Question

Suppose the S&P 500 Index portfolio pays a dividend yield of 2% annually. The index currently is 1,200. The T-bill rate is 3%, and the S&P futures price for delivery in one year is $1,233. Construct an arbitrage strategy to exploit the mispricing and show that your profits one year hence will equal the mispricing in the futures market.

Short answer

Answer

Profit will be of $11.

Step-by-step solution

Given information

Based on the input template:

Spot Price (S0) = $1200

Risk-free rate (rf) = 3% or .03

Dividend (d) = 2% or .02

Future price (F0) = ?

Calculation of initial future price

Parity value of Futures price F0= S0(1 + rf- d)T

= $1,200 (1 + .03 - .02)

= $1,212.00

But the actual futures price = $1233 i.e. overpriced by $11 (given)

Calculation of arbitrage

Buy the stock at spot price of $1,200 using borrowed money of $1,200 and short future.

Action	Initial cash flow	Cash flow at time T (one year)
Buy stock	-1,200	$S_T$ +(.02 x 1,200)
Short future	0	1,233 - ST
Borrow	1,200	-1,200 x 1.03
Total	0	11 (riskless cash flow)