## Are Your Expected Investment Returns Valid?

If you were to review the historical performance of any mutual fund, asset class, or investment portfolio over any period of time, you’d certainly notice quite a bit of variation in the returns.  Take the S&P 500 (representing the largest 500 U.S. companies), for example.  The returns from this asset class over the last five years – starting from 2013 and working backwards – were 32.2%, 15.9%, 2.1%, 14.8%, and 25.9%.  And let’s not forget 2008, when the return was negative 36.6%.  Those are some pretty huge swings and serve to illustrate the relative uncertainty one faces when attempting to estimate future performance.  Nonetheless, even putting aside the uncertainty of future predictions, if you were to utilize historical data to determine future returns of any investment (despite the caveat in all investment prospectuses that “past performance is not an indicator of future returns”), you would very likely be at risk of mathematically overestimating those returns.  Why is that?

It has to do with volatility drag, which I wrote about a couple of years ago (Volatility Is a Drag).  The problem occurs when you utilize arithmetic rather than geometric averaging for return estimates.  Let’s look at an example.  Suppose you expect your portfolio to grow 10% this year, but lose 10% next year.  The average return (calculated arithmetically) would be 0% over the two years.  However, the actual compounded (geometric) return would be negative 1%.  It might be easier to see it this way:  starting with \$100 in the portfolio, the balance would increase to \$110 after the first year.  But it would lose 10% of that \$110 in year two, or \$11, leaving only \$99, a total loss of 1%.

Volatility drag is simply the mathematical recognition that a negative return has a bigger impact on a portfolio than the equivalent-sized positive return.  It’s easier to envision using larger gains and losses.  If a portfolio drops by 50%, for example, will a 50% gain the following year bring it back to where it started?  No!  It would take a 100% increase to get there.  So that negative 50% return has a much greater impact on the portfolio than a positive 50% gain.

The formula for calculating the geometric return of an investment requires you to have access to all the historical returns across the period of interest.  This might be cumbersome to find and to calculate.  There’s a simple shortcut you can use that is based on the investment’s average return and standard deviation over the period, measures that are commonly tracked by many investment and finance sites such as Morningstar.com.  You simply reduce the return by half the variance (or half the standard deviation squared).  For example, suppose a mutual fund has an expected return of 10% (calculated arithmetically) and a standard deviation of 20%, based on historical data.  The geometric return would be 10% – (20%^2)/2 = 8%.  This would be the more accurate figure to use for your estimated future returns.  (Be aware that this shortcut does underestimate the actual geometric return somewhat, especially for short time spans).

Bottom line: if you are going to use historical returns to estimate expected future returns, don’t use arithmetic returns.  Use geometric returns instead.  Otherwise you will have set your expectations too high!

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