Question

Suppose the S&P 500 currently has a level of 875. The continuously compounded return on a 1-year T-bill is 4.25%. You wish to hedge an $800,000 stock portfolio that has a beta of 1.2 and a correlation of 1.0 with the S&P 500.

(a) What is the 1-year futures price for the S&P 500 assuming no dividends?

(b) How many S&P 500 futures contracts should you short to hedge your portfolio? What return do you expect on the hedged portfolio?

*YOU MUST ANSWER WITH DETAILED WORKING!!

Answer 1

Given in the question

Current level of S&P 500 index = 875

Risk free rate or Rf = 4.25% per ammum(Continuously compounded)

Value of the portfolio = $800000

Beta of the portfolio = 1.2

Correlation = 1 , means the portfolio moves in the direction of the Market moves.

(a)

F= Futures price

S= Sport price or current level of index

e=2.71828

r= rate of return or Rf

t = time

Hence One year Futures price of S&P 500 index=

=>One year Futures price of S&P 500 index = $913

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(b)

No of index futures to be short = [(Value of portfolio*Beta of portfolio)] / value of one futues contract

=>No of index futures to be short =($800000*1.2)/$913 = 1051 contract

Current level of S&P index = 875

Expected one year level of S&P index = 913

Expected Market return = (913-875)/875 *100 = 4.34%

Hence Expected return on portfolio = Risk free return+ Beta*(Expected market return-Risk free return)

=>Expected return on portfolio= 4.25%+1.2*(4.34%-4.25%) = 4.358%