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Portfolio Volatility and the Effect on Compound Return

Portfolio Volatility and the Effect on Compound Return

January 23, 2024

If I am a buy and hold, long-term investor, why does my portfolio volatility matter? We typically refer to volatility as “risk” in finance but, as a concept, it simply describes the degree of price movement of a financial asset or group of securities. Increased “risk” is typically associated with an increased return, but this is not always the case. Even
if risky securities provide a reasonable return in the long term, they can experience significant drawdowns in the process. A simple mathematical concept can help us understand why additional return is necessary to justify additional volatility and amplified drawdowns in our portfolios.

The compound average, also known as the geometric average, calculates increases and decreases of portfolio value in a sequence, while a simple average will sum the entire data set and divide by the number of observations.

              The difference between these two calculations is called the volatility drag.

              Compound Average Return = Simple Average Return minus Volatility Drag.

              Volatility Drag = Variance of Returns divided by 2

To demonstrate, let’s construct a few $100,000 portfolios and measure the return of each, every year for 30 years. We will target an average of 5% return per year. The zero-volatility portfolio assumes a 5% return every year.

In a portfolio of market securities, there would be some variation of returns over the years. For simplicity’s sake, we can calculate a 10% volatility portfolio as +15% return one year, -5% return the next year, and repeat the sequence for 30 years. The 15% and 20% volatility portfolios use the same methodology but with greater variation. These time series must end on a down year to generate the 5% average return.

At the end of 30 years, the 10% volatility portfolio will have lagged the zero-volatility portfolio by $55,211.31 and the 20% volatility portfolio will have lagged by $183,918.61 despite having identical simple average returns of 5%.

The logical explanation as to why this occurs is that, despite the same average annual return, asset prices need to generate higher return in the up years to reclaim the value they lost in the down years. Example – if a stock loses 50% of its value, it must go up 100% to reclaim that loss.

The effect is strong enough that, over 30 years, an investor could buy a “3.1% Return Zero-Volatility” portfolio and outperform the “5% Return 20% Volatility” portfolio by $1,620.75.

This exercise ends up being a long-winded proof that if we hold simple average returns constant, the portfolio with lower volatility will produce the higher growth rate. We must keep in mind that not all volatility is created equal, and that securities which display higher volatility and greater drawdowns often provide excess returns. Investors have been handsomely compensated for taking on additional “risk” in equities versus fixed income over the past 30 years. If an investor is not compensated adequately, however, the decision may not only cause them unnecessary emotional distress, but damage to their portfolio returns versus more efficient options, especially over a long investment horizon.

Source: Wikepedia: Thomas E Messmore (1995). "Variance Drain". The Journal of Portfolio Management. 21 (4): 104-110. doi:10.3905/jpm.1995.409536. S2CID 219239961