Q15I

Expert-verifiedFound in: Page 590

Book edition
9th

Author(s)
Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus

Pages
748 pages

ISBN
9780078034695

**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.

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)

= $1,212.00

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.

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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