投资学10版习题答案20.doc

1、Chapter 20 - Optio ns Markets: I ntroductionCHAPTER 20: OPTIONS MARKETS: INTRODUCTIONPROBLEM SETSall1. Options provide numerous opportunities to modify the risk profile of a portfolio. The simplest example of an option strategy that increases risk isnvesting in anoptions ' portfooliof at the mon

2、ey options (as illustrated in the text). The leverage provided by options makes this strategy very risky, and potentially very profitable. An example of a risk-reducing options strategy is a protective put strategy. Here, the investor buys a put on an existing stock or portfolio, with exercise price

3、 of the put near or somewhat less than the market value of the underlying asset. This strategy protects the value of the portfolio because the minimum value of the stock-plus-put strategy is the exercise price of the put.2. Buying a put option on an existing portfolio provides portfolio insurance, w

4、hich is protection against a decline in the value of the portfolio. In the event of a decline in value, the minimum value of the put-plus-stock strategy is the exercise price of the put. As with any insurance purchased to protect the value of an asset, the trade-off an investor faces is the cost of

5、the put versus the protection against a decline in value. The cost of the protection is the cost of acquiring the protective put, which reduces the profit that results should the portfolio increase in value.3. An investor who writes a call on an existing portfolio takes acovered call position. If, a

6、t expiration, the value of the portfolio exceeds the exercise price of the call, the writer of the covered call can expect the call to be exercised, so that the writer of the call must sell the portfolio at the exercise price. Alternatively, if the value of the portfolio is less than the exercise pr

7、ice, the writer of the call keeps both the portfolio and the premium paid by the buyer of the call. The trade-off for the writer of the covered call is the premium income received versus forfeit of any possible capital appreciation above the exercise price of the call.4. An option is out of the mone

8、y when exercise of the option would be unprofitable. A call option is out of the money when the market price of the underlying stock is less than the exercise price of the option. If the stock price is substantially less than the exercise price, then the likelihood that the option will be exercised

9、is low, and fluctuations in the market price of the stock have relatively little impact on the value of the option. This sensitivity of the option price to changes in the price of the stock is called the option' s delta, which is discussed in detail in C.hFaoprteorpt2io1nsthat are far out of the

10、 money, delta is close to zero. Consequently, there is generally little to be gained or lost by buying or writing a call that is far out of the money. (A similar result applies to a put option that is far out of the money, with stock price substantially greater than exercise price.)20-1A call is in

11、the money when the market price of the stock is greater than the exercise price of the option. If stock price is substantially greater than exercise price, then the price of the option approaches the order of magnitude of the price of the stock. Also, since such an option is very likely to be exerci

12、sed, the sensitivity of the option price to cha nges in stock price approaches one, in dicati ng that a $1 in crease in the price of the stock results in a $1 in crease in the price of the optio n. Un der these circumsta nces, the buyer of an opti on loses the ben efit of the leverage provided by op

13、ti ons that are n ear the mon ey. Con seque ntly, there is little in terest in opti ons that are far in the mon ey.5.CostPayoffProfita.Call option, X = $190.00$6.75$5.00-$1.75b.Pu0 opMbn?W00$0®0W$100.3.000.00-3.00c.Call option, X = $195.003.650.00-3.65d.Put optio n, X = $195.005.000.00-5.00e.Ca

14、ll option, X = $200.001.610.00-1.61f.Put optio n, X = $200.008.095.00-3.096. In terms of dollar returns, based on a $10,000 investment:Price of Stock 6 Mon ths from NowStock Price$ 80$ 100$ 110$ 120All stocks (100 shares)8,00010,00011,00012,000All options (1,000 options)0010,00020,000Bills + 100 opt

15、io ns9,3609,36010,36011,360In terms of rate of retur n, based on a $10,000 inv estme nt:Price of Stock 6 Mon ths from NowStock Price$80$100$110$120All stocks (100 shares)-20%0%10%20%All options (1,000 options)-100-1000100Bills + 100 optio ns-6.4-6.43.613.620-2Copyright ? 2021 McGraw-Hill Education.

