Question

The S-6 index is a fictitious index and is used by many investors to monitor the general behaviour of the stock market. Its value was set equal to 100 on 1 January 1975 (based on the stock prices below). In the table below we have the value of the stocks composing this index for 1 January 2015 and 30 June 2015.

	Closing market value of stock
Stock	1 January 1975	1 January 2015	30 June 2015
1	240	460	430
2	630	1120	1150
3	450	990	980
4	150	420	360
5	320	700	650
6	80	320	290

1. Calculate the value of the index for 1 January and 30 June 2015.
2. Compare the value the value of the index on those two dates with the original base of 1 January 1975.
3. Given the evolution of the index between 1 January 2015 and 30 June 2015, would you qualify that market as a bull or bear market? What is the return for six months and what would be that return on an annualised basis?
4. List a real stock index which is calculated using the same method as above? How do we call such indexes? What are the disadvantages of using such a method? Can you name an alternative method which is better?

Answer 1

a.

Closing market value of stock
Stock	01-Jan-75	01-Jan-15	30-Jun-15
1	240	460	430
2	630	1120	1150
3	450	990	980
4	150	420	360
5	320	700	650
6	80	320	290
Total	1870	4010	3860
%	100%	214%	206%
Value of Index	100	214.44	206.42

b. Value as on 1st Jan 2015 is 114% higher than 1st Jan 1975 Value while Value as on 30th Jun 2015 is 106% higher than 1st Jan 1975 Value.

c. Index value has fallen from 214.44 to 206.42 in 6 months of given period. Thus 6 months return is -8.02/214.44*100 = -3.74% and Annualised return = -3.74/6*12 = -7.48%

d.

1. Real stock index which is calculated using the same method as above - Dow Jones Industrial Average (DJIA)

2. How do we call such indexes - price-weighted index.

3. Disadvantages of using such a method -

The index is calculated by taking the sum of the prices of all 30 stocks in the index. This sum is then divided by a divisor. The divisor is adjusted based on stock splits, spinoffs or other changes in the market.

Stocks with higher prices have a larger impact on movements in the index as compared to lower-priced stocks. As a price-weighted index, no consideration is given to the relative size of the industry sector of the stock or its market capitalization. Another criticism of the DJIA is it only represents a thin slice of the blue-chip universe since it only contains 30 stocks.

4. Alternative method which is better - S&P 500 is a market-cap-weighted index. It is calculated by taking the adjusted market capitalization of all the stocks in the index and then dividing it by a divisor. Similar to the DJIA, the divisor is adjusted for stock splits, spinoffs and other market changes.