Futures-Swaps-and-Risk-M课件

1、CHAPTER 23Futures, Swaps, and Risk ManagementFutures can be used to hedge specific sources of risk.Hedging instruments include:Foreign exchange futuresStock index futuresInterest rate futuresSwapsCommodity futuresFutures2Foreign Exchange FuturesForeign exchange risk: You may get more or less home cu

2、rrency than you expected from a foreign currency denominated transaction.Foreign currency futures are traded on the CME and the London International Futures Exchange.3Figure 23.2 Foreign Exchange Futures4Interest rate parity theoremDeveloped using the US Dollar and British PoundwhereF0 is todays for

3、ward rateE0 is the current spot ratePricing on Foreign Exchange Futures5Text Pricing Example rus = 4% ruk = 5%E0 = $2.00 per pound T = 1 yrIf the futures price varies from $1.981 per pound, covered interest arbitrage is possible.6Direct Versus Indirect QuotesDirect exchange rate quote:The exchange r

4、ate is expressed as dollars per unit of foreign currencyIndirect exchange rate quote:The exchange rate is expressed as foreign currency units per dollar7Hedging Foreign Exchange RiskA US exporter wants to protect against a decline in profit that would result from depreciation of the pound. The curre

5、nt futures price is $2/1. Suppose FT = $1.90?The exporter anticipates a profit loss of $200,000 if the pound declines by $.10Short or sell pounds for future delivery to avoid the exposure.8Hedge Ratio for Foreign Exchange ExampleHedge Ratio in pounds $200,000 per $.10 change in the pound/dollar exch

6、ange rate$.10 profit per pound delivered per $.10 in exchange rate= 2,000,000 pounds to be deliveredHedge Ratio in contracts Each contract is for 62,500 pounds or $6,250 per a $.10 change$200,000 / $6,250 = 32 contracts9Figure 23.3 Profits as a Function of the Exchange Rate10Available on both domest

7、ic and international stocksSettled in cashAdvantages over direct stock purchaselower transaction costsbetter for timing or allocation strategiestakes less time to acquire the portfolioStock Index Contracts11Table 23.1 Major Stock-Index Futures12Table 23.2 Correlations among Major U.S. Stock Market I

8、ndexes 13Creating Synthetic Positions with FuturesIndex futures let investors participate in broad market movements without actually buying or selling large amounts of stock.Results:Cheaper and more flexibleSynthetic position; instead of holding or shorting all of the actual stocks in the index, you

9、 are long or short the index futures14Creating Synthetic Positions with FuturesSpeculators on broad market moves are major players in the index futures market.Strategy: Buy and hold T-bills and vary the position in market-index futures contracts.If bullish, then long futuresIf bearish, then short fu

10、tures15Exploiting mispricing between underlying stocks and the futures index contractFutures Price too high - short the future and buy the underlying stocksFutures price too low - long the future and short sell the underlying stocksIndex Arbitrage16This is difficult to implement in practiceTransacti

11、ons costs are often too largeTrades cannot be done simultaneouslyDevelopment of Program TradingUsed by arbitrageurs to perform index arbitragePermits quick acquisition of securities Index Arbitrage and Program Trading17Hedging Systematic RiskTo protect against a decline in stock prices, short the ap

12、propriate number of futures index contracts.Less costly and quickerUse the beta for the portfolio to determine the hedge ratio.18Hedging Systematic Risk ExamplePortfolio Beta = .8S&P 500 = 1,000Decrease = 2.5%S&P falls to 975Portfolio Value = $30 millionProjected loss if market declines by 2.5% = (.

