Chapter 3

Measuring returns

Once a portfolio has been established, it is important to monitor the fund’s

performance. Measuring the performance of a portfolio involves calculating

the returns achieved by the fund over a particular period of time, known as

the evaluation period. The evaluation period used to monitor performance

may be weekly, monthly, quarterly or annually. Various methods may be

used to calculate returns, each giving a different result. Parties interested in

evaluating performance use consistent and standard methods for calcu-

lating and presenting returns, several of which are reviewed below.

Performance evaluation involves comparing the performance of a fund

against a suitable yardstick or benchmark (usually a relevant index) after

adjusting for risk in order to determine how the fund manager has

performed and how the returns were actually achieved. Evaluation enables

the investor to check that the agreed investment strategy has been

followed, and to assess the skill of the fund manager.

Calculating returns

Clients, trustees of pension funds and unit trusts, board of directors of

investment trust companies and managers of fund management depart-

ments are amongst the groups interested in monitoring the capabilities of

the fund managers and analysts who contribute to the running of the funds.

Although calculating returns is simple in theory, it is relatively more

complex in practice. The methods considered are money return, time-

weighted return and money-weighted return.

Portfolio Management in Practice

Total return or money return

The first step in assessing performance is to measure the total return that

a fund has produced. To calculate this return, the value of each share in the

fund at the beginning of the evaluation period is multiplied by the number

of shares held. The sum of these values is the market value of the portfolio

at the beginning of the time period. The same procedure is carried out

using the market prices and amounts of the holdings at the end of the time

period to calculate the market value of the portfolio at the end of the

evaluation period. The total return (also known as money return) from the

portfolio is calculated as follows:

Total return r =

V

end

–V

beginning

V

beginning

where:

V

beginning

= market value of the fund at the beginning of the period

V

end

= market value of the fund at the end of the period (including

reinvested dividends or coupon payments).

If, for example, V

end

is £5 million, V

beginning

is £4 million, calculate the

money return:

r=

£5–£4

£4

× 100 = 25%

The next step to examine is what happens when clients add new money to

the fund or withdraw money from the fund. Money may be added or

withdrawn at any time during the examination period. If the money is

added just before the end of the period, the above formula would have to

be adjusted as follows:

r=

(V

end

–D)–V

beginning

V

beginning

where:

V

end

= the portfolio value at the end of the period

V

beginning

= the portfolio value at the beginning of the period

D = deposits into the fund by the investor.

34

Measuring returns

For example, if V

end

is £5 million, V

beginning

is £4 million and a cash input

(D) of £250 000 is made, the money return is calculated as:

r=

(£5 – £0.25) – £4

£4

× 100 = 12.5%

If the cash input had not been subtracted, the return quoted would have

been 25% rather than 12.5%. This would have been misleading, since part of

the increase was due to money coming into the fund and not to the fund

manager’s skill. Withdrawals from a fund or distributions made from a fund

to shareholders can also produce a distorting effect, and thus the timing of

deposits into and withdrawals from a portfolio must be taken into account.

The above example assumes distributions into and out of the fund are

made at the end of the period. This is unlikely to be true in practice, and

the following two methods overcome the problem by breaking the

evaluation period into smaller sub-periods.

Money-weighted returns

This technique discounts the cash flows for each sub-period at an interest

rate (the internal rate of return) that makes the sum of the present values

of the cash flows and value of the portfolio at the end equal to the portfolio

value at the beginning of the period. The money-weighted return may be

calculated as follows:

V

beginning

=

C1

(1+v)

+

C2

(1+v)

2

+ . . . +

Cn+V

end

(1+v)

n

where:

V

end

= the portfolio value at the end of the period

V

beginning

= the portfolio value at the beginning of the period

v = the money weighted rate of return.

Cn = the cash flow in period n.

For example, calculate the internal rate of return/money-weighted return

when V

beginning

is £4.4 m and V

end

is £4.5 m, and three distributions of

£500 000 are made at the end of years 1, 2 and 3.

35

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