8/3/2019 342 Chapter 13

1/51

Chapter 13. Risk & Return in

Asset Pricing Models

Portfolio Theory

Managing Risk

Asset Pricing Models

8/3/2019 342 Chapter 13

2/51

I. Portfolio Theory

how does investor decide amonggroup of assets?

assume: investors are risk averse additional compensation for risk

tradeoff between risk and expected

return

8/3/2019 342 Chapter 13

3/51

goal

efficient or optimal portfolio

for a given risk, maximize exp.

return OR

for a given exp. return, minimize

the risk

8/3/2019 342 Chapter 13

4/51

tools

measure risk, return

quantify risk/return tradeoff

8/3/2019 342 Chapter 13

5/51

return = R =change in asset value + income

initial value

Measuring Return

R is ex post

based on past data, and is known R is typically annualized

8/3/2019 342 Chapter 13

6/51

example 1

Tbill, 1 month holding period

buy for $9488, sell for $9528

1 month R:

9528 - 9488

9488

= .0042 = .42%

8/3/2019 342 Chapter 13

7/51

annualized R:

(1.0042)12

- 1 = .052 = 5.2%

8/3/2019 342 Chapter 13

8/51

example 2

100 shares IBM, 9 months

buy for $62, sell for $101.50

$.80 dividends 9 month R:

101.50 - 62 + .80

62= .65 =65%

8/3/2019 342 Chapter 13

9/51

annualized R:

(1.65)12/9

- 1 = .95 = 95%

8/3/2019 342 Chapter 13

10/51

Expected Return

measuring likely future return

based on probability distribution

random variable

E(R) = SUM(Ri x Prob(Ri))

8/3/2019 342 Chapter 13

11/51

example 1

R Prob(R)

10% .2

5% .4

-5% .4

E(R) = (.2)10% + (.4)5% + (.4)(-5%)

= 2%

8/3/2019 342 Chapter 13

12/51

example 2

R Prob(R)

1% .3

2% .4

3% .3

E(R) = (.3)1% + (.4)2% + (.3)(3%)

= 2%

8/3/2019 342 Chapter 13

13/51

examples 1 & 2

same expected return

but not same return structure

returns in example 1 are morevariable

8/3/2019 342 Chapter 13

14/51

Risk

measure likely fluctuation in return how much will R vary from E(R)

how likely is actual R to vary fromE(R)

measured by

variance (s2) standard deviation (s)

8/3/2019 342 Chapter 13

15/51

s2 = SUM[(Ri - E(R))2 x Prob(Ri)]

s = SQRT(s2)

8/3/2019 342 Chapter 13

16/51

example 1

s2 = (.2)(10%-2%)2

= .0039

+ (.4)(5%-2%)2

+ (.4)(-5%-2%)2

s = 6.24%

8/3/2019 342 Chapter 13

17/51

example 2

s2 = (.3)(1%-2%)2

= .00006

+ (.4)(2%-2%)2

+ (.3)(3%-2%)2

s = .77%

8/3/2019 342 Chapter 13

18/51

same expected return

but example 2 has a lower risk

preferred by risk averse investors variance works best with symmetric

distributions

8/3/2019 342 Chapter 13

19/51

symmetric asymmetric

E(R)R

prob(R)

R

prob(R)

E(R)

8/3/2019 342 Chapter 13

20/51

II. Managing risk

Diversification

holding a group of assets

lower risk w/out lowering E(R)

8/3/2019 342 Chapter 13

21/51

Why?

individual assets do not have

same return pattern combining assets reduces overall

return variation

8/3/2019 342 Chapter 13

22/51

two types of risk

unsystematic risk

specific to a firm

can be eliminated throughdiversification

examples:

-- Safeway and a strike-- Microsoft and antitrust cases

8/3/2019 342 Chapter 13

23/51

systematic risk

market risk cannot be eliminated through

diversification

due to factors affecting all assets

-- energy prices, interest rates,inflation, business cycles

8/3/2019 342 Chapter 13

24/51

example

choose stocks from NYSE listings

go from 1 stock to 20 stocks

reduce risk by 40-50%

8/3/2019 342 Chapter 13

25/51

s

# assets

systematic

risk

unsystematic

risktotal

risk

8/3/2019 342 Chapter 13

26/51

measuring relative risk

if some risk is diversifiable,

then sis not the best measure ofrisk

is an absolute measure of risk

need a measure just for the

systematic component

8/3/2019 342 Chapter 13

27/51

Beta, b variation in asset/portfolio return

relative to return of market portfolio

mkt. portfolio = mkt. index

-- S&P 500 or NYSE index

b =% change in asset return

% change in market return

8/3/2019 342 Chapter 13

28/51

interpreting b if b = 0

asset is risk free

if b = 1 asset return = market return

if b > 1 asset is riskier than market index

b < 1 asset is less risky than market index

8/3/2019 342 Chapter 13

29/51

Sample betas

Amazon 2.23

Anheuser Busch -.107

Microsoft 1.62

Ford 1.31

General Electric 1.10

Wal Mart .80

(monthly returns, 5 years back)

