Aurora Borealis
6 August 2018 Financial Analysts Journal

Volatility: It’s Worse Than You Thought (Summary)

  1. Phil Davis

This In Practice piece gives a practitioner’s perspective on the article “Volatility Lessons,” by Eugene F. Fama and Kenneth R. French, published in the Third Quarter 2018 issue of the Financial Analysts Journal.

What’s the Investment Issue?

Most investors are aware of potential high volatility in their equity investments, but they may not realize the impact over longer time horizons of volatility on portfolio performance.

It is almost axiomatic that equities will substantially outperform Treasuries over the long term. Performance data may nevertheless mask long periods of underperformance that could derail many popular investment strategies.

The authors examine the extent to which volatility impacts equity performance over short and long periods, with a particular focus on the three- and five-year periods against which asset managers are often benchmarked. They also assess the effect of volatility on the performance of widely used equity factor strategies: small size and value.

How Do the Authors Tackle the Issue?

The authors collate monthly stock returns from the NYSE, AMEX, and NASDAQ (after 1972) from 1963 to 2016.

They examine how much the equity premium changes from a one-month horizon out to a 30-year horizon, where the premium is the difference between equity returns and the performance of one-month US Treasury bills.

The authors decide on two ways of simulating and evaluating the returns. First, they calculate annual premiums based on monthly returns. In this approach, pairs of monthly equity returns and monthly Treasury returns are compared with each other to produce simulated annual equity premiums. Although the authors evaluate 642 monthly returns, by comparing pairs of returns randomly against each other, the process produces some 100,000 possible annual premiums.

The authors’ second method of measurement incorporates the uncertainty that expected returns will actually materialize. They control for this by calculating the standard error of the mean returns—a measure of uncertainty about the underlying mean.

A similar assessment is made of value and small-size premiums using a sophisticated statistical adjustment. The authors measure premiums of three value portfolios: market value (that is, all value stocks), big value (stocks that are both large and value), and small value (stocks that are small and value). They also measure the premiums for a portfolio of stocks selected on small-size criteria only.

What Are the Findings?

Volatility can have a large and negative effect on investors’ goals, depending on their investment time horizon. Because of volatility, the standard deviation of the monthly premium is 4.42%, which is almost nine times bigger than the 0.51% average monthly equity premium between 1963 and 2016. This means there is considerable doubt that realized premiums will be positive, even over longer periods.

To put this into context, for the three-year periods that are often used by investors to benchmark their fund managers, negative equity premiums occur in 28.54% of the return simulations. This falls to a smaller—but still significant—23.41% for five-year periods. Even over 10-year periods, considered very long term by many investors, negative premiums occur 15.6% of the time.

Value stocks and small stocks, meanwhile, have higher average returns than equity markets as a whole over the 1963–2016 period. The average return on a value-weighted portfolio beat the average market return by 0.29% a month. But as before, the standard deviation of this premium is substantial, at 2.19% a month, implying considerable uncertainty about the actual premiums that can be achieved, even over long periods.

For example, on a five-year horizon, the probability that small value stocks have a negative premium over the market is 11.68%, but this rises to a substantial 29.8% for small stocks. Over three years, negative premiums in small stock portfolios are estimated to occur 34.06% of time. Even over 10 years, negative premiums will occur 22.48% of the time for small-size stocks. 

When introducing uncertainty about the expected premium into their measurements, the authors find that the range of premiums is amplified—and not symmetrically. For 10-year equity premiums, for instance, the standard deviation rose from 149% to 167%.

This increased dispersion of returns is not evenly distributed: The authors find that positive returns are considerably higher, whereas negative returns are only modestly lower. Under the uncertainty method, the 95th percentile of 20-year equity premiums, for example, returned 429% above Treasuries. This result contrasts with the 5th percentile, which underperformed T-bills by a more modest 39%. Value and small stock premiums over the market also have a risk of bad outcomes, but over the longer term, outcomes are skewed toward good rather than bad outcomes.

Table 2. Summary Statistics for Monthly Value and Small Stock Returns in Excess of Market, July 1963 to December 2016 (642 Months)


Market Value

Big Value

Small Value







Std. dev.





SE mean










What Are the Implications for Investors and Investment Professionals?

Equity premiums (compared with one-month Treasuries) over three- and five-year periods are negative more often than is widely believed. The same is true of value and small stocks, which underperform the wider market over three and five years surprisingly often.

Even over longer periods, underperformance is frequent enough to make many investors reconsider the size of the equity allocations in their portfolios. In light of these findings, investors may consider more tactical approaches to equity investing, to offset periods of volatility and consequent underperformance.

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