Stock Market Indexes

1. 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?

2. 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.

3. 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

4. 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

5. 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.

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

7. Example (cont.) Index Value1 = (100 + 10)/2 = 55 Index Value2 = (100 + 11)/2 = 55.5 % 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.

8. 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

9. 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

10. Price Weighting Index • Index Value1 = (100 + 10)/2 = 55 • Index Value2 = (55 + 10)/2 = 32.5 % Change = (32.5 - 55)/55 = - 40.9% The index is down, but stock A gained 10% and stock B was unchanged.

11. 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

12. 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.

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

14. 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 is the only original stock still in the index.

15. DJIA: Composition • Today, there are 30 Companies. • Represent about 30% of the market value of U.S. Stocks • 27 stocks trade on the NYSE • 3 stocks (MSFT, INTC, and CSCO) trade on NASDAQ

16. DJIA: Composition As of Jan. 1, 2014: 3M, Nike, American Express, AT&T, Merk, Goldman Sachs, Boeing, Caterpillar, Chevron, Cisco, Coca-Cola, DuPont, ExxonMobil, GE, Visa, Home Depot, Intel, IBM, Johnson & Johnson, JP Morgan Chase, United Healthcare, McDonald’s, Microsoft, Pfizer, Procter & Gamble, Travelers, United Technologies, Verizon, WalMart, Disney

17. 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/

18. 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

19. DJIA: Index Value Suppose the Dow closes at 10,589.50 How did they arrive at this value? 30  Pi,t i = 1 DJIA Indext = --------------------- Adj. Divisor

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

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

22. 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.

23. 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

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

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

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

27. What if Instead…Case 2 Price PriceShares 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

28. Example (cont) Index Value2 = (100)(100,000) + (11)(1,000,000) ----------------------------------------- X 100 (100)(100,000) + (10)(1,000,000) = 105

29. What if a stock splits? Price Price Stock Day 1 Day 2 Shrs Out A $100 $ 55 200,000 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

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

31. 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?

32. S&P 500 http://www.standardandpoors.com/home/en/us Most famous market-value weighed index • Technically a float-weighted index • How many stocks are in the index?

33. 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.

34. S&P 500 • Stocks are selected to include leading companies in leading industries in the U.S. • U.S. firms only, though some non- U.S. firms are “grandfathered” into the index • Changes are made every few weeks • Standard and Poors (a division of McGraw-Hill) decides which companies to include in the index

35. 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

36. 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

37. 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

38. International Indexes International Equity Indexes: • MSCI World Index: 1600 stocks from 23 countries Only companies from developed countries; market value weighted • Global Dow: 150 stocks; both developed and emerging countries (but 40% from U.S.); equally-weighted

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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. 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???