solution manual for 《investment analysis and portfolio management》 ch21.doc

chapter 21an introduction to derivative markets and securitiesanswers to questions1. since call values are positively related to stock prices while put values are negatively related, any action that causes a decline in stock price (e.g., a dividend) will have a differential impact on calls and puts. specifically, an impending dividend will boost put values and depress call values.another way to consider the situation is to represent the difference between the theoretical price of a call option (c) and the theoretical price of a put option (p) as cp. this is the same as a portfolio that is long a call option and short a put option. for a firm that pays dividends, we expect that the price of its stock will decline by the amount of the dividend on the last day before the stock goes exdividend. a decline in stock price makes a call less valuable and a put more valuable, so cp will decrease.this portfolio has the same payoff as being long a forward contract with a contract price equal to the strike price. since there is no guarantee that the strike price is the forward price, this forward contract will typically have a nonzero value (i.e. the call and put will have different prices). a dividend will decrease the upfront premium for a long position in a forward contract because the expected stock price at expiration decreases. consequently, cp is decreased by dividends.2. it is generally true that futures contracts are traded on exchanges whereas forward contracts are done directly with a financial institution. consequently, there is a liquid market for most exchange traded futures whereas there is no guarantee of closing out a forward position quickly or cheaply. the liquidity of futures comes at a price, though. because the futures contracts are exchange traded, they are standardized with set delivery dates and contract sizes.if having a delivery date or contract size that is not easily accommodated by exchange traded contracts is important to a future/forward end user then the forward may be more appealing. if liquidity is an important factor then the user may prefer the futures contract.another consideration is the marktomarket property of futures. if a firm is hedging an exposure that is not markedtomarket, it may prefer to not have any intervening cash flows, hence it will prefer forwards.3. for forwards, calls and puts, what the long position gains, the short position loses, and vice versa. however, while payoffs to forward positions are symmetric, payoffs to call and put positions are asymmetric. that is to say, long and short forwards can gain as much as they can lose, whereas long calls and puts have a gain potential dramatically greater than their loss potential. conversely, short calls and puts have gains limited to the option premium but have unlimited liability.for example, if the price of wheat declines by 10%, the losses to a long position in a futures contract on wheat would be the same as the gains if the price were to increase by 10%. for an atthemoney call option, there would be an asymmetric change in value. a long position in an atthemoney call option on wheat would decline in value less for a 10% fall in wheat prices than it would increase from a 10% rise in wheat prices.position loss potential gain potential symmetrylong forward kunlimited symmetricshort forward unlimited k symmetriclong call call premiumunlimited asymmetricshort call unlimited call premium asymmetriclong put put premium k asymmetricshort put k put premium asymmetric4. cfa examination iii (1993)4(a). derivatives can be used in an attempt to bridge the 90day time gap in the following three ways:(1) the foundation could buy (long) calls on an equity index such as the s&p 500 index and on treasury bonds, notes, or bills. this strategy would require the foundation to make an immediate cash outlay for the “premiums” on the calls. if the foundation were to buy calls on the entire $45 million, the cost of these calls could be substantial, particularly if their strike prices were close to current stock and bond prices (i.e., the calls were close to being “in the money”).(2) the foundation could write or sell (short) puts on an equity index and on treasury bonds, notes, or bills. by writing puts, the foundation would receive an immediate cash inflow equal to the “premiums” on the puts (less brokerage commissions). if stock and bond prices rise as the committee expects, the puts would expire worthless, and the foundation would keep the premiums, thus hedging part or all of the market increase. if the prices fall, however, the foundation loses the difference between the strike price and the current market price, less the value of the premiums.(3). the foundation could buy (long) equity and fixedincome futures. this is probably the most practical way for the foundation to hedge its expected gift. futures are available on the s&p 500 index and on treasury bonds, notes, and bills. no cash outlay would be required. instead, the foundation could use some of its current portfolio as a good faith deposit or “margin” to take the long positions. the market value of the futures contracts will, in general, mirror changes in the underlying market values of the s&p 500 index and treasuries. although no immediate cash outlay is required, any gains (losses) in the value of the contracts will be added (subtracted) from the margin deposit daily. hence, if markets advance as the committee expects, the balances in the foundations futures account should reflect the market increase.4(b).there are both positive and negative factors to be considered in hedging the 90-day gap before the expected receipt of the franklin gift. positive factors(1). the foundation could establish its position in stock and bond markets using derivatives today, and benefit in any subsequent increases in market values in the s&p index and treasury instruments in the 90 day period. in effect, the foundation would have a synthetic position in those markets beginning today.