RETURN AND RISK:
THE CAPITAL ASSET PRICING
MODEL (CAPM)
Chapter 11

11-2
Class Problem Consider the following scenario:ScenarioProbabilityStock Return Bond ReturnRecession.20-5%+14%Normal .60+15%+8%Boom.20+25%+4%Calculate the expected return and standard deviation of returns for stocks.
2

11-3
Class Problem con’t
Scenario
Probability
Stock Return
Bond Return
Recession
.20
-5%
+14%
Normal
.60
+15%
+8%
Boom
.20
+25%
+4%
Calculate the expected return and standard deviation of returns for bonds.ER of bond = variance of bond = standard deviation Look at the way stock and bond returns move during recessions and booms. What does this mean for diversification in a portfolio of the two assets?
=
3

11-4
Individual Securities
For individual stocks we look at:
◦
Expected Return
◦
Variance and Standard Deviation
◦
Covariance and Correlation (to another security or index)

11-5
Covariance &
Correlation
Variance and Standard Deviation
◦
measure the variability of individual stocks.
Covariance and Correlation
◦
Measure how 2 random variable are
related
.
5

11-6
Covariance
Scenario
Probability
Stock
Bond
Deviations
Product (1) x (4)
(1)
(2)
(3)
(4)
Recession
.20
-.18%
.056%
-.01008
- .002016
Normal
.60
.02%
- .004%
-.00008
-.000048
Boom
.20
.12%
-.044%
-.00528
-.001056
Covariance (Rstocks,Rbonds) = - .00312
Deviations from Exp Returns
Product of
Covariance: A measure of the degree to which returns on two risky assets
move in tandem.
If the covariance is negative, the two returns tend to move in opposite directions.
If the covariance is positive, the two returns tend to move together.
Negative Covariance shows negative relationship between stock & bond returns – one
is usually above the average return when the other is below its average return
The size of the number is hard to interpret
because it is in squared deviation units

11-7
Correlation
9949
.
0
)
032
)(.
098
(.
00312
.
)
,
(
b
a
b
a
Cov
Correlation: A statistic in which the covariance is scaled to a value between +1 to -1

11-8
Correlation

11-9
The Return and Risk for
Portfolios
Note that stocks have a higher expected return than bonds and
higher risk. Let us turn now to the risk-return tradeoff of a
portfolio that is 50% invested in bonds and 50% invested in stocks.
Scenario
Probability
Stock Return
Bond Return
Recession
.20
-5%
+14%
Normal
.60
+15%
+8%
Boom
.20
+25%
+4%
ER of stock
=
13%
variance of stock = 96
standard deviation
=
9.8%
ER of bond =
8.4%
variance of bond = 10.24
standard deviation
=
3.2%

11-11
The Efficient Set
Definition:
◦