Download Risk and Return

Return and Risk:
The Capital Asset Pricing Models:
CAPM and APT
Text: Chapter 10 and 11
Portfolio Theory
Ex1, Two portfolio
 Portfolio 1: a single investment A: with expected return :
1 and variance 25
 Portfolio 2: equally weighted combination of two uncorrelated
investments: with expected return of 1, and variances 25
 Both have the same expected return : 1,
but the variance of portfolio 2 is .52*25 + .52*25 = 12.5
 Portfolio 2 is preferred than portfolio 1.
 It is because the zero covariance diversifies some of the return
volatility.
A portfolio of two risky assets
Ex2:
 Asset 1 has expected return of .22 and SD of .32
 Asset 2 has expected return of .13 and SD of .23
 Covariance is .01104
X1
0
.2
.4
.6
.8
1
X2
1
.8
.6
.4
.2
0
E(rp~)
.13
.148
.166
.184
.202
.22
(rp~)
.23
.2037
.2018
.2250
.2668
.32
Efficient Portfolio Frontier
E(R)

Efficient Sets and Diversification
E(R)
r = -1
-1 <
r<1
r =1

What about portfolio of n assets?
Expected return
of portfolio
Standard
deviation of
portfolio’s return.
Markowitz Portfolio Theory
 Combining stocks into portfolios can reduce
standard deviation below the level obtained from a
simple weighted average calculation.
 Less than perfect correlation coefficients make this
possible.
 The various weighted combinations of stocks that
create this standard deviations constitute the set of
efficient portfolios.
Combination of risk-free and risky asset
 p2 = x1212, Thus, : p = x11, x1 = p / 1
 E(rp~) = x1r1 + x2 rf = p*(r1/1) + x2 rf
Expected return
of portfolio
Asset 1
.
rf
Standard
deviation of
portfolio’s return.
Which risky asset to choose?
Capital market line
.
Y
S
X
.
Risk-free
rate (Rf )
Standard
deviation of
portfolio’s return.
Which Risky Asset To Choose?
Expected return
of portfolio
Capital market line
Borrowing
5
Lending
4
Risk-free
rate (Rf )
.
.
.
S
.
Y
X
Standard
deviation of
portfolio’s return.
The Chosen Portfolio, M
 Will different individual have different choice of different risky
portfolio asset?
 What if different individual holds the same expectation
(homogeneous expectation), that is, .market reflects all the
information?
 What does portfolio S look like?
 All investors will invest in portfolio S, regardless of their risk
aversion. But they may NOT have the same portion of their wealth
in the two assets.
Security Market Line
Expected return
on security (%)
.
T
.
Rm
Rf
Security market
line (SML)
M
.
0.8
S
1
Beta of
security
Security Market Line
 For a well diversified portfolio, the risk measure of individual
stock is not the SD of return, it is beta.
 Investors are not rewarded with any return for bearing any
unsystematic risk.
 Why should equilibrium prices of securities fall on SML?

If point A lies above the Security market line, then investors
will bid up the price until the return goes back on line

If point B lies below the security market line, then investors
will sell the security, push down the price until it goes back on
line.
Capital Asset Pricing Model
 If investors hold market portfolio, how do they measure the risk of
individual securities?
The covariance with the markets, that is Beta.
 CAPM, for any security i,
E (ri~) = rf + i [E(rm~ - rf)],
where, E(rm~ - rf) : expected market risk premium
i = COV(ri~, rm~)/m2
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1931-2002
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1931-65
SML
30
20
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
1966-2002
30
20
SML
Investors
10
Market
Portfolio
0
1.0
Portfolio Beta
Testing the CAPM
Company Size vs. Average Return
Average Return (%)
25
20
15
10
5
0
Smallest
Largest
Company
size
Testing the CAPM
Book-Market vs. Average Return
Average Return (%)
25
20
15
10
5
0
Highest
Lowest
Book-Market Ratio
About CAPM
 Why does CAPM not hold ?

Is CAPM dead?
 Expected return vs. real return
 Short term or long term effect?
 The contribution of CAPM



How the financial markets may price risky assets
How to measure a risky asset’s risk
How to calculate expected rate of return.
The Measurement Of Beta
 Choice of market proxy
 The time period
 Measurement error: the problem of overestimate for high
beta and underestimate for low beta stocks
 Instability over time
Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
Premium = r - rf
= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) +
…
Return= a + bfactor1(rfactor1) + bf2(rf2) + …
Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
(1978-1990)
Yield spread
Estimated Risk Prem ium
(rfactor  rf )
5.10%
Interest rate
- .61
Exchange rate
- .59
Real GNP
.49
Inflation
- .83
Mrket
6.36
Factor