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Frequently Asked

Frequently Asked. How Did the Stock Market Perform Yesterday? Down 1.77%? Down 1.27%? Down 1.64%?. Which is True?. Down 1.77% (DJIA) Down 2.54% (S&P 500) Down 1.64% (Nasdaq comp).

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Frequently Asked

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  1. Frequently Asked • How Did the Stock Market Perform Yesterday? • Down 1.77%? • Down 1.27%? • Down 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 • The number of stocks in the index. • The types of stocks in the index. • The weighting method used to calculate the index value.

  4. Basic Idea: Price Weighting Everyday calculate the average price (arithmetic mean price) Formula:n Indext =  Pi,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 Value1 = (100 + 10)/2 = 55 Index Value2 = (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 PriceShares Stock Day 1 Day 2 Outstanding A $100 $100 100,000 B $ 10 $ 11 1,000,000

  8. Example (cont) Index Value1 = (100 + 10)/2 = 55 Index Value2 = (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 • Why is this called price weighting? • Stock A’s Price is 10 times higher so it gets a 10 times larger weighting. • Does 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 • Index Value1 = (100 + 10)/2 = 55 • Index Value2 = (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 • From 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 • http://www.djindexes.com/jsp/index.jsp • 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 only original one. • Blue Chips (leaders in their industry)

  15. DJIA: Composition • Today are 30 Companies. • Represent about 30% of the market value of U.S. Stocks • Only two stocks (MSFT and INTC) trade on NASDAQ

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

  17. Other Dow Jones Price Weighted Indexes • Transportation (20 firms) • Utilities (15 firms) • Composite (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  Pi,t i = 1 DJIA Indext = --------------------- 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 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 PriceShares 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 Value1 = (100)(100,000) + (10)(1,000,000) ----------------------------------------- X 100 (100)(100,000) + (10)(1,000,000) = 100

  25. Market Value Example 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: 10% increase in A causes 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

  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 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%

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

  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. 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% • Represents around 80% of market value of the U.S. stock market ($ 11.8 Trillion)

  36. Other MV Weighted Indexes • NYSE Composite: All NYSE stocks • AMEX Index: All AMEX stocks • NASDAQ 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/ • From NYSE, AMEX, Most active OTC. • Originally were 5000. • Measure of overall U.S. stock market

  38. Wilshire 5000 • Represents 100% of US stocks with readily available price data. • NYSE 81% • AMEX .50% • Nasdaq 18%

  39. Other MV Weighted Indexes • Wilshire 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: • Morgan Stanley Capital Intl. (MSCI) • Dow Jones World Stock Index

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

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

  44. 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

  45. Example Using Arithmetic Mean: Average % Change = (10+0)/2 = 5% Index Value2 = 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 Value2 = 100 X 1.488 = 104.88

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

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

  49. Index Fund Formation • Price Weighted: Equal number of shares of each stock • Market Value Weighted: Invest in proportion to market capitalization. • Unweighted: Equal dollar amount in each stock

  50. Implications of Skewness Have $100 to invest  4 stocks in our world (W, X, Y & Z) • 1 will have a 300% return ($100 grows to $400) • 1 will have a 25% return ($100 grows to $125) • 1 will have a 5% return ($100 grows to $105) • 1 will have a - 20% return ($100 shrinks to $ 80)

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