Chapter 2, Problem 2WM

Summary Introduction

(a)

To calculate:

By using the price-weighted index of the five stocks, the monthly return of the five stocks.

Introduction:

The price-weighted index is an average calculated by taking a sum of prices of the stock and then dividing them by a divisor.

Answer to Problem 2WM

The monthly return of the stocks by using price-weighted index average of five stocks is $\left(12\%\right)$ .

Explanation of Solution

Given:

The prices of five different stocks on the first and last trading day of the previous month using the data source from www.nasdaq.com are:

  $\text{(In \$)}$

Date/Company	Apple	Microsoft Corp.	Facebook Inc.	Vodafone group	Netflix Inc.
$01/10/2018$	$227.26$	$115.61$	$162.44$	$21.43$	$381.43$
$31/10/2018$	$381.43$	$106.81$	$151.79$	$18.93$	$301.78$

The return using price-weighted index average can be computed by:

  $\text{Return}=\frac{{\text{Price-weighted index}}_1-{\text{Price-weighted index}}_0}{{\text{Price-weighted index}}_0}\times 100$

So, by using the above formula, the Price-weighted index at period $0$ i.e. on $01/10/2018$ is:

  $\begin{array}{c}\mathrm{Price}\text{-}weightedindex=\frac{{\displaystyle \sum _n^0\text{Prices of the five stocks }}}{\text{Number of stocks}}\\ =\frac{\$227.36+\$115.61+\$162.44+\$21.43+\$381.43}{5}\\ =\$181.634\end{array}$

So, by using the above formula, the Price-weighted index at period $1$ i.e. on $31/10/2018$ is:

  $\begin{array}{c}\text{Price-Weighted index}=\frac{{\displaystyle \sum _n^1\text{Prices of the five stocks}}}{\text{Number of stocks}}\\ =\frac{\$381.43+\$106.81+\$151.79+\$18.93+\$301.78}{5}\\ =\$159.634\end{array}$

The return of the stocks by using a price-weighted index average of five stocks:

  $\begin{array}{c}\text{Return}=\frac{{\text{Price-weighted index}}_1-{\text{Price-weighted index}}_0}{{\text{Price-weighted index}}_0}\times 100\\ =\frac{159.634-181.634}{181.634}\times 100\\ =-12\%\end{array}$

Thus, the monthly return of the stocks by using a price-weighted index average of five stocks is $\left(12\%\right)$ .

Summary Introduction

(b)

To calculate:

By using the value-weighted index of the five stocks, the monthly return of the five stocks.

Introduction:

The value-weighted index is an average return calculated by equalizing the weighted average of the returns of the stocks with the weights proportional to the market value.

Answer to Problem 2WM

The monthly return of the stocks by using value-weighted index average of five stocks is $92.02\%$ .

Explanation of Solution

Given:

The market values of five different stocks on the first and last trading day of the previous month using the data source from www.nasdaq.com are:

  $\left(\text{Amount in \$ millions}\right)$

Date/Company	Apple	Microsoft Corp.	Facebook Inc.	Vodafone group	Netflix Inc.
$01/10/2018$	$5270$	$2150$	$4270$	$265.90$	$3181.10$
$31/10/2018$	$8320$	$5450$	$9100$	$132.10$	$6063.60$

The return using price-weighted index average can be computed by:

  $\text{Return}=\frac{{\text{Value-weighted index}}_1-{\text{Value-weighted index}}_0}{{\text{Value-weighted index}}_0}\times 100$

So, by using the above formula, the Value-weighted index at period $0$ i.e. on $01/10/2018$ is:

  $\begin{array}{c}\text{Value weighted index}=\frac{{\displaystyle \sum _n^0}\text{Values of the five stocks }}{\text{Number of stocks}}\\ =\frac{\$5270+\$2150+\$4270+\$265.9+\$3181.10}{5}\\ =\$3027.40\text{ millions }\end{array}$

So, by using the above formula, the Value-weighted index at period $1$ i.e. on $31/10/2018$ is:

  $\begin{array}{c}\text{Value weighted index}=\frac{{\displaystyle \sum _n^1}\text{Values of the five stocks }}{\text{Number of stocks}}\\ =\frac{\$8320+\$5450+\$9100+\$132.10+\$6063.60}{5}\\ =\$5813.14\text{ millions}\end{array}$

The return of the stocks by using a value-weighted index average of five stocks:

  $\begin{array}{c}\text{Return}=\frac{{\text{Value-weighted index}}_1-{\text{Value-weighted index}}_0}{{\text{Value-weighted index}}_0}\times 100\\ =\frac{5813.14-3027.40}{3027.40}\times 100\\ =92.02\%\end{array}$

Thus, the monthly return of the stocks by using a value-weighted index average of five stocks is $92.02\%$ .

Summary Introduction

(c)

To explain:

The difference between the two returns computed, by comparing them.

Introduction:

The price-weighted index is based on per share value and the value-weighted index is based on the total value of shares.

Answer to Problem 2WM

The main reason behind the difference between both returns is the multiplier used in computing the index value of both returns.

Explanation of Solution

As compared to both the returns computed above in sub-part a. and b. it can be observed that there is a huge difference in the returns of the both. This difference is due to the multiplier used in calculating the values for computing return.

The multiplier used in the price-weighted index is the price per share which means that more weight age is given to the higher per share value.

The multiplier used in the value-weighted index is the value of total shares i.e. price of a share multiplied with a number of shares (volume) which means that more weight age is given to the higher market value.

Thus, due to the above mentioned reason, the returns in both indexes will be different from each other.