Value investing is a strategy of buying stocks with low price-to-fundamentals ratios and selling stocks with high ones. It has been shown that value investing is one of the few investment strategies to generate a premium in most markets and periods. Value stocks generally move in concert. This co-movement, the foundation of traditional style-based investing, limits the efficiency of the average value strategy. Die-hard proponents of the Efficient Market Hypothesis (EMH) would argue that this is an inescapable destiny; if you want to be compensated with higher return, you must take on value risk. We hold, on the contrary, that value investors are not destined to accept this risk. An implementation that is sensitive to value risk can significantly decrease the strategy’s relative exposure.

Two Nobel Theories

The 2013 list of Nobel prizewinners in economics and finance was a balanced ticket. Two of the new Laureates, Eugene Fama and Robert Shiller, have made praiseworthy contributions to our understanding of markets and prices, yet they represent very different views on unresolved issues in finance.

Eugene Fama starts from the position that markets are very efficient. If value stocks generate a premium, then in some way they must be riskier. He observes that value stocks tend to co-move with each other and reasons that the correlation of value portfolio holdings must be the locus of the risk for which market participants are compensated. The exact source of value risk has not been identified, but advocates of the EMH have variously argued that it may be related to distress, illiquidity, or some rare and elusive events.

Robert Shiller speaks for the behavioral camp, whose adherents would argue that investors subscribing to the value strategy buy cheap stocks and sell expensive ones. How do stocks become cheap or expensive? Market participants are susceptible to cognitive errors and other behavioral biases. Familiar examples include overconfidence, mental accounting, availability cascades, loss aversion, overreacting to news, and herding. It is not inconceivable that investors, behaving irrationally, can misprice some stocks or even be wrong about entire market segments.

In the presence of so many and such pervasive behavioral quirks, the question is not “how efficient are financial markets?” but “how can we trust prices to be efficient at all?” The short answer is that prices are largely efficient because arbitrageurs energetically exploit mispricing. Arbitrageurs can finance their trades against mispricing by borrowing and using investors’ capital. Nonetheless, risk arbitrage positions can remain open for a while; if borrowing is limited and investors focus on short-term performance, arbitrageurs can be fired before the mispricing is corrected.

The efficient markets and behavioral perspectives offer different interpretations of the pricing mechanism. But their explanations of value investing are similar:

  • stocks with low price-to-fundamentals ratios (value stocks) outperform stocks with high-price-to fundamentals ratios; and

  • value stocks tend to co-move with each other.

What Value Risk Is Not

Given that the predictions based upon risk and mispricing are quite tangled, it is useful to say what value risk is not. As mentioned above, EMH proponents initially suspected that the value premium might be the reward for assuming default risk. However, this proposition has been disproven. Dichev (1998) was the first to show that default risk does not generate a premium. More recently, research conducted by Piotroski and So (2012) has demonstrated that value stocks with low probability of default are responsible for the majority of the value premium.

Illiquidity was the second early suspect for the source of value risk, and in time Pástor and Stambaugh (2003) demonstrated that illiquidity does indeed earn a premium. Illiquidity risk, however, does not explain the value effect. Even after controlling for all illiquidity risk, enough excess return is left over to account for the value premium.

With no obvious culprits like distress or illiquidity remaining under suspicion, advocates of the risk explanation suggest that the value premium must be due to hard-to-measure systemic risk or the remote likelihood of a catastrophic event—the low frequency, high impact (LFHI) kind of event that risk managers find so challenging to model.

The Skein of Risk and Cheapness

The risk and mispricing theories are unhelpfully intertwined. Daniel and Titman (1997) suggested a way to disentangle them. Consider two examples.

Example 1: Eugene’s Portfolio—Safe vs. Risky. Two companies, Risky Corp. and Safe Inc., have exactly the same book-to-market (B/M) ratios of 0.6. Risky Corp. co-moves strongly with other value companies; its value loading is 0.5. Safe Inc. co-moves with growth stocks; its value loading is negative 0.5. Eugene, an investor, decides to create a long–short portfolio containing the two stocks. He goes long Risky Corp. and short Safe Inc.

Example 2: Robert’s Portfolio—Safe vs. Cheap. Two similar companies, Cheap Corp. and Expensive Inc., both have a value loading of 0.1. However, they have markedly different B/M ratios. Cheap Corp. has a B/M ratio of 0.8; Expensive Inc., 0.4. Robert, another investor, decides to go long Cheap Corp. and short Expensive Inc.

What investment outcomes should Eugene and Robert expect? Logically, these two portfolios will have very different results, depending on which theory of value is correct.

According to the risk-based theory, value risk is compensated with higher expected return. If variations in the B/M ratio do not reflect the riskiness of the portfolio, they will have no performance effect. Eugene’s strategy of buying risky securities and selling safe ones will induce a lot of value risk loading in the portfolio. Robert’s portfolio has offsetting positions in stocks with exactly the same value risk loading. If the risk theory is true, Eugene’s expected return is high, while Robert’s is zero. The performance of both portfolios is completely explained by the traditional risk factors (market, value, size, and momentum), leaving no room for risk-adjusted alpha.

According to the mispricing theory, risk loadings are irrelevant for return predictions. Rather, it is variations in B/M ratios, reflecting the relative cheapness of stocks, that help predict returns. Accordingly, Eugene’s strategy of buying risky but similarly priced securities would not translate into higher return. Robert’s approach of buying cheap and selling expensive securities would generate a premium. Moreover, adjusting for risk factors would yield quite surprising results: Eugene’s portfolio will generate negative alpha because it has a high loading on the value risk factor, which is unrewarded with high returns. Robert’s portfolio will generate positive alpha because it has a high return and no loading on value risk.

