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Stock Indexes

Stock Indices Every day we hear that the Dow was up (or down) or that the S&P was such and such. What does it mean? What is the Dow? What is the S&P?

In order to gauge how the stock market did on a particular day or a longer period, we use a market index to measure performance. Market indices take many flavors. For example, the Dow Jones Industrial average, the most famous index in the world, is a price weighted index or 30 large firms that are on the New York Stock Exchange(NYSE). Others Indexes (or indices if you prefer), such as the S&P 500 are market value based.

Market value index This type of index uses the market value of equity in calculating returns. For example:
Day 1
Shares
Stock Price o/s Market value
A 10 1,000,000 10,000,000
B 15 6,000,000 90,000,000
C 20 5,000,000 100,000,000
= 200,000,000 = Total market value of stocks in Index
We then make this the base=100
Day 2
Suppose that Stock B splits 2:1 and stock C pays a 10% stock dividend. Moreover, the prices on all of the stocks change during the day. Stock Price o/s Market value
A 10 1,000,000 10,000,000
B 7.5 12,000,000 90,000,000
C 18.18 5,500,000 100,000,000
=200,000,000 Total market value of stocks in Index
What is the new Index Value?
the same as the old. Next let’s assume that the stock prices change during the day. Stock Price o/s Market value
A 12 1,000,000 12,000,000
B 10 12,000,000 120,000,000
C 20 5,500,000 110,000,000
=242,000,000 Total market value of stocks in Index
What is the new Index Value? Beginning market value of index stocks $200,000,000

Ending value of index stocks $242,000,000 242,000,000 divided by 200,000,000= 1.21
121* 100 = new index value.
= 121 Notice that if a market value index is used, we do not need to worry about stock splits or stock dividends.
Price Index We will be using the same numbers as above but now we have a stock price index To begin off we need an initial index value. For this we can average the stock prices.
So (10 + 15+ 20)/3 = 15 So on day zero, our price index would be 15. Just like before, stock B splits and stock C pays a 10% stock dividend. The next step in calculating out index value is to adjust for these changes. If nothing else happens except for the splits (remember a stock dividend is in effect a mini stock split), our index value should not change. So we assume it does not change and reaverage .using a new denominator or divisor. Thus,
Old Index value = New Index value
(Sum of Stock Prices)/ (# stocks) = (New Sum)/New Divisor
(10 + 15 + 20) / (3) = (10 + 7.5 + 18) /Divisor
15 = (35.5) / Divisor
Divisor = 35.5 / 15
Divisor = 2.3667
Check: Prior to the Open, new index is still 15
(10 + 7.5 + 18) / 2.3667 = 15 Now account for the price changes that occur during day one to determine the closing index value.
(12+ 10+ 20) /2.3667 = 17.74
One problem with a price index is that a movement in a high priced stock has a greater influence on the index than the same percentage movement of a lower priced stock. For example:
Suppose in the above example, stock B goes up by 10% on day 3 while the other stocks do not move. What would be the new index value?
(12 + 11 + 20) / 2.3667 = 18.17
Now suppose that instead of stock B moving, stock c increases by 10%. What would the new index value be?
(12 + 10 + 22) / 2.3667 = 18.6 “Assignment”: Find what the current divisor for the Dow Jones Industrial Average is. (hint look in the Wall Street Journal usually on page c1) Of the major indicies most (but by no means all) are Market weighted. For example the FTSE (footsie) is a value-weighted index of 100 stocks on the London Stock Exchange.

BTW at the time of this writing October 2013) the divisior on the Dow was .15. For the current divisior you can see wikipedia.


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