Hull J.C. Risk management and Financial institutions

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404 Chapter 18

late 1990s. This is discussed in Business Snapshot 15.5. All insurance

companies decided to hedge their exposure to a fall in long-term rates at

about the same time. The result was a fall in long-term rates!

The chief lesson to be learned from these stories is that it is important

to see the big picture of what is going on in financial markets and to

understand the risks inherent in situations where many market partici-

pants are following the same trading strategy.

18.4 LESSONS FOR NONFINANCIAL CORPORATIONS

We conclude with some lessons applicable primarily to nonfinancial

corporations.

Make Sure You Fully Understand the Trades You Are Doing

Corporations should never undertake a trade or a trading strategy that

they do not fully understand. This is a somewhat obvious point, but it is

surprising how often a trader working for a nonfinancial corporation will,

after a big loss, admit to not really understanding what was going on and

claim to have been misled by investment bankers. Robert Citron, the

treasurer of Orange County, did this. So did the traders working for

Hammersmith and Fulham, who in spite of their huge positions were

surprisingly uninformed about how the swaps and other interest rate

derivatives they traded really worked.

If a senior manager in a corporation does not understand a trade

proposed by a subordinate, the trade should not be approved. A simple

rule of thumb is that if a trade and the rationale for entering into it are

so complicated that they cannot be understood by the manager, it is

almost certainly inappropriate for the corporation. The trades under-

taken by Procter and Gamble would have been vetoed using this

criterion.

One way of ensuring that you fully understand a financial instrument is

to value it. If a corporation does not have the in-house capability to value

an instrument, it should not trade it. In practice, corporations often rely

on their investment bankers for valuation advice. This is dangerous, as

Procter and Gamble found out. When it wanted to unwind its trans-

actions, it found it was facing prices produced by Bankers Trust's

proprietary models, which it had no way of checking.

Big Losses and What We Can Learn from Them 405

Make Sure a Hedger Does Not Become a Speculator

One of the unfortunate facts of life is that hedging is relatively dull,

whereas speculation is exciting. When a company hires a trader to

manage foreign exchange, commodity price, or interest rate risk there is

a danger that the following happens. At first the trader does the job

diligently and earns the confidence of top management. He or she

assesses the company's exposures and hedges them. As time goes by,

the trader becomes convinced that he or she can outguess the market.

Slowly the trader becomes a speculator. At first things go well, but then a

loss is made. To recover the loss, the trader doubles up the bets. Further

losses are made, and so on. The result is likely to be a disaster.

As mentioned earlier, clear limits to the risks that can be taken should

be set by senior management. Controls should be put in place to ensure

that the limits are obeyed. The trading strategy for a corporation should

start with an analysis of the risks facing the corporation in foreign

exchange, interest rate, commodity markets, and so on. A decision

should then be taken on how the risks are to be reduced to acceptable

levels. It is a clear sign that something is wrong within a corporation if

the trading strategy is not derived in a very direct way from the

company's exposures.

Be Cautious about Making the Treasury Department a

Profit Center

In the last 20 years there has been a tendency to make the treasury

department within a corporation a profit center. This seems to have much

to recommend it. The treasurer is motivated to reduce financing costs and

manage risks as profitably as possible. The problem is that the potential

for the treasurer to make profits is limited. When raising funds and

investing surplus cash, the treasurer is facing an efficient market. The

treasurer can usually improve the bottom line only by taking additional

risks. The company's hedging program gives the treasurer some scope for

making shrewd decisions that increase profits, but it should be remem-

bered that the goal of a hedging program is to reduce risks, not to

increase expected profits. The decision to hedge will lead to a worse

outcome than the decision not to hedge roughly 50% of the time. The

danger of making the treasury department a profit center is that the

treasurer is motivated to become a speculator. An outcome like that of

Orange County or Procter and Gamble is then liable to occur.

406

Chapter 18

SUMMARY

The key lesson to be learned from the losses is the importance of internal

controls. The risks taken by traders, the models used, and the amount of

different types of business done should all be controlled. It is important

to "think outside the box" about what could go wrong. LTCM, Enron's

bank counterparties, and many other financial institutions have failed to

do this, with huge adverse financial consequences.

FURTHER READING

Dunbar, N., Inventing Money: The Story of Long-Term Capital Management and

the Legends Behind It. Chichester, UK: Wiley, 2000.

Jorion, P., Big Bets Gone Bad: Derivatives and Bankruptcy in Orange County.

New York: Academic Press, 1995.

Jorion, P., "How Long-Term Lost Its Capital," Risk, September 1999: 31-36.

Ju, X., and N. Pearson, "Using Value at Risk to Control Risk Taking: How

Wrong Can You Be?" Journal of Risk, 1 (1999): 5-36.

Thomson, R., Apocalypse Roulette: The Lethal World of Derivatives. London:

Macmillan, 1998.

Zhang, P. G., Barings Bankruptcy and Financial Derivatives. Singapore: World

Scientific Publishing, 1995.

Valuing Forward

and Futures

Contracts

The forward or futures price of an investment asset that provides no

income is given by

where S

is the spot price of the asset today, T is the time to maturity of

the forward or futures contract, and r is the continuously compounded

risk-free rate for maturity T. When the asset provides income during the

life of the contract that has a present value I, this becomes

When it provides a yield at rate q, it becomes

A foreign currency can be regarded as an investment asset that provides a

yield equal to the foreign risk-free rate.

