Compute the percentage of price change for each of the stocks in Problem 1. Compute the arithmetic mean of these percentage changes. Discuss how this answer compares to the answer in Part a.

Chapter 5 Homework Tori Perugini FINC 319 Questions: 1. Discuss briefly several uses of security-market indexes. There are many uses of security-market indexes. One is to use it as a benchmark to evaluate the performance of professional money managers. Another use of securitymarket indexes is to create and monitor an index refund. You can also use securitymarket indexes to measure market rates of return in economic studies or for predicting future market movements by technicians. 2. What major factors must be considered when constructing a market index? Put another way, what characteristics differentiate indexes? When constructing a market index, some factors that should be considered are the representativeness of the sample, weighting sample members, and computations procedures. 3. Explain how a market index is price weighted. In such a case, would you expect a $100 stock to be more important than a $25 stock? Give an example. A price-weighted series is an unweighted arithmetic average of current prices of the securities included in the sample. This includes closing prices of all securities are summed and divided by the number of securities in the sample. A $100 security will have a greater influence on the series than a $25 security because a 10 percent increase in the former increases the numerator by $10 while it takes a 40 percent increase in the price of the latter to have the same effect. 5. Explain how a price-weighted index and a value-weighted index adjust for stock splits. Given a four security series and a 2-for-1 split for security A and a 3-for-1 split for security B, the divisor would change from 4 to 2.8 for a price-weighted series. Stock Before Split Price After Split Prices A $20 $10 B 30 10 C 20 20 D 30 30 Total 100/4 = 25 70/x = 25 x = 2.8 The price-weighted series adjusts for a stock split by deriving a new divisor that will ensure that the new value for the series is the same as it would have been without the split. The adjustment for a value-weighted series due to a stock split is automatic. The decrease in stock price is offset by an increase in the number of shares outstanding. Before Split Stock A B C D Total Price/Share $20 30 20 30 # of Shares 1,000,000 500,000 2,000,000 3,500,000 Market Value $20,000,000 15,000,000 40,000,000 105,000,000 $180,000,000 The $180,000,000 base value is set equal to an index value of 100. After Split Stock A B C D Price/Share $10 10 20 30 New Index Value # of Shares 2,000,000 1,500,000 2,000,000 3,500,000 Market Value $20,000,000 15,000,000 40,000,000 105,000,000 Current Market Value x Beginning Index Value $180,000,000 Base Value 180,000,000 x 100 180,000,000 100 which is exactly what one would expect since there has been no change in prices other than the split. 9. Assume a correlation of 0.82 between the Nikkei and the TSE Composite Index. Examine the correlation between the MSCI Pacific Basin Index and the DJTSM in Exhibit 5.13. Explain why these relationships differ. 11. Why is it contended that bond-market indexes are more difficult to construct and maintain than stock-market indexes? The bond-market series are more difficult to construct due to the wide diversity of bonds available. Also bonds are hard to standardize because their maturities and market yields are constantly changing. In order to better segment the market, you could construct five possible subindexes based on coupon, quality, industry, maturity, and special feature (such as call features, warrants, convertibility, etc.) Problems: 1. You are given the following information regarding prices for a sample of stocks. a. Construct a price-weighted index for these three stocks, and compute the percentage change in the index for the period from T to T + 1. Percentage change= 46.67-32.67=14/32.76= 42.85% b. Construct a value-weighted index for these three stocks, and compute the percentage change in the index for the period from T to T + 1. Period T Stock A B C TOTAL Price/Share $60 20 18 # of Shares 1,000,000 10,000,000 30,000,000 Market Value $60,000,000 200,000,000 540,000,000 $800,000,000 Period T+1 Stock A B C TOTAL Price/Share $80 35 25 # of Shares 1,000,000 10,000,000 30,000,000 Market Value $80,000,000 350,000,000 750,000,000 $1,180,000,000 Percentage change= 1,180-800/800= 380/800= 47.50% c. Briefly discuss the difference in the results for the two indexes. The percentage change for the price-weighted series is a simple average of the differences in price from one period to the next. Equal weights are applied to each price change. The percentage change for the value-weighted series is a weighted average of the differences in price from one period t to t+1. These weights are the relative market values for each stock. Thus, Stock C carries the greatest weight followed by B and then A. Because Stock B had the greatest percentage increase (75%) and the second largest weight, the percentage change would be larger for this series than the price-weighted series. 2. a. Given the data in Problem 1, construct an equal-weighted index by assuming $1,000 is invested in each stock. What is the percentage change in wealth for this portfolio? Period T Stock A B C TOTAL Period T+1 Stock A B C TOTAL Price/Share $60 20 18 # of Shares 16.67 50 55.56 Market Value $1,000,000 100,000,000 1,000,000 $3,000,000 Price/Share $80 35 25 # of Shares 16.67 50 55.56 Market Value $1,333.60 1,750 1,389 $4,472.60 b. Compute the percentage of price change for each of the stocks in Problem 1. Compute the arithmetic mean of these percentage changes. Discuss how this answer compares to the answer in Part a. c. Compute the geometric mean of the percentage changes in Part b. Discuss how this result compares to the answer in Part b