects allprices

Market risks affects all investments in aportfolio

non-diversifiable or systematic risk

Risk and ReturnIndividual Securities


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11

Portfolio Risk as a Function of theNumber of Stocks in the Portfolio

Nondiversifiable risk;

Systematic Risk;Market Risk

Diversifiable Risk;

Nonsystematic Risk;

Firm Specific Risk;

Unique Risk

n

In a large portfolio the variance terms are effectivelydiversified away, but the covariance terms are not.

Thus diversification can eliminate some, but not all of the

risk of individual securities.

Portfolio risk


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Diversification -Caveat

Diversification reduces portfolio risk is afact (as long as correlation is less than 1.0);but there are disagreements about whetherdiversifiable risk is relevant in asset

pricing.

As we increase N,marginal benefits ofportfolio diversification decreases; andtransaction and information costs increases


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13

Definition of Risk When InvestorsHold the Market Portfolio

Total security risk = systematic (non-diversifiable) risk + unsystematic(diversfiable) risk

Relevant risk = securitys contribution to

well-diversified portfolio risk The common measure of the risk of a

security in a large portfolio is the beta()ofthe security.

Beta measures the responsiveness of asecurity to movements in the marketportfolio.

)(

)(2

,

M

Mi

i

R

RRCov

b


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14

N

i

N

jij ijj

wi

wi

N

i iw

p

iwwhere

N

iiREiwpRE

1 1

2

1

22

0.11

)()(

Intuition: Marginal Contribution to risk

Portfolio variance increasingly depends on covariance

terms as N increases i.e. N variance terms vs N(N-1)covariance terms

Hence, as each security is added, the marginal

contribution to portfolio risk comes mainly from security

covariance with portfolio


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Relationship between Risk and ExpectedReturn (Capital Asset Pricing Model

(CAPM))

Expected Return on the Market:

Expected return on an individual security:

PremiumRiskMarket FM RR

)( FMiFi RRRR

Market Risk Premium

This applies to individual securities held within well-diversified portfolios.

R l ti hi B t Ri k &


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16

Relationship Between Risk &Expected Return

Expec

ted

return

%3FR

%3

1.5

%5.13

5.1 i %10MR

%5.13%)3%10(5.1%3 iR

)( FMiFi RRRR


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Summary

In a world where investors hold combinations of

riskless asset and market portfolio, risk is measuredrelative to market portfolio.

Risk of any portfolio is the risk it adds to themarket portfolio

risk is proportional to covariance term : standardising covariance

beta

What is the beta of:

market portfolio

riskier than market

riskless security?


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18

Estimation of Beta

Theoretically, the calculation of beta is

straightforward:

Market Portfolio - Portfolio of all assets in theeconomy. In practice a broad stock market index

is used to representthe market.

Beta - Sensitivity of a stocks return to the return on

the market portfolio

2)(

),(

M

MiiM

MRVarMRiRCov


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Determinants of Beta

1. Business Risk

Cyclicity of Revenues

Retailers/auto firms pro-cyclical (highbeta)

Utilities/transportless dependent onbusiness cycle (low beta)

Cyclical does not mean volatile

High std dev stocks need not havehigh beta (e.g. movie studioshitor flop)


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Determinants of Beta

2. Operating Leverage

The degree of operating leverage measureshow sensitive a firm (or project) is to its fixedcosts.

Operating leverage increases as fixed costs

rise and variable costs fall.

Operating leverage magnifies the effect ofcyclicity on beta.

The degree of operating leverage is given by:

SalesinChange

SalesinChange

EBIT

EBITDOL


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2. Operating Leverage

Sales Volume

$

Fixed costs

Total

costs

EBIT

Sales

Operating leverage increases as fixed costs rise

and variable costs fall.

Fixed costs

Total

costs


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3. Financial Leverage and Beta

Operating leverage refers to the sensitivityto the firms fixed costs of production.

Financial leverage is the sensitivity of afirms fixed costs of financing.


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Beta and Leverage

If the beta of the debt is non-zero, thenbetas of the firms equity is given by:

B = MV of Debt SL= MV of Levered Equity

TC= corporate tax rate

Financial leverage increases the equitybeta.

L

CS

BT ))(1( DebtfirmUnleveredfirmUnleveredEquity


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24

Financial Leverage and Beta: Example

Consider Grand Sport, Inc., which is

currently all-equity and has a beta of 0.90. The firm has decided to lever up to a capital

structure of 1 part debt to 1 part equity.

Since the firm will remain in the sameindustry, its asset (unlevered) beta shouldremain 0.90.

