equity trading the trouble with value

Electronic copy available at: http://ssrn.com/abstract=2700691

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Equity Trading: the Trouble with Value

Jamil Baz and Nicolas Le Roux

Abstract

Recently, liquidity-driven economic policies have mounted a challenge to time-series valueinvesting. In this paper, we examine the risk-return performance of simple value indicators.Wefind that: 1) even though long term equity returns are partially predictable, directional valueinvesting delivers mediocre results; 2) the Central Bank put is a fly in the ointment for valueinvestors; 3) relative value has broadly outperformed absolute value. Lastly, we conjecturethat the poor performance of directional value investing hides substantial overvaluations in U.S.equities.

December 7, 2015

Electronic copy available at: http://ssrn.com/abstract=2700691

2

Introduction

Graham and Dodd established the foundations for value investing in the 1930s. Value becamesubsequently the favorite investment style for the patient investor. Recently, liquidity-driven macroeconomic policies have mounted a challenge to directional value investing. In this paper, we examinethe risk-return performance of simple value indicators. We construct both directional and relativevalue portfolios and proceed to list seven stylized facts about value investing.

Stylized Fact Number 1: Long Term Equity Returns Are

Partially Predictable

We test the predictive value of our signals: the cyclically-adjusted price to earning ratio(CAPE), the current price to earning ratio (PE), the dividend yield and the replacement valueto market value ratio also known as Tobins Q. On a priori ground, all these indicators should mat-ter: indeed, the inverse of the price to earning ratio, under some assumptions, is equal the real equityyield (see appendix for a proof). All else being equal, an increase in the real yield of an asset shouldcause excess demand for that asset and therefore higher expected asset returns. Similarly, the divi-dend yield is a reasonable approximation for the equity risk premium. A high dividend yield beingan indication of equity cheapness versus bonds, will also result in higher expected equity returns.Lastly, the rationale for using Tobins Q as a value indicator is well known: as the market value ofa publicly-traded business drops below its replacement value, it pays to buy the stock rather thanbuilding the equivalent business.

It is therefore comforting that some level of predictability of equity returns is borne out by thedata. In Figure 1, the regression of S&P 10-year returns between time t and time t + 10 against theCAPE at time t shows that a high (low) CAPE predicts a low (high) equity return.

Figure 1. Regression CAPE vs. S&P Annualized 10-Year Returns

3From Table 1, it can be seen that the R-square increases with the holding period: for the CAPE,it is of order 4% for one year horizon and 34% for ten year horizon. Similarly, the PE, the dividendyield and the Tobins Q predict equity returns with the R-square increasing with the holding periodin all cases.1

Table 1: OLS Estimates, Monthly Data

Panel A: OLS EstimatesP/E DivY CAPE Tobins Q

1yr Beta (0.22%) 2.24% (0.63%) (14.21%)Cst 0.13 0.00 0.19 0.20R Square 1.20% 3.24% 4.44% 5.67%



History from Jan 1901 Jan 1901 Jan 1901 Jan 1952

Stylized Fact Number 2: Regression Signals are not trad-

able

We now try our hand at trading the signals from the above regressions. To this end, we useresults from regressions with one year, five year and ten year returns over an expanding window. Webuy equity if equity returns implied by the regression are positive and sell equity otherwise. We scalethe size of the trading positions to the expected Sharpe ratio of the trade and rebalance monthly.2

In Table 2 Panel A, we show the empirical Sharpe ratios associated with the trading of ourfour signals: the Sharpe ratios are all positive and comparable to the Sharpe ratio of a naive S&P500 long only strategy. Interestingly, the skew of the trading strategies particularly for five yearand ten year regressions is improved compared to the long only trading rule (panel B).

1But things are not that simple. The topic of equity return predictability has led to a long controversy. Boudoukh,Richardson and Whitelaw (2006) show that when regressors such as the dividend yields are persistent, the estimatorsare very highly correlated under the null hypothesis of no predictability. Under this same hypothesis, the betas andR-squares are almost proportional to the horizon - which is exactly what transpires from Table 1. According to thispaper, at best, the use of multiple horizon regressions may be redundant; at worst, long horizon predictability is justnot there. Subsequently, Cochrane (2007) offers a defense of both short-term and long-term return predictability byshowing that dividend growth is not predictable. Ang and Bekaert (2007) find that returns are predicted by dividendyields over shorter horizons but not over longer horizons.

