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«Equity Style Investing RONG, WU How to cite: Equity Style Investing, Durham theses, Durham University. RONG, WU (2013) Available at Durham E-Theses ...»

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Comparing the holdings of corresponding styles for both types of investors, it is evident that the return predictability from business cycle information tends to induce the Doctrinaires to consistently pursue extreme positions on value (small) stocks and/or growth (large) stocks than the Skeptics do. For example, in the case of two styles of small and large stocks based on monthly returns, the Skeptics would long 122.7% (168.9%) of their wealth on small stocks financed by shorting 50.6% (79.5%) of the value on large stocks, ending with 72.1% (89.4%) of the initial wealth that allocated to long equity styles and the remaining 27.9% (10.6%) allocated to cash on value-weighted (equallyweighted) portfolio scheme. The Doctrinaires, in contrast, would tilt 248.1% (345.6%) of the initial wealth to long small stocks and short 42.3% (157.8%) value of large stocks, yielding net borrowing of 105.8% (87.8%) amount of the initial wealth for value-weighted (equallyweighted) investing. Similar finding holds for quarterly horizons and for other styles. The fundamental reason for such extreme tilt is because the Doctrinaires believe the return spreads of these twinstyles can be estimated using business cycle predictors and therefore the exposure can be reduced at bad times when expected returns are low or volatility is high.

The conditional investing is quite sensitive to the state variables and these variables affect the optimal style investing in quite a different mechanism. Consider the basic style box, along the small and large dimension, regardless whether it is based on monthly or quarterly horizon, the short-term interest rate (yld) and the term spread (term) tend to induce investors to tilt to small stocks and tilt away from large stocks, both in a very important manner. On the contrary, market dividend yield (div) significantly leads investors to tilt away from small stocks to large stocks relative to their early holdings.

Along value and growth axis, variable yld, div and term all significantly or importantly suggest investors moving away from value stocks and tilt to growth stocks on the monthly rebalancing. For the quarterly frequency, the variable term becomes less informative while variable yld or div still functions the same as it does in monthly frequency case, and the default spread (def) appears to lead investors to tilt to value stocks despite that it appears to be less informative for the entire style space on monthly rebalancing frequency.

If considering style interactions and thus more detailed equity market segments, it can be seen that importantly yld and div tend to lead investors to tilt to small growth stocks (SG) and tilt away from small value stocks (SV) for both monthly and quarterly horizons. In addition, variable term appears to suggest investors moving away from large value (LV) stocks on monthly horizon or large growth (LG) stocks on quarterly rebalancing periods.

In summary, business cycle predictive variables of yld, div, term and def tend to exert significant or important impact on investors’ optimal style investing policy. To be significant in predicting optimal style allocation weight in the mean-variance framework, a state variable should ideally either predict the expected style returns or the variance of style returns. Ait-Sahalia and Brandt (2001) study the moments of the market index of S&P 500 and find that def is positively related to the variance-covariance of monthly returns and positively but not significantly related to the expected returns. They argue that div is positively related to the expected stock returns by the definition of the present value formula, and the variable term is the most important and should be positively related with expected returns and negatively related with return variance. Given the fact that the research data of Ait-Sahalia and Brandt (2001) is based on the U.S. markets and the nature that business cycle variables are country specific, the results in table 5-3 are overall consistent with the existing literature. It is also noted that the coefficients of significant state variables generally have opposite signs for counterpart style allocations, suggesting that such variables indeed exert different impact on optimal style investing policies.

Business cycle predictability could benefit investors’ dynamic style investing. Smart investors capitalising on the conditional business cycle information consistently beat those disregarding business cycle conditions, both in-sample and out-of-sample. For example, on the monthly return frequency, the average optimal monthly returns of conditional investing is 14.7%, 4% and 3.4% as compared to 2.8%, 2.2% and 1.4% of unconditional investing based on style variables of APC, BM and DY, respectively (BM and DY returns are not shown in the table and are available on request). Except for style portfolios based on BM, the corresponding one-month out-of-sample performance is 9.9% and 1.9% as compared to 2.3% and 1.0% based on APC and DY, respectively. Similar findings are shown for quarterly basis (and this time BM also outperforms in one-quarter-ahead period). It should note that the in-sample expected excess returns of optimal tangent style investing portfolio are generally significant, while out-sample average returns are not. Indeed, such predictability-based style investing typically have high volatility, nevertheless such strategy provides investors with different return-risk trade off.

Figure 5-1 displays the time-series optimal style weights of conditional and unconditional investing using equally-weighted monthly and quarterly returns (results for the value-weighted schemes are qualitatively the same). Evidently, optimal style investing policies of the two types of investors are fundamentally different. The Doctrinaires’ conditional investing policy is more dynamic giving its timing nature suggested by different economic states. Style allocations across different horizons tend to demonstrate similar characteristics, suggesting that in principle business cycle variables predict optimal style allocation in a consistent manner for different rebalancing periods. However, conditional style investing based on different return frequencies can be different due to drastic changes in the conditional volatilities and correlations of different asset classes across horizons.

Overall, by focusing directly on the optimal style weights as suggested by Brandt and Santa-Clara (2006), the Doctrinaires are able to capture the entire distributions of style returns as opposed to the expected returns only, and hence should obtain better style investing policies.

