Problems 18-19 represent a greater challenge. You may need to review the definitions of call and put options in Chapter 2.

18. You are faced with the probability distribution of the HPR on the stock market index fund given in Table 5.1 of the text. Suppose the price of a put option on a share of the index fund with exercise price of $110 and maturity of one year is $12.

a. What is the probability distribution of the HPR on the put option?

b. What is the probability distribution of the HPR on a portfolio consisting of one share of the index fund and a put option?

c. In what sense does buying the put option constitute a purchase of insurance in this case?

19. Take as given the conditions described in the previous question, and suppose the risk- free interest rate is 6% per year. You are contemplating investing $107.55 in a one-year CD and simultaneously buying a call option on the stock market index fund with an ex- ercise price of $110 and a maturity of one year. What is the probability distribution of your dollar return at the end of the year?

APPENDIX: CONTINUOUS COMPOUNDING

Suppose that your money earns interest at an annual nominal percentage rate (APR) of 6% per year compounded semiannually. What is your effective annual rate of return, account- ing for compound interest?

We find the answer by first computing the per (compounding) period rate, 3% per half- year, and then computing the future value (FV) at the end of the year per dollar invested at the beginning of the year. In this example, we get

FV (1.03)2 1.0609

The effective annual rate (REFF), that is, the annual rate at which your funds have grown, is just this number minus 1.0.

REFF 1.0609 1 .0609 6.09% per year

I. Introduction 5. History of Interest Rates and Risk Premiums

The McGraw−Hill

Companies, 2001

150 PART I Introduction

Table 5A.1

Effective Annual

Rates for APR

of 6%

Compounding Frequency n REFF (%)