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Essentials Of Investments
Found in: Page 589
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

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

See the step by step solution

Step by Step Solution

Step 1: Calculation of future price ‘a’

Based on the input template:

Spot price 1200Futures 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

Step 2: Calculation of future price ‘b’

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

Spot price1200Futures 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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