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To deepen the understanding of Brandt and Santa-Clara (2006), it is useful to compare the conditional style policies to a more traditional approach that first modelling the conditional style portfolio returns and then choose the optimal style investing weights. Specifically, unlike the previous method that uses the sample moment as expected style returns, this time the expected style returns are estimated using regressions based on the set of business cycle predictors (one-periodahead forecasts of returns), while the variance-covariance matrix is formed unconditionally (using sample analogue). In this way, the optimal style investing only takes into account the predictability of the state variables to style returns but simply ignores their impact on variance-covariance structure of different styles. Table 5-4 compares the results of the two approaches.

Table 5-4 Traditional versus Conditional Style Investing on State variables This table compares the style investing that uses business cycle information to predict the first moment of style returns to that directly predicts optimal style timing policy with same predictors. The conditional expected returns are obtained from an in-sample regression of returns on the predictors and the statistic Markowitz solution is applied to these conditional expected returns together with the unconditional variance-covariance matrix from sample analogue. Panel A displays the estimated regressions of style portfolio returns on the conditioning business cycle variables at both monthly and quarterly frequency. Panel B summarizes the two investing policies, reporting the time-series average of the weights on style portfolios and the in-sample and on-period-ahead-out-of-sample returns (monthly equivalent).

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The results in Panel A of Table 5-4 demonstrate the predictability of business cycle variables to the conditional stock returns. First, the signs of the coefficients are highly consistent for both monthly and quarterly horizons. It is noted that the regression coefficients for variables div and term are all positive and often significant. It is suggested that movements in the div series are related to long-term business conditions and hence they capture predictable components of equity style returns. Ait-Sahalia and Brandt (2001) argue that div should forecast returns on the basis of the present value formula (since div does not appear to predict dividend growth). Fama and French (1989) find that the slope of the yield curve moves in tandem with the business cycle. They show that the variable term spread (term) tends to decrease near peaks of business cycle and increases when the economy troughs. Since the expected stock returns are low when the economy peaks and high when the economy troughs, the variable term positively predict expected returns. Ait-Sahalia and Brandt (2001) also find term is positively related with expected returns.

Second, the average coefficient of variable default spread (def) is negative and often significant. This is a bit intriguing as Ait-Sahalia and Brandt (2001) find that def is positively but not significantly related to the expected returns. Fama and French (1989) document that def tracks time variations in expected stock returns that appear to be persistent beyond the short-term business cycle fluctuations.

The negative coefficients of def would arguably suggest that equity styles are unable to track the long-run trends in the business cycle.

Third, the impact of yld on the expected returns is often positive but less significant for small and value styles, and is negative but more significant for large and growth stocks. This is consistent with Fama and Schwert (1977) and Fama (1981) who document that the short interest rate is negatively related to future market returns (since market index mainly constitute large stocks on both value and growth dimensions, and momentum is most pronounced in small-growth and small-value styles). Table 5-4 also suggests that returns are more predictable with long horizons than at short horizons as the average increases with return horizons. This is because the time series of business cycle variables demonstrate slow mean-reverting properties.

Although business cycle information predicts the first moment of conditional style returns, evidently, ignoring the predictability on the variance-covariance structure of style returns could result in less better style investing performance as opposed to the conditional investing strategies parameterising on variables that arguably capture the time variation in all moments of style returns. In almost all cases the conditional style investing predominantly beat the traditional investing approach, particularly in out-of-sample periods. For example, optimal style investing based on small-large (value-growth) with monthly rebalancing yields 2.83% (1.24%) in-sample returns and 1.64% (0.39%) one-period-ahead monthly returns based on value-weighted return calculations. In contrast, the returns for optimal conditional investing is 3.75% (15.26%) and 3.92% (10.81%) for in-samples and out-of-samples, respectively. The advantage of conditional investing is also seen on the quarterly horizons.

But where does the outperformance of conditional style investing come from? To understand the mechanism as how business cycle information affecting the style allocation process with different firm characteristics, Table 5-5 compares average time-series coefficients of the state variables for the conditional style investing policy described in Table 5-2 and the coefficients from the regressions of expected style returns reported in Table 5-4 (* refers that the coefficient is significant for at least 10% level).

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It is evident that the mechanism business cycle variables predict expected style returns and in turn the optimal style allocation policy is substantially different. First, while the role default spread (def) plays is similar in both expected returns and style allocation context, it is no longer significant in the style investing decision-making despite of its significance in the expected style return distributions. In addition, although the lower expected returns for small cap stocks and higher expected returns for large cap stocks are suggested by the regression, yld predicts that a positive shock to this variable would induces investors to overweight small stocks and underweight large stocks.

However, a positive shock to yld would lead investors to tilt to growth stocks, which matches their higher expected returns signalled by changes of yld. Similarly, the dividend yield (div) statistically predicts the style allocation along both size and value dimensions. Although div has more significant (positive) impact on returns for small cap stocks (value stocks) than for large cap stocks (growth stocks), it induces investors to overweight large stocks or growth stocks and underweight small cap stocks or value stocks when experiencing positive shocks.

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