CFA 2018 level 3 schweser practice exam CFA 2018 level 3 question bank CFA 2018 r29 risk management applications of options strategies summary

fair option prices “Boxing-in” your profit! Strategy Comment Covered Call Profit Calculation Underlying+ short call Lowers risk by providing a cushion Protective Put Underling + long put Puts a floor on losses Bull Spread Long call (X1) + short call (X2) Make money if underlying goes up Bear Spread Long put (X2) + short put (X1) Make money if underlying goes down Butterfly Combine bull and bear, using three exercise prices Make money if underlying is stable VT – S0 + c0 Collar Pay for put by selling call Limits down side risk… but also cap upside VT – S0 Straddle Buy put and call with same X and same expiration Make money if underlying is volatile VT – (c0 + p0) Box Combine bull and bear, using two exercise prices Exploit arbitrage opportunity if both BSM and Binomial not hold X2 – X1 – (c1 – c2 + p2 – p1) VT – S0 – p0 VT – c1 + c2 VT – p2 + p1 VT – c1 + 2c2 – c3 Interest Rate Options Underlying is an interest rate and the exercise price is expressed in terms of a rate A call option will make money if the option expires with the underlying interest rate above the exercise rate Interest rate call option payoff: NP)max(0, Rate at expiration − Exercise rate)((Days in underlying rate ) 360 A put option will make money if the option expires with the underlying interest rate below the exercise rate Interest rate put option payoff: NP)max(0, Exercise rate − Rate at expiration)((Days in underlying rate ) 360 Effective Interest Rate Using Call Options Loan amount Underlying Spread Current Libor Expiration Exercise rate Call premium Today’s date $40,000,000 180-day Libor 200 basis points over Libor 5.5 percent 20 August (128 days later) percent $100,000 14 April For Libor of percent, the payoff is $40,000,000𝑚𝑎𝑥(0,0.08 − 0.05) 180 = $600,000 360 The compounded premium is: $100,000 + (0.055 + 0.02) 128 360 = $102,667 The effective loan proceeds are $40,000,000 – $102,667 = $39,897,333 The loan interest is: $40,000,000(0.08 + 0.02)(180/360) = $2,000,000 The effective interest rate is: $40,000,000 + $2,000,000 − $600,000 $39,897,333 365 180 − = 0.0779 Effective Interest Rate Using Put Options Loan amount Underlying Spread Current Libor Expiration Exercise rate Put premium $50,000,000 90-day Libor 250 basis points over Libor 7.25 percent May (in 47 days) percent $62,500 For Libor of percent, the payoff is: $50,000,000max (0, 0.07−0.060) (90/360) =$125,000 The compounded premium is: $62,500[1+ (0.0725+0.025) (47/360)] = $63,296 Put costs $62,500 on 15 March, which is equivalent to $63,296 on May The effective amount loaned is $50,000,000 + $63,296 = $50,063,296 With Libor at percent, the interest is: $50,000,000[(0.06+0.025)(90/360)] = $1,062,500 The loan interest plus the put payoff is the effective interest on the loan The effective rate on the loan is: $50,000,000 + $1,062,500 + $125,000 $50,063,296 365 90 − = 0.0942 10 Interest Rate Caps A floating rate loan requires periodic interest payments in which the rate is reset on a regularly scheduled basis A cap is a combination of interest rate call options designed to align with rates on a loan Each component is called a caplet It provides protection against rising interest rates over the life of the loan Date 15 April 15 October 15 April 15 October 15 April 15 October 15 April Libor 0.0900 0.0850 0.0725 0.0700 0.0690 0.0875 Loan amount Underlying Spread Current Libor Interest based on Component caplets Exercise rate Cap premium $10,000,000 180-day Libor 100 basis points over Libor percent actual days/360 five caplets expiring 15 October, 15 April, … percent $75,000 Loan Rate 0.1000 0.0950 0.0825 0.0800 0.0790 0.0975 11 Interest Rate Caps A floating rate loan requires periodic interest payments in which the rate is reset on regularly scheduled basis A cap is a combination of interest rate call options designed to align with rates on a loan Each component is called a caplet It provides protection against rising interest rates over the life of the loan Date 15 April 15 October 15 April 15 October 15 April 15 October 15 April Libor 0.0900 0.0850 0.0725 0.0700 0.0690 0.0875 Loan Rate 0.1000 0.0950 0.0825 0.0800 0.0790 0.0975 Loan amount Underlying Spread Current Libor Interest based on Component caplets Exercise rate Cap premium $10,000,000 180-day Libor 100 basis points over