Andrew Ang has published online draft versions of some sections from his forthcoming book, Asset Management, and from what I’ve read so far it promises to be a treasure trove, at least for the narrow sliver of investment managers that care about evidence over theory. His chapter on ‘Equities Market Level’ is especially interesting to us, as it explores two areas of research that we have also explored at length in many articles on this blog: statistical forecasting of long-term stock market returns, and; the observation and management of portfolio volatility. The chapter is 50 pages long, and well worth reading (here), but for brevity I want to highlight a few critically important findings: **1. Volatility is very forecastable, and it is therefore possible to effectively manage risk in portfolios.** In fact, using standard volatility forecasting methods, the correlation between the volatility estimate at the beginning of any month, and the realized volatility over the subsequent month, is 63%, which suggests more than 12x greater forecast-ability for volatility relative to returns. Long-time readers will recall that we have posted many articles that deal with this topic, and we would encourage new readers to examine some of this research. Ang used an intuitive (but somewhat complicated) method to test the performance of a strategy which actively manages the volatility of a portfolio of U.S. stocks through time based on the VIX implied volatility index, so that when the VIX is high, the portfolio holds a higher cash (t-bill) position in order to maintain the expected volatility of the portfolio in the face of large changes in the volatility distribution through time. From Ang:

If volatility is so predictable, then volatility trading should lead to terrific investment gains. It does. Despite my pessimism on predicting expected returns of the previous section, I am far more enthusiastic on strategies predicting volatilities.

…[The chart below] shows that the cumulated returns (left-hand axis) of [a] volatility timing strategy largely avoided the drawdowns of the static strategy during the early 2000s and the 2008 financial crisis. During these periods VIX (right-hand axis) was high and the volatility timing strategy shifted into T-bills. It thus avoided the low returns occurring when volatility spiked.

The mean of the static 60%-40% strategy in [the chart below] is 7.9% and its reward-to-risk ratio is 0.82. In contrast, the volatility timing strategy has a mean of 10.1% and a reward-to-risk ratio of 1.95. Volatility strategies have good performance.

Source: Ang (2012) **2. It is really difficult to forecast equity returns over time horizons that are meaningful for most investors.** While equity returns over the very long term are about 9% nominal and 6.6% real, the range of possible equity returns is very wide over shorter time frames out to 20 years or more. The following chart from our AAA whitepaper shows the distribution of rolling 20-year real returns to stocks using Professor Shiller’s database, which has stock and bond return information back to 1871.

Source: Shiller (2012) The following table from Ang quantifies the degree to which a wide variety of valuation, economic and trend-based factors explain equity returns over periods from 1 quarter to 5 years. Ang confirms our discovery that the Shiller PE is a robust explanatory variable for stock returns, with statistical significance at all horizons studied. The only other statistically significant factor tested by Ang was the Consumption-Wealth ratio, though the author correctly highlights the ‘look-ahead’ bias embedded in this measure, which means it can not be used effectively for contemporaneous forecasting.

Source: Ang (2012) Ang provides a superb summary of the implications of this analysis on forecasting stock returns for investors, and I feel it’s worth re-publishing here in its entirety. Note that the first point pertains directly to our Estimating Future Returns report, as Ang highlights the spurious confidence implied by R-squared values in studies with long-term overlapping periods. We would definitely agree with Ang’s caution, but we would also point out that estimates generated by our model are still likely to prove to be much more accurate than simple long-term average estimates in forecasting stock market returns going forward.

There are time-varying risk premiums, but they are difficult to estimate. If you attempt to take advantage of them, do the following:

- Use good statistical techniques. Overstating statistical significance, for example by using the wrong t-statistics and thereby making predictability look “too good,” will hurt you when you implement investment strategies. One manifestation of spuriously high R2 in fitted in samples is that the performance deteriorates markedly going out of sample. Consistent with the spurious high R2 s, Welch and Goyal (2008) find that the historical average of excess stock returns forecasts better than almost all predictive variables. Use smart econometric techniques that combine a lot of information, but be careful about data mining, and take into account the possibility of shifts in regime

- Use economic models. Notice that the best predictors in Table 7 were valuation ratios. Prediction of equity risk premiums is the same as prediction of economic value. If you can impose economic structure, do it. Campbell and Thompson (2008), among others, find that imposing economic intuition and constraints from economic models help.

- Be humble. If you’re trying to time the market, then have humility. Predicting returns is hard to do. Since it is difficult to statistically detect predictability, it will also be easy to delude yourself in thinking you are the greatest manager in the world because of a lucky streak (this is self-attribution bias) and this overconfidence will really hurt when the luck runs out. You will also need the right governance structure to withstand painful periods that may extend for years.
Note there are very few who have skill, especially among those who think they have skill.

**3. Cash (t-bills) represent a much better hedge against inflation than stocks.** This revelation will probably come as a major shock to equity investors who believe that their equity portfolio represents their best shot at hedging against an inflationary shock from misguided central bank intervention. The following chart from Ang clearly illustrates this point. Ang performed a robust pearson correlation analysis between, stock, bond and cash returns and inflation. Stocks exhibit negative correlation vs. inflation in absolute terms over periods less than 3 years; that is, when inflation increases, stocks react negatively in the short term. After 3 years, stocks are relatively agnostic to changes in inflation, as inflation estimates change in response to changes in inflation regime. On the other hand, t-bill yields adapt fairly quickly to changes in inflation, with correlations rising toward 0.5 after about a 3 year horizon, where they find a plateau. Conversely, when stock returns are adjusted for t-bill yields to represent excess returns, they exhibit a negative correlation vis-a-vis inflation for the entire horizon out to 10 years in the range of -0.1 to -0.2. **The incontrovertible message from this analysis is that investors should hold a healthy slug of cash in portfolios to hedge against inflation – in diametric opposition to prevailing investment dogma.**

Source: Ang (2012)

**Takeaways**

There a few big ideas here. First: focus on what you can control, and budget for what you can’t. You *can’t *control the long-term returns to markets, and the evidence above strongly suggests that you can’t even make a very good forecast about what to expect. You *can *observe, measure, and to a very large degree control the volatility of your portfolio, however. And it happens that by controlling for volatility in the right way, you will have a high probability of achieving higher absolute returns. Even if controlling for volatility doesn’t deliver higher returns over your investment horizon, it will definitely achieve two important goals: 1.You will enjoy a more stable investment experience with less anxiety, and therefore be much less likely to make highly detrimental behavioural errors under situations of extreme pressure 2.You will improve the sustainability of your retirement plan because you will substantially narrow the range of potential negative market outcomes. For more on this, we strongly encourage you to read this important article. The other important takeaway is that investment dogma is often (dare I say, mostly?) wrong, and that it is important to verify the empirical validity of many basic investment concepts before putting real money to work. For example, the volatility management tests revealed what we have known for some while: higher returns do not necessarily require higher risk. In fact, smart low risk strategies often outperform high-risk strategies in both absolute and risk-adjusted terms. Further, evidence from the above examination of correlations between stocks, t-bills and inflation directly contradicts one of the most popular myths in finance: that is, that stocks will protect your portfolio in the event of an inflationary shock, while cash will become worthless. Certainly, cash under the mattress is much more vulnerable to inflation, but cash held in cash-like instruments like high quality government Treasury bills actually offer better protection than stocks, which are likely to lose value after adjusting for inflation.