1 and 2. (double weight) An option on a stock has an exercise price exactly equal to its current
price. Compare two strategies: (a) buy a naked call on the stock; (b) buy the stock and buy a put
on it (having the exercise price equal to its current price). Is the payoff pattern of (a) the same as
the payoff pattern of (b)? Explain.
The payoff pattern of buying the naked call on the stock is the same as the payoff pattern of
buying the stock and a put on it. In each case, a decline in the stock price would lead to a loss
equal to the premium paid for the option. The call option would simply expire worthless, and the
put option would give you the ability to sell the stock at its current price if it declines in the
future, negating the loss from the decline in stock price. Both strategies will see gains if the
stock prices increases, since the call option will increase in value in the first strategy, and the
stock will increase in value in the second strategy. See the diagrams below.
3 and 4. (double-weight). This is about accrued interest on a bond. A. Does it enter into the
“haircut” (margin) calculation for a repo? B. How is accrued interest reflected, if at all, in the
quoted price of a bond or note? yield? Explain. C. How is it taken into account when bonds are
notes are delivered under a futures contract?
5.
You are given: the 100-day Tbill rate is .06. The 150-day Tbill rate is .08. What is the
“bill parity” or forward discount rate on the future 50-day bill?
6.
Show the possible profits on a graph of buying one call and two puts at the same strike
price. Under which circumstances might this strategy be sensible?
This strategy is a “straddle”, with a higher payout to the downside than to the upside. This
strategy would be sensible if you expect the volatility in the stock to increase, since the payout
increases as the stock price moves away from its original price. The strategy makes sense
particularly if you expect the stock to move lower, since it pays out even more on the downside.
See the diagram below.
7.
Why is selling a call or put more risky than buying a call or put?
Selling an option is more risky than buying one because when you buy an option, your risk is
defined. The largest loss that you can make when buying an option is the premium that you pay
for it. The largest gain that you can make when selling an option is the premium that the buyer
pays for it. However, the downside risk is infinite. For example, if you were to sell a call and
the stock price increased substantially, the buyer would exercise the option and you would have
to sell them the stock at the original strike price. The stock price can move infinitely higher, so
you have infinite risk.
8.
The profit profile or possibilities of “writing a covered call” (buying or owning a security
while selling a call against the security) is similar to writing what “naked” option
contract? Explain.
The profit profile of writing a covered call is similar to writing a naked put. They both limit the
gain if the stock moves higher, and they both have infinite risk if the stock moves lower. The
covered call strategy earns money initially by collecting the premium from the call, but it can
lose money if the stock price declines since you also own the stock. The covered call limits the
gain if the stock rises, because the buyer of the call will exercise it if it at the strike price, buying
your stock at that price.
9.
“A low-coupon security is more price-volatile [in response to a given change in yield]
that a high-coupon security.” True or false, or what? Explain carefully
10.
Bill parity: a 70-day T-bill has a discount rate of 4%. An 88-day T-bill has a discount of
4.5%. What is the bill parity or forward rate? Would you consider this forward rate the
“expected” or forecasted rate? Explain.
11. and 12. *TWO POINTS (DOUBLE CREDIT)
Fill in the rest of the table correctly (use the blank sheets, not this sheet):
Instrument
Treasury bill
Bankers Acceptance
How quoted in the marketplace
discount rate, 360 day
Commercial paper
Bank CD
Repo rate
Treasury bond with 5 years left to maturity
Treasury bond with 4 months left to maturity
13. About bonds: a. What is a low-coupon bond?
b. Does having a low coupon bond make the dollar price more volatile?
c. In what sense does having a low coupon make a bond price more
volatile?
d. What is the effect of “callability” on the yield of a bond?
Explain your answers
14.
When a bank makes a mortgage interest rate commitment, it agrees that its lending rate
will be fixed subject to the loan application’s being accepted and other conditions of the loan
being satisfied. The bank knows that if market mortgage rates rise, borrowers are likely to hold
them to their commitment; but if rates fall, borrowers can choose to finance their mortgages at
the lower rates. What options contact is a way to offset the risk the bank makes when fixing the
mortgage interest rate in advance? Explain.
15 and 16.
*(DOUBLE-WEIGHT) Predict and explain the effect on the option’s premium from the
following:
a. for a call option, a reduction in variance of the underlying security; b. for a put
option, a reduction in variance of the underlying security; c. for a call option, a lower
exercise price; d. for a put option, a lower exercise price.
A reduction in variance of the stock would reduce the premium of a call option because
the chances of a stock moving beyond a strike price at some point before expiration are
lowered. A reduction in variance has the same effect on a put option for the same reason.
A lower exercise price for a call option means a higher premium, because there is a
higher chance that the stock price will be above the strike price by expiration. A lower
strike price has the opposite effect on a put option, since there is less of a chance of the
stock price moving below the strike price.
17. Select one. If all investors were indifferent to risk, the yield curve (a) would always be
“flat;” (b) would be flat on the average; (c) would normally be upward-sloping. Explain.
18. and 19.
*(DOUBLE-WEIGHT) Consider the following “portfolio:” buy a call at the
premium Vc and buy a Treasury bill having price-per-face of β and face of E, where E is the
exercise price of the option. Now show how you would “short” this portfolio. What is the
payoff pattern? Explain.
20. Suppose a call with a particular exercise price E is written on a security that has current price
exactly the same as E. If you sell a put on this security (same maturity), will the premium be
higher or lower than the premium on the call? Explain.
It depends. If the options market is expecting the stock to go up, then the call premium would be
higher than the put premium. If the market is expecting the stock to go down, then the put
premium would be higher than the call premium.
21. Consider the following portfolio of options: buy a European call at exercise price E and sell
a put on the same underlying security at the same exercise price. What is the payoff pattern that
is created? Next: suppose the price of the underlying security is higher than in the first case
above. What will be the effect on the payoff pattern (i.e., how do you re-draw it)?
The payout pattern is simply the same as buying the underlying stock. You will gain as the stock
price goes up and lose as it goes down. See diagram below.
22. and 23. *(DOUBLE-WEIGHT)
Suppose a call option on a given stock has premium $5 per share, and the put option at the same
exercise price (E=$100) has premium $3 per share. The price of a Treasury security having the
same maturity as the options is .9900 (dollars per face). …not sure what he means by “$ per
face”…may need to doublecheck this answer.
a. What would you expect the price of the underlying security to be?
Use the put-call parity formula, shown below:
c + PV(x) = p + s
5 + 99 = 3 + s
s = 101
b. Illustrate with a graph the profit or payoff profile that would result from a “covered
call” (write call on the security your own) on this stock. Explain.
Buy the stock at $101 and sell the call at $5, essentially reducing the purchase price of the stock
to $96. If the stock is above $100 at expiration, then the stock will be call away and profit will
be limited to $4 (the $5 premium that you collected minus the $1 loss from buying the stock at
$101 and selling it at $100). If the stock falls, then profit falls too. $96 is the breakeven point.