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FIN 685: Risk Management Topic 2: How Do We Deal with Risk? Why Should We Care? Larry Schrenk, Instructor Why Manage Risk? Why Hedge? Digression: Non-Linearity What is Hedging? How to Hedge – Linear Risk – Non-Linear Risk Why Manage Risk? Why Hedge? – Commodity price risk – Equity market risk – Interest rate risk – Foreign exchange rate risk – Credit risk – Weather risk 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 5 (of 26) 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) 6 (of 26) 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 NonFinancial Firms 7 (of 26) 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. There are three major ways in which to invest as a speculator in the futures markets – Short Term – Long Term – Spreading 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. 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. 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! Lawrence P. Schrenk 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 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 Now consider a non-linear relationship. – There are an infinite number of slopes Lawrence P. Schrenk 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 We can estimate the slope at any point. A – The yellow tangent line has the slope of the tangent point (A). Lawrence P. Schrenk 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. Lawrence P. Schrenk What is Hedging? “…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?” "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 financial position taken to diminish exposure to a risk. Hedging versus Speculating Hedging as Insurance Hedging-Active; Diversification-Passive Static Hedge – Long Term Position • How Long Does It Last? Dynamic Hedge – Rebalancing • Cost versus Benefit Forward (and Futures) Contracts Options Swap Contracts – Not Here 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. 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. Perfect Hedge: All Risk Eliminated Cross Hedging: Hedged and Hedge Assets Do Not Match Exactly. – Different Assets – Different Characteristics – Different Time Periods Selective Hedging 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 Tbills 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. 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 of Short Foreign Hedge with British Pounds ______________________________________________________________________________________ Date Jan. 1 Cash position Future Hedge ____________________________________________________________ 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 Converts to U.S. dollars at $1.35 and receives $135,000 buy pound futures at $1.35 $5,000 loss Net Hedge Price= Dollar Depreciating May 1 Receives 100,000 pounds Converts to U.S. dollars at $1.45 and receives $145,000 $5,000 gain buy pound futures at $1.45 Eliminate all risk in an underlying risky investment, so risk free. Payoff on underlying asset Payoff on hedged position Payoff on hedge 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 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 91 100 4.98 360 1,000,000 $987,412 100 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 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. (Hedge initiated at time t1 and closed out at time t2) Futures Price Spot Price Time t1 t2 Basis is the difference between spot & futures Basis risk arises because of the uncertainty about the basis when the hedge is closed out 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. Proportion of the exposure that should optimally be hedged is: sS h* r sF 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. To hedge the risk in a portfolio the number of contracts (N*) that should be shorted is P N* b A where P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract The effectiveness of a hedge is measured by r2. – Perfect Hedge: • r = 1 → r2 = 100% 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. 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 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. 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 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 A B C D s 10% 20% 10% 30% r .94 .81 .80 .75 bushels/contract 1,000 1,000 500 1,000 expiration 3 months 5 months 6 months 5 months Use B, since it has the highest r of those contracts expiring after the close of the desired hedge. ss 0.15 0.81 0.6075 Ratio: h* r sF 0.20 Effectiveness: r 0.81 65.61% 2 Contracts: N* b 2 P 100,000 0.6075 60.75 A 1,000 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 A B C D s 10% 20% 10% 30% r bushels/contract expiration 1.0 1,000 5 months .90 1,000 9 months 1.0 500 8 months .95 1,000 5 months Use B, since it has the highest r of those contracts expiring after the close of the desired hedge. ss 0.25 h* r 1 2.5 Ratio: sF Effectiveness: Contracts: 0.10 r 1 100% 2 2 P 100,000 N * b 2.5 5,000 A 50 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 ($) revenues? How can you hedge this risk? 52 (of 26) Now 0 S($/₤) = 1.4794 One Year 1 F12($/₤) = 1.4513 CF = ₤18.2 million $ ??? 53 (of 26) 1. Do not Hedge 2. Hedge with Futures/Forward Contracts 3. ‘Hedge’ with Option Contracts Expected Cash Flow – E[S1($/₤)] = F1($/₤) = 1.4513 – Expected Cash Flow = 1.4513 x ₤18.2 million = $26.41 million Risk – Upside FX Exposure: – Downside FX Exposure: Yes Yes Cost of Hedge Position: $0 55 (of 26) Cash Flow ($) $28.21 $27.30 $26.41 $25.48 $24.57 1.35 1.40 1.45 1.50 1.55 S1($/₤) 56 (of 26) Known Cash Flow – E[S1($/₤)] = F1($/₤) = 1.4513 – Lock in Revenues 1.4513 x ₤18.2 million = $26.41 million Risk – Upside FX Exposure: – Downside FX Exposure: No No Cost of Hedge Position: Minimal 57 (of 26) Cash Flow ($) $28.21 $27.30 $26.41 $25.48 $24.57 1.35 1.40 1.45 1.50 1.55 S1($/₤) 58 (of 26) The relevant option has three possible strike prices: Put Options Strike 1.35 1.40 1.45 Min. Rev. Premium Cost (×18.2 M) $24.6 M $25.5 M $26.4 M $0.012 $0.026 $0.047 $221,859 $470,112 $862,771 59 (of 26) Minimum Cash Flow – E[S1($/₤)] = F1($/₤) = 1.4513 – Lock in Minimum Revenue 1.4513 x ₤18.2 million = $26.41 million Risk – Upside FX Exposure: – Downside FX Exposure: Yes No Cost of Hedge Position: $862,771 60 (of 26) Value ▪ Cash Flow ($) $28.21 Profit ▪ $27.30 $26.41 -$862,771 $25.48 $24.57 1.35 1.40 1.45 1.50 1.55 S1($/₤) 61 (of 26) Cash Flow ($) $28.21 $27.30 Forward Market Hedge $26.41 $25.48 $24.57 1.35 1.40 1.45 1.50 1.55 S1($/₤) 62 (of 26)