1. CHAPTER 4 Risk and Return- The Basics
Stand-alone risk
Portfolio risk
Risk & return: CAPM / SML

2. Risk The chance of variability of returns associated with an asset
The risk can be considered in two ways:
Stand-alone risk (risk of a single asset)
Portfolio risk (risk of an asset is combined with other assets)
ERR should compensate the investors’ perceived risk for the investment

3. Investment returns The rate of return on an investment:
(Amount received – Amount invested)
Return = ________________________
Amount invested
For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is:
($1,100 - $1,000) ÷ $1,000 = 10%.

4. Return: Calculating the expected return
Demand
Probability
Rate of Return
Strong
0.3
100%
Normal
0.4
15%
Weak
(70%)
Total
1.00
= (0.3)(100%)+(0.4)(15%)+(0.3)(-70%)=15%

5. Risk: Calculating the SD for expected return

6. Expected return and SD for historical data
Average return for the historical data is simply the average value of the returns over time
SD is calculated by applying the following formula:

7. Calculating SD for historical data
Year
Return
2002
15%
2003
-5%
2004
20%
Average return: 10%

8. Comments on SD as a measure of risk
SD (σi) measures total risk.
The larger the σi, the lower the probability that actual returns will be closer to expected returns.
The larger σi is associated with a wider probability distribution of returns.
For a one asset portfolio, the appropriate measure of risk is σi.

9. Comparing risk and return
Security
Expected return
Risk, σ
T-bills
8.0%
0.0% HT
17.4%
20.0%
Coll*
1.7%
13.4%
USR*
13.8%
18.8%
Market
15.0%
15.3%
* Seem out of place.

10. Coefficient of Variation (CV)
A standardized measure of dispersion about the expected value
It shows the risk per unit of return
A meaningful basis for comparison when:
The expected returns on two alternatives vary
The returns are expressed in different units

11. Risk rankings by CV CV T-bill 00/8.00 =0.00 HT 20/17.4 =1.15
Coll /1.7 =7.88
USR /13.8=1.36
Market 15.3/15 =1.020
Coll. has the highest amount of risk per unit of return.
HT, despite having the highest standard deviation of returns, has a relatively average CV.

12. Calculating portfolio expected return
Companies
Investment
Expected Return
Microsoft
$25,000
12%
General Electric
11.5%
Pfizer
10.0%
Coca-Cola
9.5%

13. Problems 4-1: A stock’s return has the following distribution
Demands for Products
P(Demand)
Rate of Return if Demand Occurs
Weak
0.1
(50%)
Below average
0.2
(5)
Average
0.4 16
Above average 25
Strong 60
Total Weight
1.00
Calculate the stock’s expected return, standard deviation, and coefficient of variation

14. Solutions 4-1 Demands Prob. Rate of Return Weak 0.1 (50%) -0.05
Below Avg.
0.2
(5)
-0.01
Average
0.4 16
0.064
Above Avg. 25
0.05
Strong 60
0.06
1.00
= 0.114

15. Problems and Solution 4-3
Assume that the risk-free rate is 5% and the market risk premium is 6%.
a) What is the expected return for the overall stock market?
b) What is the required rate of return on a stock that has a beta of 1.2?
Solution:
a) Expected return = 5%+(6%)(1.0)=11%
b) RRR= 5%+ (6%)(1.2)=12.2%

16. Problems and Solution 4-4
Assume that the risk-free rate is 6% and the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7?
Solution:
RRR= 6%+ (13% – 6%)(0.7)=10.9%

17. Problem 4-7 Suppose, rRF=9%, rM=14% and bi=1.3.
a) What is ri, the required rate of return on Stock i?
b) Now suppose rRF (i) increases to 10% or (ii) decreases to 8%. The slope of the SML remains constant. How would this affect
c) Now assume rRF remains at 9% but rM (i) increases to 16% or (ii) falls to 13%. The slope of the SML does not remain constant. How would these changes affect

18. Solution 4-7
a) Given
b-i)
b-ii)
c-i)
c-ii)