Effectiveness of earnings forecasts in efficient global portfolio construction

International Journal of Forecasting (

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Effectiveness of earnings forecasts in efficient global portfolio construction Hui Xia a , Xinyu Min b , Shijie Deng b,∗ a

School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China

b

Steward School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

article

info

Keywords: Consensus temporary earnings forecasts Mean–variance efficient portfolio Stock selection

abstract We analyze the effectiveness of using fundamental variables of earnings forecasts for constructing mean–variance efficient portfolios. The performances of the Markowitz mean–variance optimal portfolios are examined by selecting stocks based on the consensus temporary earnings forecasts (CTEF) data. An empirical analysis on both US domestic equities and international equities is conducted for the period 1997–2010, and we find that the CTEF variable is a statistically significant factor in generating portfolios with active returns over benchmark portfolios. © 2014 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

1. Introduction The Fama–French (1992) model formalized the framework for selecting stocks based on fundamental data such as the size and the book-to-market ratio of a company in modern portfolio management. Following the strand of the literature that includes the work of Basu (1974, 1977, 1983), Banz (1981), Banz and Breen (1986), Jaffe, Keim, and Westerfield (1989), Chan, Jegadeesh, and Lakonishok (1996), Lakonishok, Shleifer, and Vishny (1994), Fama and French (1992), Jegadeesh and Titman (1993) and Fama and French (1995), there is an extensive and growing body of work on portfolio construction based on the fundamental variables of stocks, such as earnings, book value, cash flow, sales and consensus analysts’ forecasts, as well as on behavioral factors such as price momentum. Subsequent related work, such as that of Guerard, Gultekin, and Stone (1997), has focused on extending the

∗

Corresponding author. E-mail addresses: [email protected] (H. Xia), [email protected] (S. Deng).

model of Fama and French (1992) to a ‘‘stock-picking’’ model that consists of a composite set of fundamental variables, momentum variable and earnings forecasts. Guerard, Rachev, and Shao (2013) use three stock-selection models to estimate expected return models in the US and global equity markets. Applying the mean–variance, enhanced-index-tracking techniques and mean-expected tail-loss methodologies, they generate statistically significant active returns from various portfolio construction techniques. Deng and Min (2013) analyze the performance of an optimal global portfolio constructed from a 10-factor stock selection model, as described by Guerard, Gultekin, and Xu (2012). They find that the risk-adjusted return of the efficient portfolio of the global equity universe outperforms that of the domestic equity universe. Moreover, the empirical results demonstrate that the active portfolio return increases with both investors’ risk tolerances and the systematic tracking error allowed against the benchmark portfolio. When we have a composite stock selection model that is working well in generating portfolios with active returns, it is important to understand which factors in the composite factor set play major roles in generating the active returns. Guerard (2012) finds that in a stock selection model,

http://dx.doi.org/10.1016/j.ijforecast.2014.10.004 0169-2070/© 2014 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

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βsc measures the exposure of the excess return on asset s to

earnings forecast revisions and the directions of such revisions are more important than analysts’ forecasts in identifying mispriced securities, and that analysts’ earnings per share forecasts, with their revisions and breadths, are associated with excess returns. Based on the consensus temporary earnings forecasts variable (CTEF), which is singled out from the 10-factor stock selection model utilized by Deng and Min (2013), we select a universe of stocks from the US and global equities, respectively, from which to form the Markowitz mean–variance efficient portfolios. The empirical results show that the active returns of the efficient portfolios generated by the CTEF variable are comparable to those of the efficient portfolios generated by the 10-factor stock selection model. The CTEF variable is therefore a statistically significant factor in constructing portfolios with active returns. The return attribution analysis further confirms that CTEF plays a major role in generating the active returns associated with the 10-factor stock selection model used by Deng and Min (2013). The rest of the paper is organized as follows. In Section 2, we present a detailed description of the consensus temporary earnings forecast variable in the 10-factor stock selection model. Section 3 describes the mean–variance framework for constructing the optimal portfolio over the universe of stocks selected by applying the CTEF criterion. The datasets and empirical analysis are presented in Section 4. We summarize our findings and conclude in Section 5.

