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Determination of Forward and Futures Prices

First, we’ll derive some important general results on the relationship between forward (or futures price) and spot price.

Then, we’ll use the results to examine the relationship between futures price and spot price for contract on stock indices, foreign exchange, and commodities.

1. Investment Assets vs. Consumption Assets

Investment Asset = Asset that is held for investment purposes by significant numbers of investors.

Ex.: stocks, bonds, gold & silver (in certain cases)

Consumption Asset = Asset that is held primarily for consumption.

Ex.: copper, oil, pork bellies…

We’ll see that we can use “arbitrage arguments” to determine the forward (or futures) price of an investment asset. We cannot do this for consumption assets.

Short selling

Short selling = Selling an asset that is not owned. (Possible for some – but not all – investment assets)

(CF Illustration pg 100)!!

The investor is required to maintain a “margin account” with the broker.

Margin account = Cash deposited by the investor with the broker to guarantee that the investor will not walk away from the short position if the share price increase. If the price of the asset goes up, additional margin may be required.

Margin account does not represent a cost for the investor because interest is paid on the balance in margin accounts.

Assumptions and Notation

In this chapter we will assume that:

* Market participants are subject to not transaction costs when they trade;

* Market participants are subject to the same tax rate on all net trading profits;

* Market participants can borrow money at the same risk-free rate of interest as they can lend money;

* Market participants take advantage of arbitrage opportunities as they occur.

The following notation will be used:

* T: time until delivery date in a forward or futures contract (in years)

* S0:...