3.1

Hedging Strategies Using Futures

Chapter 3

3.2

Long & Short Hedges: Anticipatory Hedging Rule

Do now in the futures market what you expect to do in the future spot market

A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price

A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

Examples of Anticipatory Hedging

Airline goes long gasoline futures to hedge a future purchase of jet fuel.

Firm that will issue 20-year bonds a year from now hedges by shorting T-bond futures.

Farmer shorts wheat futures to hedge his sale of wheat in the future.

Opposites Hedging Rule

Your position in the futures market should the opposite of your position in the spot market: if long one, short the other.

A portfolio manager hedges via a short position in stock index futures: spot long, futures short.

Company with outstanding floating-rate debt hedges via long position in T-bill futures: spot short, futures long.

3.5

Argument in Favor of Corporate Hedging

Companies should focus on the parts of their business in which they possess expertise. They should take steps to minimize risks arising from interest rates, exchange rates, and other market variables as they lack expertise in predicting these variables.

Another Argument in Favor of Corporate Hedging

Better (cheaper, more accurate) for company to hedge rather than the individual investors (shareholders) to hedge. The latter do not know the firm’s precise exposure.

3.7

Arguments against Corporate Hedging

Shareholders are usually well diversified and can make their own hedging decisions; stockholder in an airline also owns share in an oil firm.

Explaining ex-post a situation where there is a loss on the hedge and a gain on the underlying can be difficult, i.e. risk of treasurer being fired.

Another Argument against Corporate Hedging

It may increase risk to hedge when competitors do not. Firms in the industry may have the ability to pass on cost increases to customers, i.e. complete pass-thru of cost changes. The variables p (sales price) and c (cost per unit) may be highly positively correlated; a natural hedge exists.

E.g. jewelry manufacturer goes long gold futures. What if gold price subsequently drops?!

Examples of natural hedges (complete pass-through of cost)

When p and c are highly positively correlated. Thus, hedging with futures/forward is not warranted.

Gasoline refiner/retailer: retail price vs. crude oil price.

Meat packer (slaughters, processes, distributes meat to retailers): wholesale price vs. live cattle price.

3.10

Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2)

Time

Spot Price

FuturesPrice

t1 t2

3.11

Basis Risk

Basis is the difference between spot & futures: B = S - F

Basis risk arises because of the uncertainty about the basis when the hedge is closed out

Hedging involves the substitution of basis risk for spot price risk.

3.12

Long Hedge Suppose that

F1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset Price

Hedge via a long futures contract the

future purchase of an asset, risk of S2

Cost of Asset=S2 +(F1–F2) = F1 + Basis2

3.13

Short Hedge

Suppose that

F1 : Initial Futures Price

F2 : Final Futures Price

S2 : Final Asset Price

Hedge via a short futures the future sale of

an asset, risk of S2

Price Realized=S2+ (F1 – F2) = F1 + Basis2

3.14

Choice of Contract

Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge

When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price, aka Cross-hedging. There are then 2 components to the basis.

3.15

Optimal Hedge Ratio

Proportion of the exposure (a percent) that should optimally be hedged is

where

S is the standard deviation of S, the change in the spot price during the hedging period,

F is the standard deviation of F, the change in the futures price during the hedging period is the coefficient of correlation between S and F Measure of hedging effectiveness is square of

F

Sh

Analogy: Simple Regression & Optimal Hedge Ratio

A Variation to be explained

Risk to be hedged

B Explained variation

Hedged risk

C Unexplained variation

Unhedged risk

R^2 = B/A % Explained % Hedged

Perfect hedge iff no basis risk

Perfect hedge: R^2 =1. Implies that correlation between S and F = 1.

R^2 is measure of hedging effectiveness. What proportion of variance in spot price is removed by hedging?

No basis risk: variance of (S-F) = 0. Occurs when the correlation between S

and F = 1.

Derive number of contracts, N, from h

N = h (QA / QF ) QA is size of exposure QF is size of futures contract Example 3.5 p. 60 : Airline wants to hedge

purchase 2 months from now of 2M gallons of jet fuel via long position in oil futures contract. Formula, h = .928 (.0263 / .0313 ) = .78, i.e. hedge 78% of 2M gallons or 1.56M gallons. How many contracts is that?

Hedging effectiveness=.928^2 or 86%

How many contracts, N, is h=78%?

Oil futures contract involves 42,000 gallons i.e., QF= .042M

N = .78 (2M / .042M) = 37.14 or 37 contracts

Take long position in 37 oil contracts. Will remove 86% of uncertainty via this

hedge.

Tailing the Futures Hedge

Adjustment for the fact that the futures hedge generates immediate cash flows (marking to market) whereas the risk being hedged pertain to some time in the future.

NTH= h (VA/VF) = h (QA S/QF F) = N (S/F) Back to Example 3.5 p. 60 with S =

1.94/gallon F = 1.99/gallon NTH= 37.14 (1.94/1.99) = 36.22 or 36 Effect of tailing the hedge adjustment is to

reduce slightly the number of contracts

Should you tail the hedge?

Hedge now receipt/payment in the future with a futures contract? Yes!

Why? Futures hedge cash flows start occurring now & continue daily; receipt/payment occurs at future date

Hedge now receipt/payment a month from now with 1-month forward contract? No!

Hedge now receipt/payment a year from now with 1-year forward contract? No!

3.22

Rolling The Hedge Forward: Hedge a long-term exposure with a time sequence of short-term futures hedges

We can use a series of futures contracts to increase the life of a hedge

Each time we switch from 1 futures contract to another we incur a type of basis risk

Metallgesellschaft debacle: p.69

3.23

Hedging Using Index Futures

To hedge the risk (reduce to zero the ) of an investment portfolio the number of contracts that should be shorted is

where P is the value of the portfolio, is its beta, and F is the current value of one futures (=futures price times contract size)

F

P

3.24

Reasons for Hedging an Equity Portfolio

Desire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.)

Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outperform the market.)

3.25

Example

Futures price of S&P 500 is 1,000

Size of portfolio is $5 million

Beta of portfolio is 1.5

One contract is on $250 times the index

What position in futures contracts on the S&P 500 is necessary to hedge the portfolio? N=1.5(5M/.25M)=30. If short 30 contracts, beta is reduced to zero.

More general stock index futures formula

N*= number of contracts that must be held long to change beta of portfolio to beta*

N*= (beta* – beta) (P/F) Current portfolio exhibits beta If bullish, may want to raise beta P=market value of the managed portfolio F=value of the asset that underlies futures

3.27

Changing Beta of Managed Portfolio

What position is necessary to reduce the beta of the portfolio to 0.75? N=(.75-1.5)(5M/.25M)=-15; short 15 S&P 500 contracts. What if using Mini S&P 500 contracts, F=0.05M? Short 75 Mini S&P 500 contracts.

What position is necessary to increase the beta of the portfolio to 2.0? N=(2-1.5) (5M/.25M)=10; take a long position in 10 S&P500 contracts.