(2). the cost of establishing the synthetic position is relatively low, depending on the derivative strategy used. if calls are used, the cost is limited to the premiums paid. if futures are used, the losses on the futures contracts would be similar to the amounts that would be lost if the foundation invested the gift today. writing the puts is the riskiest strategy because there is an open-ended loss if the market declines, but here again the losses would be similar if the foundation invested today and stock and bond markets declined.(3). derivative markets (for the types of contracts under consideration here) are liquid. negative factors(1). the franklin gift could be delayed or not received at all. this would create a situation in which the foundation would have to unwind its position and could experience losses, depending on market movements in the underlying assets.(2). the committee might be wrong in its expectation that stock and bond prices will rise in the 90 day period. if prices decline on stocks and bonds, the foundation would lose part or all of the premium on the calls and have losses on the futures contracts and the puts written. the risk of loss of capital is a serious concern. (given that the current investment is primarily bonds and cash, the foundation may not be knowledgeable enough to forecast stock prices over the next 90 days.)(3). because there is a limited choice of option and futures derivative contract compared to the universe that the committee might wish to invest in, there could be a mismatch between the specific equities and bonds the foundation wishes to invest in and the contracts available in size for $45 million. unless the 90-day period exactly matches the 90-day period before expiration dates on the contracts, there may be a timing mismatch.(4). the cost of the derivatives is potentially high. for example, if the market in general shares the committees optimistic outlook, the premiums paid for calls would be expensive and the premiums received on puts would be lean. the opportunity cost on all derivative strategies discussed would be large if the committee is wrong on the outlook for one or both markets.(5). there may exist regulatory restrictions on the use of derivatives by endowment funds. evaluationthe negative factors appear to outweigh the positive factors if the outlook for the market is neutral; therefore, the committees decision on using derivatives to bridge the gap for 90 days will have to be related to the strength of its conviction that stock and bond prices will rise in that period. the certainty of receiving the gift in 90 days is also a factor. the committee should certainly beware that there is a cost to establish the derivative positions, especially if its expectations do not work out. the committee might want to consider a partial hedge of the $45 million.5. cfa examination ii (1991)because chen is considering adding either short index futures or long index options (a form of protective put) to an existing welldiversified equity portfolio, he evidently intends to create a hedged position for the existing portfolio. both the short futures and the long options positions will reduce the risk of the resulting combined portfolios, but in different ways.assuming that the short futures contract is perfectly negatively correlated with the existing equity portfolio, and that the size of the futures position is sufficient to hedge the risk of the entire equity portfolio, any movement up or down in the level of stock market prices will result in offsetting gains and losses in the combined portfolios two segments (the equity portfolio itself and the short futures position). thus, chen is effectively removing the portfolio from exposure to market movements by eliminating all systematic (market) risk (unsystematic (specific) risk has already been minimized because the equity portfolio is a welldiversified one). once the equity portfolio has been perfectly hedged, no risk remains, and chen can expect to receive the risk-free rate of return on the combined portfolio. if the hedge is less than perfect, some risk and some potential for return beyond the riskfree rate are present, but only in proportion to the completeness of the hedge.if, on the other hand, chen hedges the portfolio by purchasing stock index puts, he will be placing a floor price on the equity portfolio. if the market declines and the index value drops below the strike price of the puts, the value of the puts increases, offsetting the loss in the equity portfolio. conversely, if the stock market rises, the value of the put options will decline, and they may expire worthless; however, the potential return to the combined portfolio is unlimited and reduced only by the cost of the puts. as with the short futures, if the long options hedge is less than perfect, downside risk remains in the combined portfolio in proportion to the amount not covered by the puts.in summary, either short