Question

A portfolio manager expects to purchase a portfolio of stocks in 60 days. In order to hedge against the potential price increase over the next 60 days, she decides to take a long position on a 60-day forward contract on the S&P 500 stock index. The index is currently 2135. The continuously compounded dividend yield is 2%. The discrete risk free rate is 4%. (Use “Pricing_Equity Model Continuou”)

A. What is the “no-arbitrage” forward price on this forward contract?

B. 30 days into the forward contract, the S&P 500 index is 2100. What is the value of the forward contract position at this 30 days arbitrary time into the contract? (assuming the Forward contract negotiated and locked in price at the “no-arbitrage” forward price above).

C. At expiration, the S&P 500 index value is 2175. What is the value of the forward contract position at expiration?

Answer 1

Answer A .	Fair Future Price (FFP)	Spot Price*(e^(r-dy)t)
	Spot price	2135(Including Dividend)
	r	Continuously Compounding Rate of Interest = 4%
	dy	Dividend Yield = 2%
	t	time in yrs
	Explanation for above formula:
	This formula is as per continuosly Compounding :	So " e" is used and dy is deducted from ROI as for calculating Ex Dividend Spot price.
	Explanation for No Arbitage price:	No arbitage price is that where FFP is equal to Actual Future value; b'coz arbitage is possible only when FFP is not equal to Actual Future value
	Hence FFP is
	2135*(e^(4%-2%)60/360	(Assumed 1 yr=360 days)
	No Arbitage Price (FFP) =2142
Answer B.
	FFP (For 30 Days Future )	2100*e^(4%-2%)30/360
		2103
	Long Position on Contract Entered	2142
	Short Position To be Entered for square off the long position	2103
	Value of forward contract position (at 30 days)	-39
Answer C.
	Long Position on Contract Entered	2142
	short the S&P 500 Index on expiry	2175
	Value of forward contract position	33
	Profit on Settlement	33