Homework answers / question archive / Part I 1) 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

Part I 1) 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

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Part I

1) Consider the following “portfolio:” buy a call at the premium V_c 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.

2) Why does the U.S. Treasury now prefer to use “uniform price” auctions to sell its securities rather than “discriminatory price” auctions?  Explain.

3) Draw a profit profile (diagram showing the profit level for all possible prices of the underlying security of an option) for the case of written (sold) put. 

a.   Explain the shape of your diagram.

b.  Now suppose the price of the underlying security rises.  What will the profit profile look like now to someone who now writes this put?  Draw the new profit profile and explain how it is different from the previous one. 

 

 

Part II

 

 

4. An investor creates a “strangle:” she buys a European put having exercise price $80 and a European call having exercise price $90.  Suppose at the exercise date the underlying security price turns out to be $86.  What is the gain/loss for this investor? Explain. 

 

5. Find the typo: the following table lists put premiums (V_p) at six given different exercise prices ( E ).  But there is a typo for one of the put premiums; it cannot be correct.  Find the typo and explain why the number for V_p cannot be correct.  Explain.

 

HINT: What do we know about the relative size of the premiums on three options which differ only by their exercise prices?

 

 

E	Vp
90	1
95	2.1
100	2.65
105	3.5
110	4.7
115	6.0

 

 

6. Consider the “butterfly spread” profit profile below.  In class we constructed it with four call options.   For this question, explain how to construct it with four puts.  [puts]

 

 

 

Part III

 

 

7. I offer to borrow money from you for 90 days at the following interest rate quotations:

1. a discount rate of 5%.
2. a simple interest money market rate of 5.04%.
3. a “bond equivalent” yield (simple interest 365 day) rate of 5.11%.

 

     Which is the better deal from your point of view? Explain your calculation.

 

8. Suppose the (riskless) rate on Euro-denominated T-bills is higher than the U.S. Treasury bill rate.  If the spot rate S is quoted $ per Euro, would you expect that the forward rate F (also $/Euro) will be higher or lower than S?  Explain.  Does this indicate whether the Euro will rise or decline in value in the future?  Explain. 

 

9. Find a pair of options that will create a payoff profile of the following shape: 

 

 

                     

 

 

 

Explain clearly what the options are and why you get this joint shape.

Part IV

 

10. Suppose the 180-day bill rate is lower than the 90-day rate.  What does that imply about trader’s expectations of future interest rates?  Explain.

 

 

11.  An investor buys a security and writes a European call whose exercise price E makes it “on the money.”  Draw a diagram that shows the possible payoff depending on possible prices of the security at the exercise date.  Explain.

 

12. You have seen the formula for deriving the yield to maturity on a bond.  What will the formula be for a “zero-coupon” bond (one that pays no coupon, but one cash payment at the end)?  Explain.

Part V

 

 

 

13. A dealer forecasts that the discount rate on a 60-day bill will be 5.10%.     The current discount rate on a 90-day bill is 5.30%.  What is the highest 30-day repo rate the dealer can afford to pay and still expect to break even on a repo?  Explain.

 

14. and 15. *(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?

            b.  Illustrate with a graph the profit or payoff profile that would result from a “covered call” (write call on the security you own) on this stock.  Explain.

 

Part VI

 

16. In what sense is the “yield to maturity” an “interest rate?”  Explain.

 

17. “A low-coupon security is more price-volatile [in response to a given change in yield] than a high-coupon security.”  True or false, or what?  Explain carefully. 
18. True, False, or Uncertain (select one and defend your selection): “Stock prices follow a random walk process.”  Explain.