The Mathematics of Money

(Darren Dugan) #1

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


Mutual Funds


Even though there are plenty of good reasons to diversify, creating a
diversified portfolio of investments can pose some practical problems for
an investor. In the previous example Matt decided to invest 60% of his
money in stocks; but now, how does he decide which stocks? Unless Matt
is knowledgeable about how to evaluate a business’s financial strength
and prospects—not an easy task—he will not be in a position to make
good decisions about which specific stocks to buy. How will he decide
which specific stocks to buy? It might be a good thing for Matt to invest
time and effort in learning how to select the best stocks and bonds, but
doing that requires lots of time and effort. If he has an aptitude for this
and finds it interesting, great; it can be a very rewarding hobby. But most
people find they have other things they’d rather do with their time.
Also, unless Matt has a large amount of money to invest, creating a diversified portfo-
lio of individual securities may not be practical. Suppose he has $3,000 in his investment
account right now; 60% of $3,000 works out to $1,800. If he divides this money evenly
among a dozen different stocks, that works out to $150 in each stock. This is simply too
small an amount to practically invest in an individual stock. After taking into account the
commissions (stock brokers do not work for free) and other fees involved in buying stocks,
it really isn’t practical to invest less than a few thousand dollars in an individual stock.
Mutual funds are a type of investment vehicle that addresses these difficulties. A mutual
fund is an investment portfolio that pools money from many different investors. The decisions
of which securities to invest in are made by the fund’s portfolio manager. By owning shares
in the mutual fund, each investor effectively owns a piece of the overall investment portfo-
lio. If Matt invests $1,800 in a stock mutual fund, he may find his investments diversified
among hundreds of different stocks owned by the fund.
Like a stock, the ownership of a mutual fund is divided into shares. Each share is
entitled to an equal percent of the overall fund’s assets.^8 The value of one share of a fund is
determined by dividing the value of the fund’s overall assets by the total number of shares
outstanding. This called the fund’s net asset value (or NAV ).

Example 6.4.2 The Nesoh Capital Equity Fund has assets totaling $15,735,962.
There are 845,362 shares. What is the fund’s NAV?

To fi nd the NAV we simply divide $15,735,962/845,362 to get $18.61.

An open-end mutual fund does not have a fixed number of shares. New shares are
created whenever someone invests money in the fund, old shares cease to exist when
someone pulls money out of the fund. Most mutual funds in the United States today are
open-end funds. Closed-end funds, on the other hand, have a fixed number of shares.
When someone wants to invest in a closed-end fund, no new shares are created; instead,
that investor must buy existing shares from someone else. Closed-end funds can be
bought and sold just like stocks. Unlike open-end funds, though, they do not necessar-
ily sell for their net asset value. The selling price of a closed-end fund is determined by
what the market will bear. Closed-end funds may sell for more, or less, than their net
asset values.

Example 6.4.3 If Matt invests $1,800 in the open-end Nesoh Capital Equity Fund,
how many shares will be created?

The investment of $1,800 divided by $18.61 per share works out to 96.7221937. A mutual
fund can have fractional shares; the number of shares is often carried out to three decimal
places. Assuming this, Matt would have 96.722 shares in this fund.

(^8) Some mutual funds do have different classes of shares, which may not all be of equal value, but this is the
exception, not the rule.
6.4 Mutual Funds and Investment Portfolios 295
Mutual funds are a popular way to build a diversifi ed
investment portfolio. © Royalty-Free/CORBIS/DIL

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