You are given the following data on three securities, A, B, and the market, M: Security Expected Return Standard Deviation Covariance with “M” A 10% 15% 225 B 10% 15% 180 M 10% 15% 225 Note: The...

Fin 81 Midterm Exam
*Show all work where required.
1.
(25 points)
You are given the following data on three securities, A, B, and the market, M:
    Security
    Expected
Return
    Standard Deviation
(
)
s
    Covariance with “M”
(
)
M
i
R
R
Cov
,
    A
    10%
    15%
    225
    B
    10%
    15%
    180
    M
    10%
    15%
    225
Note: The risk-free rate is
%
5
=
F
R
.
a. Compute the correlation between A and the market, and B and the market. (6 points)
Correlation between A and the market = Cov(Ri,RM)/
(
)
s
A*
(
)
s
M
= 225/15*15
= 1
Correlation between B and the market = Cov(Ri,RM)/
(
)
s
B*
(
)
s
M
= 180/15*15
= 0.8
b. Based on your answer to part (a), which of the two securities, A or B, is better to be combined into a portfolio with M? Explain briefly. (5 points)
Security B is better to combined with portfolio M.
Correlation between security A and market is 1 so in case of bull market this portfolio will good return, but in a bear market it will negative return.
In case of security B, it isn’t perfectly correlated with market, so it diversifies the portfolio and offers safety to the investor.
c. Compute the expected return and standard deviation for a portfolio formed between M and your choice in part (b). Then compute the weighted-average standard deviation of this portfolio and explain why the portfolio’s actual standard deviation is less than just holding any of the three securities, all of which have a standard deviation of 15% and an expected return of 10%. (10 points)
(
)
s
p2 = W2M
(
)
s
M2 + W2B
(
)
s
B2 + 2 WMWB WMWA*Correlation Coeff
Assuming a 50:50 portfolio between M and B, then
= 0.52*152 + 0.52*152 + 2*0.5*15*0.5*15*0.8
= 14.23%
Portfolio’s standard deviation is less than all the 3 above mentioned assets because of risk diversification due to addition of B to M.
Assuming a 50:50 portfolio between M and B, then,
50% *10% + 50% * 10% = 10%
So, expected return on total portfolio is 10%.
d. Compute the systematic risk
(
)
b
CAPM expected return for your choice in part (b). Why is it less than 10%? Explain in the context of systematic and total risk. (4 points)
Expected Return = Risk free rate + (return on market – risk free rate)*
(
)
b
10% = 5% + (10% - 5%) *
(
)
b

(
)
b
= 1

(
)
b
is a measure of the volatility of a stock in relation to the market. It is the index of systematic risk, indicating the sensitivity of return on a portfolio to return from the market. If Beta is 1, it means a defensive portfolio.
Total risk = systematic risk + non-systematic risk
2.
(25 points)
You are given the following data for options on a common...