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### FIN 685: Risk Management

Topic 2: How Do We Deal with Risk? Why Should We Care?

Larry Schrenk, Instructor

Topics

- Why Manage Risk? Why Hedge?
- Digression: Non-Linearity
- What is Hedging?
- How to Hedge
- Linear Risk
- Non-Linear Risk

Some of the Risks that can be hedged

- Commodity price risk
- Equity market risk
- Interest rate risk
- Foreign exchange rate risk
- Credit risk
- Weather risk

Why Hedge? Con

- Hedging is Irrelevant or Wasteful
- Diversified shareholders don’t care about firm-specific risks (CAPM)
- Since markets are efficient, risk management does not add to firm value
- Active risk management wastes resources
- Agency cost
- Increase risk when competitors do not hedge

Why Hedge? Pro

- Hedging creates Value
- Transaction Costs
- Helps ensure that cash is available for positive NPV investments
- Reduces dependence on (expensive) external finance
- Reduces probability of financial distress
- Firms should focus on core business
- Non-Linearity
- Reduces tax obligation
- No Diversification
- A company whose owners are not well diversified may benefit from hedging. (example: privately owned)

Do Firms Hedge?

- Overall, Firms’ Behavior Diverse
- 50% of surveyed firms do use derivatives for risk management
- especially large firms (83%), and
- especially for FX risk.
- Mainly hedging, but some speculation.
- 1998 Wharton/CIBC World Markets Survey of Financial Risk Management by US Non-Financial Firms

Hedging versus Speculating

- Speculating
- Speculators in futures markets do not own or control the underlying commodity.
- They invest in futures markets to try and capture profits from price movements/price forecasting.
- The major attraction of speculative investors to the futures market is the leverage made possible by the margin system.

Investing as a speculator

- There are three major ways in which to invest as a speculator in the futures markets
- Short Term
- Long Term
- Spreading

Short term speculators

- The most celebrated of all day traders are the scalpers (also known as locals)
- Mostly exchange members
- Trade on very small price movements and concentrate on a large volume of trade to generate income
- Locals usually end the day without holding any open position, i.e., they offset all the trade by the end of the day.

Spreaders

- Spreading involves price relationships in two or more markets and tries to take advantage of any abnormality.
- Spread investing is relatively less risky because gains made on either the buy or sell side are usually offset by losses on other side.
- Spreader will spread temporal, spatial, form and substitutional relationships.

Types of spread

- Temporal Spread: Relationships Involving Carrying Charges such as Storable Commodities
- Spatial Spread: Price Relationship between Gold trading in New York Futures Gold and Chicago Futures Gold
- Substitutional Spread: Near Substitutes

Digression: Non-Linearity

- It is essential to appreciate the importance of this non-linearity, i.e., ‘curvature’
- Non-linearity is our worst enemy!

Digression: Non-Linearity(cont’d)

- First, consider a linear relationship.
- The slope (rise over run) is 1
- If the x value increases by one, then the y value increases by one–everywhere.

Digression: Non-Linearity

- In a linear relationship, all we need to know is the slope to predict how a change in x will affect the value of y.
- In particular, we do not need to know the current value of x in order to predict how a change in x will affect the value of y.

Digression: Non-Linearity

- Now consider a non-linear relationship.
- There are an infinite number of slopes

Digression: Non-Linearity

- In a non-linear relationship:
- No one slope characterizes the entire relationship
- We DO need to know the current value of x in order to predict how a change in x will affect the value of y.
- Any prediction will be
- Only an approximation, and
- Only ‘locally’ valid.

Digression: Non-Linearity

- We can estimate the slope at any point.
- The yellow tangent line has the slope of the tangent point (A).

A

Digression: Non-Linearity

- But the more x changes, the less valid is the prediction of y based upon the slope at x0.
- The accuracy of any prediction will depend upon:
- The magnitude of the change in x, and
- The degree of convexity in the relationship.

Financial risk

- “…can be defined as the exposure of a company’s earnings, cashflow or market value to external factors such as interest rates, exchange rates, or commodity prices.” Tufano and Headley, “Why Manage Risk?”