2The expected Sharpe ratio is calculated as the return predicted by the regression divided by the volatility of S&P500 monthly returns over the most recent 12-month window

4Table 2: Empirical Results for Regression Based Trading

Panel A: Sharpe RatiosP/E DivY CAPE Tobins Q Avg

Regression 1yr 0.44 0.33 0.33 0.18 0.32

Regression 5y 0.60 0.52 0.49 0.36 0.50

Regression 10yr 0.67 0.63 0.62 0.37 0.57S&P long Only 0.50 0.50 0.50 0.70

Panel B: SkewsP/E DivY CAPE Tobins Q Avg

Regression 1yr -1.94 -0.56 -0.81 0.31 -0.75

Regression 5y -0.28 0.29 0.56 0.77 0.34

Regression 10yr -0.90 -0.39 0.17 0.20 -0.23S&P long Only -0.95 -0.95 -0.95 -0.78

While these results are interesting, major difficulties appear upon further inspection of thedata: first, if one uses, as we do, an expanding window to estimate the regression parameters, theparameter estimates tend to move less and less as we add data points. The trading strategy becomesstale to a certain extent: for example, using the signal from the ten year return regression againstthe dividend yield, the strategy has been invariably long S&P 500 since 1962. Indeed, looking at theregression equation in Figure 2, it would take a dividend yield of -1.97% to predict negative returnsover the next ten years. This simply means that estimates from a simple regression should not betaken too seriously if only because when an index like the S&P 500 has a good run (as has largelybeen the case since 1901), the regression simply extrapolates past good noise into the future. Inother words, the regression with many data points puts the trading strategy on automatic pilot.

Figure 2. Regression DivY vs. S&P 10-Years Returns

In an attempt to resolve this problem, we replace the expanding window with a twenty yearmoving window. Here again, Sharpe ratios are comparable to a long-only strategy with no appreciablereduction in skewness. This spells the need for a new trading rule.

5Table 3: Empirical Results for Regression Based Trading (using a twenty year moving window)


Regression 1yr 0.52 0.55 0.53 -0.13 0.36

Regression 5y 0.54 0.59 0.56 0.17 0.47

Regression 10yr 0.59 0.62 0.58 0.36 0.54S&P long Only 0.53 0.53 0.53 0.63


Regression 1yr -1.94 -0.56 -0.81 0.31 -0.75

Regression 5y -0.28 0.29 0.56 0.77 0.34

Regression 10yr -0.90 -0.39 0.17 0.20 -0.23S&P long Only -0.95 -0.95 -0.95 -0.78

Stylized Fact Number 3: Rule-Based Trading Does not

Perform

To avoid the stale trading positions inherent to regression, we test a trading strategy basedon the z-score of the signals. We calculate the z-scores of the PE, the CAPE, the dividend yieldand the Tobins Q at each point of time by comparing the present signal value to the average valuefrom an expanding window, then normalized by the volatility of the signal. When the z-score thusobtained is greater than one in absolute value, we trade the signal; otherwise, we do not and keepa cash position. We test two strategies one binary where we either buy or sell one unit and onelinear where the trading size is proportional to the z-score. Note that, as in the regression case, thestrategy trades the mean reversion of the signals.

The results, summarized in Table 4, are quite disappointing as the strategy Sharpe ratio is notsignificantly different from zero across all signals. Furthermore, it underperforms a long-only naivestrategy. We will revisit these results below (stylized fact 6).

Table 4: Empirical Results (Z-Score Strategy)


Z-Score (Binary, 1StDev) 0.35 -0.12 0.10 -0.53 -0.05

Z-Score (Linear, 1StDev) 0.15 -0.03 -0.01 -0.67 -0.14S&P long Only 0.50 0.50 0.50 0.70


Z-Score (Binary, 1StDev) 0.92 0.07 0.42 0.37 0.45

Z-Score (Linear, 1StDev) -3.76 1.16 -0.83 -0.78 -1.05S&P long Only -0.95 -0.95 -0.95 -0.78

6Stylized Fact Number 4: Results are Similar in the US,

Europe and Japan

To make sure that our results are not U.S. specific, we compare results from regression-basedand ruled-based trading across a number of national stock indices: in the U.S., Japan, the UK,Germany and France.

From Table 5, it appears that the negative relationship between PEs and subsequent returnsis broadly negative with a couple of minor exceptions. UK regressions fits surprisingly well, both interms of regression coefficients and R-squares.