EPt is the earnings–price ratio at time t, calculated as earnings per share divided by the price per share at time t;

2. Forecast stock returns with earnings forecasts

BPt is the book–price ratio at time t, calculated as the book value per share divided by the price per share at time t;

It has become common practice for portfolio managers to select stocks based on asset return forecasting models in modern portfolio management. The return forecasting models evolved from the single factor models of Sharpe (1964), Lintner (1965) and Mossin (1966) to the multifactor models of Rosenberg (1974), Ross (1976), Roll and Ross (1980), Fama and French (1992), Bloch, Guerard, Markowitz, Todd, and Xu (1993) and Fama and French (1995). The fundamental theory supporting these models states that the return from holding a financial asset consists of the reward for having exposures to one or several systematic risk sources as a result of holding the asset. By establishing reliable estimates of a much smaller set of risk factors, forecast models for asset returns can be developed and used to screen out suitable stocks for portfolio construction. In a general multi-factor asset return model, the excess return on an asset (namely, the amount in excess of the risk-free return rate) is attributed to its exposure to a set of Nc non-diversified systematic risk factors. Specifically,

⃗rs =

Nc 

βsc ⃗fc + ϵ⃗s ,

(1)

c =1

where

⃗rs is the excess return on the sth asset; ⃗fc is the rate of return on the cth systematic risk factor; ϵ⃗s is the asset-specific residual after removing the impact of all factors from the excess return on asset s, and represents the diversifiable risk that is specific to asset s; and

the systematic risk-factor c, and is termed the factor beta. Risk factors correspond to different types of observable variables. Connor and Korajczyk (2010) provide an extensive review of the risk factor models. There are several alternative approaches for determining systematic risk factors in a multi-factor model setting. Common practice is to use a mixture of macroeconomic variables and firm-characteristic variables for modeling the risk factors. Guerard et al. (2012) use a 10-factor model to test the effectiveness of utilizing fundamental variables for generating reliable return forecasts for the construction of optimal equity portfolios. Using the same 10-factor stock selection model, Deng and Min (2013) analyzed the mean–variance efficient portfolio constructed from a set of stocks selected by their total return (TR). Let TRt +1 denote the total return of a security in time period t + 1. TRt +1 is specified as being linearly dependent on a set of ten risk factors, where a0 , a1 , . . ., a10 are the factor loading coefficients, see Eq. (2). TRt +1 = a0 + a1 EPt + a2 BPt + a3 CPt + a4 SPt

+ a5 REPt + a6 RBP6 + a7 RCPt + a8 RSPt + a9 CTEFt + a10 PMt + ϵt ,

(2)

where

CPt is the cash flow–price ratio at time t, calculated as the cash flow per share divided by the price per share at time t; SPt is the sales–price ratio at time t, calculated as net sales per share divided by the price per share at time t; REPt is calculated as the current EP ratio divided by the average EP ratio over the past five years; RBPt is calculated as the current BP ratio divided by the average BP ratio over the past five years; RCPt is calculated as the current CP ratio divided by the average CP ratio over the past five years; RSPt is calculated as the current SP ratio divided by the average SP ratio over the past five years; CTEFt is the consensus earnings per share I/B/E/S forecast, revisions and breadth; PMt is the price momentum; and

ϵt is the random innovation term. It has been found that the information in relation to a firm’s earnings that is provided by financial analysts who are following the firm can be important in forecasting the firm’s stock return. While Abarbanell (1991) studies the formulation of financial analysts’ earnings forecasts following security price changes, and draws the conclusion that there is a positive association between analysts’ forecast revisions and prior stock price changes, Guerard (2012) finds that earnings forecast revisions and the directions of such revisions are more important than analysts’ forecasts in a stock selection model that aims to identify mispriced securities for inclusion in the universe of stocks for the construction of optimal portfolios.

