三级CFA考试SS15复习笔记.pdf

SS15 Risk Management Applications of Derivatives 讲师 石奇 CFA 日期 2011年4月 地点 上海 北京 深圳 讲师 石奇 CFA 日期 2011年4月 地点 上海 北京 深圳 上海金程国际金融专修学院上海金程国际金融专修学院上海金程国际金融专修学院上海金程国际金融专修学院 2 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Topic in CFA Level III PERFORMANCE EVALUATION AND ATTRIBUTIONSS 17 PRIVATE WEALTH MANAGEMENTSS 4 PORTFOLIO MANAGEMENT FOR INSTITUTIONAL INVESTORSSS 5 CAPITAL MARKET EXPECTATIONS IN PORTFOLIO MANAGEMENTSS 6 ECONOMIC CONCEPTS FOR ASSET VALUATION IN PORTFOLIO MANAGEMENT SS 7 GLOBAL INVESTMENT PERFORMANCE STANDARDS EXECUTION OF PORTFOLIO DECISIONS MONITORING AND REBALANCING RISK MANAGEMENT APPLICATIONS OF DERIVATIVES RISK MANAGEMENT ALTERNATIVE INVESTMENTS FOR PORTFOLIO MANAGEMENT EQUITY PORTFOLIO MANAGEMENT PORTFOLIO MANAGEMENT OF GLOBAL BONDS AND FIXED INCOME DERIVATIVES MANAGEMENT OF PASSIVE AND ACTIVE FIXED INCOME PORTFOLIOS ASSET ALLOCATION BEHAVIORAL FINANCE ETHICS the value of the equity position increased by 1 6 and the value of the futures price increased by 2 1 These values correspond exactly to what we would expect with the provided betas of 0 8 and 1 05 What is the effective beta 11 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Adjusting Portfolio Allocation EquityCashBonds Mid cap Equity Cash Small cap Equity To reallocate an amount from equity to bonds 1 Remove all systematic risk from the position beta 0 by shorting equity futures 2 Add duration to the position MD 0 by going long bond futures To reallocate an amount from bonds to equity 1 Remove all duration from the position MD 0 by shorting bond futures 2 Add systematic risk to the position beta 0 by going long equity futures 12 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example3 Altering Debt And Equity Allocations A manager has a 50 million portfolio that consists of 50 stock and 50 bonds The beta of the stock position is 0 8 The modified duration of the bond position is 6 8 The manager wishes to achieve an effective mix of 60 stock i e 30 million and 40 bonds Since the move is only temporary and rather than having to decide which bonds to sell and which stocks to buy to achieve the desired mix the manager will use futures contracts The price of the stock index futures contract is 300 000 including the multiplier and its beta is 1 1 The price modified duration and yield beta of the futures contracts are 102 000 8 1 and 1 respectively Determine the appropriate strategy 13 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Pre investing Pre investing is the practice of taking long positions in the futures contracts to create an exposure that converts a yet to be received cash position into a synthetic equity and or bond position Example 4 A portfolio manager knows that 5 million in cash will be received in a month The portfolio under management is 70 invested in stock with an average beta of 0 9 and 30 invested in bonds with a duration of 4 8 The most appropriate stock index futures contract has a total price of 244 560 and a beta of 1 05 The most appropriate bond index futures have a yield beta of 1 00 an effective duration of 6 4 and a total price of 99 000 Determine the appropriate strategy to pre invest the 5 million in the same proportions as the current portfolio 14 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Synthetic Stock Index Fund And Synthetic Cash Synthetic Equity Long risk free asset Stock index futures Synthetic Cash Long stock Stock index futures 15 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example5 Creating Synthetic Equity A manager has 120 million in Treasury bills with a yield of 3 For the next six months the manager wishes to have a synthetic equity position approximately equal to this value The manager chooses S if LIBOR 5 55 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Caplet is a European call option on interest rates Floating rate loan borrowers long caplets to hedge interest rates increasing Cap is a combination of caplets with each caplet expiring at the date on which the floating loan rate will be reset and with the same strike rate cap rate Floorlet is a European put option on interest rates Floating rate loan lender long floorlets to hedge interest rates decreasing Floor is a combination of floorlets with each floorlet expiring at the date on which the floating loan rate will be reset and with same strike rate floor rate An interest rate Collar is a combination of a long short cap and a short long floor on the same underlying rate with the same expiring dates Interest Rate Caps Floors And Collars 56 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism A floating rate borrower can be use a cap to limit interest expense during the life of cap The payoff to the cap buyer is P max 0 NP LIBOR cap strike actual days 360 A floating rate investor can be use a floor to limit reductions in interest income during the life of floor The payoff to the floor buyer is P max 0 NP floor strike LIBOR actual days 360 Where P Periodic payment NP notional principal Compute The Payoff For A Cap And A Floor 57 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example19 Interest Rate Cap Suppose that a 1 year cap has a cap rate of 8 and a notional amount of 100 million The frequency of settlement is quarterly and the reference rate is 3 month LIBOR The contract begins on January 1 Determine the payoffs on April 1 July 1 October 1 and the following January 1 for the indicated LIBOR rates on those dates in the figure below 928 3 Jan 1 year 2 928 6 Oct 1 918 4 July 1 908 0 Apr 1 7 7 Jan 1 PayoffDt3 Month LIBOR Date 58 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example20 Interest Rate Cap A borrower is combining a cap with a 2 year floating rate 20 million loan The floating rate on the loan is LIBOR plus 200 bp to be paid semiannually The loan is made on March 1 when LIBOR is 5 The cap begins on that day also and the strike rate is 6 The loan payments and cap settlement dates are September 1 and March 1 over the next two years LIBOR on the next three settlement dates are 6 1 6 4 and 6 0 Calculate the actual interest rate payments settlements and effective interest payments 59 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example21 Interest Rate Collar For a 1 year maturity it has found the optimal combination is to set a floor strike at 3 7 and a call strike at 5 1 The premiums