16、All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.7. a. From put-call parity:P C S0X(1rf)T10 100100251.10$7.65b. Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the straddle is $10 + $7.65 = $17.658. a. Fro

17、m put-call parity:CPS。X(1rf)T4 5050251.10$5.18b.Sell a straddle, i.e., sell a call and a put, to realize premium in come of$5.18 + $4 = $9.18If the stock ends up at $50, both of the options will be worthless and your profit will be $9.18. This is your maximum possible profit sin ce, at any other sto

18、ck price, you will have to pay off on either the call or the put. The stock price can move by $9.18 in either direct ion before your profits become n egative.c. Buy the call, sell (write) the put, le nd $50/(1.10)/420-3The payoff is as follows:Positi onImmediate CFCF in 3 mon thsS T <XSt > XCa

19、ll (lo ng)C = 5.180St -50Put (short)-P = 4.00-(50 -S t)0Lending positi on5048 8250501/448821.10TotalC -P +5C°/450.00S TS T1.10By the put-call parity theorem, the initial outlay equals the stock price:S0 = $50In either scenario, you end up with the same payoff as you would if you bought the stoc

20、k itself.9. a. i. A long straddle produces gains if prices move up or down and limited losses if prices do not move. A short straddle produces significant losses if prices move significantly up or down. A bullish spread produces limited gains if prices move up.b. i. Long put positions gain when stoc

21、k prices fall and produce very limited losses if prices in stead rise. Short calls also gain whe n stock prices fall but create losses if prices in stead rise. The other two positi ons will not protect the portfolio should prices fall.10. Note that the price of the put equals the revenue from writin

22、g the call, net initial cash outlays = $38.00Positionst < 3535 st 4040 < stBuy stockStStStWrite call ($40)0040 - stBuy put ($35)35-St00Total$35st$4020-411. An swers may vary. For $5,000 in itial outlay, buy 5,000 puts, write 5,000 calls:Positi onSt = $30St = $40St =$50Stock portfolio$150,000$2

23、00,000$250,000Write call(X=$45)00-$25,000Buy put (X=$35)$25,00000In itial outlay-$5,000-$5,000-$5,000Portfolio value$170,000$195,000$220,000Compare this to just holdi ng the portfolio:Positi onSt = $30St = $40St =$50Stock portfolio$150,000$200,000$250,000Portfolio value$150,000$200,000$250,00012. a.

24、OutcomeSt <XSt> XStockSt + DSt + DPutX -St0TotalX + DSt + Db.OutcomeSt <XSt > XCall0St -XZerosX + DX + DTotalX + DSt + DThe total payoffs for the two strategies are equal regardless of whethSrr exceedsX.c. The cost of establish ing the stock-plus-put portfolio is® + PThe cost of est

25、ablishing the call-plus-zero portfolio is:C + PV(X + D)20-5Therefore:S0 + P = C + PV(X + D)This result is ide ntical to equati on 20.2.13. a.X2?XiXi x2Positi onS t < X1X1S t X2X2 < S T X3X3 < S tLong call (X1)0St -X1S T -X1St -X1Short 2 calls (X2)0042(S t -X2)-(St -X2)Long call (X3)000St -X

26、3Total0St -X12X2 -X1 -St(X2 -<1) -(X3 咲2) = 0Payoffb.Positi onS t < X1X1 St X2X2 < S TBuy call (X2)00St -X2Buy put (X1)X1 -S T00TotalX1 -S T0St -X220-6PayoffXiX214.Buy call (X2)Sell call (X1)00S t -X20-S t -X1)-St -X1)Total0X1 -S tX1 -X2Positi onSt < X1X1S t X2X2 < S tSt15. a.By writ

27、ing covered call opti ons, Jones receives premium in come of $30,000.If, i n Janu ary, the price of the stock is less tha n or equal to $45, the n Jones will have his stock plus the premium in come. But themost he can have at that time is ($450,000 + $30,000) because the stock will be called away fr

28、om him if the stock price exceeds $45. (We are ignoring here any in terest earned over this short period of time on the premium in come received from writi ng the opti on.) The payoff structure isStock pricePortfolio valueless than $4510,000 times stock price + $30,000greater than $45$450,000 + $30,

29、000 = $480,000This strategy offers some extra premium in come but leaves Jones subject to substa ntial dow nside risk. At an extreme, if the stock price fell to zero, Jones20-7would be left with only $30,000. This strategy also puts a cap on the finalvalue at $480,000, but this is more than sufficie

