Finance Question - Financial Market
AmazingExpert
financial-markets.doc*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 ( ) R |
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)
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)
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)
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)2. (25 points)
You are given the following data for options on a common stock;
102
$
=
S
75
$
=
X
%
5
.
2
=
r
months
T
3
=
2
.
=
s
a. Use the Black-Scholes Option Pricing Model to find the price of the options.
(i) Find
T
T
r
X
S
d
s
s
÷
÷
ø
ö
ç
ç
è
æ
+
+
÷
ø
ö
ç
è
æ
=
2
ln
2
1
andT
d
d
s
-
=
1
2
(6 points)(ii) Use your answers from a(i) to find
(
)
1
d
N
and(
)
2
d
N
. Note: Round your answers to 2 decimal places before looking the values up in the tables. (4 points)(iii) Use the Black-Scholes OPM to find C. (5 points)
(iv) Use the put-call parity relationship to find the value of
P
. (4 points)b. State the intrinsic value and the speculative premium for the call and put options. Why is the speculative premium so small for each option? (5 points)
3. (25 points)
A call option has a value of
5
$
=
C
and a put has a value of3
$
=
P
. Both options have an exercise price of20
$
=
X
. The options are to expire today.e. Compute the payoff schedule for the call option using the following stock prices,
S
, and draw a graph of the payoff schedule. (7 points)
|
S |
10 |
15 |
20 |
25 |
30 |
|
Intrinsic Value |
|
|
|
|
|
|
Payoff |
|
|
|
|
|
f. Compute the payoff schedule for the call option using the following stock prices,
S
, and draw a graph of the payoff schedule. (7 points)|
S |
10 |
15 |
20 |
25 |
30 |
|
Intrinsic Value |
|
|
|
|
|
|
Payoff |
|
|
|
|
|
g. Suppose that you buy the share for $20, but you would like to hedge your downside risk. Choose either the call or put option to eliminate some of the potential loss, and complete the table below. State what the resulting payoff schedule looks like. (11 points)
|
S |
10 |
15 |
20 |
25 |
30 |
|
Gain/loss on share |
|
|
|
|
|
|
Intrinsic Value (Call or Put) |
|
|
|
|
|
|
Payoff |
|
|
|
|
|
4. Provide a description of the three forms of the Efficient Market Hypothesis using the picture below. Do you think the markets are efficient?
Look at the graph below. It depicts the price adjustment at the time of the announcement of Martha’s Stewart’s conviction on Friday, March 5, 2004.
Bonus question: (5 points)
Revalue the call option using
0
=
s
so that there is no volatility. All other input values for the option remain the same as in question 2.
