The Mathematics of Money

298 Chapter 6 Investments

A. Portfolio Diversifi cation

Exercises 1 to 6 are based on the table below, showing the prices of the stocks of four different companies on January 1,

2006 and January 15, 2007. No stock splits occurred for any of these companies.

East Corp. West Corp. North Corp. South Corp.

1/15/06 $40.00 $25.00 $10.00 $100.00

1/15/07 $45.00 $20.05 $15.50 $81.50

1. On a percentage basis, which of the four companies listed in the table above was the best performer? Which company
   was the worst performer?


2. Suppose that I invested $5,000 in East Corp. on January 15, 2006. How many shares would I get for this investment?
   How many shares would I have got for $5,000 invested in West Corp.? North? South?


3. Calculate the value on January 15, 2007, of a $5,000 investment made in East Corp. on January 15, 2006. Do the
   same for each of the other three companies.


4. Suppose that instead of investing $5,000 in just one of the companies, I instead invested $1,250 in each of the four.
   What would the value of this portfolio have been on January 15, 2007?


5. Suppose that instead of investing $5,000 in just one of the companies, I instead decided to invest in a mix of the four.
   However, since I felt a little stronger about some of the companies than others, I did not invest equal amounts in all
   four. I invested $1,500 each in East and South, and $1,000 each in West and North. What was the value of my portfolio
   on January 15, 2007?

EXERCISES 6.4

average based on multiplication instead of addition. The arithmetic mean does not work

out quite right in this case because it is based on addition, whereas compound growth is

based on multiplication.

This “average” issue can lead to misunderstandings about investment performance.

Example 6.4.8 A mutual fund that I own had a really bad year in 2005; it

lost 40% of its value that year. In 2006 things went much better though, and the

fund gained 40%. Over the course of the 2 years, what was the fund’s overall

performance?

Common sense says that if I lost 40% one year and gained 40% the next, I wound up where I

started. This is not correct, though; in saying this I am using the logic that 40% and 40%

average out to 0%.

In actuality, $100 invested in this fund at the start would have become:

FV 
 $100(0.60)(1.40) 
 $84

Overall, I lost $16 on a $100 investment, and overall loss of 16%. Though the question did

not ask for an average rate of return, we can calculate it to be 8.35%.