chapter 12

Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Chapter 12

Global Performance Evaluation

Copyright © 2009 Pearson Prentice Hall. All rights reserved. 12 - 2

Calculating a Rate of Return

One approach to calculating a rate of return if there are no cash flows in or out of the portfolio:

There are two approaches to calculating a rate of return in the presence of an interim cash flow.

The money-weighted return (MWR)

The time-weighted return (TWR)

0

01

V

VVr


Example 12.1

Consider a simple portfolio with a single cash flow during the measurement period. For simplicity, the measurement period is supposed to be one year. What would be the rate of return? The details on the portfolio are as follows:

Value at start of the year is V0 = 100

Cash withdrawal on day t is Ct = -50

The cash outflow takes place 30 days after the start of the period, or at t = 30/365 = 0.082 year

Value on day t, before the cash flow is Vt = 95

Final value at end of the year is V1 = 60

%40100

10060

rAns: incorrect answer


Money Weighted Return (MWR)

Captures the return on average invested capital.

It measures net enrichment of the client.

Sometimes called the dollar-weighted rate of return (in the U.S).

Sometimes called an internal rate of return.


MWR (formula)

The MWR is defined as:

r = MWR,

V1 = final value,

Ct = cash flow at time t

V0 = initial value.

The cash flow convention is a “+” if it represents a contribution by the client, and a “-” if it is a cash flow withdrawal by a client.

10 1(1 ) (1 )

tt

C VV

r r


Example 12.2 (MWR)

Consider the example 12.1. Calculate the money weighted return.

Answer:

30/365

50 60100

(1 ) 1

18.37%

r r

r


Approximation of MWR

Dietz Method is defined as:

MWR1=

MWR2=

1 0

0 (1 )

tt

tt

V V Cprofit

average invested capital V t C

1 0

10 2

tt

tt

V V Cprofit

average invested capital V C


Example 12.3(Approximation of MWR)

Dietz Method

365 30365

60 100 50 1018.48%

100 50 54.11

MWR1

MWR2 12

60 100 50 1013.33%

100 50 75


Time Weighted Return (TWR)

Is the performance per dollar invested (or per unit of base currency).

It measures the performance of the manager independently of the cash flows to or from the portfolio.

Obtained by calculating the rate of return between each cash flow date and chain linking these rates over the total measurement period.


TWR (formula)

The formula over the measurement period is:

When there is only one cash flow Ct at time t.

11

0(1 ) (1 )(1 )

( )t

t tt t

V Vr r r

V V C


Example 12.4

Consider the example 12.2. Calculate the TWR based on the given information.

Answer:

95100

601 45

1

1

0.95 1.3333 1 1.2667 1 26.67%

t

t

r

r

r


MWR versus TWR

MWR is useful for measuring the return of invested capital.

MWR gives an assessment of the client’s net enrichment over the measurement period.

TWR is the preferred method for measuring and comparing the performance of money managers.

TWR should be used for performance evaluation.


Example 12.5. Valuing Stock Selection

Ability on a Japanese Equity Portfolio Consider a £10 million fund that is restricted to a 10% investment in Japan. ¥100 million (£1 million) is invested in the Japanese stock market and managed by a local money manager. The British fund’s trustee wants to evaluate the manager’s security selection skill in this market. Assuming a fixed exchange rate (i.e., ¥100 per £1 rate), we will consider the following scenario. The Japanese manager invests ¥100 million in the Japanese stock index, via an index fund, thereby exactly tracking the index. After two weeks, the index rises from 100 to 130, and the fund’s trustee ask the manager to transfer ¥30 million to a falling market (such as the U.K. market) in order to keep within the 10% limitation on Japanese investment and rebalance the asset allocation to its desired target. Over the next two weeks, the Japanese index loses 30% of its value (falling to 91), so that by the end of the month, the Japanese portfolio is down to ¥70 million. The MWR approximation, using the Dietz method, and the TWR of the portfolio are indicated in Exhibit 12.1. If a consultant performed a GPE using the Dietz method, what would be his conclusion regarding the security selection ability of the manager in Japan? Would his conclusion be correct?


Exhibit 12.1: TWR and Dietz Approximation to MWR for a Hypothetical Japanese Portfolio


Solution

TWR=

MWR1=

The TWR is -9% that is the performance of the Japanese index, so the Japanese index was perfectly tracked.

The MWR is 0%, so the consultant will wrongly imply that the manager outperformed the Japanese market and has great skills in Japanese stock selection.

In fact, the manager precisely tracked the Japanese market and no more.

365 15365

130 701 9%

100 10070 100 30

0%100 30

chapter 12

Documents