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.
Profit will be of $11.
Based on the input template:
Spot Price (S0) = $1200
Risk-free rate (rf) = 3% or .03
Dividend (d) = 2% or .02
Future price (F0) = ?
Parity value of Futures price F0= S0 (1 + rf - d)T
= $1,200 (1 + .03 - .02)
But the actual futures price = $1233 i.e. overpriced by $11 (given)
Buy the stock at spot price of $1,200 using borrowed money of $1,200 and short future.
Initial cash flow
Cash flow at time T (one year)
+(.02 x 1,200)
1,233 - ST
-1,200 x 1.03
11 (riskless cash flow)
Reconsider the determination of the hedge ratio in the two-state model (Section 16.2), where we showed that one-third share of stock would hedge one option. What would be the hedge ratio for each of the following exercise prices: $120, $110, $100, $90? What do you conclude about the hedge ratio as the option becomes progressively more in the money?
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