This is a question in reading 40 on schweser that I need help on.
- A portfolio manager expects to receive funds from a new client in 30 days. These assets are to be invested in a basket of equities. He decides to take a long position in 20, 30-day forward contracts on the S&P 500 stock index to hedge against an increase in equity prices. The index is currently at 1,057. The continuously compounded dividend yield is 1.50%, and the discrete risk-free rate is 4%. Fifteen days later the index value is 1,103. The value of the forward position after 15 days, assuming no change in the risk-free rate or the dividend yield, is closest to: A. $831.60. B. $860.80. C. $898.60. The discrete risk-free rate is given in the problem, so the first thing to do is calculate the continuously compounded risk-free rate and the forward price at initiation:
=ln(1.04)=0.0392
FP=1.057*e(0.0392-.015)*(30/365)=1059.10 The value of one contract after 15 days is:
V15=(1103/e(0.01515/365)-(1059.1/e0.039215*365)=44.93 The value of 20 contracts is 44.93 × 20 = $898.60.
I just want to make sure that I got the question correctly,
1. we need to know the value of the forward contract at time 15 which is 15 days from the initiation (at the value of 1057) and 15 days from the forward contract expiration at time 30 days.
2. Accordingly, we want to calculate the future value of the current price worth 1057 at time 15 when the contract value is worth 1103.
3. If the above assumptions are correct, why do we discount the 1103 for 15 days? And why do we discount it by the dividend yield?