Risk & Return

Stand-alone and Portfolio Considerations

Efficient Market Hypothesis

Securities are in equilibrium: “Fairly priced” 100,000+ analysts (MBAs, CFAs, PhDs)

work for investment firms Analysts have access to data and $$

to invest Thus, price reflects news almost

instantaneously

One cannot “beat the market” except through good luck or inside information.

Doesn’t mean you can’t make money.

Weak Form EMH Any information in historical prices is

reflected in stock prices Semi-Strong Form EMH

All public information is reflected in stock prices

Strong Form EMH All information, even inside info, is

embedded in stock prices

EMH

Return Total dollar return

income from investment + capital gain (loss)

Percentage return dividend yield + capital gains yield

You bought a stock for $35 and you received dividends of $1.25. The stock now sells for $40. What is your dollar return?

What is your percentage return?

Risk Returns generally are uncertain. The greater the chance of a return

below the expected return, the greater the risk.

Risk Premium “Extra” return earned for taking on risk Return above the risk free rate (Treasury

bills are considered risk-free)

Probability Distribution

Rate ofreturn (%) 50150-20

Stock X

Stock Y

Distribution of Annual Returns

Expected Returns Expected returns are based on the

probabilities of possible outcomes “Expected” means average if the

process is repeated many times

n

iiiRpRE

1

)(

Example: Expected Returns

What are the expected returns for Stocks C & T? State Probability C

T Boom 0.3 15%

25% Normal 0.5 10

20 Recession??? 2 1

RC = RT =

Variance and Standard Deviation

Both measure the volatility of returns Variance is the weighted average of

squared deviations

Std. Dev. is the square root of the variance (σ)

n

iii RERp

1

22 ))((σ

Example: Variance and Std. Dev.

E(RC) = 9.9%; E(RT) = 17.7%

Stock C

Stock T

n

iii RERp

1

22 ))((σ

Example State Prob. ABC, Inc. (%)

Boom .25 16 Normal .50 8 Slowdown .15 5 Recession.10 -3

What is the expected return, variance, and std dev? E(R) = Variance = Standard Deviation =

Portfolio Return & Variance

m

jjjP REwRE

1

)()(

n

iii RERw

1

22 ))((σ

Example Evenly split investment between A &

B State Prob. A B Boom .4 30% -5% Bust .6 -10% 25%

Expected return and standard deviation Each state

The portfolio

Another Example

State Prob. X Z Boom .25 15% 10% Normal .60 10% 9% Recession.15 5% 10%

What are the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Z?

Types of Risk Systematic

Risk factors that affect a large number of assets

Non-diversifiable risk, Market risk

Unsystematic Risk factors affecting a limited number

of assets Unique risk, Asset-specific risk,

Idiosyncratic risk

Portfolio Diversification Investment in several different

asset classes 50 internet stocks - not diversified 50 stocks across 20 industries -

diversified Can substantially reduce returns

variability without reducing expected returns

A minimum level of risk cannot be diversified away

Unsystematic Risk Diversifiable or unsystematic risk

can be eliminated by combining assets into a portfolio

Total risk = systematic risk + unsystematic risk Std. dev. of returns measures total risk If diversified, unsystematic risk is very

small

Systematic Risk Reward for bearing risk

No reward for unnecessary risk Beta (β) measures systematic risk

Relative to overall market What does beta tell us?

β =1: asset has ____systematic risk as the market

β < 1: asset has ____systematic risk than the market

β > 1: asset has ____systematic risk than the market

Total versus Systematic Risk

Std Dev Beta Security C 20% 1.25 Security K 30% 0.95

Which has more total risk? Which has more systematic risk? Which should have the higher

expected return?

Example: Portfolio BetasSecurity Weight Beta A .2 2.7 B .3 0.2 C .1 2.0 D .4 1.5

What is the portfolio beta? βP = w1β1 + w2β2 + w3β3 +… =

Beta and the Risk Premium

Risk premium = expected return – risk-free rate

Higher beta ~ higher risk premium Can estimate the expected return

when we know this relationship

Beta & Returns

Rf

E(RA)

A0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

Exp

ecte

d R

etur

n

Slope = Rise / Run = (E(RA) – Rf) / (A – 0)

Reward to Risk Ratio

Slope of beta & return relationship Reward to risk ratio or the risk

premium

What if an asset has a reward-to-risk ratio of 8 (asset plots above the line)?

What if an asset has a reward-to-risk ratio of 7 (asset plots below the line)?

Security Market Line

SML represents market equilibrium In equilibrium, all assets and portfolios must

have the same reward-to-risk ratio SML slope is the reward-to-risk ratio:

(E(RM) – Rf) / M = E(RM) – Rf = mkt risk premium

M

fM

A

fA RRERRE

)()(

SML

r (%)

bi

8

1.0

Risk Compensation

Riskfree Rate

Market Risk Premium

Premium for Riskier Stock

1.9

Capital Asset Pricing Model

CAPM - relationship between risk and return

E(RA) = Rf + A(E(RM) – Rf) Risk free rate Return for bearing systematic risk Amount of systematic risk

If we know an asset’s systematic risk, we can use the CAPM to determine its expected return

r (%)

0 0.5 1.0 1.5 b

1412

7 5

New SML

Δ Inflation = 2%

Impact of Inflation on SML

Original SML

rM = 18%

rM = 15%SML1

r (%) SML2 : Increased Risk Aversion

Risk, β

18

15

8

1.0

Δ RPM = 3%

Impact of Risk Aversion on SML

Example - CAPM

If the risk-free rate is 3% and the market risk premium is 8%, what is the expected return for each?

Security

Beta

A 2.7 B 0.4 C 2.1 D 1.6

Expected Return

3% + 2.7*8%3% + 0.4*8%3% + 2.1*8%3% + 1.6*8%

New Example

If the risk-free rate is 4% and the market risk premium is 6%, what is the expected return for each?

Security

Beta Expected Return

A 2.0

B 0.8