8/3/2019 342 Chapter 13

30/51

measuring b estimated by regression

data on returns of assets

data on returns of market index estimate

b= mRR

8/3/2019 342 Chapter 13

31/51

problems

what length for return interval?

weekly? monthly? annually?

choice of market index? NYSE, S&P 500

survivor bias

8/3/2019 342 Chapter 13

32/51

# of observations (how far back?)

5 years? 50 years?

time period?

1970-1980?

1990-2000?

8/3/2019 342 Chapter 13

33/51

III. Asset Pricing Models

CAPM

Capital Asset Pricing Model

1964, Sharpe, Linter quantifies the risk/return tradeoff

8/3/2019 342 Chapter 13

34/51

assume

investors choose risky and risk-freeasset

no transactions costs, taxes

same expectations, time horizon

risk averse investors

8/3/2019 342 Chapter 13

35/51

implication

expected return is a function of

beta

risk free return market return

8/3/2019 342 Chapter 13

36/51

]R)R(E[R)R(E fmf b=

or

]R)R(E[R)R(E fmf b=

fR)R(E is the portfolio risk premium

where

fm R)R(E is the market risk premium

8/3/2019 342 Chapter 13

37/51

so if b >1,

portfolio exp. return is larger thanexp. market return

riskier portfolio has larger exp.return

fR)R(E fm R)R(E

)R(E )R(Em

>

>

8/3/2019 342 Chapter 13

38/51

so if b

8/3/2019 342 Chapter 13

39/51

so if b =1,

portfolio exp. return is same thanexp. market return

equal risk portfolio means equal exp.return

fR)R(E fm R)R(E

)R(E )R(Em

=

=

8/3/2019 342 Chapter 13

40/51

so if b = 0,

portfolio exp. return is equal to riskfree return

fR)R(E

)R(Ef

R

= 0

=

8/3/2019 342 Chapter 13

41/51

example

Rm = 10%, Rf = 3%, b = 2.5]R)R(E[R)R(E

fmf

b=

%]3%10[5.2%3)R(E =

%5.17%3)R(E =

%5.20)R(E =

8/3/2019 342 Chapter 13

42/51

CAPM tells us size of risk/returntradeoff

CAPM tells use the price of risk

8/3/2019 342 Chapter 13

43/51

Testing the CAPM

CAPM overpredicts returns

return under CAPM > actual return

relationship between and return? some studies it is positive

some recent studies argue no

relationship (1992 Fama & French)

8/3/2019 342 Chapter 13

44/51

8/3/2019 342 Chapter 13

45/51

other factors important in

determining returns January effect

firm size effect

day-of-the-week effect ratio of book value to market value

8/3/2019 342 Chapter 13

46/51

problems w/ testing CAPM

Roll critique (1977)

CAPM not testable

do not observe E(R), only R

do not observe true Rm

do not observe true Rf results are sensitive to the sample

period

8/3/2019 342 Chapter 13

47/51

APT

Arbitrage Pricing Theory

1976, Ross

assume: several factors affect E(R)

does not specify factors

8/3/2019 342 Chapter 13

48/51

implications

E(R) is a function of severalfactors, F

each with its own bNN332211f F....FFFR)R(E bbbb=

8/3/2019 342 Chapter 13

49/51

APT vs. CAPM

APT is more general

many factors

unspecified factors

CAPM is a special case of the APT

1 factor

factor is market risk premium

8/3/2019 342 Chapter 13

50/51

testing the APT

how many factors?

what are the factors?

1980 Chen, Roll, and Ross industrial production

inflation

yield curve slope other yield spreads

8/3/2019 342 Chapter 13

51/51

summary

known risk/return tradeoff

how to measure risk?

how to price risk?

neither CAPM or APT are perfect orfree of testing problems

both have shown value in assetpricing