Extending the Analysis to Global Results

A study by Chaves, Hsu, Kalesnik, and Shim (2013) simulated the performance of Eugene and Robert’s strategies in 23 developed countries. For each country, the starting year was selected by identifying the longest time horizon that contained at least 25 stocks in all subsequent months.1Table 1 reports summary statistics.

Eugene’s expanded portfolio, which had a material value risk factor loading but was indifferent to B/M characteristics, generated a statistically insignificant return of only 79 bps per annum. After controlling for traditional factor exposures, Eugene’s portfolio generated negative and statistically significant alpha of –1.74%.

Robert’s strategy was appreciably more fruitful. His expanded portfolio yielded an annualized return of 7.61% with a t-statistic of 4.65. The strategy delivered positive value added in all 23 developed countries. After controlling for the four traditional factors, Robert’s portfolio had an alpha of 3.01% with a highly significant t-statistic of 4.02.

Value risk exposures are of little use in predicting returns. Book-to-market characteristics, on the other hand, are quite useful in return forecasting. These findings strongly suggest that mispricing is the dominant driver of the value premium.

A Low-Correlation Value Portfolio

Apart from intellectual curiosity, why should we care whether risk or mispricing drives the value premium? Because if (as is the case) mispricing and not risk is responsible for value returns, then we can construct more efficient and powerful strategies to extract the value premium.

Let us first draw an intuition from the fixed income world. Fixed income securities have predetermined payment structures. If we are planning to hold a default-free bond to maturity, then (given that we know the payment structure) the current market price is the only variable we need to calculate the bond’s yield over its entire remaining term. All the information the market may have used to value the bond, such as its estimated volatility and factor correlations—all this information is irrelevant once we know the price.

Similarly, Eugene and Robert’s portfolio results suggest that a company’s price-to-fundamentals ratios contain all the information we need. We know that value stocks tend to co-move with each other (as, of course, do growth stocks). Identifying stocks with cheap valuations which are not marching to the same drummer as other value stocks can diversify an otherwise unexceptional value strategy.

Figure 1 illustrates this concept by representing the two dimensions of interest: the B/M ratio on the vertical axis and value loading on the horizontal axis. Each dot represents a fictitious company. In this mockup, there is a dense cloud going from the lower left corner to upper right. Cheap value companies tend to have higher value loadings, and more expensive growth companies tend to have negative loadings on the value factor.

On the chart we also marked two separate groups of stocks with distinctive colors and symbols. The companies represented by orange triangles have high B/M ratios and tend to co-move more strongly with growth companies (negative value loading). The companies indicated by blue squares are generally expensive growth companies which tend to co-move with value companies.

The stocks in Figure 1 are made-up. However, Dell at some point in time might be taken as an example of an orange-triangle company. Despite Dell’s strong fundamentals, the market was not very optimistic about its prospects. So, on several fundamentals-to-price ratios, Dell was a value company. Nonetheless, as a technology company, Dell tends to co-move strongly with other tech companies, and they generally have low B/M ratios.

In the same way, Berkshire Hathaway might exemplify a blue-square company. The general public believes that CEO Warren Buffett has the Midas touch, and at some point in time Berkshire Hathaway was priced as an expensive company. All the same, it is still a financial company. If most other financial companies were priced cheaply, Berkshire Hathaway would be strongly co-moving with value companies.

Consider a portfolio which buys cheap stocks that tend to co-move with growth stocks (orange-triangle companies) and sells expensive companies which tend to co-move with value stocks (blue-square companies). We call this a low-correlation value portfolio.

Table 2 displays the four-factor alpha of this strategy simulated in 23 developed markets. The average alpha of the low-correlation strategy is 7.52% per annum. The alpha is positive in 20 out of 23 developed markets and statistically significant in 7 out of 23 countries. In the United States, where we had by far the longest back-test period (1927–2011), the alpha is 5.43%, and it is highly statistically significant.


Empirical evidence suggests that the value premium is driven by mispricing and that fundamentals-to-price ratios are good indicators of future outperformance. The more value stocks are correlated, the harder it is for risk arbitrageurs to squeeze out mispricing. But risk does not cause mispricing. An effective implementation of the value strategy can significantly mitigate the active risk. The low-correlation value strategy proposed here is one way to manage value risk and achieve superior risk–reward characteristics.


1. The average number of stocks for a particular country was 445, and the average starting year was 1983.


Chaves, Denis B., Jason Hsu, Vitali Kalesnik, and Yoseop Shim. 2013. “What Drives the Value Premium? Risk versus Mispricing: Evidence from International Markets.” Journal of Investment Management, vol. 11, no. 4 (Fourth Quarter):1–18.

Daniel, Kent, and Sheridan Titman. 1997. “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns.” Journal of Finance, vol. 52, no. 1 (March):1–33.

Dichev, Ilia D. 1998. “Is the Risk of Bankruptcy a Systematic Risk?” Journal of Finance, vol. 53, no. 3 (June):1131–1147.

Pástor, Ľuboš, and Robert F. Stambaugh. 2003. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy, vol. 111, no. 3 (June):642–685.

Piotroski, Joseph D., and Eric C. So. 2012. “Identifying Expectation Errors in Value/Glamour Strategies: A Fundamental Analysis Approach.” Review of Financial Studies, vol. 25, no. 9 (September):2841–2875.

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