IPM Quiz2 A Solution Spring 2013
BUS 431a: Investment and Portfolio Management
SPRING 2013, AUBG
Quiz 2(a)
Solution Guide
Problem 1 (5 points)
You are face with probability distribution of the HPR on the stock market index fund given in Spreadsheet 5.1 in the textbook. Suppose that the risk-free interest rate is 6% per year. You are contemplating investing $107.55 in a 1-year CD and simultaneously buying a call option on the stock market index fund with an exercise price of $110 and expiration of 1 year. What is the probability distribution of your dollar return at the end of the year?
Solution:
The probability distribution of the dollar return on CD plus call option is:
State of the Economy
Probability
Year-end price of stock
Ending Value of CD
Ending Value of Call
Total (combined) Value
Excellent
0.25
126.50
$ 114.00
$16.50
$130.50
Good
0.45
110.00
$ 114.00
$ 0.00
$114.00
Poor
0.25
89.75
$ 114.00
$ 0.00
$114.00
Crash
0.05
46.00
$ 114.00
$ 0.00
$114.00
Note: The call option will be executed and the stock fund purchased only when the market price exceeds the exercise price of $110.
Problem 2(5 points)
You manage a risky portfolio with expected return of 18% and standard deviation of 28%. The T-bill rate is 8%. Suppose that your risky portfolio includes the following investment in the given proportions: Stock A – 25%; Stock B: 32%; and Stock C – 43%.
What are the investment proportions of your client’s overall portfolio, including the proportions in T-bills (30%)? What is the reward-to-variability ratio (S) of your risky portfolio?
Solution:
Investment proportions:
30.0% in T-bills
Risky portfolio
0.7 × 25% =
17.5% in Stock A
0.7 × 32% =
22.4% in Stock B
0.7 × 43% =
30.1% in Stock C
Your reward-to-volatility ratio:
Problem 3 (10 points): Consider the two securities listed below:
Risky security: E(R) = 10%, σ = 20%.
Risk-free security: Rf = 5%.
You wish to form a portfolio combining the risky security and the risk-free security such that you earn an expected return of 15%.
a.
SPRING 2013, AUBG
Quiz 2(a)
Solution Guide
Problem 1 (5 points)
You are face with probability distribution of the HPR on the stock market index fund given in Spreadsheet 5.1 in the textbook. Suppose that the risk-free interest rate is 6% per year. You are contemplating investing $107.55 in a 1-year CD and simultaneously buying a call option on the stock market index fund with an exercise price of $110 and expiration of 1 year. What is the probability distribution of your dollar return at the end of the year?
Solution:
The probability distribution of the dollar return on CD plus call option is:
State of the Economy
Probability
Year-end price of stock
Ending Value of CD
Ending Value of Call
Total (combined) Value
Excellent
0.25
126.50
$ 114.00
$16.50
$130.50
Good
0.45
110.00
$ 114.00
$ 0.00
$114.00
Poor
0.25
89.75
$ 114.00
$ 0.00
$114.00
Crash
0.05
46.00
$ 114.00
$ 0.00
$114.00
Note: The call option will be executed and the stock fund purchased only when the market price exceeds the exercise price of $110.
Problem 2(5 points)
You manage a risky portfolio with expected return of 18% and standard deviation of 28%. The T-bill rate is 8%. Suppose that your risky portfolio includes the following investment in the given proportions: Stock A – 25%; Stock B: 32%; and Stock C – 43%.
What are the investment proportions of your client’s overall portfolio, including the proportions in T-bills (30%)? What is the reward-to-variability ratio (S) of your risky portfolio?
Solution:
Investment proportions:
30.0% in T-bills
Risky portfolio
0.7 × 25% =
17.5% in Stock A
0.7 × 32% =
22.4% in Stock B
0.7 × 43% =
30.1% in Stock C
Your reward-to-volatility ratio:
Problem 3 (10 points): Consider the two securities listed below:
Risky security: E(R) = 10%, σ = 20%.
Risk-free security: Rf = 5%.
You wish to form a portfolio combining the risky security and the risk-free security such that you earn an expected return of 15%.
a.