How Do You Define "Investment Return"?

When speaking about investments, you often hear terms like "real returns", "absolute returns", "compound returns", "average returns", and "absolute returns." This short note explains what they mean.

There are many different, yet equally accurate, ways you can answer the question, "what was the return on my portfolio?" To make this easy to follow, we'll use the example described in this table:

	Year 1	Year 2	Year 3	Year 4	Year 5	Simple Average	Std. Dev.
Nominal Return on Asset Class	3.0%	4.0%	-2.0%	10.0%	4.0%	3.8%	4.3%
Inflation	2.0%	3.0%	4.0%	2.0%	-1.0%	2.0%	1.9%
Nominal Return on Short Term Government Security	2.1%	3.0%	4.2%	2.0%	0.5%	2.4%	1.4%
Real Return	1.0%	1.0%	-6.0%	8.0%	5.0%	1.8%	5.3%
Excess Return	0.9%	1.0%	-6.2%	8.0%	3.5%	1.4%	5.2%
Nominal Value of Initial 1,000 Investment	1,030	1,071	1,050	1,155	1,201
Real Value of Initial 1,000 Investment	1,010	1,020	959	1,036	1,087
Compound Annual Nominal Return					3.73%
Compound Annual Real Return					1.69%

The first row shows the "nominal return" on an asset class. This return is composed of two parts: the "real return", which is the return in the absence of inflation, and the effect of inflation on the reported "nominal" return. There are two ways to remove the affect of inflation from the reported nominal return, in order to calculate the "real return." The easy approach is to simply subtract inflation from the nominal rate of return. This is the one we use in the table. However, if you assume that, during the course of a year, inflation accumulates at the same rate as the real return, then you should (to be technically correct) divide (1+Nominal Return) by (1+Inflation) and then subtract one to obtain a more accurate measure of real return. The difference between the two approaches is usually insignificant.

As you can see in the column labeled "Year 5", the nominal versus real return issue can get quite confusing when the overall price level is falling (deflation) rather than rising (inflation). Since you subtract the change in the price level from the nominal return to obtain the real return, deflation produces real returns that are higher than the reported nominal return. In contrast, under inflation, real returns are lower than nominal returns.

In contrast to real return, "excess return" is the additional return on an asset class above the return on a short-term risk free government security. Excess return is the same whether the asset class and government security returns are expressed in nominal or real terms. Since the return on short-term government securities tends to track inflation quite closely (but not perfectly), the "real return" and "excess" return on an asset class will typically be quite similar.

Now let's move on to the subject of averaging returns. As shown in the column labeled "Simple Average", the simple or "arithmetic" average is calculated by adding up the annual returns and dividing this by the number of observations (i.e., five in our example). The standard deviation is a measure of how widely the individual returns are distributed around this average. The higher the standard deviation, the wider the dispersion of returns around the average (also known as the mean). Assuming the distribution is normally shaped (i.e., it looks like the familiar bell-shaped curve), about sixty seven percent of the annual returns should fall within the range defined by the average plus or minus one standard deviation. About ninety five percent of the time, the annual return on the asset class should be within the average plus or minus two standard deviations.

In contrast to the simple (arithmetic) average, the compound average measures the annualized change in the value of an investment over a specified period of time. To put it differently, if the arithmetic return measures the average return in any one year, the compound return measures the return you actually received over a multi-year holding period. The compound return is also known as the "geometric average" return. Just to make matters even more confusing, it is also sometimes referred to as the "annualized" or "internal" rate of return.

If an investment is held for just one year, then the average annual return equals the compound annual return. In addition, if the standard deviation of returns for an investment equals zero, then over any multi-year period the average annual return and the compound average return will also be the same.

However, in the presence of risk (a non-zero standard deviation), the compound average return will always be lower than the simple average annual return, as shown in the table above. For example, the simple average real return is 1.8%. In contrast, the compound average real return is 1.69%. The difference between the simple and compound average return is caused by the variability of returns. For example, if the simple average annual real return (1.8%) was earned every year for five years, the future value of 1,000 would be about 1,093 (1,000*1.018⁵). However, as you can see in the table, the actual final value is only 1,087. A quick way to estimate the future compound annual return for an asset class is to subtract one half of the square of the standard deviation from the simple average annual return. For example, the simple average annual return in our example is 1.8%, with a standard deviation of 5.3%. The square of this number is 0.28%, and half that is 0.14%. Finally, 1.8% less 0.14% is about 1.66%, which is about equal to the actual compound annual real return of 1.69%.

So what, then, does "absolute return" mean? As you have, by now, no doubt come to expect, there isn't a simple answer to this question. Quite a few hedge fund managers refer to themselves as "absolute return" managers. However, what this often means in practice is that they are seeking to deliver at least a minimum return above short term government securities, under all different kinds of market conditions - what we would refer to as "excess return." In their view, this differentiates them from active mutual fund managers, whose objective is usually to outperform a comparable asset class index - say, the S&P 500 or Wilshire 5000 for an equity fund.

In contrast, our target real return model portfolios are also seeking to deliver an "absolute return." However, in our case, the absolute return in question is the minimum compound annual real rate of return needed to fund an investor's liabilities (e.g., to have accumulated a target amount of money at the end of a defined period of time).

If all this seems more than a little confusing, that's because, unfortunately, it is. The financial services industry still has a long way to go when it comes to using clear language that average investors can understand. But hopefully this brief overview has helped to cut through the confusion and enabled you to decipher the multiple possible meanings of "the return on my portfolio."

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