1. Frequently Asked zHow Did the Stock Market Perform Yesterday? zDown 1.77%? zDown 1.27%? zDown 1.64%?

2. Which is True? Down 1.77% (DJIA) Down 2.54% (S&P 500) Down 1.64% (Nasdaq comp).

3. Need to Know Regarding Stock Market Indexes zThe number of stocks in the index. zThe types of stocks in the index. zThe weighting method used to calculate the index value.

4. Basic Idea: Price Weighting Everyday calculate the average price (arithmetic mean price) Formula: n Index t =  P i,t divided by n i = 1 where i indexes stocks, and there are n stocks in the index

5. Price Weighting: Example Price Price Stock Day 1 Day 2 Shrs A $100 $110 100,000 B $ 10 $ 10 1,000,000

6. 10% Increase in Stock A Index Value 1 = (100 + 10)/2 = 55 Index Value 2 = (110 + 10)/2 = 60 % Change Index = (60 - 55)/55 = 9.1% 10% increase in A caused a 9.1% increase in the index.

7. Example: What if Instead... Price Price Shares Stock Day 1 Day 2 Outstanding A $100 $100 100,000 B $ 10 $ 11 1,000,000

8. Example (cont) Index Value 1 = (100 + 10)/2 = 55 Index Value 2 = (100 + 11)/2 = 55.5 %Change Index = (55.5 - 55)/55 =.91% 10% increase in B caused a.91% increase in the index.

9. Price Weighting zWhy is this called price weighting? zStock A’s Price is 10 times higher so it gets a 10 times larger weighting. zDoes this make Economic Sense??

10. Price Weighting: Example Price Price Stock Day 1 Day 2 # Shrs Out A $100 $ 55 200,000 B $ 10 $ 10 1,000,000 Stock A has a 2-for-1 split at the close of Day 2

11. Price Weighting: Example zIndex Value 1 = (100 + 10)/2 = 55 zIndex Value 2 = (55 + 10)/2 = 32.5 % Change = (32.5 - 55)/55 = - 40.9% Appears that something bad happened when in fact, value was created.

12. Adjust the Divisor Adjust Divisor Before Split, sum of prices Day 2 = 110 + 10 = 120 and 120/2 = 60 After Split, sum of prices Day 2 = 55 + 10 = 65 and 65/(adj divisor) = 60 Adj Divisor = 1.083333

13. Adj Divisor zFrom now on, add the prices of the stocks in the index and divide by the adjusted divisor to get the index value 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.

14. DJIA: History zhttp://www.djindexes.com/jsp/index.jsphttp://www.djindexes.com/jsp/index.jsp zOldest barometer of the stock market. zPrice Weighted Index zStarted in 1896 by Charles Dow with 12 stocks. (He and Jones started Dow Jones & Company.) GE only original one. zBlue Chips (leaders in their industry)

15. DJIA: Composition zToday are 30 Companies. zRepresent about 30% of the market value of U.S. Stocks zOnly two stocks (MSFT and INTC) trade on NASDAQ

16. DJIA: Composition zHow are the firms in the index selected? zScientifically??? (Editors of the Dow Jones owned WSJ select the stocks)

17. Other Dow Jones Price Weighted Indexes zTransportation (20 firms) zUtilities (15 firms) zComposite (65 firms)

18. DJIA: Weighting DJIA index closed at 10,589.50 This signifies what?? Is this the average price??

19. DJIA Index Value 30  P i,t i = 1 DJIA Index t = --------------------- Adj. Divisor

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

21. Index Value t n  (P i,t ) x (#Out Shrs i,t ) i = 1 Index t = ----------------------------- X Base n Value  ( P i,b ) X (#Out shrs i,b ) i = 1

22. Index Value t zt indexes days zb is the base day zi indexes stocks zBase 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 Shares Stock Day 1 Day 2 Outstanding A $100 $110 100,000 B $ 10 $ 10 1,000,000 [Designed so that each has the same mkt value]

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

25. Market Value Example Index Value 2 = (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: 10% increase in A causes a 5% increase in the index.

