Chapter 18, Problem 12PS

Summary Introduction

(a)

To calculate:

The total value added arrived due to the decisions taken by all the managers.

Introduction:

The total value added is computed by calculating excess (deficit) return ascertained by return as per manager's weights over the return as per MSCI weights.

Answer to Problem 12PS

The total value added is $-1.3\%$ .

Explanation of Solution

Given Information:

Results for a given month are in the following table:

Country	Weights (MSCI)	Weights (Manager's)	Manager's return in Country	Return of stock index for that Country
U.K.	$0.15$	$0.30$	$20\%$	$12\%$
Japan	$0.30$	$0.10$	$15\%$	$15\%$
U.S.	$0.45$	$0.40$	$10\%$	$14\%$
Germany	$0.10$	$0.20$	$5\%$	$12\%$

The formula for total value added is:

  $\text{Total Value Added}=\text{Return as per manager's weights}-\text{Return as per MSCI weights}$

Now, Return as per manager's weight is:

  $\begin{array}{c}\text{Return}=\left(0.30\times 20\%\right)+\left(0.10\times 15\%\right)+\left(0.40\times 10\%\right)+\left(0.20\times 5\%\right)\\ =0.06+0.015+0.04+0.01\\ =12.50\%\end{array}$

Return as per MSCI weight is:

  $\begin{array}{c}\text{Return}=\left(0.15\times 12\%\right)+\left(0.30\times 15\%\right)+\left(0.45\times 14\%\right)+\left(0.10\times 12\%\right)\\ =0.018+0.045+0.063+0.012\\ =13.80\%\end{array}$

Thus, as per the above calculation, the total value added for all managers' decision is:

  $\begin{array}{c}\text{Total Value Added}=12.50\%-13.80\%\\ =-1.3\%\end{array}$

Summary Introduction

(b)

To calculate:

The value added arrived due to the decisions taken by her country allocations.

Introduction:

The value added by allocation of country decision is computed by calculating excess (deficit) weight of manager's portfolio over the portfolio of MSCI and get it multiplied with MSCI return.

Answer to Problem 12PS

The value added is $-0.70\%$ .

Explanation of Solution

Given Information:

Results for a given month are in the following table:

Country	Weights (MSCI)	Weights (Manager's)	Manager's return in Country	Return of stock index for that Country
U.K.	$0.15$	$0.30$	$20\%$	$12\%$
Japan	$0.30$	$0.10$	$15\%$	$15\%$
U.S.	$0.45$	$0.40$	$10\%$	$14\%$
Germany	$0.10$	$0.20$	$5\%$	$12\%$

The following table is showing computation of value added:

  

Thus, the value added for country allocation is $-0.70\%$ .

Summary Introduction

(c)

To calculate:

The value added arrived due to the ability of the stock selection within the country.

Introduction:

The value added by ability of stock selection is computed by calculating excess (deficit) return of manager's return over the return of MSCI and get it multiplied with weights of manager's portfolio.

Answer to Problem 12PS

The value added is $-0.60\%$ .

Explanation of Solution

Given Information:

Results for a given month are in the following table:

Country	Weights (MSCI)	Weights (Manager's)	Manager's return in Country	Return of stock index for that Country
U.K.	$0.15$	$0.30$	$20\%$	$12\%$
Japan	$0.30$	$0.10$	$15\%$	$15\%$
U.S.	$0.45$	$0.40$	$10\%$	$14\%$
Germany	$0.10$	$0.20$	$5\%$	$12\%$

The following table is showing computation of value added:

  

Thus, the value added for country allocation is $-0.60\%$ .

Summary Introduction

(d)

To determine:

The value added arrived due to the decisions taken by her country allocations and ability of the stock selection within the country is equal, under or over performance with the total value added computed on all manager's decision.

Introduction:

The total value added is computed by calculating excess (deficit) return ascertained by return as per manager's weights over the return as per MSCI weights

The value added by allocation of country decision is computed by calculating excess (deficit) weight of manager's portfolio over the portfolio of MSCI and get it multiplied with MSCI return

The value added by ability of stock selection is computed by calculating excess (deficit) return of manager's return over the return of MSCI and get it multiplied with weights of manager's portfolio.

Answer to Problem 12PS

The total of value added of country allocation decision and stock selection is equal to total value added.

Explanation of Solution

The total of value added of country allocation decision and stock selection is equal to total value added is confirmed by as follows:

  $\begin{array}{c}\text{Total value added}=\text{Value added }\left(\text{Country decision}\right)+\text{Value added }\left(\text{Stock selection}\right)\\ -1.3\%=\left(-0.70\%\right)+\left(-0.60\%\right)\end{array}$

Thus, the contributions of both value added is confirmed to be equal to total value added.