The value of a forward contract where the holder has the right to buy

the asset for a price of K is in all cases

where F is the forward price. The value of a forward contract where the

408

Appendix A

holder has the right to sell the asset for a price of K is similarly

Example A.1

Consider a six-month futures contract on the S&P 500. The current value of

the index is 1200, the six-month risk-free rate is 5% per annum, and the

average dividend yield on the S&P 500 over the next six months is expected to

be 2% per annum (both rates continuously compounded). The futures price is

1200e

(0.05 - 0.02)x0.5

, or 1,218.14.

Example A.2

The current forward price of gold for a contract maturing in nine months is

$550. A company has a forward contract to buy 1,000 ounces of gold for a

delivery price of $530 in nine months. The nine-month risk-free rate is 4% per

annum continuously compounded. The value of the forward contract is

1,000 x (550 - 530)e

-0.04x9/12

, or $19,409.

Valuing Swaps

An interest rate swap can be valued by assuming that the interest rates

that are realized in the future equal today's forward interest rates. As an

example, consider an interest rate swap has 14 months remaining and a

notional principal of $100 million. A fixed rate of 5% per annum is

received and LIBOR is paid, with exchanges taking place every six

months. Assume that (a) four months ago the six-month LIBOR rate

was 4%, (b) the forward LIBOR interest rate for a six-month period

starting in two months is 4.6%, and (c) the forward LIBOR for a six-

month period starting in eight months is 5.2%. All rates are expressed

with semiannual compounding. Assuming that forward rates are realized,

the cash flows on the swap are as shown in Table B.l. (For example, in

eight months the fixed-rate cash flow received is 0.5 x 0.05 x 100, or

$2.5 million; the floating-rate cash flow paid is 0.5 x 0.046 x 100, or

Table B.1 Valuing an interest rate swap by assuming forward

rates are realized.

Time

2 months

8 months

14 months

Fixed cash flow

($ million)

2.5

Floating cash flow

($ million)

-2.0

-2.3

-2.6

Net cash flow

($ million)

0.5

0.2

-0.1

410

Appendix B

Table B.2 Valuing a currency swap by assuming forward exchange rates are

realized (all cash flows in millions).

Time

USD

cash flow

-0.6

-10.0

GBP

cash flow

0.2

5.0

Forward

exchange rate

1.8000

1.8400

1.8800

USD value of

GBP cash flow

0.360

0.368

0.376

9.400

Net cash flow

in USD

-0.240

-0.232

-0.224

-0.600

$2.3 million.) The value of the swap is the present value of the net cash

flows in the final column.

An alternative approach (which gives the same valuation) is to assume

that the swap principal of $100 million is paid and received at the end of

the life of the swap. This makes no difference to the value of the swap but

allows it to be regarded as the exchange of interest and principal on a

fixed-rate bond for interest and principal on a floating-rate bond. The

fixed-rate bond's cash flows can be valued in the usual way. A general rule

is that the floating-rate bond is always worth an amount equal to the

principal immediately after an interest payment. In our example, the value

of the floating rate bond is worth $100 million immediately after the

payment in two months. This payment (determined four months ago) is

$2 million. The value of the floating-rate bond is therefore $102 million

immediately before the payment at the two-month point. The value of the

swap is therefore the present value of the fixed-rate bond less the present

value of a cash flow of $102 million in two months.

Currency Swaps

A currency swap can be valued by assuming that exchange rates in the

future equal today's forward exchange rates. As an example consider a

currency swap in which 4% will be received in GBP and 6% will be paid

in USD once a year. The principals in the two currencies are 10 million

USD and 5 million GBP. The swap will last for another three years. The

swap cash flows are shown in the second and third columns of Table B.2.

The forward exchange rates are (we assume) those shown in the fourth

column. These are used to convert the GBP cash flows to USD. The final

Note that this is not perfectly accurate because it does not take account of day count

conventions and holiday calendars.

Valuing Swaps

411

column shows the net cash flows. The value of the swap is the present

value of these cash flows.

An alternative approach (which gives the same valuation) is to regard

the swap as a long position in a GBP bond and a short position in a USD

bond. Each bond can be valued in its own currency in the usual way and

the current exchange rate can be used to convert the value of the GBP

bond from GBP to USD.

Valuing

European Options

The Black-Scholes-Merton formulas for valuing European call and put

options on an investment asset that provides no income are

and

where

The function N(x) is the cumulative probability distribution function for

a standardized normal distribution (see tables at the end of the book).

The variables c and p are the European call and European put price, S

the stock price at time zero, K is the strike price, r is the continuously

compounded risk-free rate, is the stock price volatility, and T is the time

to maturity of the option.

When the underlying asset provides a cash income, the present value of

the income during the life of the option should be subtracted from S

When the underlying asset provides a yield at rate q, the formulas become

and

where

Options on a foreign currency can be valued by setting q equal to the

foreign risk-free rate.

Table C.l gives formulas for the Greek letters. N'(x) is the standard

normal density function, given by

Example C.1

Consider a six-month European option on a stock index. The current value of

the index is 1200, the strike price is 1250, the risk-free rate is 5%, the dividend

yield on the index is 2%, and the index volatility is 20%. In this case,

= 1200, K = 1250, r = 0.05, q = 0.02, = 0.2, and T = 0.5. The value of

414 Appendix C

Table C.1 Greek letters for options on an asset that provides a yield at rate q.