13、8) (2.5%) = 2%2% of $30 million = $600,000Each S&P500 index contract will change $6,250 for a 2.5% change in the index. (The contract multiplier is $250).19Hedge Ratio ExampleH = =Change in the portfolio valueProfit on one futures contract$600,000 $6,250= 96 contracts short20Figure 23.4 Predicted Va

14、lue of the Portfolio as a Function of the Market Index 21Uses of Interest Rate HedgesA bond fund manager may seek to protect gains against a rise in rates.Corporations planning to issue debt securities want to protect against a rise in rates.A pension fund with large cash inflows may hedge against a

15、 decline in rates for a planned future investment.22Hedging Interest Rate Risk ExamplePortfolio value = $10 millionModified duration = 9 yearsIf rates rise by 10 basis points (.1%), thenChange in value = ( 9 ) ( .1%) = .9% or $90,000Price value of a basis point (PVBP) = $90,000 / 10 = $9,000 per bas

16、is point23Hedge Ratio ExampleH = = PVBP for the portfolioPVBP for the hedge vehicle $9,000 $90= 100 T-Bond contracts24HedgingThe T-bond contracts drive the interest rate exposure of a bond position to zero.This is a market neutral strategy. Gains on the T-bond futures offset losses on the bond portf

17、olio.The hedge is imperfect in practice because of slippage the yield spread does not remain constant.25Figure 23.5 Yield Spread26SwapsSwaps are multi-period extensions of forward contracts.Credit risk on swapsAn interest rate swap calls for exchanging cash flows based on a fixed rate for cash flows

18、 based on a floating rate.The foreign exchange swap calls for an exchange of currencies on several future dates.27Interest Rate Swap: Text Example28The Swap DealerDealer enters a swap with Company APays fixed rate and receives LIBORDealer enters another swap with Company B Pays LIBOR and receives a

19、fixed rateWhen two swaps are combined, dealers position is effectively neutral on interest rates.29Figure 23.6 Interest Rate Swap30Figure 23.7 Interest Rate Futures31Swaps are essentially a series of forward contracts.We need to find the level annuity, F *, with the same present value as the stream

20、of annual cash flows that would be incurred in a sequence of forward rate agreements.Pricing on Swap Contracts32Figure 23.8 Forward Contracts versus Swaps 33Credit Default SwapsPayment on a CDS is tied to the financial status of one or more reference firms.Allows two counterparties to take positions

21、 on the credit risk of those firms.Indexes of CDS have now been introduced.34Commodity Futures Pricing General principles that apply to stocks apply to commodities. HoweverCarrying costs are more for commodities.Spoilage is a concern.35Commodity Futures PricingLet F0 = futures price, P0 = cash price

22、 of the asset , and C = Carrying cost 36Futures PricingF0 = P0(1+rf+c) is a parity relationship for commodities that are stored.The formula works great for an asset like gold, but not for electricity or agricultural goods which are impractical to stockpile.37Figure 23.9 Typical Agricultural Price Pa

23、ttern over the Season 38Example 2.8 Commodity Futures PricingThe T-bill rate is 5%, the market risk premium is 8%, and the beta for orange juice is 0.117.Orange juice discount rate is 5% + .117(8%) = 5.94%.Let the expected spot price in 6 months be $1.45.$1.45/(1.0594)0.5= $1.409 = PV juiceF0/(1.05)

24、0.5= 0.976F0 = PV futures0.976F0 = $1.409F0 =$1.44439CHAPTER 24Portfolio Performance EvaluationTwo common ways to measure average portfolio return:Time-weighted returnsDollar-weighted returnsReturns must be adjusted for risk.Introduction41Time-weighted returnsThe geometric average is a time-weighted

25、 average.Each periods return has equal weight.Dollar- and Time-Weighted Returns42Dollar-weighted returnsInternal rate of return considering the cash flow from or to investmentReturns are weighted by the amount invested in each period:Dollar- and Time-Weighted Returns43Example of Multiperiod Returns4

26、4Dollar-weighted Return (IRR):Dollar-Weighted Return-$50-$53$2$4+$10845Time-Weighted ReturnThe dollar-weighted average is less than the time-weighted average in this example because more money is invested in year two, when the return was lower.rG = (1.1) (1.0566) 1/2 1 = 7.81%46The simplest and most