Table 5: OLS Estimates for P/Es of Several Countries Equity Indices

Panel A: OLS EstimatesU.S. Japan UK Germany France

1yr Beta (0.22%) (0.02%) (1.26%) (0.14%) (0.04%)Cst 0.13 0.10 0.30 0.12 0.09R Square 1.20% 3.41% 15.38% 0.33% 0.03%

5yr Beta (0.49%) (0.07%) (5.16%) 0.04% 0.64%Cst 0.53 0.41 1.32 0.49 0.22R Square 1.46% 5.04% 43.50% 0.01% 2.43%

10yr Beta (4.21%) (0.16%) (9.82%) (1.84%) (1.56%)Cst 1.53 0.82 2.56 1.36 1.10R Square 25.60% 12.51% 86.99% 14.64% 11.61%

History from Jan 1901 Jan 1956 Jan 1979 Jan 1969 Jul 1987

Sharpe ratios in Table 6 show insignificant to negative gains from trading the z-score whereasregression-based (expanding window) trading broadly underperforms long-only trading, except in theU.S.

Table 6: Empirical Results using P/E Indicator

Panel A: Sharpe ratiosU.S. Japan UK Germany France Avg

Z-Score (Binary, 1StDev) 0.35 -0.37 -0.32 0.27 -0.34 -0.08

Z-Score (Linear, 1StDev) 0.15 -0.26 -0.24 0.16 -0.12 -0.06

Regression 1yr 0.44 -0.06 0.56 0.42 0.13 0.30

Regression 5yr 0.60 0.21 0.43 0.26 0.11 0.32

Regression 10yr 0.67 0.28 0.68 0.44 0.50 0.51

Indices long Only 0.50 0.43 0.69 0.52 0.43

Panel B: SkewsU.S. Japan UK Germany France Avg

Z-Score (Binary, 1StDev) 0.92 -0.86 -0.74 1.07 -1.47 -0.22

Z-Score (Linear, 1StDev) -3.76 -0.70 -0.89 0.91 -1.10 -1.11

Regression 1yr -1.94 -3.71 -0.42 0.49 -0.24 -1.16

Regression 5yr -0.28 2.66 -0.84 -0.75 -0.44 0.07

Regression 10yr -0.90 2.64 0.03 0.11 0.09 0.40

Indices long Only -0.95 -0.26 -0.93 -0.85 -0.67

7Actually, all indicator (PE, dividend yield and CAPE) results are mediocre and underperformthe long-only strategy (see appendix).

How do our results agree with the widespread belief that equity value trading has been asuccessful proposition? Our results are derived in a stock index, macro directional framework: indeed,the results from a value trading strategy will be different in a single stock, relative value framework.We will explore a relative value (cross-sectional) strategy later in this paper.

Stylized Fact Number 5: The Fed Put is the Fly in the

Ointment

So far, we have mostly reported (mediocre) results from trading value, but have not speculatedabout the reasons for failure of value as an investment signal. Clearly, the prime candidate expla-nation is the relentless upward trend of stock prices throughout the data sample. But this trend ishardly surprising: by looking at the US, we are looking at an order statistic. The US, after all, isthe best student in the class and this may be why all analysts keep studying the same data sample.Indeed, if the stock market keeps rallying aggressively, even after indicators show it is fully valued,then value trading will fail by construction.

Exactly when and why did US stocks continue performing despite value predictors pointingotherwise? One can conjecture that this era of quasi-permanent expensiveness3 kicked off after theGreenspan Fed nomination in 1987. One can also surmise that around that time, wealth-effectbecame, although never officially, a prime target of Fed policy.

To check whether this was the case, we simply test our ruled-based trading strategies4 forthe periods before and after August 1987. The results are telling, to say the least: the strategyresults worsen for every single indicator after 1987 compared to the pre-Greenspan era. The averagedifference in Sharpe ratios is a full 0.75. Surely, there are other explanations too. Two possibleexplanations could be: 1) people figured out value trading was correct after a couple of decades ofBuffetts successful investing, and as more people traded value, the premium compressed and 2) riskhas decreased.