H. Xia et al. / International Journal of Forecasting (

The consensus temporary earnings forecasting (CTEF) variable in the 10-factor return forecasting model in Eq. (2) was created by Guerard et al. (1997). It consists of the forecasted earnings yield (FEP), earnings revisions (EREV), and BR (earnings breadth), which represents the direction of revisions and can also be identified as the breadth. Specifically,

• FEP1/FEP2: one-/two-year-ahead forecast earnings per share/price per share; • EREV1/EREV2: one-/two-year-ahead forecast earnings per share monthly revision/price per share; • BR1/BR2: one-/two-year-ahead forecast earnings per share monthly breadth; • CTEF: equally weighted sum of FEP1, FEP2, EREV1, EREV2, BR1, and BR2. Shao, Rachev, and Mu (2014) use a sophisticated time series model which combines ARMA, GARCH and multivariate normal tempered stable innovations to model the CTEF variable for portfolio construction, and then examine the performances of optimal portfolios based on the meanexpected-tail-loss criterion. Beheshti (2014) considers the mean–variance efficient frontier for the earnings forecast models and investigates how the integration of the alpha alignment factor improves the efficient frontier. It is natural to investigate the question of how effective it would be to use the historical values of the CTEF variable directly to construct the mean–variance efficient portfolio, in terms of generating active returns over a benchmark portfolio. 3. The mean–variance efficient portfolio framework Markowitz (1959) introduces the concept of constructing portfolios based on their risk-reward trade-offs, which establishes the foundation for quantitative portfolio management. In the framework of Markowitz (1959), the reward and risk of investing in a financial asset are measured by the expected return and the variance of the return over a certain period, respectively. Over the past decades, there has been extensive research aiming to extend various aspects of the original framework, such as adopting alternative measures for risk-reward trade-offs in portfolio management. 3.1. The mean–variance efficient portfolio Given a universe of stocks (for instance, all stocks in the US), an investor must decide on a portfolio of the stocks to invest in that balances the reward and the risk of the investment properly. The risk-reward balance is modeled by penalizing the expected return with a risk-tolerance λ weighted variance of the return in the objective function of the mean–variance portfolio optimization problem in Eq. (3). The goal is to maximize the risk-adjusted expected return of the portfolio, with the risk being measured by the variance of the portfolio return. By varying the risk-tolerance level λ, the corresponding optimal portfolios with their associated expected return and risk form the mean–variance efficient frontier of all portfolios. The

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efficient frontier represents the best returns achievable at each given risk level. In its original form, the mean–variance optimal portfolio is obtained by solving the following optimization problem, which maximizes the risk-adjusted return of a portfolio. minimize

w ⃗ T Ωw ⃗ − λw ⃗ T α⃗

subject to

w ⃗ T ⃗e = 1, w ⃗ ≥ 0,

w ⃗

(3)

where

w ⃗ is the vector of portfolio weights on each security in the security universe,

α⃗ is the vector of expected returns for each security in the security universe,

Ω is the covariance matrix of the returns of all securities, λ is the risk tolerance parameter, and ⃗e is a vector consisting of all ones. 3.2. Practical portfolio constraints In the real world, it is well-known to portfolio managers that the solution to the original optimal portfolio problem in Eq. (3) is often not practical to implement. For instance, the mean–variance optimal portfolio solved from Eq. (3) may turn itself over many times in a year, which would incur huge transaction costs. Practical constraints are incorporated into Eq. (3) in order to make the solution more relevant to practice. As portfolio managers are typically evaluated according to the performances of their portfolios relative to that of some chosen benchmark portfolio (for instance, a portfolio corresponding to a market index), the optimal portfolio needs to meet its investment goal while tracking the performance of its benchmark portfolio closely. In practice, the following constraints are commonly imposed.

