Question

A portfolio manager expects to purchase a portfolio of stocks in 60 days. In order to hedge against a 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 at 1150. The continuously compounded dividend yield is 1.85 percent. The discrete risk-free rate is 4.35 percent. Calculate the no-arbitrage forward price on this contract.

Answer 1

SOLUTION:

From given data,

A portfolio manager expects to purchase a portfolio of stocks in 60 days. In order to hedge against a 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 at 1150. The continuously compounded dividend yield is 1.85 percent. The discrete risk-free rate is 4.35 percent.

= $ 1150

T = 60/365

r = 4.35% = 4.35/100 = 0.0435

= ln (1+r) = ln (1+0.0435) = 0.04258

= 1.85 % = 1.85/100 = 0.0185

Calculate the no-arbitrage forward price on this contract.

the no-arbitrage forward price = * e^-*T * e^*T

the no-arbitrage forward price = 1150 * e^{-0.0185*(60/365)} * e^{0.04258*(60/365)}

The no-arbitrage forward price = $ 1154.561