Q12I

Expert-verifiedFound in: Page 589

Book edition
9th

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

Pages
748 pages

ISBN
9780078034695

**The Excel Applications box in the chapter (available at www.mhhe.com/bkm ; link to Chapter 17 material) shows how to use the spot-futures parity relationship to find a “term structure of futures prices,” that is, futures prices for various maturity dates.**

**a. Suppose that today is January 1, 2012. Assume the interest rate is 1% per year and a stock index currently at 1,200 pays a dividend yield of 2%. Find the futures price for contract maturity dates of February 14, 2012, May 21, 2012, and November 18, 2012.**

**b. What happens to the term structure of futures prices if the dividend yield is lower than the risk-free rate? For example, what if the interest rate is 3%?**

**Answer**

a.

$1,198.67 |

$1,195.30 |

$1,189.43 |

b.

$1,201.31 |

$1,204.66 |

$1,210.55 |

Based on the input template:

Spot price | 1200 | Futures price vs maturity | |

Income yield(d) (%) | 2 | ||

Interest (r)(%) | 1 | ||

Today's date | 01-01-2012 | Spot Price | $1,200 |

Maturity date 1 | 02-14-2012 | Futures 1 | $1,198.67 |

Maturity date 2 | 05-21-2012 | Futures 1 | $1,195.30 |

Maturity date 3 | 11-18-2012 | Futures 1 | $1,189.43 |

Time to maturity 1 | 0.11 | ||

Time to maturity 2 | 0.39 | ||

Time to maturity 3 | 0.88 |

Time to maturity is calculated by dividing the number of days from today’s date to maturity date by 365(number of days in year).

Formula used: F0 = S0 (1 + r - d)T

Based on the input template (if dividend rate was lower than risk free rate):

Spot price | 1200 | Futures price vs maturity | ||

Income yield (%) | 2 | |||

Interest (%) | 1 | |||

Today's date | 01-01-2011 | Spot Price | $1,200 | |

Maturity date 1 | 02-14-2012 | Futures 1 | $1,201.31 | |

Maturity date 2 | 05-21-2012 | Futures 1 | $1,204.66 | |

Maturity date 3 | 11-18-2012 | Futures 1 | $1,210.55 | |

Time to maturity 1 | 0.11 | |||

Time to maturity 2 | 0.39 | |||

Time to maturity 3 | 0.88 |

Time to maturity is calculated by dividing the number of days from today’s date to maturity date by 365(number of days in year).

Formula used:

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