Matt's Money Tips

There are generally two different ways to measure average returns, either geometric, or arithmetic. When is it appropriate to use which type of return? The answer depends on the nature of the question. Geometric returns include volatility while arithmetic returns do not. Generally, for a one year or short time frame an arithmetic estimate can make sense. For instance, if I was to ask you, what is the expected return for the FTSE 100 in 2024, it makes sense to use the arithmetic average return over the last n years as an expectation. However, if you were to ask the question, what would my holding period return be if I invest my portfolio in the FTSE 100 over the next 10 years? To answer that question we need to know the expected volatility of the FTSE; here is an intuitive example as to why :

• Invest $100 at year 0
• Return in Year 1 is 50%
• Portfolio Value in Year 1 is $150
• Return in Year 2 is -50%
• Portfolio Value in Year 2 is $75

In the above example, the expected return is , however, as we can tell the ending loss on this portfolio is $25. This is because the variance of the portfolio is . Assuming that returns are normally distributed (in the real world they are not but it is close enough for the approximation) then the geometric return is , or in this case .

The annualized volatility of the US Stock market is which means that the annual geometric return is approximately or less than the arithmetic average. The takeaway here is that if you are expecting an average return of say 10% over the next 10 years, that really becomes about 8% when compounded annually due to market volatility.