On June 23, citizens of the United Kingdom voted to leave the European Union. While there has been much speculation leading up to and since the vote, many of the longer-term implications of the referendum remain unclear, as the process for negotiating what the UK exit may look like is just beginning. In keeping with our proven approach to market changes, we urge caution in allowing short-term volatility to affect long-term asset-allocation. Long-term investors recognize that risks of uncertainty are ever present in the markets.

Understanding the volatility of stock returns is an important ingredient to maintaining a disciplined investment approach. People invest their capital hoping to earn a rate of return above that of just holding cash, and there is ample evidence that capital markets reward disciplined investors. For example, Exhibit 1 illustrates what investing $1 in 1926 into various asset classes would have translated to through the end of 2015. Even so, returns can be negative for days, months, and even years based on short term conditions. After such episodes, investors are often exposed to stories proclaiming the next looming financial crisis.

Exhibit 1: Monthly Growth of Wealth ($1)
1926-2015

Exhibit 1: Monthly Growth of Wealth ($1) 1926-2015

When volatility spikes, remaining disciplined can be challenging as pundits link volatility to any number of impending “crises.” They predict poor short-term returns. Their advice for investors is often “sell now” to avoid these poor returns. But as Professor Eugene Fama points out, “The onset of high volatility should be associated with price declines that increase expected returns going forward (to compensate investors for the higher volatility).”1 That is, volatility often increases after a price decline, which may increase expected returns. So these pundits are reflecting what has already occurred, not what will occur.

But we can examine historical data to see 1) if there have been statistically reliable differences in average returns or equity premiums between more volatile and less volatile markets, 2) if a strategy that attempts to avoid equities in times of high volatility adds value over a market portfolio, and 3) if there is any relation between current volatility and subsequent returns.

Exhibit 2: Exhibit 2. US Equity Market
January 1927–April 2016

Exhibit 2: Exhibit 2.	US Equity Market - January 1927 - April 2016

A simple indicator of these relationships is average returns across different market environments. In Exhibit 2, we take monthly returns for the US equity market (represented by the Fama/French US Total Market Index) and break them up based on the previous month’s standard deviation (computed using daily stock market returns). Average returns in months when the previous month had higher volatility (75th percentile or above) were slightly higher than when the previous month had lower volatility (25th percentile or below). This conforms with the intuition presented by Fama.

But, because stock returns have been noisy, these differences in average returns have not been reliably different from zero. In other words, at a glance there is not an economically meaningful difference in average equity returns based on the volatility of the prior month.

Is the equity premium (the return over US Treasury bills, or “T-bills”) also similar across different levels of volatility? Exhibit 3 shows the average monthly returns for the US equity market and T-bills from January 1927 through April 2016. The full sample is further broken out into average returns for months following a “high volatility” month (75th percentile or above) and the remaining months.

Exhibit 3: Average Monthly Returns
January 1927 – April 2016

Exhibit 3.	Average Monthly Returns - January 1927 – April 2016

We see that the average monthly equity premium has been higher after high volatility months. Nevertheless, the difference with all other months is not reliably different from zero—meaning we cannot reliably say that the premium is higher or lower after months with high volatility.2 These results suggest it is unlikely we can learn anything about this month’s equity premium based on last month’s volatility.

What if we had a trading strategy that attempted to avoid investing in equities when volatility was high? How would such a strategy perform relative to the market? Exhibit 4 shows returns and standard deviations for the US equity market, T-bills, and a hypothetical trading strategy that bails out of equities and invests in T-bills when the previous month’s volatility was high—a strategy that “flies to safety.” If the previous month’s volatility was high (75th percentile or above), the strategy invests in T-bills. If the previous month’s volatility was not high, the strategy invests in US equities.

Exhibit 4: Performance
January 1927 – April 2016

Exhibit 4: Performance January 1927 – April 2016

Over the period from January 1927 through April 2016, the volatility of the “fly to safety” strategy, as measured by its standard deviation, was lower than the volatility of the US equity market (12.21% vs. 18.66% annualized). This makes sense because the fly to safety strategy is invested in T-bills one quarter of the time, so we expect it to have lower volatility. However, this lower volatility came with lower returns, as the fly to safety strategy had an annualized return of 8.22%, compared to 9.75% for US equities. A strategy investing 75% in the market and 25% in T-bills would have performed similarly to the fly to safety strategy, as illustrated in the last column of Exhibit 4.

Consistent with the analysis presented thus far, Exhibit 5 shows the randomness of the relation between recent volatility and future returns. The relation between them looks “flat.” So recent volatility offers no indication if future returns will be “high” or “low.” This is confirmed through regression analysis, which further indicates there has been no reliable relation between recent volatility and future returns.

Exhibit 5: US Equity Market Volatility
This Month vs. Return Next Month

 Exhibit 5: US Equity Market Volatility - This Month vs. Return Next Month

What can we take away from this analysis? Put simply, we can expect volatility when investing in stocks. There is considerable evidence that an investment strategy attempting to forecast short-term price movements is unlikely to be successful. Forecasting short-term stock market performance based on current volatility is no different. We believe that developing an asset allocation to match up with your desired risk tolerance and investment objectives, staying disciplined, and rebalancing in all market environments remains an effective way to pursue your long-term investment goals.


Appendix
Glossary

Equity premiums: The excess return expected, or realized, from owning stocks over bonds. Realized equity premiums are typically measured by the difference of return from a broad stock market index and government-issued bonds considered to represent a risk-free rate of return.

Standard deviation: A measurement of historical return volatility for a security or portfolio. A volatile stock with large differences over time from its historical average return would tend to have a high standard deviation.

Regression analysis: A statistical process for estimating the strength of the relationship between one variable, such as a portfolio’s return, and one or more other variables, such as that portfolio’s exposure to market premiums.

Index Definitions

Fama/French US Total Market Index: Value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t.