Stock Market Indexes If we want to know how the stock market did today, what should we look at? The Dow Jones Industrial Average? The S&P 500 Index? The Nasdaq Composite Index?

What We Need to Know to Understand an Index The number of stocks in the index. The types of stocks in the index. The weighting method used to calculate the index value.

Price Weighting Start by calculating the average price (arithmetic mean) of the stocks in the index at time t N Index valuet =  Pi,t divided by N i = 1 where the stocks in the index at time t go from 1 – N

Price Weighting: An Example Price Price Stock Day 1 Day 2 Shrs Out. A $100 $110 100,000 B $ 10 $ 10 1,000,000 Note that the market cap of each stock is $10 million on Day 1

Price Weighting: An Example Index Value1 = (100 + 10)/2 = 55 Index Value2 = (110 + 10)/2 = 60 % Change Index = (60 - 55)/55 = 9.1% A 10% increase in the price of stock A caused a 9.1% increase in the index.

What if Instead... Price Price Stock Day 1 Day 2 Shares Out. A $100 $100 100,000 B $ 10 $ 11 1,000,000

Example (cont.) Index Value1 = (100 + 10)/2 = 55 % Change in Index = (55.5 - 55)/55 = .91% A 10% increase in the price of stock B caused a 0.91% increase in the index.

Price Weighting Stock A’s Price is 10 times higher so it gets a 10 times larger weighting. But both companies are the same size. Stock prices can be altered by changing shares outstanding through splits and repurchases

Price Weighting: Another Example Price Price Stock Day 1 Day 2 Shares Out A $100 $ 55 200,000 B $ 10 $ 10 1,000,000 Price of Stock A goes up to $110 on day 2, and at the close of trading, it has a 2-for-1 stock split, cutting the price in half while doubling the shares outstanding

Price Weighting Index Index Value1 = (100 + 10)/2 = 55 % Change = (32.5 - 55)/55 = - 40.9% The index is down, but stock A gained 10% and stock B was unchanged.

The Solution: Adjust the Divisor Adjust the Divisor so that the index gives us the value it would have had without the split: Before the Split, the index would have been: 110 + 10 = 120 and 120/2 = 60 After the Split, sum of prices Day 2 = 55 +10 = 65 65/(adjusted divisor) = 60 Adjusted Divisor = 1.083333

The Adjusted Divisor From now on, we need to add the prices of the stocks in the index and divide by the adjusted divisor to get the index value. We continue to use this adjusted divisor until another stock splits, or until one of the stocks in the index is replaced, or if there is a spin-off or an acquisition that alters the stock’s price.

Price Weighting The Dow Jones Industrial Average does Do any major indexes use a Price Weighting System? Yes The Dow Jones Industrial Average does

DJIA: History http://www.djindexes.com Oldest barometer of the stock market. Price Weighted Index Started in 1896 by Charles Dow with 12 stocks. (He and Jones started Dow Jones & Company.) GE was the last original stock in the index.

DJIA: Composition Today, there are 30 Companies. Represent about 30% of the market value of U.S. Stocks 25 stocks trade on the NYSE 5 stocks (AAPL, MSFT, INTC, WBA, and CSCO) trade on NASDAQ

DJIA: Composition As of Aug. 1, 2018: 3M, Nike, American Express, Apple, Merck, Goldman Sachs, Boeing, Caterpillar, Chevron, Cisco, Coca-Cola, DuPont, ExxonMobil, Wallgreens, Visa, Home Depot, Intel, IBM, Johnson & Johnson, JP Morgan Chase, United Healthcare, McDonald’s, Microsoft, Pfizer, Procter & Gamble, Travelers, United Technologies, Verizon, Wal-Mart, Disney

DJIA: Composition Editors of the Dow Jones-owned WSJ select the stocks. Dow Jones is now a subsidiary of News Corp. What are their current prices? http://money.cnn.com/data/dow30/

Other Dow Jones Price Weighted Indexes Transportation (20 firms) Started in 1884 Utilities (15 firms) Started in 1929 Composite (65 firms) Stocks in the Industrial, Transportation and Utilities indexes

DJIA: Index Value Suppose the Dow closes at 24,589.50 How did they arrive at this value? 30  Pi,t i = 1 DJIA Indext = --------------------- Adj. Divisor

Market Cap Weighted Indexes Market Capitalization = Market Value DEFINITION: #shares outstanding X Price per Share

Index Value t  (P i,t ) x (#Out Shrsi,t ) i = 1 Indext = ----------------------------- X Base n Value  ( Pi,b ) X (#Out shrsi,b )

Index Value t t indexes days b is the base day i indexes stocks Base day value needs to be arbitrarily set to something by the firm starting the index. 10 or 100 are common.