27、 popular way to adjust returns for risk is to compare the portfolios return with the returns on a comparison universe.The comparison universe is a benchmark composed of a group of funds or portfolios with similar risk characteristics, such as growth stock funds or high-yield bond funds.Adjusting Ret

28、urns for Risk47Figure 24.1 Universe Comparison481) Sharpe IndexRisk Adjusted Performance: Sharperp = Average return on the portfolio rf = Average risk free ratep= Standard deviation of portfolio return492) Treynor MeasureRisk Adjusted Performance: Treynorrp = Average return on the portfolio rf = Ave

29、rage risk free ratep = Weighted average beta for portfolio50Risk Adjusted Performance: Jensen3) Jensens Measurep= Alpha for the portfoliorp = Average return on the portfoliop = Weighted average Betarf = Average risk free raterm = Average return on market index portfolio51Information RatioInformation

30、 Ratio = ap / s(ep)The information ratio divides the alpha of the portfolio by the nonsystematic risk.Nonsystematic risk could, in theory, be eliminated by diversification.52M2 MeasureDeveloped by Modigliani and ModiglianiCreate an adjusted portfolio (P*)that has the same standard deviation as the m

31、arket index.Because the market index and P* have the same standard deviation, their returns are comparable:53M2 Measure: ExampleManaged Portfolio: return = 35%standard deviation = 42%Market Portfolio: return = 28%standard deviation = 30% T-bill return = 6%P* Portfolio:30/42 = .714 in P and (1-.714)

32、or .286 in T-billsThe return on P* is (.714) (.35) + (.286) (.06) = 26.7%Since this return is less than the market, the managed portfolio underperformed.54Figure 24.2 M2 of Portfolio P55It depends on investment assumptionsIf the portfolio represents the entire risky investment , then use the Sharpe

33、measure. 2) If the portfolio is one of many combined into a larger investment fund, use the Jensen or the Treynor measure. The Treynor measure is appealing because it weighs excess returns against systematic risk.Which Measure is Appropriate?56Table 24.1 Portfolio PerformanceIs Q better than P?57Fig

34、ure 24.3 Treynors Measure58Table 24.3 Performance Statistics59Interpretation of Table 24.3If P or Q represents the entire investment, Q is better because of its higher Sharpe measure and better M2.If P and Q are competing for a role as one of a number of subportfolios, Q also dominates because its T

35、reynor measure is higher.If we seek an active portfolio to mix with an index portfolio, P is better due to its higher information ratio.60Performance Measurement for Hedge FundsWhen the hedge fund is optimally combined with the baseline portfolio, the improvement in the Sharpe measure will be determ

36、ined by its information ratio:61Performance Measurement with Changing Portfolio CompositionWe need a very long observation period to measure performance with any precision, even if the return distribution is stable with a constant mean and variance.What if the mean and variance are not constant? We

37、need to keep track of portfolio changes.62Figure 24.4 Portfolio Returns63Market TimingIn its pure form, market timing involves shifting funds between a market-index portfolio and a safe asset.Treynor and Mazuy:Henriksson and Merton:64Figure 24.5 : No Market Timing; Beta Increases with Expected Marke

38、t Excess. Return; Market Timing with Only Two Values of Beta.65Figure 24.6 Rate of Return of a Perfect Market Timer66Style AnalysisIntroduced by William SharpeRegress fund returns on indexes representing a range of asset classes.The regression coefficient on each index measures the funds implicit al

39、location to that “style.”R square measures return variability due to style or asset allocation. The remainder is due either to security selection or to market timing.67Table 24.5 Style Analysis for Fidelitys Magellan Fund68Figure 24.7 Fidelity Magellan Fund Cumulative Return Difference69Figure 24.8 Average Tracking Error for 636 Mutual Funds, 1985-198970Evaluating Performance EvaluationPerformance evaluation has two key problems:Many observations are needed for significant results.Shifting parameters when portfolios are actively m