Finance practice
MGF402 Homework 3
Due date: Thursday October 31st
1. Calculate EAR and APR for the following questions.
a. You have an APR of 7.5% with continuous compounding. What is the EAR?
b. You have an EAR of 9%. What is the equivalent APR with continuous compounding?
c. The buyer of a new home is quoted a mortgage rate of 0.5% per month. What is the APR on the loan?
d. A loan for a new car costs the borrower 0.8% per month. What is the EAR?
Answer:
a.
1 + EAR = eAPR => EAR = eAPR - 1 = e.075 - 1 = 7.79%
b.
1 + 9% = eAPR => Ln(1.09) = Ln(eAPR) = APR
APR = Ln(1.09) = 8.62%
c.
0.5% x 12 = 6%
d.
(1.008)12 - 1 = 10.03%
2. Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 3 should invest entirely in a risky portfolio with a standard deviation of 24% only if the risky portfolio’s expected return is at at least ______.
Answer: 3 = (E[rQ] - .04)/(.242) => E[rQ] = (.242) x 3 + .04 = 21.28%
3. You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a Treasury bill with a rate of return of 5%.
a. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%?
b. How much money should be invested in the risky asset to form a portfolio with a standard deviation of 9%?
Answer:
a.
E[rC] = yE[rp] + (1 - y)rf
11% = y x 15% + (1 - y) x 5% y = 60%.
Invest $10,000 x 60% = $6,000 in the risky asset.
b. σC = yσp
9% = y x 21% y = 45%.
Invest $10,000 x 45% = $4,500 in the risky asset.
4. You have $500,000 available to invest. The risk-free rate, as well as your borrowing rate, is 8%. The return on the risky portfolio is 16%. The standard deviation on the risky portfolio is 50%.
a. If you wish to earn a 22% return, how much money should you borrow?
b. If the standard deviation on the complete portfolio is
Due date: Thursday October 31st
1. Calculate EAR and APR for the following questions.
a. You have an APR of 7.5% with continuous compounding. What is the EAR?
b. You have an EAR of 9%. What is the equivalent APR with continuous compounding?
c. The buyer of a new home is quoted a mortgage rate of 0.5% per month. What is the APR on the loan?
d. A loan for a new car costs the borrower 0.8% per month. What is the EAR?
Answer:
a.
1 + EAR = eAPR => EAR = eAPR - 1 = e.075 - 1 = 7.79%
b.
1 + 9% = eAPR => Ln(1.09) = Ln(eAPR) = APR
APR = Ln(1.09) = 8.62%
c.
0.5% x 12 = 6%
d.
(1.008)12 - 1 = 10.03%
2. Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 3 should invest entirely in a risky portfolio with a standard deviation of 24% only if the risky portfolio’s expected return is at at least ______.
Answer: 3 = (E[rQ] - .04)/(.242) => E[rQ] = (.242) x 3 + .04 = 21.28%
3. You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a Treasury bill with a rate of return of 5%.
a. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%?
b. How much money should be invested in the risky asset to form a portfolio with a standard deviation of 9%?
Answer:
a.
E[rC] = yE[rp] + (1 - y)rf
11% = y x 15% + (1 - y) x 5% y = 60%.
Invest $10,000 x 60% = $6,000 in the risky asset.
b. σC = yσp
9% = y x 21% y = 45%.
Invest $10,000 x 45% = $4,500 in the risky asset.
4. You have $500,000 available to invest. The risk-free rate, as well as your borrowing rate, is 8%. The return on the risky portfolio is 16%. The standard deviation on the risky portfolio is 50%.
a. If you wish to earn a 22% return, how much money should you borrow?
b. If the standard deviation on the complete portfolio is