Risk & Return Good Overview

8/4/2019 Risk & Return Good Overview

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Risk & Return in

Asset Pricing Models

Portfolio Theory

Managing Risk

Asset Pricing Models


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I. Portfolio Theory

how does investor decide among group of

assets?

assume: investors are risk averse

additional compensation for risk

tradeoff between risk and expected return


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goal

efficient or optimal portfolio

for a given risk, maximize exp. return

OR

for a given exp. return, minimize the risk


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tools

measure risk, return

quantify risk/return tradeoff


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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


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example 1

T bill, 1 month holding period

buy for Rs.9488, sell for Rs.9528

1 month R:

9528 - 9488

9488

= .0042 = .42%


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annualized R:

(1.0042)

12

- 1 = .052 = 5.2%


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example 2

100 shares IBM, 9 months

buy for Rs. 62, sell for Rs.101.50

Rs.80 dividends

9 month R:

101.50 - 62 + .80

62= .65 =65%


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annualized R:

(1.65)

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- 1 = .95 = 95%


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Expected Return

measuring likely future return

based on probability distribution

random variable

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


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example 1

R Prob(R)

10% .2

5% .4

-5% .4

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

= 2%


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example 2

R Prob(R)

1% .3

2% .4

3% .3

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

= 2%


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examples 1 & 2

same expected return

but not same return structure

returns in example 1 are more variable


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Risk

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

how likely is actual R to vary from E(R)

measured by variance (s2)

standard deviation (s)


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

s = SQRT(s2)


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example 1

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

= .0039

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

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

s = 6.24%


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example 2

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

= .00006

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

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

s = .77%


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same expected return

but example 2 has a lower risk

preferred by risk averse investors

variance works best with symmetric

distributions


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symmetric asymmetric

E(R)R

prob(R)

R

prob(R)

E(R)


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II. Managing risk

Diversification

holding a group of assets

lower risk w/out lowering E(R)


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Why?

individual assets do not have same return pattern

combining assets reduces overall return variation


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two types of risk

unsystematic risk

specific to a firm

can be eliminated through diversification

examples:

-- Safeway and a strike

-- Microsoft and antitrust cases


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systematic risk

market risk cannot be eliminated through diversification

due to factors affecting all assets

-- energy prices, interest rates, inflation, business

cycles


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example

choose stocks from NSE listings

go from 1 stock to 20 stocks

reduce risk by 40-50%


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s

# assets

systematic

risk

unsystematic

risktotal

risk


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measuring relative risk

if some risk is diversifiable,

then sis not the best measure of risk

is an absolute measure of risk

need a measure just for the systematic

component


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Beta, b

variation in asset/portfolio returnrelative to return of market portfolio

mkt. portfolio = mkt. index

-- NSE index

b =% change in asset return

% change in market return


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interpreting b

ifb = 0

asset is risk free

ifb = 1

asset return = market return

ifb > 1

asset is riskier than market index

b < 1

asset is less risky than market index


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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)


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problems

what length for return interval?

weekly? monthly? annually?

choice of market index?

NSE

survivor bias


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# of observations (how far back?)

5 years? 50 years?

time period?

1970-1980? 1990-2000?


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assume

investors choose risky and risk-free asset

no transactions costs, taxes

same expectations, time horizon

risk averse investors


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implication

expected return is a function of

beta

risk free return

market return


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]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


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so ifb


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so ifb =1,

portfolio exp. return is same than exp. market

return

equal risk portfolio means equal exp. return

fR)R(E fm R)R(E

)R(E )R(Em

=

=


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so ifb = 0,

portfolio exp. return is equal to risk free

return

fR)R(E

)R(Ef

R

= 0

=


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example

Rm = 10%, Rf= 3%, b = 2.5

]R)R(E[R)R(Efmf

b=

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

%5.17%3)R(E =

%5.20)R(E =


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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)


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other factors important in determining

returns

January effect

firm size effect

day-of-the-week effect

ratio of book value to market value


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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


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APT

Arbitrage Pricing Theory

1976, Ross

assume:

several factors affect E(R)

does not specify factors


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implications

E(R) is a function of several factors, Feach with its own b

NN332211f F....FFFR)R(E bbbb=


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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


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testing the APT

how many factors?

what are the factors?

1980 Chen, Roll, and Ross

industrial production

inflation

yield curve slope

other yield spreads


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summary

known risk/return tradeoff

how to measure risk?

how to price risk?

neither CAPM or APT are perfect or free of

testing problems

both have shown value in asset pricing

Risk & Return Good Overview

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