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# Forwards in the share / equity market

There is only one type of forward contract in the share market, and this is the outright forward. An outright forward is simply the sale of shares at some date in the future at a price agreed at the time of doing the deal. The mathematics is straightforward (= cost of carry model):

where

FP = forward price

SP = spot price

t = term, expressed as number of days / 365

ir = interest rate per annum for the term (expressed as a unit of 1).

An example is required: a pension fund believes the price of Company XYZ shares will increase over the next 85 days when its cash flow allows the purchase of these shares. It requires 100 000 shares of the company and approaches a broker-dealer to do an 85-day forward deal. The broker-dealer buys the 100 000 shares now at the spot price of LCC94 per share and finances them by borrowing the funds from its banker at the prime rate of 12.0% pa for 85 days. It offers the pension fund a forward deal based on the following (assumption: non-dividend paying share):

SP = 100 000 shares of Company XYZ at LCC94.0 per share = LCC9 400 000 t = 85 days

ir = 12.5% = 0.125 (note that the it includes a margin of 0.5%) FP = LCC9 400 000 x [1 + (0.125 x 85 / 365)] = LCC9 400 000 x 1.029110

= LCC9 673 634.00.

After 85 days the pension funds pays the broker-dealer this amount for the 100 000 Company XYZ shares, and the broker-dealer repays the bank:

Consideration = LCC9 400 000 x [1 + (0.12 x 85 / 365)]

= LCC9 400 000 x 1.027945

= LCC9 662 684.92.

The broker-dealer makes a profit of LCC10 949.07 (LCC9 673 634.00 - LCC9 662 684.92).

Clearly, the pension fund at the start of the deal is of the opinion that the price of the shares will increase by more than the price of money for the period. Pension funds mainly do outright forward share transactions and this is because they are not permitted to incur borrowings. The pension fund would also "shop around" to find the best deal.

# Forwards in the foreign exchange market

## Introduction

Foreign exchange is deposits and securities in a currency other than the domestic currency, and an exchange rate is an expression of units of a currency in terms of one unit of another currency. An example is USD / LCC 7.5125, which means that LCC 7.5125 is required to buy USD 1.016. The 1.0 is left out of the expression because it is known to be 1.0. The one unit currency is called the base currency and the other the variable currency.

There are two broad types of deals in foreign exchange, spot and forward, and there are four types of forwards. The five deal types in foreign exchange are:

• Spot foreign exchange transactions.

• Forward foreign exchange transactions:

- Outright forwards

- Foreign exchange swaps (not to be confused with "proper" currency swaps)

- Forward-forwards

- Time options (not to be confused with "normal" options).

A spot foreign exchange transaction is a deal done now (on T+0) for settlement on T+2 (an international convention), and essentially amounts to the exchange of bank deposits in two different countries. Investments or the purchase of goods then occur as a second phase, i.e. the foreign bank deposit is used to buy the foreign investment or goods. A forward foreign exchange transaction is a transaction that takes place (i.e. is settled) on a date in the future other than the spot settlement date of T+2, but the price and amount is agreed on the deal date (i.e. now = T+0). This transaction is called an outright forward. This type of forward foreign exchange transaction and the other slight variations on the main theme are discussed next.17

## Outright forwards

### Introduction

As noted, outright forwards are forward foreign exchange contracts, i.e. contracts between the market making banks18 and clients, and may be defined as contracts in terms of which the banks undertake to deliver a currency or purchase a currency on a specified date in the future other than the spot date, at an exchange rate agreed upfront. The formula is:

where

SP = spot exchange rate

irvc = interest rate on variable currency

irbc = interest rate on base currency

t = term, expressed as number of days / 365.

The above is the standard formula, because the vast majority of forwards are done for standard periods of less than a year (30-days, 60-days, 90-days, 180-days, etc). When the period is longer than a year, the formula becomes:

(where the period is broken years, for example 430 days, then n = 430 / 365).

It will have been noted that the principal here is the PV / FV concept, with the difference being that there are two interest rates that are to be taken into account. If the rate on the variable currency is higher than the rate on the base currency, then the units of the variable currency will be higher, i.e. it takes more LCC to buy one USD on a forward date. Conversely, it takes less USD to buy one LCC on the forward date. An example is called for.

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