332 Performance Measurement in Finance

The numerator still yields the net amount of money realized while the denom-

inator gives us the amount of money that was available to the manager for

the period.

This approach only prices the portfolio at the start and end of the period.

To enhance the return’s accuracy, we should revalue whenever a ﬂow occurs.

The true daily rate of return formula

ROR =

EMV

1

BMV

1

+

EMV

2

BMV

2

+···+

EMV

n

BMV

n

(12.6)

is intended to produce an accurate rate of return, devoid of the affects of ﬂows

or market volatility.

Each individual fraction demarcates the periods from one ﬂow to the next,

starting with the beginning period market value and ending with the period’s

ending value. The tricky part is determining whether or not the ﬂow occurred

at the start or end of the day. But we’ll discuss this further below.

There are other methods available, such as the modiﬁed BAI, ICAA and unit

value formulae. Space does not permit going into these in detail. However, the

ones described above are the most commonly used ones and will be discussed

further below.

12.3 CONTRASTING THE METHODS

12.3.1 The scenario we’ll use

We’ll use the following example to contrast the various approaches and to

demonstrate the importance of properly handling cash ﬂows:

31 May: End-of-month market value = $100,000

4 June: End-of-day market value = $100,500

5 June: Cash ﬂow of $500,000

End-of-day market value (without cash ﬂow) = $130,500

End-of-day market value (with cash ﬂow included) = $630,500

30 June: End-of-month market value = $640,000

The portfolio ended the month of May with a market value of $100,000.

During the month of June, a single (but very large) cash ﬂow of $500,000

occurred; this happened on 5 June. The market value from the preceding

day was $100,500 (i.e. the portfolio had increased by $500 from the start of

month). At the end of 5 June, there was an appreciation of $30,000. If we

add this amount to the start-of-day value, we get $130,500; if we add it to

the start-of-day plus the cash ﬂow, we get $630,500. The market value at the

end of June was $640,000.

The rate-of-return formula can make a difference 333

12.3.2 Mid-point Dietz

We’ll begin by using the ‘mid-point Dietz’ method. It assumes that all cash

ﬂows occur at the middle of the period. As noted earlier, the formula is pretty

straightforward:

ROR

MPD

=

EMV −BMV − C

BMV +0.5 ×C

(12.7)

where:

ROR

MPD

= the rate of return, using the mid-point Dietz method

EMV = the ending period market value

BMV = the beginning period market value

C = the sum of the cash ﬂows for the period.

The ‘0.5’ in the denominator is what causes the cash ﬂows to be treated as if

they occurred at the middle of the period.

If we substitute the values from above, we get:

ROR

MPD

=

640,000 −100,000 −500,000

100,000 +0.5 × 500,000

=

40,000

350,000

= 11.43%

(12.8)

The advantage of this method is its simplicity. It requires you to calculate

only two market values: the starting and ending. And you simply sum all the

cash ﬂows and treat them as if they occurred in the middle.

While some people have used this method in the past for periods as long

as a calendar quarter or even a full year, it’s been more appropriate of late to

use it for calculating monthly returns. It is, however, also suitable for shorter

periods.

The main problem with this approach is that it treats ﬂows as if they

occurred in the middle of the period. This is obviously not always the case.

The accuracy of this approach diminishes when (1) the actual ﬂow date moves

farther away from the middle of the month and (2) when the size of the ﬂow,

relative to the starting market value, is large.

Traditionally, the industry has accepted ‘large’ to mean 10% or more of the

market value.

7

In our case, a cash ﬂow of $10,000 (10% of $100,000) would

qualify as large. Therefore, a ﬂow of $500,000 would have to be described

as very large. And, given that the actual ﬂow date was 5 June, a whole

10 days earlier than the mid-point of 15 June, we’d expect the accuracy to be

questionable.

7

This is one of those ‘unwritten’ rules that has become a de facto standard.

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