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
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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