6.27.2005

Q&A: Suppose there is a price-weighted market index...

composed of two stocks, with stock A selling for $100, and stock B $25.

  • What's the price of the index?
  • What's the rate of return if stock A increases by 10%, and B increases by 20%? What if stock A decreases by 5%, stock B increases by 20%?
  • What if stock A splits two for one? If the divisor stays unchanged?

  • the price index = (100 + 25) / 2 = 62.5, with the divisor being 2
  • RoR = 70 - 62.5) / 62.5 = 12%
    • the price index = ( 100*(1+10%) + 25*(1+20%) ) / 2 = 70
    • if stock A decrease by $5 and B increase by 5$, RoR = 0 since they cancel out.
  • The divisor must be reduced to a value that leaves the average unaffected by the split (otherwise the average would fall, indicating incorrectly a fall in the general level of market prices)
    • divisor = (50 + 25) / 62.5 = 1.2 * If the divisor stays unchanged: stock A = 100/2 = 50. price index = (50+25)/2 = 37.5. Thus, a simple split will cause a price-weighted index to go down unless the divisor is reflected.

Bonus Points

  • Price-weighted market index is an arithmetic average of current prices.
    • Dow Jones Industrial Average is the best-know price-weighted series: computed by adding the prices of the 30 companies of NYSE and dividing by a "divisor".
    • Nikkei-Dow Jones Average: 225 stocks on the First Section of the Tokyo Stock Exchange.
  • High-priced stocks have greater impact on the index than low-priced stocks, as the scheme assumes that an investor purchases an equal number of shares for each stock in the index.
  • Since the weight of each firm in the index is proportional to the share price, Successful firms consistently lose weight within the index as they tend to split their stocks more often. Over time, low growth, small firms with high prices will dominate the index.

Category: C++ Quant > Financial Markets

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