1. 1 Finance School of Management Chapter 11: Hedging, Insuring and Diversifying Objective To explain market mechanisms for implementing hedges, insurance and diversification

2. 2 Finance School of Management The purpose of this chapter is to give more detailed and concrete understanding of all the three methods of transferring risk and how they are used in practice. Hedging Insuring Diversifying

3. 3 Finance School of Management Chapter 11 Contents  Using Forward and Future Contracts to Hedge Risk  Hedging Foreign-Exchange Risk with Swap Contracts  Hedging Shortfall Risk by Matching Assets to Liabilities  Minimizing the Cost of Hedging  Insuring versus Hedging  Basic Features of Insurance Contracts  Financial Guarantees  Options as Insurance  The Diversification Principle  Diversification and the Cost of Insurance

4. 4 Finance School of Management Hedging  The action taken to reduce exposure to a loss but also give up the potential of a gain  Financial markets offer a variety of mechanisms for hedging against the risks. – Forward and futures contracts – Swap contracts – Matching assets to liabilities

5. 5 Finance School of Management A Simple Example  You are planning a trip from Boston to Tokyo a year from now.  You make your flight reservation now.  You can either lock in a price of $1,000 by committing now or wait to do nothing.  In either case, payment will not take place until the day of flight.  In entering the forward contract you eliminate the risk of the airfare going above $1,000.  However, you will have to pay the $1,000 even if the price turns out to be $500 on the day of your flight.

6. 6 Finance School of Management Forward Contracts  Any time two parties agree to exchange some item in the future at a prearranged price, they are entering into a forward contract.  No money is paid in the present by either party to the other.

7. 7 Finance School of Management Terminology  Forward price  Spot price  Face value  Long position  Short position

8. 8 Finance School of Management Forward Contract vs. Spot Contract Delivery price (fixed) T To exchange the asset (delivery) A spot contract is an agreement to buy or sell an asset immediately. Time Price To enter into the contract (quantity, price and future date) 0

9. 9 Finance School of Management An Illustration: A Forward Contract  A farmer has planted her fields with wheat, and the size of her crop is reasonably certain.  It is now a month before harvest.  A large fraction of her wealth is tied up in her wheat crop.  She want to eliminate the risk associated with uncertainty about its future price by selling it now at a fixed price for future delivery.  A baker will need wheat a month from now to produce bread.  A large fraction of his wealth is tied up in his bakery business.  The way for him to reduce the price risk is to buy wheat now for future delivery.  The baker is a natural match for the farmer to enter into a forward contract.

10. 10 Finance School of Management  Suppose the size of the the farmer’s wheat crop is 100,000 bushels.  The forward price is $2 per bushel.  At the end of the month, the farmer will deliver 100,000 bushels wheat to the baker and receive $200,000 from the baker in return.  Both parties eliminate the risk associated with the uncertainty about the spot price of wheat at the delivery date.

11. 11 Finance School of Management Difficulties to Match a Forward Contract  The farmer and the baker may be separated by a great distant. – The farmer is located in Kansas, and usually sells her wheat to a local distributor in Kansas. – The baker is located in New York, and usually buys wheat from a local supplier in New York.  The exactly matched quantity  The credit risk

12. 12 Finance School of Management Futures Contracts  A future contract is a standardized forward contract that is traded on an organized exchange. – Standardization of the terms of the future contracts (e.g., quantity, quality and delivery date ) ; – The exchange interposes itself between the buyer and the seller as an intermediary; – The margin requirement and the mechanism of ‘mark-to-market’.

13. 13 Finance School of Management Further Illustration: A Future Contract

14. 14 Finance School of Management Further Illustration: A Future Contract

15. 15 Finance School of Management

16. 16 Finance School of Management  Whether a transaction reduces or increases risk depends on the particular context in which it is undertaken.  Both parties to a risk-reducing transaction can benefit by it even though in retrospect it may seem as if one of the parties has gained at the expense of the other.  Even with no change in total output or total risk, redistributing the way the risk is borne can improve the welfare of the individuals involved.

17. 17 Finance School of Management Margin and Marking to Market

18. 18 Finance School of Management Another Illustration: A Series of Forward Contracts  Suppose you own a computer-software business in the United States.  A Germany company wants to acquire the right to produce and market your software in Germany.  The Germany company agrees to pay your company DM 100,000 each year for the next ten years for these rights.  If you want to hedge the risk of fluctuation in the dollar value of your expected stream of revenues, what can you do? – Enter into a series of forward contracts. – Enter a currency swap now to exchange your future stream of marks for a future stream of dollars at a or a set of pre- specified exchange rate(s).