Financial Engineering

- "the design, development and implementation of innovative financial instruments and processes, and the formulation of creative solutions to problems in finance“ John Finnerty (1988)
- "the development and creative application of financial technology to solve financial problems and exploit financial opportunities." IAFE

A hedgE

- …a financial position taken to diminish exposure to a risk.
- Hedging versus Speculating
- Hedging as Insurance
- Hedging-Active; Diversification-Passive

Static versus Dynamic

- Static Hedge
- Long Term Position
- How Long Does It Last?
- Dynamic Hedge
- Rebalancing
- Cost versus Benefit

Instruments

- Forward (and Futures) Contracts
- Options
- Swap Contracts
- Not Here

Forward (and Futures) Contracts

- An Forward (and Futures) Contract is the Agreement to Buy or Sell a Quantity of an Asset at (or within) a Specified Period of Time at a Specified Price.

Options

- An Option Contract Gives the Right (but Not the Obligation) to Buy Or Sell to Buy or Sell a Quantity of an Asset at (or within) a Specified Period of Time at a Specified Price.
- A Call Option is the Right to Buy.
- A Put Option is the Right to Sell.

Types of Hedges

- Perfect Hedge: All Risk Eliminated
- Cross Hedging: Hedged and Hedge Assets Do Not Match Exactly.
- Different Assets
- Different Characteristics
- Different Time Periods
- Selective Hedging

Long versus short positions

- A long hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price.
- Example: An insurance company plans to buy T-bills two months from now and faces the risk that the price of the bills may increase (interest rates may fall). Hedge: buy T-bill futures.
- A short hedge is appropriate when you know you will sell an asset in the future & want to lock in the price.
- Example: An oil producer agrees to sell 50,000 bbl/mo for each of the next 6 months at spot prices. Presently, the price of oil is $48.50/bbl, but it may fall over the next 6 months. Hedge: Sell a strip of crude oil futures.

Example: perfect hedge

- A U.S. firm that has an export sale to U.K. with payment to be made in British pounds faces the risk that pound, relative to dollar, will depreciate.
- Example: At the current rate of $1.4 per pound, U.S. exporter has agreed to receive 100,000 pounds ($140,000) for the merchandise. If the exchange rate changes to $1.35, the exporter still receive 100,000 pounds. But exchange rate fluctuations has reduced his profit by $5,000.

The perfect hedge

- Eliminate all risk in an underlying risky investment, so risk free.

Payoff on underlying asset

Payoff on hedged position

Payoff on hedge

Example: T-Bills

- Pricing (Discount Basis)
- (1 – discount x (91/360) x $1million
- Mar 19 w/ 27 days to Maturity priced at a discount of 4.68.
- Price on $1 million Face:
- (1 – 0.0468(27/360)) x 1,000,000 = $996,490

T-Bill Futures

- Delivery of 91-day T-Bill at maturity date.
- So, a March futures delivers a June T-Bill.
- Pricing on a discount basis, but quoted %.
- Feb. 19, March 95.02, so discount = 4.98

Hedging a $25MM T-Bill Purchase

- Previous T-Bill futures has us buy:
- $25mill / $987,412 = 25.3187 contracts
- If rates at delivery are 5.5%, T-Bills cost:
- (1-(.055*91/360)) x $1mill = $986,097
- Futures lost:
- (986,097 - 987,412) x 25.3187 = (33294), leaving $24,966,706 for T-Bills
- But this still buys us:
- $ 24,966,706 / $986,097 = 25.3187 $1 mill. T-Bills

Hedging a T-Bill Purchase

- If rates at delivery are 4.5%, T-Bills cost:
- (1-(.045*91/360))*$1mill = $988,625
- Futures gained:
- (988,625 - 987,412)*25.3187 = +30,712,
- Leaving $25,030,712 for T-Bills
- This just buys us:
- $25,030,712/$988,625 = 25.3187 $1 mill. T-Bills
- So, whether rates go up or down, buying March T-Bill futures locks in delivery.

Convergence of Futures to Spot

(Hedge initiated at time t1 and closed out at time t2)

Futures

Price

Spot

Price

Time

t1

t2

Basis Risk

- Basis is the difference between spot & futures
- Basis risk arises because of the uncertainty about the basis when the hedge is closed out

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. This is known as cross hedging.

Optimal Hedge Ratio

Proportion of the exposure that should optimally be hedged is:

where

h* is the optimal hedge ratio,

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

sF is the standard deviation of DF, the change in the futures price during the hedging period

r is the coefficient of correlation between DS and DF.