30、nt to purchase the house.b. By buying put options with a $35 strike price, Jones will be paying $30,000 in premiums in order to ensure a minimum level for the final value of his positio n. That mi nimum value is ($3510,000) x$30,000 = $320,000.This strategy allows for upside gain, but exposes Jones

31、to the possibility of a moderate loss equal to the cost of the puts. The payoff structure is:Stock pricePortfolio valueless than $35$350,000 - $30,000 = $320,000greater than $3510,000 times stock price-$30,000c.The net cost of the collar is zero. The value of the portfolio will be as follows:Stock p

32、riceless than $35betwee n $35 and $45 greater tha n $45Portfolio value$350,00010,000 times stock price $450,000If the stock price is less than or equal to $35, then the collar preserves the $350,000 prin cipal. If the price exceeds $45, the n Jones gains up to a cap of $450,000. In between $35 and $

33、45, his proceeds equal 10,000 times the stock price.The best strategy in this case would be (c) since it satisfies the two requireme nts of preserv ing the $350,000 in prin cipal while offeri ng a cha nee of getting $450,000. Strategy (a) should be ruled out since it leaves Jones exposed to the risk

34、 of substa ntial loss of prin cipal.Our ranking would be: (1) strategy c; (2) strategy b; (3) strategy a.Stock PricesBeg inning MarketPrice116.5En di nq Market Price130Buying Opti ons:Call Optio ns StrikePricePayoffProfitRetur n %11022.8020.00-2.80-12.28%12016.8010.00-6.80-40.48%13013.600.00-13.60-1

35、00.00%14010.300.00-10.30-100.00%Put Optio ns StrikePricePayoffProfitRetur n %11012.600.00-12.60-100.00%12017.200.00-17.20-100.00%13023.600.00-23.60-100.00%14030.5010.00-20.50-67.21%16. Using Excel, with Profit Diagram on next page.PriceProfitEn di ngStraddle5042.806032.807022.808012.80902.80100-7.20

36、110-17.20120-27.20130-37.20140-27.20150-17.20160-7.2020-8StraddlePricePayoffProfitRetur n %11035.4020.00-15.40-43.50%12034.0010.00-24.00-70.59%13037.200.00-37.20-100.00%14040.8010.00-30.80-75.49%Selli ng Opti ons:Call Options StrikePricePayoffProfitRetur n %11022.80-202.8012.28%12016.80-106.8040.48%

37、13013.60013.60100.00%14010.30010.30100.00%Put Optio ns StrikePricePayoffProfitRetur n %11012.60012.60100.00%12017.20017.20100.00%13023.60023.60100.00%1702.8018012.8019022.8020032.8021042.80En di ngBullishStock PriceSpread50-3.260-3.270-3.280-3.290-3.2100-3.2110-3.2120-3.21306.814030.501040.50132.79%

38、Money SpreadPricePayoffProfitBullish SpreadPurchase 120 Call16.8010.00-6.80Sell 130 Call13.60013.60Comb ined Profit10.006.801406.81506.81606.81706.81806.81906.82006.82106.8Profit diagram for problem 16:20-917. The farmer has the opti on to sell the crop to the gover nment for a guara nteed minimum p

39、rice if the market price is too low. If the support price is deno tedPS and the market pricePm then the farmer has a put option to sell the crop (the asset) at an exercise price ofPs even if the price of the underlying asset Pm) is less thanPs.18. The bon dholders have, in effect, made a loa n that

40、requires repayme nt Bfdollars,where B is the face value of bon ds. If, however, the value of the firm V) is less tha n B, the loa n is satisfied by the bon dholders tak ing over the firm .In this way, the bon dholders are forced toB (irptihe'se nse that the loa n is can celled) in returnfor an a

41、sset worth only V. It is as though the bon dholders wrote a put on an asset worth V with exercise price B. Alter natively, one might view the bon dholders as giving the right to the equity holders to reclaim the firm by paying off the B dollar debt. The bon dholders have issued a call to the equity

42、holders.19. The man ager receives a bonus if the stock price exceeds a certa in value and receives nothing otherwise. This is the same as the payoff to a call opti on.20. a.Positi onS t < 190190 S t 195S t > 195Write call, X :=$19500-S t -195)Write put, X =:$190-190 -St)00TotalSt -1900195 -S t