However, assuming a zero beta for its debt,

and zero tax rate, its equity beta wouldbecome twice as large:

Equity

Debt 1AssetEquity 80.1

1

1190.0


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Stability of Beta

Most analysts argue that betas are

generally stable for firms remaining inthe same industry use industrybetas

Thats not to say that a firms beta

cant change. Changes in product line

Changes in technology

Deregulation Changes in financial leverage


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Main sources of capital

Equity Capital

Retained Earnings

New equity

Debt Capital

Existing debt capacity vs new debt Bank borrowing

Issue bonds


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Cost of Debt

Cost of debt borrowing depends on:

Interest rate levels

Default risk of firm e.g. Bond ratings

Tax rates

Tax advantage of debt

Hybrid securities

e.g. Convertibles


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The Cost of Capital with Debt

The Weighted Average Cost of Capital is givenby:

)1(CBSWACC

TrBS

Br

BS

Sr

rs= cost of equity rB= cost of debt

S = market value of equity

B = market value of debt TC= corporate tax rate

Why do we multiply the last term by (1- TC)?

Estimating International Papers


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Estimating International PapersWACC

First, we estimate the cost ofequity and the cost of debt.

Estimate an equity beta, thenestimate the cost of equity.

We can often estimate the costof debt by observing the YTM ofthe firmsdebt.

Second, we determine the WACCby weighting these two costsappropriately.


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Estimating IPs Cost of Capital

The industry average beta is 0.82;the risk free rate is 8% and the

market risk premium is 9.2%. Thus the cost of equity capital is

%54.15

%2.982.0%8)(

FMiFe RRRr


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Estimating IPs Cost of Capital

The yield on the companys debtis 8% and the firm is in the 37%marginal tax rate.

The debt to value ratio is 32%)1(

CBSWACC Tr

BS

Br

BS

Sr

12.18 percent is Internationals cost of capital. It should be

used to discount any project where one believes that the

projects risk is equal to the risk of the firm as a whole, and the

project has the same leverage as the firm as a whole.

%18.12

)37.1(%832.0%54.1568.0


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Reducing the Cost of Capital

What is Liquidity?

Liquidity, Expected Returns and

the Cost of Capital What the Corporation Can Do


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Liquidity Expected Returns and the


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Liquidity, Expected Returns and theCost of Capital

The cost of trading an illiquidstock reduces the total returnthat an investor receives.

Investors thus will demand a highexpected return when investingin stocks with high trading costs.

This high expected return impliesa high cost of capital to the firm.


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Liquidity and the Cost of Capital

Liquidity

An increase in liquidity, i.e. a reduction in trading costs,

lowers a firms cost of capital.


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What the Corporation Can Do

The corporation has an incentive tolower trading costs since this would

result in a lower cost of capital. A stock split would increase the

liquidity of the shares.

This idea is a new one and empirical

evidence is not yet in.


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What the Corporation Can Do

Companies can also facilitate stock

purchases through the Internet. Direct stock purchase plans and

dividend reinvestment plans handled

on-line allow small investors theopportunity to buy securities cheaply.

The companies can also disclosemore information. Especially to

security analysts, to narrow the gapbetween informed and uninformedtraders. This should reduce spreads.

Th A bit P i i M d l


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The Arbitrage Pricing Model

Logic : investors are rewarded for taking non-diversifiable risks

Firm-specific risks are diversifiable and hence, notpriced

Expected return depends on systematic factors orunanticipated factor shocks (surprise)

Multiple sources of systematic risks (m)

Example: Uncertainty about general economicoutlook

unanticipated changes in GNP, inflation, (real)interest rates changes, changes in default risk,etc

Ri k S t ti d U t ti


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Risk: Systematic and Unsystematic

Systematic Risk; m

Nonsystematic Risk;

n

Total risk; U

We can break down the risk, U, of holding a stock into two

components: systematic risk and unsystematic risk:

riskicunsystemattheisrisksystematictheis

where

becomes

m

mRR

URR

Systematic Risk and Betas


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Systematic Risk and Betas

For example, suppose we have identifiedthree systematic risks on which we want to

focus:1. Inflation

2. GDPgrowth

3.The dollar-euro spot exchange rate, S($,)

Assume returns follow this process:

riskicunsystemattheis

betarateexchangespottheis

betaGDPtheis

betainflationtheis

FFFRR

mRR

S

GDP

I

SSGDPGDPII


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Arbitrage Pricing Model

)(

)()()(

fRSRS

fRGDPRGDPfRIRIfRRE

b

bb


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Documents

Risk and Return Review Lecture