cancel zero cost collar The value of the portfolio is now 90 million and payments are received quarterly based on LIBOR plus 320 basis points Today is July 1 and the next payment dates are October 1 January 1 April 1 and July 1 Current LIBOR is 4 5 The values of LIBOR on the next three settlement dates are 6 4 and 3 Calculate the actual interest rate payments to the bank which needs to effectively place a lower limit on the interest it earns on a portfolio of floating rate loans it has made settlements and effective interest payments 60 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Delta Hedging Delta hedging a derivative position means combining the option position with a position in the underlying asset to form a portfolio whose value does not change in reaction to changes in the price of the underlying over a short period of time Deltacall C S C1 C0 S1 S0 61 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example22 Delta Hedge During the last 20 minutes of trading shares of a stock have risen from 51 30 to 52 05 and a given call option on the stock has risen from 1 20 to 1 60 in price Calculate the delta of the call option Call options on the stock in the previous example have a delta of 0 533 If the stock price rises by 1 50 calculate the approximate change in the price of the option Call options on the stock in the previous example have a delta of 0 533 A dealer is short 100 contracts or 10 000 calls Calculate the number of shares of the stock to delta hedge this portfolio 62 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Delta Hedging Delta hedging is not easy for three very important reasons Delta is only an approximation of the relative price changes of the stock and option and is less accurate for larger changes in stock price Delta changes as market conditions change including changes in S Delta changes over time without any other changes 63 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Example23 Delta Hedge The initial value of a call is 1 40 which has a delta of 0 5739 and 30 days to maturity A dealer sells 200 contracts or 20 000 calls To delta hedge the position the dealer purchases 20 000 0 5739 11 478 shares of the stock at 100 share A day later the price of the stock is the same Using the data below calculate the initial value of the position and its value on the next day 64 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Calculating Delta With B S Model For call option Delta increased with the increase in S Delta decreased with the decrease in S Delta and the value of the call decline with the passage of time 65 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Gamma change in delta change in S Gamma is largest when an option is at the money and or near expiration When gamma is large delta will be changing rapidly Actual change in call price from an increase in S Deltacall S Actual change in call price from an decrease in S Deltacall S A manager would want to consider adjusting the hedge to include the gamma effect if the option is at the money and or the option is near expiration Gamma Effect 66 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism SS15 Risk Management Applications of Derivatives R43 Risk Management Applications of Swap Strategies Framework of SS15 67 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Interest Rate Swap Duration Each counterparty in a swap is essentially either of the following Long a fixed cash flow and short a floating cash flow Short a fixed cash flow and long a floating cash flow For fixed rate instrument duration will be higher For floating rate instruments duration is close to zero At inception or just after a settlement for a quarterly reset swap we estimate the duration of the floating payments as 0 25 in general we also use 0 125 68 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism For fixed rate receiver in a swap duration can be express as D pay floating D fixed D floating 0 For fixed rate payer in a swap duration can be express as D pay fixed D floating D fixed 0 Interest Rate Swap Duration 69 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Interest Rate Swap Risks Cash flow risk is inherent in floating cash flows uncertainty regarding the size of cash flows is a concern with floating rate instruments Unsure of the amount of future cash flows but market values do not change with changing interest rates Market value risk is a concern with fixed rate instruments Present values change with interest rates but cash flows are known no cash flow risk 70 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Using Swaps To Change Duration swapPPTP MDNPMDVMDV swap PT P MD MDMD VNP Example24 Determining the notional principal A manager of a 60 million fixed income portfolio with a duration of 5 2 wants to lower the duration to 4 0 The manager chooses a swap with a net duration of 3 1 What NP should the manager choose for the swap to achieve the target duration 71 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Interest Swaps Application 72 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Interest Swaps Application 73 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Currency Swap 74 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Currency Swap 75 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Use a currency swap to convert a series of foreign cash receipts into domestic cash receipts Does not require an exchange of notional principals The amounts exchange are a function of both the current exchange rate and interest rates swap rates in the countries involved Currency Swaps Without Notional Principals Example25 Currency Swaps Without Notional Principals A U S firm that wishes to convert its quarterly cash flows of 6 million each to dollars upon receipt The exchange rate is currently 0 8 and the swap rates in the United States and Europe are 4 8 and 5 respectively What is the swapped dollar cash flow 76 82100 Contribution Breeds Professionalism100 Contribution Breeds Professionalism Party A Party B Counterparty Equity Return Fixed rate on Notional Principal Stock Portfolio Equity Return A manager can swap all or part of the return on a portfolio for the return on a domestic equity index the return on a foreign index or the return on a fixed income index Equity Swap 77 82100 Contribution Breeds Professionalism100 Contribution Br