2-Financial Markets Page 48 Wednesday, February 4, 2004 1:15 PM
48 The Mathematics of Financial Modeling and Investment Managementinclusion in each of these indexes is solely a firm’s market capitalization.
The most comprehensive index is the Wilshire 5000, which actually
includes more than 6,700 stocks now, up from 5,000 at its inception.
The Wilshire 4500 includes all stocks in the Wilshire 5000 except for
those in the S&P 500. Thus, the shares in the Wilshire 4500 have
smaller capitalization than those in the Wilshire 5000. The Russell 3000
encompasses the 3,000 largest companies in terms of their market capi-
talization. The Russell 1000 is limited to the largest 1,000 of those, and
the Russell 2000 has the remaining smaller firms.
Two methods of averaging may be used. The first and most common
is the arithmetic average. An arithmetic mean is just a simple average of
the stocks, calculated by summing them (after weighting, if appropriate)
and dividing by the sum of the weights. The second method is the geo-
metric mean, which involves multiplication of the components, after
which the product is raised to the power of 1 divided by the number of
components.Trading Arrangements
Below we describe the key features involved in trading stocks.Types of Orders
When an investor wants to buy or sell a share of common stock, the
price and conditions under which the order is to be executed must be
communicated to a broker. The simplest type of order is the market
order, an order to be executed at the best price available in the market.
The danger of a market order is that an adverse move may take
place between the time the investor places the order and the time the
order is executed. To avoid this danger, the investor can place a limit
order that designates a price threshold for the execution of the trade.
The key disadvantage of a limit order is that there is no guarantee that it
will be executed at all; the designated price may simply not be obtain-
able. The limit order is a conditional order: It is executed only if the
limit price or a better price can be obtained.
Another type of conditional order is the stop order, which specifies
that the order is not to be executed until the market moves to a desig-
nated price, at which time it becomes a market order. There are two
dangers associated with stop orders. Stock prices sometimes exhibit
abrupt price changes, so the direction of a change in a stock price may
be quite temporary, resulting in the premature trading of a stock. Also,
once the designated price is reached, the stop order becomes a market
order and is subject to the uncertainty of the execution price noted ear-
lier for market orders. A stop-limit order, a hybrid of a stop order and a