Alternative Investments. Black Keith H.

changes in risk premiums or market inefficiency. It is beyond the scope of this chapter to discuss the academic and industry findings regarding the sources of predictability in asset returns. It suffices to say that studies have not been able to conclusively rule out that some asset return predictabilities using low-frequency data (e.g., annual frequency) represent temporary inefficiencies in markets (Asness, Moskowitz, and Pedersen 2010; Hull and Qiao 2015). The effectiveness of a TAA strategy is largely dependent on constructing a good model. As mentioned, the first step in developing a TAA strategy is to forecast excess returns by constructing fundamental and technical models that can predict asset class returns, using a set of explanatory variables for fundamental models and signals for technical models.12

      Models may have varying predictive strengths during different economic regimes. In addition, according to the FLOAM, the potential value added of TAA is increased if the models' errors are not correlated with each other. Therefore, multiple forecasting models should be used to maximize the value added by the TAA strategy. A good forecasting model must include economically meaningful signals and have a research process that correctly identifies those signals. In addition, the model must have performed well in the past using out-of-sample data.

      2.1.5.2 Three Notable Characteristics of Sound TAA Model Development

      The following are three important characteristics of sound model development:

      1. USE OF ECONOMICALLY MEANINGFUL SIGNALS. Economically meaningful signals are those signals with rational, intuitive explanations for their expected predictive power. For example, the term spread, as an indicator of the business cycle, is intuitive and rational. Theoretically, a flat or downward-sloping yield curve is associated with a lower inflation rate and slower economic activity. A model that uses inputs with a strong basis in economic theory is likely to provide signals that identify fundamental shifts in the economy.

      2. ABSENCE OF DATA MINING. The manager should be able to confirm that the predictive results are not due to data mining. This could occur if the manager tries a variety of models and explanatory variables to see which one performs best and chooses the most accurate one to implement the TAA strategy. Ex post, it is possible to find explanatory variables that can predict the most random processes. The question is whether there are economic reasons to think that ex ante the model would have worked. More important, out-of-sample validations must be done to guard against data mining. Out-of-sample tests of the strategy, such as in other time periods or countries, can help confirm that the strategy's success is not simply the result of fitting the model to explain one historical period.

      3. AVOIDANCE OF OVERFITTING. Models that have a large number of explanatory variables can produce impressive r-squareds, especially when there is limited data. While models with smaller numbers of explanatory variables are likely to produce less impressive r-squareds using the same sample data, they are more likely to reproduce their in-sample predictive power out of sample. In addition, models that use fewer variables are more likely to be stable through time; that is, the estimated relationship does not change radically because of small changes in the data.

      2.1.5.3 Fundamental Analysis Underlying TAA Models

      Linear regression is the most common approach for testing and developing fundamental models. Linear regressions are the simplest way to create conditional expectations of asset returns. Unlike unconditional expected returns, which use the average historical returns on the asset to form expectations, conditional expectation models obtain estimates of expected returns that are functions of the current values of a set of predictive variables.

      Suppose we have collected a long time series of monthly returns on an emerging equity market, and we run the unusual regression in which the dependent variable is the equity return and the explanatory variable is the constant one. This regression has a single coefficient, the intercept, and it will be the unconditional expected return on the asset, and will be exactly equal to the historical average monthly return. The intercept may change slightly as new data is observed and added to the sample, but it will remain mostly unchanged, especially if a very long series is used.

EXHIBIT 2.1 S&P 500 Returns versus Lagged Dividend Yield

      Suppose the same asset returns are now regressed against the constant one, and lagged values of the term spread in the local bond market. The expected return on this emerging market conditioned on the term spread is now equal to the estimated intercept plus the estimated slope coefficient times the current value of the term spread. We can think of TAA as SAA when conditional expected returns are used as inputs in the asset allocation process. For example, in a mean-variance model, conditional expected returns are used to generate tactical weights. These weights may change drastically if there is a fundamental change in economic conditions leading to substantial changes in the conditioning variables.

For example, annual returns on the S&P 500 Index are regressed against lagged dividend yields on the S&P 500 using data from January 1919 to December 2015. The regressions results are presented in Exhibit 2.1.

      As expected, this simple model lacks significant predictive power, as the slope coefficient, 1.04, is not statistically significant (the t-stat is 0.97). Still, it can be used to demonstrate how to employ such models. The unconditional mean return on the S&P 500 is 7.7 % per year. To calculate the conditional mean, we need the current value of the dividend yield, which was about 2.11 % in December 2015. Therefore, the conditional mean return on the S&P 500 in December 2015 is:

      The conditional mean return on the S&P 500 for 2016 is estimated to be 5.5 %. Should the dividend yield be different in December 2016, the conditional expectation of S&P 500 returns for 2017 will change accordingly.

      2.1.5.4 Technical Analysis Underlying TAA Models

      While regression models based on fundamental economic relationships can be useful in implementing TAA strategies, models based on technical analysis can be used to supplement these models; in some cases, research has shown that they may even perform better than fundamental models. Faber (2013) has produced one of the most cited studies in this area. The approach employed in the paper is very simple but has produced results that seem to indicate that technical analysis could serve as the basis of TAA. The model uses six asset classes: U.S. large cap (S&P 500), non-U.S. developed markets (MSCI EAFE), U.S. 10-year government bonds, commodities (S&P GSCI), real estate investment trusts (NAREIT Index), and 90-day U.S. Treasury bills. There is an expanded version of the model that uses more asset classes.

EXHIBIT 2.2 Global Tactical Asset Allocation

      Source: Based on results from Faber (2013).

      The strategy examines a very simple quantitative TAA model, which is based on a trend-following model. The objective is to build a simple model that can be used to highlight the use of technical signals in performing TAA for traditional asset classes. The model is mostly a risk-reduction technique that signals when a portfolio manager should reduce exposure to a risky asset class in favor of a less risky investment. The model uses the following buy and sell rules:

      

Increase exposure to 20 % of the portfolio if the current price is above the 10-month simple moving average.

      

Reduce exposure to 0 % of the portfolio if the current price is below the 10-month simple moving average.

The model is updated monthly, and the cash not allocated to risky strategies is invested in Treasury bills. Exhibit 2.2 presents the results reported using data covering 1973–2012.

      The buy-and-hold strategy is an equally weighted portfolio. The model has certainly performed well in the past. It is important

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This section is partly based on Tokat, Wicas, and Stockton (2007).