Libor percent actual days/360 five caplets expiring 15 October, 15 April, … percent $75,000 Days in Period Interest Due Caplet Payoffs Effective Interest 183 182 183 182 183 182 $508,333 455,000 419,375 404,444 401,583 455,000 $508,333 480,278 419,375 404,444 401,583 492,917 $25,278 0 37,917 12 Interest Rate Floor An interest rate floor is a series of interest rate put options that expire on various interest rate reset dates Each component is called a floorlet It provides protection to the lender against falling interest rates Date 15 April 15 October 15 April 15 October 15 April 15 October 15 April Libor 0.0900 0.0850 0.0725 0.0700 0.0690 0.0875 Loan Rate 0.1000 0.0950 0.0825 0.0800 0.0790 0.0975 Loan amount Underlying Spread Current Libor Interest based on Component floorlets Exercise rate Floor premium $10,000,000 180-day Libor 100 basis points over Libor percent actual days/360 five floorlets expiring 15 October, 15 April, etc percent $72,500 Days in Period Interest Due 183 182 183 182 183 182 $508,333 480,278 419,375 404,444 401,583 492,917 Floorlet Payoffs Effective Interest $0 38,125 50,556 55,917 $508,333 480,278 457,500 455,000 457,500 492,917 13 Interest Rate Collar A collar combines a long position in a cap with a short position in a floor The sale of a floor provides a premium that can be used to offset the purchase of a cap In this strategy, the borrower pays for the cap by giving away some of the gains from the possibility of falling interest rates A collar establishes a range Any rate increases above the cap exercise rate will have no net effect, and any rate decreases below the floor exercise rate will have no net effect Date Libor Loan Rate 15 April 0.0900 0.1000 15 October 0.0850 15 April Loan amount Underlying Spread Current Libor Interest based on Component options Exercise rate Premium $10,000,000 180-day Libor 100 basis points over Libor percent actual days/360 five caplets and floorlets expiring 15 October, 15 April, etc 8.625 percent on cap, 7.5 percent on floor no net premium Days in Period Interest Due 0.0950 183 $508,333 0.0725 0.0825 182 480,278 $0 $0 480,278 15 October 0.0700 0.0800 183 419,375 –12,708 432,083 15 April 0.0690 0.0790 182 404,444 –25,278 429,722 15 October 0.0875 0.0975 183 401,583 –30,500 432,083 182 492,917 6,319 486,598 15 April Caplet Payoffs Floorlet Payoffs Effective Interest $508,333 14 Strategy Comment Interest Rate Calls with Borrowing Used by a borrower Establishes a maximum rate for a loan to be taken out in future Interest Rate Puts with Lending Used by a lender Establishes a minimum rate for a loan to be given out in future Interest Rate Cap with Floating Rate Loan Used by a borrower It provides protection against rising interest rates over the life of the loan Interest Rate Floor with Floating Rate Loan Used by a lender It provides protection against falling interest rates Interest Rate Collar with Floating Rate Loan Used by a borrower It establishes a range, if interest rates move beyond this range it will have no net effect on the borrower 15 Delta Hedging Delta = Change in option price Change in underlying price To delta hedge a call option position, the number of shares to purchase can be found using the following equation: 𝑁𝑐 =− 𝑁𝑆 ∆𝑐 ∆𝑆 Delta changes with price Hence we need to change position when underlying price changes Delta also changes with the passage of time Hence we need to adjust the delta hedge as expiration approaches 16 Gamma Gamma measures sensitivity of delta to change in underlying Gamma = Change in delta Change in underlying price High gamma means that the delta changes a lot for a given change in underlying This creates a problem for delta hedgers Gamma is relatively high for at the money options Gamma is highest near expiration for at the money options 17 ... $40,000,000 – $102,667 = $39 ,897 ,33 3 The loan interest is: $40,000,000(0.08 + 0.02)(180 /36 0) = $2,000,000 The effective interest rate is: $40,000,000 + $2,000,000 − $600,000 $39 ,897 ,33 3 36 5 180 − = 0.0779... days /36 0 five floorlets expiring 15 October, 15 April, etc percent $72,500 Days in Period Interest Due 1 83 182 1 83 182 1 83 182 $508 ,33 3 480,278 419 ,37 5 404,444 401,5 83 492,917 Floorlet Payoffs... 1 83 $508 ,33 3 0.0725 0.0825 182 480,278 $0 $0 480,278 15 October 0.0700 0.0800 1 83 419 ,37 5 –12,708 432 ,0 83 15 April 0.0690 0.0790 182 404,444 –25,278 429,722 15 October 0.0875 0.0975 1 83 401,583