19. 19 Finance School of Management Hedging Foreign-Exchange Risk with Swap Contracts  A swap contract is an agreement between two parties (counterparties) to exchange (or swap) a series of cash flows at specified intervals over a specified period of time.  No immediate payment of money to either party  Based on principal (notional) amount  The swap contract is equivalent to a series of forward contracts.

20. 20 Finance School of Management Hedging Foreign-Exchange Risk with Swap Contracts: An Illustration  Suppose that the dollar/mark exchange rate is currently $.50 per mark.  It also applies to all forward contracts covering the next ten years.  By entering the swap contract, you lock in a dollar revenue of $50,000 on the settlement date each year.  Suppose one year from now on the settlement date, the spot rate of exchange is $.40 per mark. –The counterparty is obliged to pay you 100,000×($.50-.40)=$10,000.  If the spot rate of exchange in the second year is $.70 per mark. –You will be obliged to pay the counterparty 100,000×($.70-.50)=$20,000.

21. 21 Finance School of Management Interest Rate Swap: An Illustration  The cost of financing of two corporations with different credit ratings.  AAA corp. has relative advantage in fixed rate financing, while BBB corp. has relative advantage in floating rate financing.  BBB wants to have fixed rate liability, while AAA wants to have floating rate liability.

22. 22 Finance School of Management Hedging Shortfall-Risk by Matching Assets to Liabilities  Financial intermediaries (such as insurance companies) need to assure their customers that the product they are buying is free of default risk.  Hedge their liabilities by investing in assets that match the characteristics of their liabilities.

23. 23 Finance School of Management An Illustration  An insurance company sells a customer a guaranteed investment contract that promises to pay $1,000 five years from now for a one-time premium today of $783.53 (interest rate=5%).  The insurance company can match its assets to this liabilities by buying a five-year government zero-coupon bond for less than $783.53.  However, if the insurance company invests the premium in a portfolio of stocks, there will be a risk of shortfall.

24. 24 Finance School of Management Other Hedging Instruments to Match Assets to Liabilities  A savings bank has customer liabilities that are short- term deposits earning an interest rate that changes with market conditions (floats).  Hedging instruments – To buy a floating-rate bond – A strategy of “rolling over” short-term bonds – To invest in long-term fixed bonds and enter a swap contract to swap the fixed rate for a floating rate

25. 25 Finance School of Management Minimizing the Cost of Hedging  You live in Boston and are planning to move to Tokyo a year from now.  An apartment you agreed to buy it for ¥10.3 million.  The dollar/yen exchange rate is currently $0.01 per yen.  You have just sold your condominium in Boston for $100,000, and have invested the money in one-year U.S. Treasury bills at an interest rate of 3%.  You plan to use the money to pay for the apartment in Tokyo.

26. 26 Finance School of Management  The risk of exchange rate has been fluctuating, as low as $.008 per yen and as high as $.011.  Two ways to eliminate your exposure to the risk of a rise in the dollar price of the yen – To enter a forward contract, the forward price is $.01 per yen; – To get the owner of the Tokyo apartment to sell it to you for a price fixed in U.S. dollars.  The mechanism chosen to implement the hedge should be the one that minimizes the cost of achieving the desired reduction of risk.

27. 27 Finance School of Management Insuring versus Hedging  When you hedge, you eliminate the risk of loss by giving up the potential for gain.  When you insure, you pay a premium to eliminate the risk of loss and retain the potential for gain.

28. 28 Finance School of Management An Illustration  A trip from Boston to Tokyo a year from now.  You make your flight reservation now and lock in a price of $1,000.  By entering the forward contract you eliminate the risk of the price going above $1,000.  But …  Alternatively, the airline offer you the possibility of paying $20 now for the right to purchase your ticket a year from now at a price of $1,000.  If the price turns out to be more than $1,000, you will exercise the right.  Otherwise you will let it expire. Hedging Insuring

29. 29 Finance School of Management The Farmer’s Wheat Crop Hedging versus Insuring against Price Risk: The Farmer

30. 30 Finance School of Management The Farmer’s Wheat Crop  By insuring, the farmer retains much of the economic benefit of an increase in the price of wheat while eliminating the downside risk.  This benefit comes at the cost of paying a premium for the insurance.

31. 31 Finance School of Management Basic Features of Insurance Contracts  Exclusions are losses that might seem to meet the conditions for coverage under the insurance contract but are specifically excluded.  Caps are limits placed on compensation for particular losses covered under an insurance contract.  A deductible is an amount of money that the insured party must pay out of his or her own resources before receiving any compensation from the insurer.  A copayment feature means that the insured party must cover a fraction of the loss.

32. 32 Finance School of Management Financial Guarantees  Financial guarantees are insurance against credit risk, which is the risk to you that the counterparty to your contract will default.  Examples of guarantees – Credit card: guarantees of banks to merchants; – Residential mortgages: guarantees of payment by government.