Back to Example: Case 1 Price Price Stock Day 1 Day 2 Shares Out. A $100 $110 100,000 B $ 10 $ 10 1,000,000 Again, note that each stock has the same market value on day 1

Market Value Example – Day 1 Index Value1 = (100)(100,000) + (10)(1,000,000) ----------------------------------------- X 100 = 100

Market Value Example – Day 2 Index Value2 = (110)(100,000) + (10)(1,000,000) ----------------------------------------- X 100 (100)(100,000) + (10)(1,000,000) = 105

Market Value Example % Change = (105 - 100)/100 = 5.0% NOTE: a10% increase in Stock A caused a 5% increase in the index.

What if Instead…Case 2 Price Price Shares Stock Day 1 Day 2 Outstanding A $100 $100 100,000 B $ 10 $ 11 1,000,000 Instead of stock A going up by 10%, stock B does

Example (cont) Index Value2 = (100)(100,000) + (11)(1,000,000) (100)(100,000) + (10)(1,000,000) = 105

What if a stock splits? Price Price Stock Day 1 Day 2 Shrs Out B $ 10 $ 10 1,000,000 Stock A goes up to $110 and then has a 2- for-1 split at the close of Day 2

Market Value Example Index Value2 = (55)(200,000) + (10)(1,000,000) (100)(100,000) + (10)(1,000,000) = 105

Market Value Example % Change = (105 - 100)/100 = 5.0% Since stocks A and B have the same market value, they receive the same weight in the index What indexes use this weighting system?

S&P 500 http://money.cnn.com/data/markets/sandp/ Most famous market-value weighed index Technically a float-weighted index How many stocks are in the index?

S&P 500 1928 was S&P 90. In 1957 it became S&P 500. Is used by 97% of U.S. money managers and pension plan sponsors as a proxy for the U.S. stock market.

S&P 500 Stocks are selected to include leading companies in leading industries in the U.S. U.S. firms only Changes are made every few weeks Standard and Poors (a division of McGraw-Hill) decides which companies to include in the index

Other MV Weighted Indexes NYSE Composite: All NYSE stocks NASDAQ Composite: All stocks listed on NASDAQ (Roughly 3,000 stocks) Wilshire 5000: All stocks traded in the United States

Other MV Weighted Indexes Wilshire 4500: Wilshire 5000 stocks with the S&P 500 stocks removed. S&P 400: A mid-cap index S&P 600: A small-cap index

Other MV Weighted Indexes Russell Indexes: U.S. Stocks from NYSE, AMEX, and Nasdaq http://www.russell.com/indexes Russell 3000: 3000 largest U.S. firms Russell 2000: 2000 smallest of Russell 3000 Russell 1000: 1000 largest of Russell 3000

International Indexes International Equity Indexes: MSCI World Index: 1600 stocks from 23 countries Market-value weighted Does not include emerging markets Global Dow: 150 stocks; both developed and emerging countries (but 40% from U.S.); equally-weighted

Equally-weighted Indexes Each stock receives the same weight. Indexes done either with arithmetic or geometric averages of % changes in stock prices.

Back to Example: Case 1 Price Price Stock Day 1 Day 2 Shares Out.

Example Stock A increased 10% in price and Stock B had a price change of 0%. Assume a starting index value of 100 on day 1, so Index Value1 = 100

Example Using Arithmetic Mean: Average % Change = (10+0)/2 = 5% Since the stocks in the index went up by an average of 5%, the index must go up by 5% Index Value2 = 100 X 1.05 = 105 Used in academic studies

Example Using Geometric Mean: Average % Change [(1.10)(1.0)]1/2 - 1 = 4.88% Index Value2 = 100 X 1.0488 = 104.88 Used by Value Line

Index Fund Formation Price Weighted: Equal number of shares of each stock Market Value Weighted: Invest in proportion to market capitalization. Equally-weighted: Equal dollar amount in each stock

Implications of Skewness Suppose there are only 4 stocks in our index: W, X, Y & Z   W has a 300% return X has a 25% return Y has a 5% return Z has a - 20% return

Implications of Skewness What if we have an equally-weighted index? Index Return: .25(300%) + .25(25%) + .25(5%) + .25(-20%) = 77.5%   The “typical” stock in your index was not up 77.5% The outstanding performance of W drove the results

Implications of Skewness  Many indexes have skewed returns     Often get a narrow market. Strong returns for an index may be primarily due to one or two industries

Implications of Skewness  For any price-weighted or value-weighted index, as a stock’s price goes up (relative to other stocks) it receives a higher weighting in the index. This means that if there is a “bubble” in one sector, the index will tilt more heavily toward the stocks in that sector. For those who invest in the index, it means placing a greater weight on those stocks which have gone up in price the most. Is that good or bad???