• Tracking error constraint: the characteristics of the managed portfolio must track those of a designated benchmark index closely, see Fabozzi, Gupta, and Markowitz (2002). Specifically, the deviations between the portfolio weights and those of the benchmark portfolio must fall within the allowed bounds. • Total turnover constraint: frequently trading in and out of stocks to rebalance a portfolio can cause significant transaction costs, which reduces the total return on the portfolio. By imposing constraints on the amount that the weights on the stocks in a portfolio can change when rebalancing the portfolio, the turnover in the optimal portfolio, and thus the transaction costs, are effectively controlled to whatever level is deemed acceptable. The implementation detail of these constraints is given in the following empirical analysis section. 4. Empirical analysis of portfolio performance We employ the US expected returns (USER) dataset of Guerard et al. (2012) and the global expected returns (GLER) dataset of Guerard et al. (2013) for the period

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1997–2009. The universe of stocks for constructing the mean–variance (MV) optimal portfolio is based solely on the ranking of the CTEF values of the stocks in the two datasets. The MV model with constraints on the tracking error and the total turnover is solved by the Sunguard APT solver. 4.1. Portfolio optimization and implementation of the tracking error (TE) constraint As was explained in Section 3.2, the tracking error measures the degree to which the return on a portfolio deviates from that of a benchmark over time. In the APT solver, the tracking error is defined as the standard deviation of the difference between a portfolio’s return and the benchmark’s return. The tracking error can also be interpreted as the volatility of the target portfolio’s active returns over the benchmark portfolio. We illustrate this point through the derivation below. Let p and b denote the portfolio weight vectors of the target portfolio and the benchmark portfolio, respectively. Under the multi-factor model in Eq. (1) for the stock returns, the active return of portfolio p over the benchmark portfolio return rb , denoted by rp−b , is: rp−b = rp − rb

=

Ns 

wsp rs −

s =1

Ns 

wsb rs

s =1

  Ns Nc   = (wsp − wsb ) βsc Cc + ϵs s =1 Nc

c =1





Ns

  = (wsp − wsb )βsc Cc c =1

s =1

+

Ns 

(wsp − wsb )ϵs

s=1

  Nc Ns Ns    = (wsp − wsb )βsc Cc + (wsp − wsb )ϵs . c =1

s =1

s=1

Then, the variance of rp−b is: Var(rp−b ) = σp2−b = E[(rp − rb − E[rp − rb ])2 ]

 2 Nc Ns   = (wsp − wsb )βsc Var(Cc ) c =1

s=1 Ns

+

 (wsp − wsb )2 Var(ϵs ) s=1

 2 Nc Ns   = (wsp − wsb )βsc c =1

s=1

Ns  + (wsp − wsb )2 Var(ϵs ) s=1

≡ σβ,p−b + σϵ,2 p−b . 2

It is clear from the above expression that Var(rp−b ) is identical to the squared value of the tracking error TEp,b between portfolios p and b. Namely, TEp,b =



Var(rp−b ) = σp−b .

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Table 1 Factor attribution of the MV-optimal USER portfolio (λ = 200, total turnover = 8%, systematic tracking error = 8%). Return

