Question

For each question use the following data: A fund manager has a portfolio worth $50 million with a beta of 0.80. The manager is concerned about the performance of the market over the next three months and plans to use three-month put options with a strike price of 1950 on a well-diversified index to hedge its risk. The current level of the index is 2,000, one contract is on 100 times the index, the risk-free rate is 4% per annum, and the dividend yield on the index is 2% per annum.

Calculate the effect of your strategy on the fund manager’s returns if the level of the market in three months is 1,900.

(a) How many put option contracts should the fund manager purchase?

(b) What is the cash flow associated with options position, rounded to the nearest dollar?

(c) What is the percent return on the market index (including dividends)?

(d) What is the predicted return on the equity portion of the portfolio, as predicted by the CAPM?

Answer 1

A) Number of put option to be purchased = beta of portfolio* value of portfolio/ value of index

= 0.87* 50,000,000/ 2000*100

= 217.5 i.e.217(after rounding off)

b) current value of index= 2000

strike price = 1950

2 months price = $1900

Cash flow associated with the option position = (1900-2000) *217*100 = ($2170000)

c) Return in the form of dividend = 2%*3/12 = 0.50%

Return in the form of capital gain = 1900-2000/2000 = -5%

Total market return = -4.50%

d) Return as per CAPM-

Return = Rf + beta( Rm-Rf)

4% +0.80 (-4.50-4)

= -2.8%