Chapter 17, Problem 27C

Summary Introduction

(A)

Adequate Information:

Indexed Contract price/Spot price - $1800

Risk free interest rate - 3%

Dividend yield - $25

To calculate:

The value by which the contract is mispriced.

Introduction:

The contract is said to be mispriced if there is discrepancy in parity value of the futures contract and the value of future price of stock-index. The parity value for future price of the contract states that if an asset purchased today and held until the maturity of the futures contract, the value of the future contract is equal to the current spot price adjusted for the variables such as interest rate, dividends, etc. In simple mathematical equation:

  $\text{Parity value=Spot price}\times \text{(1+Risk free interest rate-dividend yield)^time period in years}$

Summary Introduction

(B)

To formulate:

A zero net-investment arbitrage portfolio to show riskless profit equal to future mispricing.

Introduction:

A zero net investment arbitrage portfolio is a situation where an investor can realize arbitrage profits or riskless profits which require no initial net investment. This can be pursued by following a strategy involving selling the stock in strategy A and in strategy B buying stock and then lend in short future position.

Summary Introduction

(C)

To formulate:

An arbitrage portfolio if the investor does not receive any interest on the funds.

Introduction:

Arbitrage opportunity is a strategy of buying and selling of same asset to make profit from price difference.

Summary Introduction

(D)

To formulate:

An arbitrage portfolio if there is no band for stock futures price.

Introduction:

A no-arbitrage band specifies limits on financial portfolio prices i.e. how high and how low can future prices be excluding the possibility of making no arbitrage opportunity.