futures or long options (puts) can be used to reduce or eliminate risk in the equity portfolio. use of the options (put) strategy, however, permits unlimited potential returns to be realized (less the cost of the options) while use of the short futures strategy effectively guarantees the riskfree rate but reduces or eliminates potential returns above that level. neither strategy dominates the other; each offers a different risk/return profile and involves different costs. arbitrage ensures that, on a riskadjusted basis, neither approach is superior.6.cfa examination ii (1997)three prominent pricing inconsistencies are apparent in the table for the furniture city call options:1. the june call option at a strike price of $110 is undervalued. a call option that is in the money should be worth at least as much as its intrinsic value. the intrinsic value of a call option is the maximum of either zero or the difference between the security price and the exercise price (s - e). the june $110 option, therefore, should be worth at least $119.50 - $110.00, or $9.50. the current price of $8 7/8 implies that the option is undervalued.2.the august call option at a strike price of $120 is undervalued. call options having the same strike price but with longer maturities are more valuable than those with shorter maturities because the stock has more time in which to rise above the strike price; that is, the time value increases with maturity. the august $120 option of $3 is below the july $120 option of $3 3/4; therefore, the august $120 option is undervalued. alternatively, the july $120 option could be said to be overvalued.3.the september call option at a strike price of $130 is overvalued. call options having the same maturity but with higher strike prices that are more out of the money are worth less because a larger and less likely move in the stock price will be needed for the option to pay off. the september $130 option is priced higher than the september $120 option; therefore, the september $130 option is overvalued. alternatively, the september $120 option could be said to be undervalued.(note: candidates receive full credit for identifying other, less prominent, pricing inconsistencies.)7.the important distinction is whether the option is a covered or uncovered position. if the option is added to a portfolio that already contains the underlying asset (or something highly correlated), then the option will frequently be a covered position and, consequently, lower overall risk. for example, selling a call without owning the underlying asset leaves the seller open to unlimited liability and (probably) increases portfolio price fluctuation (risk). but if the seller of the call owns the underlying asset, then selling the call neutralizes the portfolio from price changes above the strike price and (probably) decreases risk.because options are bets that an assets price will be above or below some level (the strike price), they represent a way of leveraging ones subjective view on the assets future price. options always cost less than the underlying asset and consequently can change in price more (on a percentage basis) than the underlying asset does. this provides the same effect as borrowing money to buy the asset or selling the asset short and investing the proceeds in bonds. (in fact, this is how option pricing theory values options, by replicating the price of an option using the underlying asset and bonds.)8.call options differ from forward contracts in that calls have unlimited upside potential and limited downside potential, whereas the gains and losses from a forward contract are both unlimited. therefore, since call options do not have the downside potential of forwards, they represent only the “good half” (the upside potential) of the forward contract. the “bad half” of the long forward position is the unlimited downside potential that is equivalent to being short a put. this is consistent with putcall parity where being long a call and short a put yields the same payoff as a forward contract.9.since options have nonlinear (kinked) payoffs, broad market movements may have different relative effects on the value of a portfolio with options depending on whether the market moves up or down. for example, a portfolio that is putprotected may not move down much if the market declines 10% but may move up nearly 10% if the market rises 10%. consequently, the returns are asymmetric or skewed. this makes standard deviation a less informative statistic because it reveals information only about the degree of variation and not the “direction” of the variation. since investors usually care about downside risk (standard deviation), investors probably will not care as much if all of the variation is in the upside return. the standard deviation statistic could be modified to only measure the variation in negative returns (the socalled semivariance) so that it was a measure of downside risk only.10.a synthetic offmarket forward contract with a forward price of $25 could be created using putcall parity. buying a call struck at $25 and selling a put struck at $25 assures the investor of buying the stock at the expiration date for $25. this portfolio then has the same requirements as the offmarket forward at $25. cp is onehalf of the putcal1 parity relationship, and we know it has to equal spv(k). since s = $32 and the risk freerate can be calculated as (3532)/32 = 9.375%, we can calculate that the offmarket forward is worth sp($25) = $32$25 / (1 +