Assignment

Question 1 (20 marks)

Elaine opens a margin account with BG Securities Ltd to purchase 500 shares of AMG stock at $55 per share. She borrows $10,000 from the brokerage firm to help pay for the purchase. The interest rate is 1% per month.

a. Briefly discuss the pros and cons of buying stocks on margin. (4 marks)

b. What is the margin in Elaine's account when she first purchases AMG stock? (3

marks)

c. What is the remaining margin in her account if AMG share price falls to $40 per

share after a month? Will she receive a margin call if the maintenance margin

requirement is 35%? (9 marks)

d. Determine the rate of return on her investment. (4 marks)

Question 2 (20 marks)

Midas is considering two stocks. The expected return on LAN is 15% with a standard

deviation of 32%. The expected return on GBT is 9% with a standard deviation of 23%.

The correlation between the returns on LAN and GBT is 0.15. The betas of LAN and

GBT are 1.2 and 0.8 respectively.

a. Assume that Midas would like to have a portfolio with a beta of 0.9. Recommend

how he can invest in two stocks to achieve his objective. Determine the expected

return and standard deviation on this portfolio. (12 marks)

b. Now suppose the T-bill rate is 4.5%. Recommend how Midas can construct a new

portfolio with a beta of 0.6 by investing in both the portfolio in (a) and the T-bills.

Determine the expected return and standard deviation on the new portfolio. (8 marks)

Question 3 (20 marks)

a. A 10-year 5% coupon bond has a yield of 8% and a duration of 7.85 years. If the

bond yield increases by 60 basis points, what is the percentage change in the bond

price? (3 marks)

b. Alpha Insurance Company is obligated to make payments of $2 million, $3 million,

and $4 million at the end of the next three years, respectively. The market interest

rate is 8% per annum.

i. Determine the duration of the company's payment obligations. (10 marks)

ii. Suppose the company's payment obligations are fully funded and

immunized using both 6-month zero coupon bonds and perpetuities.

Determine how much of each of these bonds the company will hold in the

portfolio. (7 marks)

Question 4 (20 marks)

a. ALM Property stock has a beta of 1.5 and an expected return of 13%. The risk-free

rate is 4%. Assume the CAPM is valid.

i. Determine the market risk premium. (6 marks)

ii. Suppose UCC stock has a beta of 0.6. What is the expected return on the

UCC stock? (4 marks)

b. A fund manager of IMD Securities Ltd quoted:

'GC Tech has a very high beta since its stock has traded as high as $253 and

as low as its current $64 during this year.'

Do you agree with the fund manager? Explain. (10 marks)