There are
several ways to measure the return achieved on an investment and it is
important to understand what each measure is telling you. Let’s use a basic
example. At the beginning of year 1 you deposit $100,000 with a
portfolio manager. At the end of year 1 you have a balance of
$110,000 before withdrawals. You decide to withdraw $20,000 at the
end of year 1 leaving $90,000 invested. At the end of year 2 you
have a balance of $94,500. How did you do?
Holding
Period Return
One of
the simplest measures of performance is a holding period return which compares
your ending wealth to your beginning wealth adjusted for withdrawals. In
this case, your holding period return for the two years combined is 14.5%
(($94,500+20,000-100,000)/$100,000).
You can
compute the holding period return for each year individually as follows:
Year
1 10%
(($90,000 +20,000-100,000)/100,000)
Year
2 5%
(($94,500-90,000)/90,000)
Note that
the holding period return for the two years of 14.5% is different than if you
summed the two years individual holding period returns. This is
because a different amount was invested in each of those years.
Arithmetic
Average Return
The
arithmetic average return is the simple average of the year’s returns (the sum
of the holding period returns divided by the number of years). The
arithmetic average for this example is 7.5%.
Geometric
Average Returns
A
geometric return is a better measure of the performance of a portfolio over
time. There are two types of geometric returns: an internal rate of
return and a time-weighted return.
The
internal rate of return is calculated using a financial calculator of computer
and considers the value in each period as well as deposits and
withdrawals. It measures the compound average return achieved by the
investor. For this example the internal rate of return is
7.72%. Note that this exceeds the simple average in this case. The
reason is that you (the investor) withdrew part of you funds after the high
return year and had fewer funds invested in the lower return year. In
hindsight this was a good decision.
That decision to withdraw should not be reflected in the portfolio managers
return. The time-weighted return computes a geometric average which
removes the impact of deposits and withdrawals. In this example the
time-weighted return would be 7.2%. So the portfolio manager is
responsible for a compound average return of 7.2%. The investor,
however, earned 7.72% considering the timing of the withdrawal.
Risk
Adjusted Returns
It is
also useful to consider the return generated by a portfolio relative to its
risk. One measure could simply be the average return divided by the
standard deviation of returns, or return relative to risk. The
higher this ratio the more return was generated per unit of risk. A
popular metric is the Sharpe ratio which subtracts the risk free rate from the
portfolio average return before dividing by the standard deviation. The
Sharpe ratio measures the excess return per unit of risk. A higher
positive number is desirable (Sharpe ratios must be computed for a portfolio
and benchmark for the same period to see which is higher).