27. 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

28. Example (cont) Index Value 2 = (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 has a 2-for-1 split at the close of Day 2

30. Market Value Example Index Value 2 = (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%

32. S&P 500 http://www.standardandpoors.com Most famous market value weighed index of the U.S. stock market. zHow many stocks are in the S&P 500? zWhy is it so hard to beat?

33. S&P 500 z1928 was S&P 90. In 1957 it became S&P 500. zIs 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 zStocks are selected to include leading companies in leading industries in the U.S. z“U.S.” firms. Some are “grandfathered” non-U.S. firms, but no new ones will be added. Chrysler was removed from the index when it was acquired by Daimler (German firm).

35. S&P 500 424 NYSE stocks 85.7% 74 NASDAQ stocks 14.1% 2 AMEX stocks.2% zRepresents around 80% of market value of the U.S. stock market ($ 11.8 Trillion)

36. Other MV Weighted Indexes zNYSE Composite: All NYSE stocks zAMEX Index: All AMEX stocks zNASDAQ Composite: OTC stocks that meet requirements (Roughly 5,000 stocks)

37. Other MV Weighted Indexes Wilshire 5000: All U.S. headquartered firm stocks with readily available price data. Started in 1974. http://www.wilshire.com/Indexes/Broad/ zFrom NYSE, AMEX, Most active OTC. zOriginally were 5000. zMeasure of overall U.S. stock market

38. Wilshire 5000 zRepresents 100% of US stocks with readily available price data. zNYSE 81% zAMEX.50% zNasdaq 18%

39. Other MV Weighted Indexes zWilshire 4500: Wilshire 5000 stocks with the S&P 500 stocks removed.

40. Other MV Weighted Indexes Russell Indexes: U.S. Firm Stocks Only NYSE,AMEX,OTC http://www.russell.com/US/indexes Russell 3000: 3000 largest U.S. firms Russell 2000: (2000 smallest mkt cap of Russell 3000) Russell 1000: (1000 largest market cap of Russell 3000)

41. Intl. Market Value Indexes International Equity Indexes: zMorgan Stanley Capital Intl. (MSCI) zDow Jones World Stock Index

42. Unweighted Indexes zEach stock receives the same weight. zIndexes done either with arithmetic or geometric averages of % changes in stock prices.

43. Back to Example: Case 1 Price Price Shares Stock Day 1 Day 2 Outstanding A $100 $110 100,000 B $ 10 $ 10 1,000,000

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

45. Example Using Arithmetic Mean: Average % Change = (10+0)/2 = 5% Index Value 2 = 100 X 1.05 = 105 (Used in academic studies)

46. Example Using Geometric Mean: Average % Change = [(1.10)(1.0)] 1/2 = (1.10) 1/2 = 1.0488 - 1 = 4.88% Index Value 2 = 100 X 1.488 = 104.88

47. Unweighted Indexes (geometric mean) zValue Line: NYSE, AMEX, OTC

48. Index Funds zHold all of the stocks in an index. z$750 billion indexed to the S&P 500!!

49. Index Fund Formation zPrice Weighted: Equal number of shares of each stock zMarket Value Weighted: Invest in proportion to market capitalization. zUnweighted: Equal dollar amount in each stock

50. Implications of Skewness Have $100 to invest 4 stocks in our world (W, X, Y & Z) z1 will have a 300% return ($100 grows to $400) z1 will have a 25% return ($100 grows to $125) z1 will have a 5% return ($100 grows to $105) z1 will have a - 20% return ($100 shrinks to $ 80)

51. Implications of Skewness z What if put 1/4 in each?? z.25(300%) +.25(25%) +.25(5%) +.25(-20%) E(R) = 77.5% ($100 grows to $177.50) z Will have more than if put all in X, all in Y or all in Z, but less than if all in W.

52. Related Facts z  Over past 15 years, the S&P 500 annual return would be almost cut in half by dropping the best 50 firms in each year. z  Often get a narrow market. In the late 1990s it was the technology stocks. They had huge returns and had driven the market returns up. More recently has been energy stocks.