“Chapter # 5, Risk and Return - Problems”
QUESTION # 01
Jerome J. Jerome is considering investing in a security that has the following distribution of possible one-year returns:
Probability of Occurrence|0.10|0.20|0.30|0.30|0.10|
Possible return|-0.10|0.00|0.10|0.20|0.30|
a. What is the expected return and standard deviation associated with the investment?
b. Is there much “downside” risk? How can you tell?
SOLUTION:-
(a) Data
Pi = 0.10, 0.20, 0.30, 0.30, 0.10
Ri = -0.10, 0.00, 0.10, 0.20, 0.30
= ??
= ??
R2
Formula
= RiPi
=

POSSIBLE RETURN, Ri|PROBABILITY OF OCCURRENCE, Pi|(Ri) (Pi)|(Ri - )2 (Pi)|
-0.10|0.10|-.01|(-.1 -.11)2(.10)|
0.00|0.20|.00|( .00 - .11)2(.20)|
0.10|0.30|.03|( .10 - .11)2(.30)|
SOLUTION:-
Data
Rf = 0.07 m = 0.12 β = 1.67
= ??
Formula
= Rf + (m + Rf) β

Expected return = .07 + (.12 - .07) (1.67) = .1538, or 15.38%

QUESTION # 06
Currently, the risk free rate is 10 percent and the expected return on the market portfolio is 15 percent. Market analysts’ return expectations for four stocks are listed here, together with each stock’s expected beta.
STOCK|EXPECTED RETURN|EXPECTED BETA|
1. Stillman Zinc Corporation|17.0%|1.3|
2. Union Paint Company|14.5|0.8|
3. National Automobile Company|15.5|1.1|
4. Parker Electronics, Inc.|18.0|1.7|
a. If the analysis’ expectations are correct, which stocks (if any) are overvalued? Which (if any) are undervalued?
b. If the risk-free rate were suddenly to rise to 12 percent and the expected return on the market portfolio to 16 percent, which stocks (if any) would be overvalued? Which (if any) undervalued? (Assume that the market analysts’ return and beta expectations for our four stocks stay the same.)

SOLUTION:-
The best way to visualize the problem is to plot expected returns against beta. A security market line is then drawn from the risk-free rate through the expected returns for the market portfolio which has a beta of 1.0.

a)

For a 10% risk-free rate and a 15% market return, indicates that stock 1 and 2 are