48E** Calc & analyze the value and return of an index given its weighting method

Question 1

Weighting Method Issues

Answer 1

Which securities get the greatest weight? • What investment strategy would produce the portfolio returns equal to the index returns?

Question 2

Weighting Methods

Answer 2

• Price-weighted indices • Market capitalization-weighted indices – Free-float weighted indices • Equal weighted indices • Fundamental value-weighted indices

Question 3

Price-Weighted Indices

Answer 3

• Sum the prices and divide by a given divisor. • If a stock splits, you have to adjust the divisor. • If the composition of the index list changes, the divisor must change to ensure that the index level does not change.

What is the price-weighted index of the following three stocks? Given Stock price, shares outstanding but 0 splits - It’s The price-weighted index equals [(50 + 35 + 110) / 3] = 65….or stock price sum / # of stocks, NOT SHARES OUTSTANDING

An index was recently begun with the following two stocks:

Company A – 50 shares valued at $2 each.

Company B – 10 shares valued at $10 each.

Given that the value-weighted index was originally set at 100 and Company A’s stock is currently selling for $4 per share while Company B’s stock is still at $10 per share, what is the current value of the price-weighted index and the market-cap-weighted index?

Price weight = [(4) + (10)] / 2 = 7

Question 4

Market Capitalization Indices (aka Value-Weighted Indices) = Equal-weighted index = (1 + average percentage change in index stocks) × initial index value.

Answer 4

• Sum the total market capitalizations and divide by the divisor. – Total market capitalization is price × shares outstanding. • If a stock splits, you do not have to adjust the divisor because splits should not change total capitalization. • If the composition of the index list changes, you have to adjust the divisor.

At the beginning of the year, the value of a market-cap weighted index of these three stocks was 100. The index value at year-end is closest to: Market-cap weighted index = (ending market capitalization / beginning market capitalization) × beginning index value.

Beginning market capitalization = (10)(10,000) + (50)(5,000) + (100)(500) = 400,000

Ending market capitalization = (15)(10,000) + (50)(5,000) + (85)(500) = 442,500

Index value = (442,500 / 400,000) × 100 = 110.625

If the initial index value is 100, the current index is closest to:

First calculate the return relatives and then find the mean of the relatives. The number of shares is irrelevant in this question.

5/5 = 1
12.5/10 = 1.25
10/7.50 = 1.33
8/5 = 1.60

(1 + 1.25 + 1.33 + 1.60) / 4 = 1.295

100 × 1.295 = 129.5

This Q has #shares, Initial Cost, Current Cost

An index was recently begun with the following two stocks:

Company A – 50 shares valued at $2 each.

Company B – 10 shares valued at $10 each.

Given that the value-weighted index was originally set at 100 and Company A’s stock is currently selling for $4 per share while Company B’s stock is still at $10 per share, what is the current value of the price-weighted index and the market-cap-weighted index?

Market-cap weight = [(4)(50) + (10)(10)] / (2)(50) + (10)(10) = 150

What is the market-cap weighted index of the following three stocks assuming the beginning index value is 100 and a base value of $150,000?

As of December 31

Company Stock Price Shares Outstanding

X $1 5,000

Y $20 2,500

Z $60 1,000

The market-cap weighted index = (($1)(5,000) + ($20)(2,500) + ($60)(1,000))/$150,000

= ($115,000/$150,000)(100)

= (0.767)(100)

= 76.67 or 77

Question 5

Float-Adjusted Market Capitalization Indices

Answer 5

• Market float refers to the shares that are available to the investing public. – It generally excludes shares held by controlling shareholders, other corporations, and governments. • To computed a free float adjusted index, use the float instead of the shares outstanding. • If the float is expressed as a percentage

Question 6

Equal-Weighted Indices

Answer 6

• Average the percentage change in each of the securities in the universe, then use this average to gross up the value of the index. • If a stock splits, you only have to compute the return to the stock appropriately. • If the composition of the index list changes, you do not have to do anything other than find the appropriate set of returns to average.

Question 7

Weights for Fundamental- Weighted Return Indices

Answer 7

•