And why do we use Average Returns?

Most advisors think in terms of annualized returns, not average returns.  However, monte carlo analysis relies on average returns.  It’s important to understand what these two numbers are, how they are different, and why do we use average returns?

The first thing to understand is what these two numbers are.  Annualized, or geometric average, returns take volatility into account.  It is essentially the annual rate of return that takes you from your beginning value to your ending value, no matter what happened in the middle.  If you’re curious you can see the formula on Investopedia.

Average returns, also known as the mean return or simple average return, is simply adding up all of the annual returns and dividing by the number of years.

Because of the smoothing inherent in annualized return, average returns will always be greater, except when the standard deviation is zero.  The greater the standard deviation the larger the divergence will be between average returns and annualized returns.

So if advisors are used to thinking about annualized returns, why do we use average returns?

We use average returns because that is how monte carlo analysis works.  To generate annual returns for the simulation the system builds a normal curve using the specified return and standard deviation.  A number is then picked from the curve, and that is the annual return for that year.  The average return is the midpoint of this distribution.  Because the annualized return already incorporates the negative effect of variance it would negatively skew the distribution, and we would be using returns that were lower than we intended.