5. You are given the following information concerning four stocks: Stock A B C D
ID: 2778800 • Letter: 5
Question
5. You are given the following information concerning four stocks:
Stock A B C D
Shares outstanding 1,000 300 2,000 400
Price 20X0 50 30 20 60
20X1 50 30 40 60
20X2 50 60 20 60
Using 20X0 as the base year, construct three aggregate measures of the market that simulate the Dow Jones Industrial Average, the S & P 500 stock index, and the Value Line stock index (i.e., a simple average, a value-weighted average, and a geometric average).
a) What is the percentage change in each aggregate market measure form 20X0 to 20X1, and 20X0 to 20X2? Why are the results different even though only one stock's price changed and in each case the price that changed doubled?
b) If you were managing funds and wanted a source to compare your results, which market measure would you prefer to use in 20X2?
Explanation / Answer
Dow Jones is a simple price weighted index. Since 2010 is the base year, the value of the index in 2010 is assumed to be 100.
Value of index in 2010 = 100
Value in index in 2011 = (45 * 100)/40 = 112.5
Value of index in 2011 = (47.5 * 100)/40 = 118.75
S&P500 is a market capitalisation based weighted average index. In this the weights of individual components are determined by their market capitalisations that is, no of shares * price for each stock
Assuming value of index in 2010 to be 100;
Value of Index in 2011 =(163000/123000)* 100 = 132.52
Value of Index in 2012 = (132000/123000)* 100= 107.32
Value Line Stock index is the equally weighted geometric average index. In this, each component is given an equal weightage.
Value of index in 2010 = 100
Value of Index in 2011 = [(1+ 0%) * (1+ 0%) * (1+ 100%) * (1+ 0%)]1/4 * 100 = 21/4 * 100 = 118.92
Value of index in 2012 = [(1+ 0%) * (1+100%) * (1+ 0%) * (1+ 0%)]1/4 * 100 = 21/4 * 100 = 118.92
a)
The results are different even though only one stock's price changed and in each case the price that changed doubled because the method to calculate the value of the index is entirely different in each case.
S&P 500 depends not only on the price but also the number of shareand hence the value in 2011 is very big because of the price of C doubled and the number of shares of C is maximum (2000). In 2012, the value did not change that much because the price of stock B doubled , however, the no of shares of B is minimum (300)..
Dow Jones and Value Line Composite do not depend on the number of shares. Dow Jones is weighted by price. Thus higher the price pf shares, higher the index value. Value Line Composite is equally weighted based on the geomeric average.Since each share is equally weighted, that is why the value of index is same in both 2011 and 2012 since the price of only one stock doubled in both the years.
b) I would prefer to use S&P 500 as the benchmark for comparing the results in 2012 since it not only uses the price of shares but also the number of shares in the market.
In case of Dow Jones if one stock splits, the value of the index will change entirely. This will not be a case in S&P 500 as it uses market capitalisation to calculate the index value.
Also, when we manage funds we do net necessarily allocate equal wightage to all the stocks in the portfolio. Thus, the returns of the portfolio will not only depend on what stocks we buy but also on how much funds we have allocated to each stock which is not captured by Value Line Composite as it is an equal - weighted index. However, S&P500 is a market capitalisation weighted index rather than an equal - wighted index and hence is a more relevant measure in comparing the results.
Year 1000 300 2000 400 Price weighted Average 2010 50 30 20 60 40 2011 50 30 40 60 45 2012 50 60 20 60 47.5Related Questions
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