## CFA Reading on Derivatives – FRA and Futures Markets & Contracts

CFA Level 2 – Derivatives; Study Session 16, Reading 61 in 2011 curriculum/Reading 59 in 2010 – Futures Markets & Contracts

I will go over FRAs and Futures in this post. (FRA is part of previous reading)

**Forward Rate Agreements (FRA)**

FRA is yet another derivative product. The underlying in an FRA is an interest rate on a deposit or on a loan i.e. the price of an FRA is an interest rate. The deposit/loan can be for any period in the future and the beginning of this period can also be any period in the future. It is the beginning and ending of these periods that form the notation of an FRA.

For example, 2 x 5 FRA means that the derivative contract expires in 2 months and the underlying deposit or loan is initiated at the end of 2 months (from now) and ends at the end of 5 months (from now) i.e. the deposit/loan period is for 5 – 2 = 3 months and (it is worth repeating) those 3 months start 2 months from now. (confusing I know but it is imperative you get your head around this)

An FRA is a forward contract in which the long, agrees to pay a fixed interest payment at a future date and receive an interest payment at a rate to be determined at expiration of the contract (not the expiration of the deposit/loan).

*Value of an FRA from CFA Institute:*

The value of an FRA based on a Eurodollar deposit is the present value of $1 to be received at expiration minus the present value of $1 plus the FRA rate to be received at the maturity date of the Eurodollar deposit on which the FRA is based, with appropriate (days/360) adjustments.

The payment made at the expiration of the FRA is the difference between the Value of the FRA and the agreed upon price of the FRA, adjusted by the notional principal and the number of days.

The payoff is also discounted, however, to reflect the fact that the underlying rate on which the instrument is based assumes that payment will occur at a later date… remember that the period of deposit/loan starts at the expiration of the FRA contract and the interest payment on this deposit/loan is made at the end of the period.

Let’s move on to Futures Markets and begin by establishing the difference between Futures & Forwards

Figure 2 http://psc.ky.gov/agencies/psc/training/Risk/sld012.htm

Pricing Futures is similar to Forwards, **future price for an asset with no storage costs** is given by:

The market price of a Forward contract is the amount a party to the transaction is willing to pay to terminate the contract. However, because futures are traded on an exchange and are settled and marked-to-market daily , the Futures contract have zero value at the end of the day and have non-zero value during the day.

Value of a futures contract = Current Futures price – Futures price at last mark-to-market

Because of the daily settlement feature of futures, cash is exchanged daily between the long and the short and this cash can be invested to earn a return. And because of this futures prices are sometimes higher than forwards for an identical contract.

The following table illustrates the difference:

**Costs & Benefits of holding the underlying asset**

If holding an underlying asset results in monetary costs and benefits (net cost), futures price is:.

If holding an underlying asset results in non-monetary benefits (convenience yield), futures price is:

All other formulas (dividend paying asset, coupon paying asset, etc) for pricing futures are similar to forwards.

In the next topic, I will discuss contango and backwardation.

Source of all formulas: Schweser Notes

## What is the theoretical relation among various rates in Economics?

I have been reviewing study session 4 in CFA Level 2 Economics and I can’t seem to get my head around all the parity relations… hence a post to clarify my thoughts and develop a clear understanding.

All parity relations are a function of exchange rates, nominal interest rates, real interest rates and inflation rates between the a pair of countries/currencies.

**Interest Rate Parity – Exchange Rate > Nominal Interest Rate**

Covered Interest Rate Parity:

*forward exchange rate* as a function of the spot exchange rate and nominal interest rates.

Uncovered Interest Rate Parity:

*expected spot exchange rate* as a function of the current spot exchange rate and nominal interest rates

**International Fischer Relation – Inflation Rate > Nominal Interest Rate**

difference in nominal interest rates should be equal to difference in expected inflation rates because real rates as equal

**Purchasing Power Parity (PPP) – Exchange Rate > Inflation Rate**

Absolute PPP

price of a basket of similar goods between two countries should be equal (rarely is in practice)

Relative PPP

*expected spot exchange rate* as a function of the current spot exchange rate and inflation rates (note similarity to uncovered interest rate parity)

Approximate Relative PPP

difference in inflation rates is equal to the *expected appreciation/depreciation *of the currency

The above stuff is easy on its own but gets tricky when combined with International Asset Pricing reading from study session 18 on Portfolio Management.

**Real Exchange Rate**

explains the changes in nominal exchange rate not explained by the *difference in* *price levels* i.e.

(Note here that the price levels are already adjusted for inflation, hence if real exchange rates are constant then any change in nominal exchange rate is explained by the difference in inflation)

Also,

% Change in Real Exchange Rate = % Change in Nominal Exchange rate – (Inflation in DC – Inflation in FC)

**Foreign Currency Risk Premium – Exchange Rate > Real Interest rates**

is the difference between the % change in exchange rates and the difference in real interest rates

I think that should clarify the interplay of different rates.

## loving the silver freefall

What goes up vertically… comes down vertically (almost).

Disclosure: no position in silver or silver related securities