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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
Why Manage Risk? Why Hedge?
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
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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
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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)
7 (of 26)
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 Surve
y 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
Lawrence P. Schrenk
DIGRESSION: NON-LINEARITY
• It is essential to appreciate the importance of this non-linearity, i.e., ‘curvature’
• Non-linearity is our worst enemy!
Lawrence P. Schrenk
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.
Lawrence P. Schrenk
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.
Lawrence P. Schrenk
DIGRESSION: NON-LINEARITY
• Now consider a non-linear relationship.
– There are an infinite number of slopes
Lawrence P. Schrenk
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.
Lawrence P. Schrenk
DIGRESSION: NON-LINEARITY
• We can estimate the slope at any point.
– The yellow tangent line has the slope of the tangent point (A).
A
Lawrence P. Schrenk
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.
What is Hedging?
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.
EXAMPLE: PERFECT HEDGEExample of Short Foreign Hedge with British Pounds ______________________________________________________________________________________
Date Cash position Future Hedge ____________________________________________________________ Jan. 1 U.S. firm agrees to sale in pound. Sell one contract of pound futures at $1.4 Sale price 100,000 pounds (current exchange rate $1.4/pound) Dollar Appreciating May 1 Receives 100,000 pounds buy pound futures at $1.35 Converts to U.S. dollars at $1.35 and receives $135,000 $5,000 loss Net Hedge Price= Dollar Depreciating May 1 Receives 100,000 pounds buy pound futures at $1.45 Converts to U.S. dollars at $1.45 and receives $145,000 $5,000 gain
THE PERFECT HEDGE
• Eliminate all risk in an underlying risky investment, so risk free.
Payoff on underlying asset
Payoff on hedge
Payoff on hedged position
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
91100 4.98
3601,000,000 $987,412
100
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)
Time
Spot Price
FuturesPrice
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 periodr is the coefficient of correlation between DS and DF.
* S
F
h
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
*P
NA
HEDGE EFFECTIVENESS
The effectiveness of 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 peform the 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 HEDGEYour 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 s r 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:
0.15* 0.81 0.6075
0.20s
F
h
22 0.81 65.61%
100,000* 0.6075 60.75
1,000
PN
A
EXAMPLE 2: PERFECT HEDGEYour 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 s r 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:
0.25* 1 2.5
0.10s
F
h
22 1 100%
100,000* 2.5 5,000
50
PN
A
52 (of 26)
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 ($) revenues? How can you hedge this risk?
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TIMELINE
Now One Year 0 1
S($/₤) = 1.4794 F12($/₤) = 1.4513
CF = ₤18.2 million
$ ???
THREE POSSIBILITIES
1. Do not Hedge
2. Hedge with Futures/Forward Contracts
3. ‘Hedge’ with Option Contracts
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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
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POSSIBILITY 1: PAYOFF
1.40 1.45
$26.41
S1($/₤)
Cash
Flo
w (
$)
1.50 1.551.35
$25.48
$24.57
$27.30
$28.21
57 (of 26)
POSSIBILITY 2: FORWARD MARKET HEDGE
• Known Cash Flow– E[S1($/₤)] = F1($/₤) = 1.4513
– Lock in Revenues1.4513 x ₤18.2 million = $26.41
million• Risk
– Upside FX Exposure:No– Downside FX Exposure: No
• Cost of Hedge Position: Minimal
58 (of 26)
POSSIBILITY 2: PAYOFF
1.40 1.45
$26.41
S1($/₤)
Cash
Flo
w (
$)
1.50 1.551.35
$25.48
$24.57
$27.30
$28.21
59 (of 26)
POSSIBILITY 3: OPTION MARKET HEDGE
• The relevant option has three possible strike prices:
Put OptionsStrike 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 $862,771
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POSSIBILITY 3: OPTION MARKET HEDGE
• Minimum Cash Flow– E[S1($/₤)] = F1($/₤) = 1.4513
– Lock in Minimum Revenue1.4513 x ₤18.2 million = $26.41
million• Risk
– Upside FX Exposure:Yes– Downside FX Exposure: No
• Cost of Hedge Position: $862,771
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POSSIBILITY 3: PAYOFF
1.40 1.45
$26.41
S1($/₤)
Cash
Flo
w (
$)
1.50 1.551.35
$25.48
$24.57
$27.30
$28.21 Value ▪
Profit ▪
-$862,771
62 (of 26)
PAYOFF COMPARISONS
1.40 1.45
$26.41
S1($/₤)
Cash
Flo
w (
$)
1.50 1.551.35
$25.48
$24.57
$27.30
$28.21
Opt
ion
Mar
ket Hed
ge
Forward Market Hedge
No Hed
ge
