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are an estimate of the percentage of outstanding principal that will be prepaid in a given

year. In other words, if the odds of prepayment are 6 percent for any given mortgage, then

we expect that 6 percent of all mortgages will prepay, meaning that 6 percent of the

principal in a mortgage pool will be prepaid per year.

16. We calculate SMMs as follows:

= 1 в€’ (1 в€’ CPR )

1 / 12

SMM

Given the answers in the previous problem, itвЂ™ mostly a matter of plug and chug. The

s

answers are .254 percent (50 PSA), 1.06 percent (200 PSA), and 2.26 percent (400 PSA).

Notice that the 400 PSA is not simply double the 200; thereвЂ™ a compound interest-type

s

effect in the calculation.

17. A collateralized mortgage obligation (CMO) is a mortgage-backed security with cash

flows that are divided into multiple securities. They exist because they provide a means of

altering some of the less desirable characteristics of MBSвЂ™ thereby increasing

s,

marketability to a broader class of investors. More fundamentally, they exist because

investment banks (the creators and marketers) have found them to be a profitable product!

18. Every mortgage payment has an interest portion and a principal portion. IO and PO strips

are very simple CMOвЂ™ the interest and principal portions are separated into distinct

s;

payments. Holders of IO strips receive all the interest paid; the principal goes to holders of

PO strips. If interest rates never change, the IO stripsвЂ“especially the longer dated onesвЂ“are

vastly more risky. With PO strips, the only uncertainty is when the principal is paid. All

PO strips-holders will receive full payment. With an IO strip, however, prepayment means

that no future interest payments will be made, so the amount of interest that will be

received is unknown.

FUNDAMENTALS OF INVESTMENTS B-47

19. PO strips have greater interest rate risk, where we define interest rate risk to mean losses

associated with interest rate increases and gains associated with decreases. When interest

rates go up, prepayments slow down, thereby postponing the time until principal is

received. IO strips can actually behave like вЂњinverse floaters,вЂќ their value tends to rise

when interest rates increase. The reason is that slowing prepayments increases the interest

that will be received by IO strips-holders.

20. The A-tranche will essentially receive all of the payments, both principal and interest until

it is fully paid off. The Z-tranche receives nothing until the A-tranche is paid off. After

that, the Z-tranche receives everything. The Z-tranche is much riskier because the size and

timing of the payment is not known.

21. With a protected amortization class (PAC) CMO, payments are made to one group of

investors according to a set schedule. This means that the protected class investors have

almost fully predictable cash flows. After protected class investors are paid, all the

remaining cash flow goes to non-PAC investors, who hold PAC support or PAC

companion bonds. In essence, one group of investors receives fixed payments, the other

group absorbs all (or virtually all) the uncertainty created by prepayments.

22. Macaulay duration assumes fixed cash flows. With MBSвЂ™ and CMOвЂ™ the payments

s s,

depend on prepayments, which in turn depend on interest rates. When prepayments pick

up, duration falls, and vice versa. Thus, no single measure is accurate.

B-48 CORRADO AND JORDAN

Chapter 14

Stock Options

Answers to Questions and Problems

Core Questions

1. Assuming American-style exercise, a call option confers the right, without the obligation,

to buy an asset at a given price on or before a given date. An American-style put option

confers the right, without the obligation, to sell an asset at a given price on or before a

given date. European-style options are the same except that exercise can only occur at

maturity. One reason you would buy a call option is that you expect the price of the asset

to increase. Similarly, you would buy a put option if you expect the price of the asset to

decrease. In both cases, other reasons exist, but these are the basic ones. A call option has

unlimited potential profit, while a put option has limited potential profit; the underlying

asset's price cannot be less than zero.

2. a. The buyer of a call option pays money for the right to buy....

b. The buyer of a put option pays money for the right to sell....

c. The seller of a call option receives money for the obligation to sell....

d. The seller of a put option receives money for the obligation to buy....

3. Your options are worth $60 - $50 = $10 each, or $1,000 per contract. With five contracts,

the total value is $5,000. Your net profit is $5,000 less the $1,000 (5 contracts at $200

each) you invested, or $4,000.

4. Your options are worth $30 - $20 = $10 each, or $1,000 per contract. With eight

contracts, the total value is $8,000. Your net profit is $8,000 less the $2,400 (8 contracts

at $300 each) you invested, or $5,600.

5. The stock costs $100 per share, so if you invest $10,000, youвЂ™ get 100 shares. The

ll

option premium is $5, so an option contract costs $500. If you invest $10,000, youвЂ™ get ll

$10,000/500 = 20 contracts. If the stock is selling for $120 in 90 days, your profit on the

stock is $20 per share, or $2,000 total. The percentage gain is $2,000/10,000 = 20%.

Similarly, in this case, your options are worth $20 per share, or $2,000 per

contract. However, you have 20 contracts, so your options are worth $40,000 in all. Since

you paid $10,000 for the 20 contracts, your profit is $30,000. Your percentage gain is a

pleasant $30,000/$10,000 = 300%.

If the stock is selling for $100, your profit is $0 on the stock, so your percentage

return is 0%. Your option is worthless (why?); the percentage loss is -100%. If the stock

is selling for $80, verify that your percentage loss on the stock is -20% and your loss on

the option is again -100%.

FUNDAMENTALS OF INVESTMENTS B-49

6. 60 contracts at $700 per contract = $42,000

7. Stock price = $95: option value = 60(100)($95 вЂ“ $80) = $90,000

Stock price = $86: option value = 60(100)($86 вЂ“ $80) = $36,000.

8. Initial cost= 25(100)($4.25) = $10,625; maximum gain= 25(100)($80)вЂ“$10,625 =

$189,375. Terminal value= 25(100)($80 вЂ“ $55) = $62,500; net gain = $62,500 вЂ“ $10,625

= $51,875

9. Stock price = $55: net loss = $10,625 вЂ“ $62,500 = вЂ“ $51,875.

Stock price = $100: net gain = $10,625.

The breakeven stock price is the $80 exercise price less the premium of $4.25, or $75.75.

For terminal stock prices above $75.75, the premium received more than offsets any loss,

so the writer of the put option makes a net profit (ignoring the effects of the time value of

money).

10. In general, the breakeven stock price for a call purchase is the exercise price plus the

premium paid. For stock prices higher than this, the purchaser realizes a profit. For a put

purchase, itвЂ™ the strike price less the premium. For stock prices lower than this, the

s

purchaser realizes a profit.

Intermediate Questions

11. If you buy a put option on a stock that you already own, you guarantee that you can sell

the stock for the strike price on the put. Thus, you have in effect insured yourself against

stock price declines beyond this point. This is the protective put strategy.

12. The intrinsic value of a call option is max{S вЂ“ K,0}. It is the value of the option at

expiration.

13. The value of a put option at expiration is max{K вЂ“ S,0}. By definition, the intrinsic value

of an option is its value at expiration, so max{K вЂ“ S,0} is the intrinsic value of a put

option.

14. You get to keep the premium in all cases. For 20 contracts and a $2 premium, thatвЂ™ s

$4,000. If the stock price is $30 or $40, the options expire worthless, so your net profit is

$4,000. If the stock price is $50, you lose $10 per share on each of 2,000 shares, or

$20,000 in all. You still have the premium, so your net loss is $16,000.

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