# Stocks for the Long Run? Maybe Not So Much

## Lubos Pastor takes Jeremy Siegel to task...

BY Scot Blythe | June 29, 2011

Through the long equity boom, from 1982 to 2000, stocks looked not only attractive, but safe, particularly as bond yields fell from their inflated heights. That conventional wisdom was codified, in a way, in Jeremy Siegel’s 1994 book, *Stocks for the Long Run*.

Two arguments emerged from that book, which has been updated four times. The first is that, over long time periods, stocks always outperform bonds and cash. The second is that the longer the time horizon, the less volatility an investor will experience in stock returns.

Lubos Pastor contests Siegel’s conclusions on two grounds, but he’s not refuting the accuracy of the data. Over the long term, stocks have indeed yielded a 2% to 4% excess return over bonds, and more over cash. Will that equity risk premium persist? Probably not, he suggests.

Pastor, the Charles P. McQuaid Professor of Finance at the Booth School of Business at the University of Chicago, was in Toronto this month presenting at a seminar sponsored by Dimensional Fund Advisors.

A basic reason for Pastor’s downbeat message is that the past has limited predictive value for the future. Realized returns have two components: expected returns and unexpected returns.

Unexpected returns result from such things as increased productivity, the absence of global wars and so on – things unpredictable or the luck of the draw. Were Siegel’s data transposed from the U.S. to another country, such as Germany, the long-term stock returns – after 200 years of data – might not look so compelling. The concept of an unexpected return isn’t esoteric. It can be applied to bonds: the coupon is known – and expected — but a shock may increase or decrease the capital value of the bond.

Expected stock returns, basically the equity risk premium, depend on the perceived riskiness of holding equities over bonds. In the past, investors demanded a premium because stocks were not transparent, they were not liquid and trading costs were high. The premium today is much lower, he thinks, and he expects stocks to average between 2% and 3% less than in the past. According to Siegel’s data, U.S. stocks have returned on average about 7% a year. We can’t count on the beneficent unexpected returns bestowed in the past, nor is there the same degree of risk in stocks as there once was.

But there’s another element to the stocks for the long run argument. Historically, the longer the holding period, the less the volatility investors experienced. Annual volatility, for example, is greater than volatility tracked over a decade. But volatility can be analyzed in three ways.

If stocks did indeed follow a random walk, as posited in the efficient market hypothesis, volatility should be constant. By contrast, the conventional wisdom is that volatility drops because of mean reversion — negative shocks are eventually offset by positive shocks, or more exactly, expected and realized returns are negatively correlated. Pastor, however, says it’s the exact opposite. From the investor’s point of view, volatility will be higher over longer time periods, not lower.

That’s because the investor today does know the parameters of tomorrows’ stock returns. Estimates of volatility based on historical data ignore this parameter uncertainty: volatility is computed around an average realized return. Future returns, however, are unknown. Since the future return is unknown, investor uncertainty is compounded. This uncertainty means that the investor expects greater, rather than lesser volatility, the longer the time horizon.

Pastor bases his argument on predictive variance. Predictive variance has two components. The first is true conditional variance, where the mean return and the parameters – the factors that predict stock returns – are known. But parameter uncertainty and return uncertainty both affect the expected true variance. Predictive variance is thus the true conditional variance, which is based on historical data, plus the variance of that expected variance, which is not known beforehand. Using Siegel’s 200-year data series, Pastor suggests that predictive variance is 25% higher than realized variance. If that’s the case, investors will lessen their stock allocation.

To illustrate his point, Pastor takes a special case of predictive variance, where the random walk applies. Variance is known. But predictive variance still increases over time because the mean is unknown.

He decomposes predictive variance into five elements: the random walk, mean reversion, uncertainty about the future equity premium, uncertainty about the current equity premium – nobody provides a daily summary of the current equity risk premium — and estimation risk.

Estimation risk is based on the predictive value of three components: dividend yields, term spreads and “bond yields” a term defined as the “minus” of the current 30-year bond yield over its 12-month moving average. Each factor has robust predictive value; but each is also imperfect because of the presence of unexpected returns – the effect of market shocks, good or bad.

In his analysis say, Pastor finds that random walk effects on future variance are outweighed by mean reversion. However, the positive contribution of mean reversion in reducing volatility is overhwelmed by the other three components: uncertainty about the current and future equity premium, and imperfect predictors used to estimate the equity risk premium.

As a result, the long-term volatility of the market is 21% at a 30-year horizon – higher than the 17% experienced over one-year periods.

This has consequences, particularly for target-date funds. At the heart of target-date funds is the notion that a longer time horizon means a higher allocation to stocks, which is gradually reduced as the fund approaches maturity. Thus, a 30-year target date fund would have an initial allocation to stocks of 80% , which would taper off to about 30% at maturity. Once one introduces parameter uncertainty, the initial allocation to stocks falls to 60% of the portfolio, while the final allocation would be less than 20%.

The situation looks different if one incorporates a human capital approach. That assumes that a young worker is vested with a bond – an earning capacity that pays a regular coupon — at the beginning of their working life whose value falls as they approach retirement As a result, to diversify their portfolio, they need almost 100% in stocks at the beginning of their working life, and roughly 70% at the end, as their human capital is depleted.

So stocks can have a good long run, but not for everyone. And if the past is not indicative of the future, investors are likely to see stocks as riskier than they have been historically.