3See stylized fact number 64We do not compare the subsamples for regression-based trading: as mentioned, regressions yield overwhelming

long positions

8Table 7: Pre and post Greenspan Comparison

Panel A: Sharpe ratios before 1986P/E DivY CAPE Tobins Q Avg

Z-Score (Binary, 1StDev) 0.59 0.11 0.39 -0.27 0.20

Z-Score (Linear, 1StDev 0.54 0.15 0.31 -0.43 0.14

S&P long Only 0.46 0.46 0.46 0.75

Panel B: Sharpe ratios after 1986P/E DivY CAPE Tobins Q Avg

Z-Score (Binary, 1StDev) -0.23 -0.53 -0.56 -1.06 -0.60

Z-Score (Linear, 1StDev -0.26 -0.47 -0.48 -1.04 -0.56

S&P long Only 0.65 0.65 0.65 0.65

Skew results are also worth reporting: not only does the skew of value strategies deteriorate inthe post-Greenspan era; the skew of the S&P returns deteriorates as well. To summarize, it wouldappear that Fed policy is the most potent enemy of the directional value investor.

Panel C: Skew ratios before 1986P/E DivY CAPE Tobins Q Avg

Z-Score (Binary, 1StDev) 1.53 -0.01 0.67 0.58 0.69

Z-Score (Linear, 1StDev 2.71 1.67 0.16 -0.02 1.13

S&P long Only -0.86 -0.86 -0.86 0.27

Panel D: Skew ratios after 1986P/E DivY CAPE Tobins Q Avg

Z-Score (Binary, 1StDev) 0.65 0.58 -0.02 -1.25 -0.01

Z-Score (Linear, 1StDev -2.71 0.23 -1.11 -1.69 -1.32

S&P long Only -1.59 -1.59 -1.59 -1.59

Stylized Fact Number 6: The Failure in the Value Factor

is Hiding Substantial Overvaluation

In light of the above, one may reasonably wonder whether central banks are not permanently devoted tostimulating wealth; in other words, it may be that directional value investing is permanently doomed to failure.

Not quite so, we believe. It is likely that the failure of directional value over the last three decades is hidinga structural overvaluation. Witness to that four standard value indicators: dividend yield, CAPE, Tobins Q andmarket cap to GDP . We show below the time-series for each indicator including the last point and the average. Wealso compute the indicators half-life, meaning the expected time it takes to travel half the distance to the average.

The results of the exercise are very clear: the US stock market appears to be overvalued by 57% to 102%depending on the value indicator under consideration.

9Figure 3. Dividend Yield Time-Series

Figure 4. CAPE Time-Series

Figure 5. Tobins Q Time-Series

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Figure 6. Market Cap to GDP Time-Series

Table 8: Fair Values

Panel A: Fair ValuesCurrent Average % Overvalued Half-Life

DivY 2.0% 4.1% 102.0% 3.9

CAPE 27.5 16.0 71.3% 7.5

Tobins Q 1.1 0.7 57.1% 6.2

Market Cap / GDP 1.27 0.70 81.4% 5.7

Here, two remarks are in order: first, it is never comforting statistically to just rely on a limited data sample tomake sweeping inferences about value in the stock market. After all, it is well-known that the equity return estimateis aicted with a high standard error equal to

Twhere is the market volatility and T the length of the sample. If

is 20% and T is 115 years, then the actual excess return could be 3.7% higher or lower than the point estimate fromthe sample with a 95% probability confidence interval. Viewed from this perspective, a 115 year sample is too small;second it can always be claimed that a historically stock market value is associated with lower risk.

While these two objections are perfectly valid, recall that we are dealing with the U.S. data sample: the U.S.is an order statistic compared to other countries. If the current price is too high compared to the average historicalprice and if that average historical price has beaten all average historical prices from other national samples, then thepresumption of expensiveness is even higher. And while it may be true that risk is lower today, the current contextmacro-economic context where asset prices are subsidized by unsustainably stimulative policies and very high leverageseems to dispel the notion of lower risk.

Also, we made implicitly the usual all else equal assumption (where all else was dividends, earnings movingaverage, replacement costs and GDP) to infer the extent of the overvaluation. Things can get worse however. Whatif all else is not equal? To take an example, the CAPE, as seen before, is 71% above average at unchanged earnings;reversion to the mean would imply a fall of about 42% in the index value. But this assumes that earnings did notadjust. If, as shown in the below graph, the earnings to GDP ratio reverses back to average, earnings should fall by36% at constant GDP. Under these conditions, for the long term CAPE to adjust with both the numerator and thedenominator converging to the mean, stock prices should hence fall by 1 58% 64% = 63%.

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Figure 7. Profit after Tax to GDP Time-Series

Stylized Fact Number 7: Relative Value Outperforms

Directional Value Trading

We now try our hand at one last trading simulation. If directional value investing does not work, what aboutrelative value investing?