43、STb. Proceeds from writi ng optio ns:Call:-$2.99Put:$1.75Total:-$1.2420-10If IBM sells at $198 on the option expiration date, the call option expires in the mon eycash outflow of $3, result ing in a profit of -$1.24. If IBM sells at $208 on the option expiration date, the call written results in a c

44、ash outflow of $10 at expiration and an overall profit of: -$1.24 -$10.00 = -$11.24c. You break even when either the put or the call results in a cash outflow of -$1.24. For the put, this requires that:-$1.24 = $190.00 -StSt = $191.24For the call, this requires that:-$1.24 = S t -$195.00St = $193.76

45、d. The investor is betting that IBM stock price will have low volatility. This positi on is similar to a straddle.21. The put with the higher exercise price must cost more. Therefore, the net outlay to establish the portfolio is positive.Positi onSt < 9090 S t 95S t > 95Write put, X = $90-90 -

46、St)00Buy put, X = $9595 -S t95 -S t0Total595 -S t0T22. Buy the X = 62 put (which should cost more but does not) and write the = 60 put. Since the options have the same price, your net outlay is zero. Your proceeds at expirati on may be positive, but cannot be n egative.Positi onSt < 6060 S t 62S

47、t> 62Buy put, X = $6262 -S t62 -S t0Write put, X = $60-60 -St)00Total262 -S t020-1123. Put-call parity states that:P C S0PV (X) PV (Divide nds)Solvi ng for the price of the call optio n: C S) PV(X) PV (Divide nds)C $100 型00皂 $7(1.05)(1.05)$9.8624. The followi ng payoff table shows that the portfo

48、lio is riskless with time-T value equal to $10:Positi onSt < 10St > 10Buy stockS TS TWrite call, X = $100-S t -10)Buy put, X = $1010 -S T0Total1010Therefore, the risk-free rate is: ($10/$9.50)-1 = 0.0526 = 5.26%25. a., b.Positi onS T < 100100 S t 110St> 110Buy put, X =$110110 -ST110 -St0

49、Write put, X=$100-100 -St)00Total10110 -St0The net outlay to establish this positi on is positive. The put you buy has a higher exercise price tha n the put you write, and therefore must cost more tha n the put that you write. Therefore, net profits will be less than the payoff at time T.20-12c. The

50、 value of this portfolio gen erally decreases with the stock price. Therefore, its beta is n egative.26. a. Joe' s strategyPositi onCostPayoffSt 1,200S t > 1,200Stock in dex1,200StStPut optio n, X = $1200601,200 -St0Total-1,2601,200StProfit = payoff -$1260-0S t -1,260Sally ' s strategyPos

51、iti onCostPayoffSt 1,170S t > 1,170Stock in dex1,200S tStPut opti on, X = $1,270451,170 -St0Total1,2451,245StProfit = Payoff -6S t -1,245$1,245b. Sally does better whe n the stock price is high, but worse whe n the stock price is low.c. Sally ' s strategy has greater systematic Piskfits are m

52、ore sensitive to the value of the stock in dex.20-1327. a., b. (See graph)This strategy is a bear spread. In itial proceeds = $9$3 = $6The payoff is either n egative or zero:Positi onS t < 5050 S t 60S t > 60Buy call, X = $6000S t -60Write call, X = $500-S t -50)-St -50)Total0-S t -50)-0c. Bre

53、akeve n occurs whe n the payoff offsets the in itial proceeds of $6, which occurs at stock priceS t = $56. The investor must be bearish: the position does worse whe n the stock price in creases.20-1428. Buy a share of stock, write a call withX = $50, write a call with X = $60, and buy a call with X

54、= $110.Positi onSt < 5050 S t 6060 < S t 110St > 110Buy stockS tS tStS tWrite call, X = $500-S t -50)-St -50)-S t -50)Write call, X = $6000-St -60)-S t -60)Buy call, X = $110000St -110TotalS t50110 -S t0The investor is making a volatility bet. Profits will be highest when volatility is low and the stock priceS t is betwee n $50 and $60.29. a.PositionSt W1,179St > 1,170Buy stockStStBuy put1,170 -S t0Total1,170StPositi onSt <1,260St > 1,260Buy call0St