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 options to be purchased is given by:

  

Given portfolio value=$50mn, target beta=NIL, portfolio beta=0.8, price of future=2,000,future multiplier=100.

Thus 200 put contracts should be sold.

b) Current price of index=2,000 and price after 3 months=1,900

Cash inflow by selling put=$(2,000-1,900)*200*100=$20,00,000

c) Market index = Dividend yield + Capital gain yield, given dividend yield on index=2% per annum, current level of index is 2,000 and level in three months will be 1,900.

= 2/100*3/12+ (1,900-2,000)/2,000

= 0.005 +(-0.05)

= -0.045 or -4.5%

d) Return on equity as per CAPM is given by:

  

Given risk free rate=4%, Market index=-4.5% as calculated in (c) and portfolio beta=0.8.

  

Thus loss in value of portfolio=$50mn*2.8%=$14,00,000

Cash inflow from put option=$20,00,000 as calculated in (a).

Total gain=$(20,00,000-14,00,000)=$6,00,000