33. 33 Finance School of Management Caps and Floors on Interest Rates  You have $5,000 on deposit in a bank money-market account.  The interest rate you earn is adjusted on a daily basis.  The risk is that the interest rate will fall.  Insurance policy: interest-floor  You took a $100,000 adjustable-rate mortgage loan for a house.  The mortgage interest rate is tied to the one- year U.S.Treasury bill rate.  Insurance policy: interest-cap

34. 34 Finance School of Management Options as Insurance  A option is the right (not the obligation) to purchase or sell something at a specified price (the exercise price) in the future. – A call and a put – Strike or exercise price – Expiration or maturity date – European- or American-type

35. 35 Finance School of Management Put Options on Stocks  Lucy is a manager working for XYZ corporation.  She has received shares of XYZ stock as compensation in the past and now owns 1,000 shares.  The current market price of XYZ is $100 per share.  She can buy XYZ puts at an exercise price of $100 per share expiring in one year.  The current price of a one-year European put on a share of XYZ with a $100 exercise price is $10.  By choosing a put with a lower exercise price (such as $95), she will increase the ‘ deductible ’ but lower the cost of the insurance.

36. 36 Finance School of Management Put Options on Bonds  We know that the prices of bonds will fluctuate substantially because of changes in possible losses to bondholders from default (the default risk) and changes in the level of risk-free interest rates.  However, a put option on a bond can provide insurance against losses stemming from either source of risk, and thus the bondholders are guaranteed a minimum price which is the exercise price of put option on the bond.

37. 37 Finance School of Management The Diversification Principle  Diversifying means splitting an investment among many risky assets instead of concentrating it all in only one.  The diversification principle states that by diversifying across risky assets people can sometimes achieve a reduction in their overall risk exposure with no reduction in their expected return.

38. 38 Finance School of Management Diversification with Uncorrelated Risks  Investing in a single drug. – initial capital: $100,000 – probability of success: 50% – uncertainty: $400,000 or nothing  Possible outcomes and payoffs: – fail with probability 0.5 and with no payoff – succeed with probability 0.5 and with $400,000

39. 39 Finance School of Management Diversification with Uncorrelated Risks Expected Payoff =$200,000 Standard Deviation =$200,000 Expected Payoff =$200,000 Standard Deviation =$200,000  Investing in two drugs （ diversifying by holding a portfolio ） – initial capital: $100,000 （ $50,000 per drug ） – probability of success: 50% – uncertainty: $200,000 or nothing – independence of successes  Possible outcomes and payoffs: – No drugs succeed with probability 0.25 and with no payoff; – One drug succeeds with probability 0.5 and with $200,000; – Both drugs succeed with probability 0.25 and with $400,000.

40. 40 Finance School of Management Diversification with Uncorrelated Risks Expected Payoff =$200,000 Standard Deviation =$200,000 Expected Payoff =$200,000 Standard Deviation =$200,000 Expected Payoff =$200,000 Standard Deviation =$141,421 Expected Payoff =$200,000 Standard Deviation =$141,421 Standard Deviation falls

41. 41 Finance School of Management Diversification with Uncorrelated Risks  Generalizing the argument, it is easy to prove that the standard deviation in the case of N drugs is:  Conclusion: Given the facts of this example, the risk may be made as close to zero as we wish if there are sufficient securities!  In reality, however, N is must be finite, and pharmaceutical projects have a non-zero correlations.

42. 42 Finance School of Management Nondiversifiable Risk  The part of the portfolio volatility that can be eliminated by adding more stocks is the diversifiable risk.  The part that remains no matter how many stocks are added is the nondiversifiable risk.

43. 43 Finance School of Management Correlated Homogeneous Securities  Pharmaceutical projects do have positive correlation. (Why?)  Loosen the assumptions made about the correlation, and set it to ρ, and use the generalization of  With the homogeneous securities, we have diversifiable risk: firm-specific risk nondiversifiable risk: systematic risk Perfect correlation (ρ=1) does not reduce risk!

44. 44 Finance School of Management Diversifiable Security Risk Nondiversifiable Security Risk 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 05101520253035404550 Portfolio Size Standard Deviation of Portfolio Rate of Return Diversifiable Security Risk Nondiversifiable Security Risk

45. 45 Finance School of Management

46. 46 Finance School of Management Diversifiable (Unique) risk 0 51015 Number of Securities Portfolio standard deviation The effect of increasing the number of securities in a portfolio Nondiversifiable (Market) risk Approx. 20% Diversification of Risk

47. 47 Finance School of Management Diversification and the Cost of Insurance  The more diversified are the risks in a portfolio of a given size, the less it will cost to insure the portfolio against a loss. – Insuring each stock separately would cost twice as much as insuring the portfolio of two stocks. In chapter 12, you will learn how to select an efficient portfolio.