The Mathematics of Money

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

The following table compares $10,000 invested in each of the four stocks (500 shares

each) with $10,000 invested by putting $2500 (125 shares each) into each stock.

$10,000 in

Axerixia

$10,000 in

Blunderbluff

$10,000 in

Caughdenoy

$10,000 in

DDKind

$2500 in

each

Start $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

1 $8,885.00 $11,250.00 $11,235.00 $10,625.00 $10,498.75

2 $9,015.00 $13,375.00 $9,880.00 $10,085.00 $10,588.75

3 $11,990.00 $9,025.00 $10,995.00 $13,275.00 $11,321.25

4 $12,120.00 $7,220.00 $14,325.00 $12,995.00 $11,665.00

5 $14,275.00 $6,325.00 $16,565.00 $10,530.00 $11,923.75

6 $13,135.00 $5,820.00 $18,705.00 $10,555.00 $12,053.75

7 $12,515.00 $4,735.00 $19,815.00 $12,220.00 $12,321.25

8 $14,010.00 $5,215.00 $20,780.00 $10,005.00 $12,502.50

9 $16,385.00 $3,090.00 $21,230.00 $9,555.00 $12,565.00

10 $17,545.00 $1,805.00 $21,715.00 $9,250.00 $12,578.75

11 $15,910.00 $1,025.00 $24,615.00 $9,385.00 $12,733.75

12 $14,260.00 $770.00 $25,490.00 $10,000.00 $12,630.00

By putting equal amounts into each stock, you would end up with $12,630. This is not as

good as the $14,260 you would have ended up with if you have put all your money into

Axerixia, or the $25,490 you would have had from Caughdenoy, but it beats the $10,000

you would have had with DDKind and positively kills the $770.00 you would have wound

up with in Blunderbluff. By spreading your investment across these four stocks, you guar-

antee that you will not do as well as if you have put all your money in the best performers,

but you also ensure that you will not do as badly as if you hand put all your money into the

poorer performers.

Of course Blunderbluff’s losses eat up some of Caughdenoy’s gains. Owning a mix

averages the performance of all the stocks together. This makes it very unlikely that you

will end up with an extraordinary return (any mix is bound to contain mediocre performers

like DDKind and clunkers like Blunderbluff). But it also makes it unlikely that you will

end up with an appallingly bad return (the mix is likely to contain good performers like

Axerixia and Caughdenoy to balance to duds).

Diversification can not only affect the end result of an investment, it can also affect

the volatility along the way. From month to month, the prices of each of these stocks

varied, as did the value of the mixture. However, from the table above we can see that

the month-to-month variation was greater for the investments in individual stocks than

for the combined investment. This can also be seen by looking at a graph of the month-

by-month values:

Single Stock Portfolios

Time

$0.00

$5,000.00

$10,000.00

$15,000.00

$20,000.00

$25,000.00

$30,000.00

Value

Axerixia Blunderbluff Caughdenoy Dedekind

6.4 Mutual Funds and Investment Portfolios 291