Question

Suppose you manage an equity portfolio. You are concerned that equities, as an asset class, are temporarily overvalued, so you implement a hedge, utilizing the S&P 500 index futures contract. Other important information is as follows:

Your equity portfolio is $5M and has a beta equal to 1.5.

The riskless rate is 4% per annum.

The S&P 500 index is currently equal to 1,000 and has a dividend yield of 1% per annum.

The S&P 500 index futures price is 1,010 witha multiplier of 250 (for delivery in four months);

Your hedge will be in place for three months.

You short 30 contractsto hedge the portfolio (rounded to the nearest integer).

Suppose that three months later, the S&P 500 index is 900 and the S&P 500 index futures priceis 902.

(a) _+810,000___What is the cash flow associated with the futures position(and indicate positive or negative)?(

b) ___-9.75%_____What is the percent return on the S&P 500 market index (including dividends)?

(c) ____-15.125%___What is the predicted percent return on the equity portfolio, as forecasted by the CAPM?

(d) __$-756,250________What is the cash flow on the equity portfolio?

The answers are given, I need help on how to workout problems b,c and d.

Thanks.

Answer 1

Few observations to be noted:

For CAPM -

It is important to note that market return of -4.5% is for 3 months whereas risk free rate is per annum. risk free rate for 3 months would be 4/4 = 1%.

CAPM = 1 + 0.9 (-4.5-1) = 3.95%

Cash flow from equity portfolio = 100million * 3.95% = 3,950,000 ---- Answer 3

Cash flow from hedged position = 3,950,000 - 4,922,500 = 972,500

Percent return = 972500 / 100 million / 100 = 0.97% for 3 months --- Ans