## 18 Nov [CLIENT GUIDE] Explaining The Difference Between Average Annual Return and Compounded Annual Growth Rate (CAGR).

I was on the phone with an advisor two weeks ago and he was bemoaning the lack of client education surrounding the difference between average annual return and compounded annual growth rate (CAGR).

His argument was that the leading measure used to evaluate financial products was “completely broken”. The result being sub-optimal investment selection at its best and fraud at its worst. I decided to investigate.

There is no denying that by using an average annual return statistic, investments tend to have a higher performance percentage (as you will see below). Yet its also true few clients fully understand CAGR and its implications.

If everyone understood CAGR then I believe it would be a better measure than average annual growth rate and you will see this in the examples. But first I want to you copy, print or download the guide below that will simply explain the difference between average annual return and compounded annual growth rate.

**Average Annual Return**

The average annual return for a set of investment years is calculated by summing the results of each year and dividing by the total number of years. Below is an example based on the returns of Vanguard’s Total Stock Market ETF (VTI) from 2004-2013.

| 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 |

| 12.73% | 6.15% | 15.70% | 5.36% | -36.81% | 28.73% | 17.28% | 1.00% | 16.45% | 33.48% |

The average annual return calculation would be….

12.73% + 6.15% + 15.70 + 5.36% + -36.81% + 28.73% + 17.28% + 1.00% + 16.45% + 33.48% Divided by 10 years = 10.01%

Source: Vanguard.com

**Compounded Annual Growth Rate**

The compounded annual growth rate (CAGR) measures performance over a series of years and represents what you actually get from your investments at the end of the investing period. It accounts for compounding and volatility (unlike the simpler average annual return calculation). This is best explained with an example.

If you invest $100,000 dollars over two years and the returns are 10% and -10% the average annual return is 0% (10% + -10% / 2 = 0%). However, this doesn’t represent what you actually get at the end of the two year investing period.

At the end of the first period you will have $110,000 dollars but after a 10% decline at the end of the second year, which is $11,000, you will have a loss ending on 99,000.

Year | End of Year 1 | End of Year 2 |

Return | 10% | -10% |

Investment | $110,000 | $99,000 |

The average annual return statistic would have you believe that you ended the two period on $100,000 (because of the 0% average annual return) but this isn’t the case. The compounded annual growth rate formula would have picked this up and given you an annual return of -0.5%. So if you returned -0.5% in the first year and -0.5% in the second year you would have $99,000. Which is exactly what you got at the end of the period.

Investment | $100,000 |

CAGR -0.05% – End of Year 1 | $99,500 |

CAGR -0.05% – End of Year 1 | $99,000 |

The formula for CAGR is outlined below. It is a little complicated so you can use an online calculator at websites such as Investopedia.

** CAGR = (B/A) ^{1/n }– 1**

A = Original investment amount

B = Value of your investment at the end of the period

n = number of periods (e.g. years).

**Implications for Investors**

In the example above we only used a two year period however the difference between the average annual return and the CAGR tends to grow larger over longer time periods and periods of volatility. Using the example of the Vanguard Total Stock Market ETF quoted earlier the average annual return is 10.01% but the CAGR is 8.13%. Put simply, average annual return ignores compounding, which is critical factor in an investor’s returns. **So what should an investor do?**

- Where possible calculate the CAGR before selecting any investment product.
- Expect your return to be a little less than any quoted average annual return statistic.
- When evaluating investments do your best to evaluate like with like.

Download our free client guide to help you explain the difference between annual average return and compounded annual growth rate to your clients.

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