# CAGR Illusions

The compound annual growth rate (CAGR) is a useful but often misleading metric, especially when calculation periods are chosen purposely by sales and marketing people. Below is an introduction to CAGR, an example that shows how ambiguity arises and how it can affect real asset performance comparisons.

CAGR is defined as follows:

To calculate CAGR we take the ratio of the final price of an asset or investment to its initial price and raise it to the inverse of the number of years N between the two values and subtract 1 from the result.

Note the CAGR is also equal to/known as:

• Year-over-year growth rate
• Annualized return
• Compound annual return (CAR)
• Mean annual growth rate
• Annualized rate
• Geometric return

Note that CAGR does not depend on path followed but only on initial and final values. This is important because two assets can produce the same CAGR in a given period of time but with totally different behavior. In other words, CAGR is a measure of returns but says nothing about risk arising from variability of returns.

An example

Below is an example of two assets, A and B, which have the same CAGR but very different behavior:

Both assets A and B start at a value of 2 and after 10 years reach a value of 10. However, asset B has 50% drawdown during the first year and asset A 25% drawdown during the seventh year. But notice how the latter drawdown looks larger than the former although it is only 25% versus 50% for asset B.

CAGR for both assets stating for the whole period is equal to:

(10/2)^(1/10) – 1 = 17.4619%

Next we repeat the CAGR calculations starting at the end of year 1:

CAGR(A) = (10/3) ^(1/9) = 14.3135%

CAGR(B) = (10/1)^(1/9) = 29.1549%

Therefore, by changing the initial point we get nearly twice as high CAGR for asset B although this asset also has twice as high drawdown.

The large drawdown actually contributes to a higher CAGR because the calculation involves a much lower initial value.

Is the above just a manufactured example or does it relate to real life?

Below is a graph of the growth of \$1 for the index of all hedge funds, long/short equity hedge funds and S&P 500 TR since 1997 based on yearly net return data from BarclayHedge (see related article here):

Data source: BarclayHedge www.barclayhedge.com

As shown in the quoted article, if CAGR calculations start at 1997, hedge funds have outperformed S&P 500 total return on the average on both absolute and risk adjusted basis.

However, sales people, usually those from passive index fund departments, start their calculation at 2009 or 2010. In this way they avoid the huge drawdown periods from 2000 to 2009 in equities during which long/short hedge funds performed relatively well.

Actually, long/short hedge fund investors had higher probability of staying invested and realizing a smaller but reasonable CAGR after 2009. On the other hand, many equity investors hit uncle point during the first or the second drawdown and never enjoyed the hypothetical large CAGR arising from changing the starting point of calculation. In other words, the large CAGR does not reflect the risks.

Conclusion

CAGR depends on initial values and suitable selection of a starting point can offer a misleading picture of the performance of an asset by excluding periods of high risk. A better metric of performance is MAR (ratio of CAGR to maximum drawdown.) Always be skeptical of high CAGR values, especially above 10%. There is high probability of selection of a suitable starting point, or even look-ahead bias, in the case of backtested results. The latter is not rare, as it has found its way even in seminal publication about momentum investing. See this article and this article for more details.

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