Question

You short an equity portfolio worth $50 million with a market beta of 0.7. The market index is currently at 1000.

b. Suppose you buy 150 futures contracts to buy the market index one year from now. The contract multiplier is 250. What is the delta of the futures?

c. What is the dollar change in the value of your equity portfolio if the market index increases by 50 points (5%)?

d. What is the dollar change in the payoff of your futures position if the market index increases by 50 points (5%)?

Answer to C: If the market index increases by 50 points or 5% , then the portfolio should increase in value by (5 x 0.7) =3.5 % Therefore, increase in $ value of portfolio = 50 x (1.035) = $ 1750000.
Answer to D: Cash Ouflow when Futures are bought = 150 x 250 x 1000 = $ 37500000. Cash Inflow when Futures are sold after 50 point increase = 150 x 250 x 1050 = $ 39375000. Change in Payoff = 39375000 - 37500000 = $ 1875000

e. Based on your answers in parts c and d, do you conclude that you have a favorable deal, or are you facing any risk?

f. If you want to hedge away your risk completely, what changes in your futures position should you make?

Answer 1

Answer

(a) Delta of the portfolio (or any financial asset) is the change in the price of the portfolio for a unit change in the price of the underlying asset.

In this case the equity portfolio is assumed to be have the market index as the underlying asset.

The beta of the portfolio is 0.7 which implies that for a 1% change in value of the market index (underlying asset) the value of th equity portfolio changes by beta x 1% = 0.7%

Hence, Portfolio Delta = 0.7

(b) The delta of the futures portfolio is equal to the change in value of futures position for a unit change in the value of the underlying asset. The underlying asset in this case is the market index, which however has no intrinsic spot value as it is intangible. The intangible nature ensures that market index value is decipherable only if its is attached to a futures based on this index. Such a future is infact the futures position that the investor undertakes (by buying 150 of these futures) and hence the underlying asset (ndex based futures) is same as the futures on it. Therefore, the futures position will have a beta of 1 as the derivatives and its underlying asset are one and the same in this case(because the underlying is intangible in nature and has no intrinsic spot value).

(c) If the market index increases by 50 points or 5% , then the portfolio should increase in value by (5 x 0.7) =3.5 %

Therefore, increase in $ value of portfolio = 50 x (1.035) = $ 1750000

(d) Cash Ouflow when Futures are bought = 150 x 250 x 1000 = $ 37500000

Cash Inflow when Futures are sold after 50 point increase = 150 x 250 x 1050 = $ 39375000

Change in Payoff = 39375000 - 37500000 = $ 1875000

(e) It can be risky as if market index gies down the value of futures will also go down but not in ame ratio as equity.

(f) It can be risky as if market index gies down the value of futures will also go down but not in ame ratio as equity. So, need to balance the remaining value of change using more short of equity portfolio.