Risk

IR

t-stat

Portfolio Benchmark Active

10.43% 2.78% 7.65%

21.07% 22.11% 7.13%

0.91

3.27

Factor

1.43%

5.30%

0.20

0.72

1.17% 0.43% −0.26% 0.15% 0.00% −0.07%

4.90% 0.74% 2.52% 0.54% 0.00% 0.32%

0.19 0.59 −0.08 0.31 0.00 −0.20

0.67 2.11 −0.27 1.10 0.00 −0.72

6.22%

4.76%

1.07

3.82

Style Country Industry Currency Local Market Specific

Another insight is that the tracking error consists of two parts: the systematic tracking error σβ,p−b , contributed by the volatility of the fundamental risk factors, and the idiosyncratic tracking error σϵ,p−b , contributed by the volatility of the idiosyncratic factors that are orthogonal to all risk factors. 4.2. Factor attribution of the optimal USER and GLER portfolios In using the APT solver to obtain the MV optimal portfolios for both datasets of USER and GLER, we set the CTEF to be the tilt variable, and set the risk tolerance level to be λ = 200, the monthly turn-over rate to be no more than 8%, and the systematic tracking error to be no more than 8%. Based on the US equity universe contained in the USER dataset, Table 1 summarizes the factor attribution for the optimal USER portfolio, where the information ratio (IR) is defined as the ratio of the excess return on the portfolio to the volatility of the excess return, and the t-statistic (t-stat) is defined as the ratio of the bias of the estimated parameter from its notional value to its standard deviation. It also illustrates the return decomposition of this portfolio. The breakdown of the contributions to the achieved active return of the USER portfolio by various style factors is shown in Table 2. Tables 1 and 2 present several useful empirical observations. The MV-optimal USER portfolio with CTEF as the tilt variable produces an annualized return of 10.43%, whereas the Russell 3000 growth benchmark return is only 2.78% over the period 1997–2009. This corresponds to an active return of 7.65%. The information ratio of the active return is 0.91 and the corresponding t-statistic is 3.27, which indicates the statistical significance of the results. Moreover, the active return is decomposed into stock specific returns of 6.22% (with a t-statistic of 3.82) and a factor-return of 1.43% (with a t-statistic of 0.72), where the factor-return is not statistically significant. In terms of the breakdown of the active return to the style factors, the medium-term momentum has a positive exposure (0.2893) and produces a return of 2.05%, which is highly statistically significant (t-statistic = 4.02); the value factor offers an exposure of 0.4538 and a factor return of 2.29%, which is statistically significant with a t-statistic of 7.10; the exposure to the growth factor is 0.0972, with the corresponding factor-return being 0.35% (also statistically

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Table 2 Active-return breakdown by style factors for the MV-optimal USER portfolio (λ = 200, total turnover = 8%, systematic tracking error = 8%). Style

Contribution

Avg exposure

HR

IR

t-stat

Medium-term momentum Value Size Growth Short-term momentum Liquidity Exchange rate sensitivity Leverage Volatility

2.05% 2.29% −1.78% 0.35% −1.02% 0.24% 0.00% 0.04% −0.99%

0.2893 0.4538 −0.7378 0.0972 0.0490 0.0921 0.0177 0.0153 0.1585

66.23% 71.43% 50.00% 62.34% 35.71% 53.25% 47.40% 48.70% 40.26%

1.12% 1.98% −0.31% 1.15% −0.62% 0.51% −0.02% 0.19% −0.72%

4.02 7.10 −1.11 4.10 −2.23 1.82 −0.05 0.69 −2.59

Table 3 Factor attribution of the MV-optimal GLER portfolio (λ = 200, total turnover = 8%, systematic tracking error = 8%). Return Portfolio Benchmark Active Factor Style Country Industry Currency Local Market Specific

6.84% 0.43%

Risk

IR

t-stat

16.84% 20.80%

6.41%

8.23%

0.81

2.78

0.90% 1.27% −0.29% −0.23% 0.04% 0.24% −0.13%

7.36% 4.09% 4.41% 2.06% 2.84% 0.55% 0.59%

0.11 0.24 −0.06 −0.09 0.01 0.36 −0.21

0.38 0.84 −0.21 −0.30 0.05 1.25 −0.72

5.51%

3.68%

1.18

4.06

significant, with a t-statistic of 4.10). Note that the average weighted exposure to the size factor is negative, which indicates that the USER portfolio favors the small-cap equities. For the global equity universe contained in the GLER dataset, Table 3 summarizes the factor attribution for the MV-optimal GLER portfolio, and illustrates the return decomposition of the portfolio. The break-down of the contribution by the style factors to the active return of the GLER portfolio is shown in Table 4. Empirical results which are similar to those obtained in the USER portfolio are presented in Tables 3 and 4. The active return on the MV-optimal GLER portfolio is 6.41% per annum. The information ratio of the active return is 0.81, and the corresponding t-statistic is 2.78, which indicates the statistical significance of the results. The contributions of the medium-term momentum, value and liquidity to the active return are all statistically significant, at the respective levels of 4.72%, 6.30%, and −3.76%. The average weighted exposure to the size factor

