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Essentials Of Investments
Found in: Page 590
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

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Short Answer

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.

Answer

Profit will be of $11.

See the step by step solution

Step by Step Solution

Step 1: 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) = ?

Step 2: 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)

Step 3: 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

+(.02 x 1,200)

Short future

0

1,233 - ST

Borrow

1,200

-1,200 x 1.03

Total

0

11 (riskless cash flow)

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