At a conference I attended recently, the question “do you have too much equity risk?” came up during a risk parity discussion. One of the investors said his portfolio wasn't over allocated to equity risk since he had a long-term investment horizon.
His claim: equities are less risky for long-term investors. He reasoned that with a long enough investment horizon, the good and bad return years cancel each other out, leaving the investor with an almost guaranteed return. This logic resonated with many of the other conference attendees.
(More: Don't project your risk tolerance on your clients)
When I heard this line of reasoning, it reminded me of four other rationales used over the years by other well-respected investors and asset managers:
Time Diversification: Adding uncorrelated sources of return to a portfolio lowers risk. Similarly, if returns are uncorrelated through time, a long-term investor benefits more from time diversification and, thus, equities are lower risk for long-term investors.
Average Returns: As investment horizon increases, the average (or annualized) stock return becomes less risky, justifying a larger stock allocation. This is a simple application of the law of large numbers.
Sharpe Ratio: Expected returns grow linearly with investment horizon (i.e., the two-year expected stock return equals two times the one-year expected return). Volatility, a measure of risk, grows with the square root of time (i.e., the two-year volatility equals the one-year volatility multiplied by the square root of two). As a result, Sharpe Ratios (i.e., return per unit risk) grow with investment horizon, making it worthwhile for long-term investors to hold more risky assets, such as equities.
Permanent Loss of Capital: Volatility is a poor risk measure for long-term investors who care more about permanent loss of capital. Investors with these risk preferences should hold more equities, all else being equal.
MISGUIDED
At first read, all of the statements above make intuitive sense, which is probably why they continue to have traction within the investment community. While there are many reasons for risk to vary with investment horizon, the logic above is misguided or, at least, materially incomplete.
To help understand this, it is critical to understand the difference between a random walk and mean reversion. Under a random walk, the return from one year has no impact on future returns. In other words, returns are uncorrelated through time. This implies that risk scales linearly with investment horizon, and risk per period is constant irrespective of investment horizon. Short and long horizon investors face the
same risk per period under a random walk.
(Also: Advisers' role in constructing smarter portfolios to combat volatility)
Now that we understand the basics of a random walk, let's quickly revisit the misguided and incomplete logic presented at the aforementioned conference. Under a random walk environment, returns are uncorrelated through time,
average (not cumulative) returns have lower risk with longer horizons, and Sharpe Ratios increase with investment horizon.
All of these are true statements under a random walk, but they are
irrelevant for measuring long horizon risk. The risk of
cumulative returns (the relevant risk measure for investors) grows with investment horizon, and the risk per period is constant. Additionally, in contrast to the rationale above, volatility is a good measure of permanent loss of capital under a random walk. All price movements are permanent under a random walk, i.e., when a stock drops in price, it's not expected to recover. Thus, the logic from the conference does not warrant a larger equity allocation for long-term investors, all else equal. End of story.
If a longer time horizon in itself doesn't lower risk, what else is necessary? Mean reversion. In a mean reverting environment, future returns depend on prior year returns. Returns are negatively correlated through time. Unusually good years tend to be followed by unusually bad years. Thus, under mean reversion, risk scales with investment horizon more slowly than a random walk, and risk per period declines with investment horizon. Long horizon investors face less risk per period under mean reversion.
Which view of the world, random walk or mean reversion, is more accurate? According to the last 40 years of data and my simple model, the degree of mean reversion in the historical data is large for the S&P 500 and Barclays Aggregate. A 10-year, 78/22 stock/bond investor experiences the same risk per period as a 1-year, 60/40 investor.
ESTIMATING WITH ERRORS
However, historical measures of mean reversion require estimates of means, variances, and correlations (“parameters”), and we inevitably estimate them with error. This error accumulates quickly over time, making assets look more risky to long-horizon investors. Investors need to address this reality and model parameter uncertainty. Once parameter uncertainty is incorporated, the degree of prospective mean reversion is dramatically reduced – the 10-year, 78/22 stock/bond allocation from before changes to 64/36.
In sum, don't pursue another strategic asset allocation study without a thorough discussion on investment horizon, how returns are assumed to evolve over time (i.e., random walk or mean reversion), and parameter uncertainty. Even if it's unintentional, most asset allocation work implicitly assumes a one-year investment horizon, a random walk, and/or no parameter uncertainty. These material assumptions do not typically reflect reality.
Peter Hecht is managing director and senior investment strategist at Evanston Capital Management. For more on this topic, you can refer to his white paper.