To answer this question, we go long the three most valuable indices and short the three least valuable indices ina universe of 25 national stock indices. The data sample starts in 1990. We rebalance on a daily basis. We then formthree portfolios ranked according to three indicators: price to book, dividend yield and price to earnings ratio. Weshow in figure 23 the results of the simulation. The Sharpe ratio of the total portfolio is 0.54; interestingly, the skew ispositive and the beta of the strategy is negative. As a result, combining an S&P long position with the relative valueportfolio doubles the Sharpe ratio from 0.39 to 0.78 while taking the skew from negative to positive territory.

Of course, such a strategy will not stand on its own and should be part of a wider array of investments styleswithin a broad portfolio. Relative value trading appears however to have desirable risk-return characteristics. Baz etal. (2015) compare in more detail directional and cross section performances across asset classes.

Table 9: Relative Value Trading Results

Panel A: Signals AlonePB DivY P/E CAPE All S&P

Correl w. S&P (33.2%) (10.5%) 7.3% 0.6% (24.6%) 100.0%

Sharpe 0.37 0.47 0.02 0.09 0.54 0.39

Skew (Daily) 0.40 0.47 0.87 0.76 1.26 -0.24

Skew (50bds) 1.44 0.88 0.26 1.80 1.63 -0.84

Panel B: CombinationPB + S%P DivY + S%P P/E + S%P CAPE + S%P All + S%P

Avg 6.2% 6.5% 2.6% 4.1% 7.2%

StDev 8.8% 10.1% 11.1% 10.6% 9.2%

Sharpe 0.71 0.65 0.24 0.39 0.78

Skew (Daily) 0.21 0.03 0.44 0.18 0.46

Skew (50bds) 0.94 0.27 -0.64 0.43 0.56

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Conclusions

This paper finds that, even though long term equity returns are partially predictable, directional value investingremains challenging. We show that the Central Bank put is a fly in the ointment for value investors. We alsofind that relative value has broadly outperformed absolute value. Lastly, we conjecture that the poor performance ofdirectional value investing hides substantial overvaluations in U.S. equities.

References

1. Ang, A., and Bekaert, G. (2007). Stock Return Predictability: Is it There? Review of Financial Studies,651-707

2. Baz, J., Granger, N., Harvey, C.R., Le Roux, N., and Rattray, S. (2015). Dissecting Investment Strategies inthe Cross Section and Time Series http://ssrn.com/abstract=2695101

3. Cochrane, J.H. (2008). The Dog That Did Not Bark: A Defense of Return Predictability. Review of FinancialStudies , 1533-1575

4. Boudoukh, J., Richardson, M., and Whitelaw, R.F. (2008). The Myth of Long-Horizon Predictability. Reviewof Financial Studies , 1576-1605

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Appendix

.1 Why the Real Equity Yield is equal to the Earnings Yields

A stock price P is the value of a dividend stream, with initial dividend D growing at a real rate g and discountedat a real equity yield r.

P =

0

Degtertdt =D

r g (1)

It follows that r is:

r =D

P+ g (2)

With R designating the real bond yield, the equity risk premium is:

ERP = r R = DP

+ g R (3)

g, the real dividend growth, is equal to:g = bi (4)

where i is the real internal rate of return and b is the dividend retention rate (b = 1 DE , where E is earnings). Firmswill keep investing until the real internal rate of return matches the real equity yield, hence i = r. We thus have :

P =D

r br =D

r(1 b) =E

r(5)

Therefore:E

P= r (6)

.2 Regression and Back-Testing Results

Figure 8. Regression Table (DivY)

.2 Regression and Back-Testing Results 14

Figure 9. Sharpe Ratios (DivY)

Figure 10. Skew (DivY)

Figure 11. Regression Table (CAPE)

Figure 12. Sharpe Ratios (CAPE)

.2 Regression and Back-Testing Results 15

Figure 13. Skew (CAPE)

IntroductionStylized Fact Number 1: Long Term Equity Returns Are Partially PredictableStylized Fact Number 2: Regression Signals are not tradableStylized Fact Number 3: Rule-Based Trading Does not PerformStylized Fact Number 4: Results are Similar in the US, Europe and JapanStylized Fact Number 5: The Fed Put is the Fly in the OintmentStylized Fact Number 6: The Failure in the Value Factor is Hiding Substantial OvervaluationStylized Fact Number 7: Relative Value Outperforms Directional Value TradingConclusionsReferencesAppendixWhy the Real Equity Yield is equal to the Earnings YieldsRegression and Back-Testing Results

equity trading the trouble with value

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