Optimal contracts

To hedge the risk in a portfolio the number of contracts (N*) that should be shorted is

where P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract

Hedge effectiveness

- The effectivenessof a hedge is measured by r2.
- Perfect Hedge:
- r = 1 → r2= 100%

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 out peformthe market.

Hedging Price of an Individual Stock

- Similar to hedging a portfolio
- Does not work as well because only the systematic risk is hedged
- The unsystematic risk that is unique to the stock is not hedged

Why Hedge Equity Returns

- May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio
- Suppose stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.

Rolling The Hedge Forward

- 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

Example 1: cross hedge

Your company has contracted to buy 100,000 bushels of corn in four months at the then current spot rate (sS = 15%). If you have the following forward contacts available, which is the most effective hedge? Also, calculate the optimal hedge ratio, hedge effectiveness and optimal number of contracts.

Contract sr bushels/contract expiration

A 10% .94 1,000 3 months

B 20% .81 1,000 5 months

C 10% .80 500 6 months

D 30% .75 1,000 5 months

Solution 1: Cross hedge

- Use B, since it has the highest r of those contracts expiring after the close of the desired hedge.
- Ratio:
- Effectiveness:
- Contracts:

Example 2: perfect hedge

Your company has contracted to buy 100,000 lbs. of lard in six months at the then current spot rate (sS = 25%). If you have the following forward contacts available, which is the most effective hedge? Also, calculate the optimal hedge ratio, hedge effectiveness and optimal number of contracts.

Contract sr bushels/contract expiration

A 10% 1.0 1,000 5 months

B 20% .90 1,000 9 months

C 10% 1.0 500 8 months

D 30% .95 1,000 5 months

Solution 2: perfect hedge

- Use B, since it has the highest r of those contracts expiring after the close of the desired hedge.
- Ratio:
- Effectiveness:
- Contracts:

Example: FX Hedging

- Your company, headquartered in the U.S., supplies auto parts to Jaguar PLC in Britain. You have just signed a contract worth ₤18.2 million to deliver parts next year. Payment is certain and occurs at the end of the year.
- The $/₤ exchange rate is currently S($/₤) = 1.4794.
- How do fluctuations in exchange rates affect dollar ($) revenues? How can you hedge this risk?

Three possibilities

- Do not Hedge
- Hedge with Futures/Forward Contracts
- ‘Hedge’ with Option Contracts

Possibility 1: Do Not Hedge

- Expected Cash Flow
- E[S1($/₤)] = F1($/₤) = 1.4513
- Expected Cash Flow =

1.4513 x ₤18.2 million = $26.41 million

- Risk
- Upside FX Exposure: Yes
- Downside FX Exposure: Yes
- Cost of Hedge Position: $0

Possibility 2: Forward Market Hedge

- Known Cash Flow
- E[S1($/₤)] = F1($/₤) = 1.4513
- Lock in Revenues

1.4513 x ₤18.2 million = $26.41 million

- Risk
- Upside FX Exposure: No
- Downside FX Exposure: No
- Cost of Hedge Position: Minimal

Possibility 3: Option Market Hedge

- The relevant option has three possible strike prices:

Put Options

Strike Min. Rev. Premium Cost (×18.2 M)

1.35 $24.6 M $0.012 $221,859

1.40 $25.5 M $0.026 $470,112

1.45 $26.4 M $0.047 $862,771

Possibility 3: Option Market Hedge

- Minimum Cash Flow
- E[S1($/₤)] = F1($/₤) = 1.4513
- Lock in Minimum Revenue

1.4513 x ₤18.2 million = $26.41 million

- Risk
- Upside FX Exposure: Yes
- Downside FX Exposure: No
- Cost of Hedge Position: $862,771

Possibility 3: Payoff

Value ▪

$28.21

Cash Flow ($)

$27.30

Profit ▪

$26.41

-$862,771

$25.48

$24.57

S1($/₤)

1.35

1.40

1.45

1.50

1.55

Payoff Comparisons

$28.21

No Hedge

Option Market Hedge

Cash Flow ($)

$27.30

Forward Market Hedge

$26.41

$25.48

$24.57

S1($/₤)

1.35

1.40

1.45

1.50

1.55

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