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.
Buy call
buy stock + put
Yes, it’s the same. Protective put is a synthetic call
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?
(** same question as in previous document. See response there)
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?
1
150
1
(1 + 𝑟2 )𝑡2 𝑡2−𝑡1
(1 + .08) ⁄360 150⁄360−100⁄360
1.0326 7.2
𝑓 = ([
]
)
−
1
=
([
]
)
−
1
=
(
) − 1 = .1214
100
(1 + 𝑟1 )𝑡1
1.0163
(1 + .06) ⁄360
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?
Strips are unlimited profit, limited risk options trading strategies that are used when the options trader
thinks that the underlying stock price will experience significant volatility in the near term and is more
likely to plunge downwards instead of rallying.
Large profit is attainable with the strip strategy when the underlying stock price makes a strong move
either upwards or downwards at expiration, with greater gains to be made with a downward move
Maximum loss for the strip occurs when the underlying stock price on expiration date is trading at the
strike price of the call and put options purchased. At this price, all the options expire worthless and the
options trader loses the entire initial debit taken to enter the trade.
7.
Why is selling a call or put more risky than buying a call or put?
A naked option position is much more risky than writing a simple covered option because you have
essentially sold the right to something that you do not own. You aim to make a profit by collecting the
premium, however you face unlimited loss if the option becomes in the money.
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.
** same question as previous document. See answer there
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
** same question as previous document. See answer there
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.
1
1
88
(1 + 𝑟2 )𝑡2 𝑡2−𝑡1
(1 + .045) ⁄360 88⁄360−70⁄360
1.0108 20
𝑓 = ([
]
)
−
1
=
([
]
)
−
1
=
(
) − 1 = .0634
70
(1 + 𝑟1 )𝑡1
1.0077
(1 + .04) ⁄360
forward rate is the forecasted rate
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
discount
Commercial paper
discount, 360 day
Bank CD
compounding rate, 365
Repo rate
Treasury bond with 5 years left to maturity
discount, 360
Discount, 360
Treasury bond with 4 months left to maturity
discount 360
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
a) a low coupon bond is one that has low yield, which in turn means high duration.
b) the low coupon bond is more volatile because the incoming cash flows from the bond are
lower (used to aid in pricing the bond) and are more sensitive to interest rate shifts
c) Callability refers to the issuers ability to call or buy back the bond from investors at a pre-specified call
price. Bonds are usually called during low interest rate environments when companies see that they can
issue bonds at cheaper rates. Because of callability, a bond’s yield is usually quoted as yield-to-worst.
YTW is therefore either the yield-to-maturity or the yield-to-call
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.
(** same question as in previous document. See response there)
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.
** for a and b see previous document
c) lower strike = higher premium
d) lower strike = lower premium
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.
The curve should be flat. If investors are risk-neutral they are indifferent to buying long term or
short term bonds and there would be no risk premium. If there was a risk premium, then it could
be upward sloping
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.
**see question 7 from previous doc, essentially same question
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.
** similar to question 1 on previous doc (should be the same)
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)?
Buy call & sell put at same strike (long synthetic)
next scenario (should resemble a call but w/o the line below 0)
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).
a. What would you expect the price of the underlying security to be?
C + Xe−rT = S0 + P
5 + 100 ∗ 𝑒 −.01∗1 = 𝑆0 + 3
𝑆0 = 8 + 99.9167 = 107.0050 ≈ 107.01
** here r = .01 and assumed T to be 1 yr. (question is really poor). Feel like information is
missing
b. Illustrate with a graph trhe profit or payoff profile that would result from a “covered
call” (write call on the security you own) on this stock. Explain.
You own the stock
Sell a call at strike price A
Using the covered call option strategy, the investor gets to earn a premium writing calls while at the same
time appreciate all benefits of owning the underlying stock. The profit potential is limited because selling
the call obligates you to sell stock you already own at strike price A.