The Impact of Volatility on Portfolios – Part II

In part I we saw that two portfolios that averaged 10% per year had different ending amounts of wealth. Part II will examine why.

While both portfolios had the same average return we must explain that it was an identical arithmetic average. This is the average that most of us are familiar with – the one where you sum all the numbers and then divide by the number of observations. Implicit in this type of average is that each “event” is independent. This type of average is commonly used for test scores for a class. Each test is an independent event as Billy’s score should not affect Sally’s score (unless they are cheating).

Investment returns (and consequently your account balance) don’t work this way because the “events” of yearly returns are not independent. A poor return in year one will decrease the amount of capital used to generate returns in year two. This means we have to use a different average measure for investment returns – the geometric average.

Assuming we had a return of 75% in year one and -55% in year two, the geometric average is calculated as follows: [((1+.75)*(1+-.55))^1/2]-1. It looks complex but, really all we have to do is add 1 to each yearly return and raise their product to the power of one divided by the number of years and then subtract one (okay, maybe it is a little complex –let’s look at it another way).

Take a look at the picture below to see the difference between a zero-volatility and high-volatility portfolio with an arithmetic average of 10%. These numbers were purposely chosen to show how different your ending wealth can be when high volatility is present.

As you can see the arithmetic returns are identical at 10%, but the geometric returns are very different: 10% vs. -11.3%! That means an account balance of $121,000 vs. $78,750.

Two important points to take from part II-

1. The geometric average will ALWAYS be less than the arithmetic average unless there is zero volatility (in which case they will be the same).
2. You pay your bills based on the geometric average.

The Impact of Volatility on Portfolios – Part I

You and your buddy both have $100,000 to invest for two years. You talk strategy but differing opinions on risk cause you to take separate strategies. After deciding to take the more conservative route, you invest your 100k and earn 10% in year one. Your buddy takes a riskier route with his money and earns 20% in the first year. He then makes fun of you endlessly.

In year two, you continue to earn 10%, but your friend’s risky strategy makes nothing.

Over the course of two years you both averaged 10% per year [(10%+10%)/2=10% and (20%+0%)/2=10%], BUT your account balance reads $121,000 and his is $120,000. Who is laughing now?

In part two we will look at why this happens (hint- the answer lies in volatility).