The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


1.4 Time Value of Money 289


  1. Debbie took a position short 10,000 ounces of August silver at $10.43 an ounce. At the delivery date, the spot price
    was $10.72 an ounce.


a. Did Debbie make or lose money on this deal?
b. Calculate Debbie’s profi t or loss.
c. Assuming the usual initial margin requirements, calculate Debbie’s return as a percent.
d. Assuming a term of 114 days, calculate Debbie’s return as a simple interest rate.


  1. If you expect nickel prices to rise, would you want to be long or short nickel futures? If you believe that a stock price is
    likely to decline, would you want to own puts or calls on that stock?


F. Additional Exercises


  1. In Example 6.3.4 we calculated Luis’s rate of return from a futures transaction as a simple interest rate. Calculate his
    rate of return from this example as an effective compound interest rate.

  2. Suppose that the stock of Ganargua Hydro presently trades for $35 a share. You believe that between now and October
    the stock will rise in value, and have $2.500 you want to put into an investment based on this belief. Suppose that you
    consider three different alternatives: investing all of your money in the company’s actual stock, buying calls with a strike
    price of $35, or buying calls with a strike price of $50. Calculate the number of shares or options contracts you could
    buy with $2,500, using the prices shown in the options chain for this company given in the text. Then, for each of these
    alternatives, evaluate how things would work out for you if the stock price dropped to $30, if it stayed at $35, if it rose
    to $45, and if it rose to $60. Discuss any conclusions you can draw from this.


6.4 Mutual Funds and Investment Portfolios


Savings and wise investments provide a solid road to financial well-being. Yet that
broad statement hides an awful lot of difficult details. Obviously if you knew the future
it would be easy to pick the best investments today and become fabulously wealthy.
Sadly, knowing the future is not an option for any of us. So when we make investment
decisions (or any other ones for that matter), we have to settle for basing our choices
on informed and educated guesses of what the future holds. No matter how informed
and educated our guesses may be, we have to deal with the possibility that they will
turn out to be wrong.
In Section 6.1, we considered an investment in the stock of Zarofire Systems, and found
that this investment worked out extremely well. Over the course of 7 years, we would have
earned an approximately 25% overall rate of return. This is absolutely wonderful! From
our previous work we know that this kind of rate, compounded over time, can result in
fabulous investment gains.
Now if we had known from the start how things would work out, we would have been
wise to pour all of our money into Zarofire stock. The problem, of course, is that there
is no way that we could have known this in advance. When we first bought the stock,
we must have thought that the company had good prospects, that it would be a success-
ful business and profitable investment—otherwise, why buy its stock? But there was no
way that you could know for sure that the company’s management would not make mis-
guided decisions, that a competitor with even better products and better prices would not

6.4 Mutual Funds and Investment Portfolios 289
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