is negative, which indicates that the GLER portfolio favors the small-cap equities as well. The above analysis illustrates that the majority of the active return on both the optimal USER portfolio and the optimal GLER portfolio, all constructed based on the CTEF variable, comes from the stock-specific return instead of the factor returns. In other words, the active return is generated mainly by using CTEF as the stock-selection criterion, instead of by the common beta-factors such as style, country, industry, currency, local and market. While the overall exposure of the CTEF-based portfolio to the whole factor set is not statistically significant, the factor-specific exposures of the portfolio to the ‘‘medium-term momentum’’ and ‘‘value’’ factors are statistically significant in both the USER and the GLER portfolios. The exposure to the growth factor is significant for the USER portfolio, and the exposure to the volatility factor is significant for the GLER portfolio. Fig. 1 plots the cumulative active return, the factorreturn, and the stock-specific return of the MV-optimal GLER portfolio over the simulation time horizon. 5. Conclusion We analyze the performances of optimal global portfolios constructed from the consensus temporary earnings forecast variable. Under the Markowitz mean–variance framework, applied optimization techniques are employed to obtain the optimal portfolios which satisfy practical requirements on risk-tolerance, the turnover rate, and the tracking error. Our empirical analysis demonstrates the effectiveness of the consensus temporary earnings forecast variable in selecting stocks for constructing mean– variance optimal portfolios with significant active returns. In particular, the CTEF variable with a simple forecast based

Table 4 Active-return break-down by style factors for the MV-optimal GLER model (λ = 200, total turnover = 8%, systematic tracking error = 8%). Style

Contribution

Avg exposure

HR

IR

t-stat

Medium-term momentum Value Size Growth Short-term momentum Liquidity Exchange rate sensitivity Leverage Volatility

1.60% 1.36% −1.51% 0.04% −0.56% −1.02% −0.08% 0.06% 1.39%

0.2137 0.2793 −0.4632 0.0313 0.0291 −0.2871 0.0361 0.0311 −0.0149

65.49% 71.13% 47.89% 52.11% 48.59% 37.32% 47.18% 52.11% 49.30%

1.37% 1.83% −0.37% 0.37% −0.40% −1.09% −0.36% 0.21% 0.70%

4.72 6.30 −1.27 1.27 −1.38 −3.76 −1.23 0.73 2.40

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Fig. 1. Cumulative active return and the returns on the decomposed components of the MV-optimal GLER portfolio.

on historical data is capable of generating portfolios with active returns that are comparable to those generated by sophisticated multi-factor return forecast models. Regardless of the risk-reward trade-off measure used for obtaining the optimal portfolio, the approach of modeling the joint distribution of the returns of a universe of stocks directly, then solving for the corresponding optimal portfolio weights, is not only difficult to implement when the number of assets is large, but also susceptible to noisy data, yielding notoriously unstable results. Recent research has begun to investigate the important role of stocks’ characteristics in the selection of a portfolio. Brandt, Santa-Clara, and Valkanov (2009) propose an approach that models the portfolio weight in each asset directly as one single function of the asset’s characteristics, in order to obtain the optimal portfolio for a large number of assets. Their approach is computationally straightforward and readily extendable. It produces sensible portfolio weights, and offers a robust performance both in- and out-of-sample. Hjalmarsson and Manchev (2012) study empirical mean–variance optimization when the portfolio weights are assumed to have a certain functional relationship with the underlying stock characteristics such as value and momentum, and find that the direct approach for estimating portfolio weights clearly beats a naïve regression-based approach that models the conditional mean. By demonstrating the effectiveness of using the CTEF variable alone to construct efficient portfolios which can generate active returns, we make the investigation of the functional dependency between the optimal portfolio weights and the CTEF variable a promising direction to pursue for future research. References Abarbanell, J. S. (1991). Do analysts earnings forecasts incorporate information in prior stock price changes? Journal of Accounting and Economics, 14(2), 147–165. Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9(1), 3–18.

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