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

Answer to Question (a)
No. of cotracts = Value of spot invastment X Beta / Value of one contract
Value of one contract = 1950X 100 = $195,000
No. of contracts = $50,000,000 X 0.80 / $195,000				205.1282051282
Rounded to 205 Contract
Answer to Question (b)
The question is silent about the premium on put option, So it is ignored.
Since the index became $1900, which is below the strike price of 1950, then the put option can be exercised.
The profit from exercising the put option = (1950-1900)X 100 X205					$10,25,000.00
Answer to Question (c)
Period = 3 months
Return from market = ((Closing value - Opening Value)/ Opening value) X 12 / period +Annualized %return of divident
%return of divident = annual = 2%,
((Closing value - Opening Value)/ Opening value) X 12 /period = ((1900-2000)/2000) X 12/3						-20.00%
Add : Annualized %return of divident						2.00%
percent return on the market index (including dividends)						-18.00%
The Annualized percentage is worked out
Answer to (d),
As per CAPM Predicted return = Rf+ (BetaX (Rm-Rf))
CAPM = 4% + (0.8 X (-18%-4%)			-13.60%

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