5

The Blueprint to Long-Term Performance

PORTFOLIO MANAGEMENT IS INHERENTLY a question of asset pricing, the field of economics concerned with understanding how financial asset prices are determined by investors’ preference and the structure of financial markets. Understanding investors’ preferences is crucial to portfolio management: it explains how prices are formed in financial markets and which risk factors F are compensating investors with positive average returns. It also highlights investor biases and errors that lead to mispriced assets. Simply put, understanding investors’ preferences is paramount to portfolio management.

In chapter 4 we saw that as investors we need to understand the limitations of forecasting (especially at short horizons) and that successful forecasts of extreme events are often a one-time phenomenon. The poor track record of forecasters brought Howard Marks of Oaktree Capital to declare: “You can’t predict but you can prepare.”¹ What can be predicted to some extent are the characteristics of the probabilities of events.

A majority of investors prefer the most basic of these characteristics: higher average portfolio returns. To illustrate the source of average returns, our return equation from chapter 2 is once again helpful. From this equation, the return we can expect every period by investing in an asset is

E[R] = R_f + α + β_m × Ε[F_m] + β₂ × Ε[F₂] +…

where Ε represents the return R that is expected. The difference between Ε and the average return is a question of timing: Ε indicates what we expect the average return to be before it is realized, whereas the average return is the average of the realized returns after the fact. Clearly, when choosing a portfolio, we are forced to consider expected returns, not the yet-to-be-realized average returns or the historical returns. In this equation, we have the risk-free rate of return R_f, the mispricing α, the expected return of each factor Ε[F], which is called a risk premium, and the asset’s exposure to these factors β. The stock-specific shock ε is absent because it is purely an unpredictable (idiosyncratic) shock with an expected return of zero, and hence the average return unrelated to common risk factors is entirely captured by α. As a reminder, α can also be defined as the excess return attributed to a specific manager’s skills and/or to his luck or the result of the portfolio exposure to risk factors that have yet to be properly identified and documented. In the end, it captures the mispricing of an asset.

This is not the whole story; another characteristic of the probabilities of events shows up on our radar: the risk of our portfolio. Again using our return equation, we can use the variance of returns, given by

Var[R] = Var[β_m × F_m + β₂ × F₂ +…] + Var[ε],

to measure the risk of our investment. In a nutshell, the variance measures the variability of realized return around what is expected. Just as we did in chapter 4, we often use its close parent the volatility (or standard deviation), which is the square root of variance. We prefer assets with lower variance because we are more certain that realized returns will be close to what was expected. In this equation, the mispricing α is absent because it is a constant and has no risk (assuming you can identify its value). We use volatility as a risk measure for our portfolio, but keep in mind that most of the intuitive reasoning discussed shortly remains if we use a more sophisticated measure of risk.

These last two equations are key to understanding why there are three sources of sustainable long-term performance, whatever the asset class, and that they are all related to a form of diversification: diversification of unrewarded risks, diversification of priced sources of risk, and diversification of mispricing risk.

This chapter will show that these three forms of diversification can be used to explain the long-term average return of most factor-based products (now referred to in the industry as smart beta products) and fundamental management styles without assuming that portfolio managers have any forecasting skill. Although forecasting can be useful, we need not explicitly forecast expected returns to outperform. In this chapter we discuss each form of diversification in detail. The more financially knowledgeable readers will notice that we are not reinventing anything here, but merely presenting all sources of performance in a consistent framework. Most investors are familiar with these sources of performance, though they are usually presented in a less explicit fashion.

The field of asset pricing is often ignored when dealing with portfolio management techniques, but these last two equations show why it should not be. Before we explain why it matters so much, let’s consider how modern portfolio theory developed in the 1950s and 1960s. The cornerstone of modern portfolio theory comes from the work of Harry Markowitz, who showed how to optimally combine assets in a portfolio to maximize reward (expected returns) for a given level of risk (variance in this case). The efficient frontier, which presents a set of optimal risk/return portfolios, is derived from this exercise. This is now considered the most basic portfolio management technique.

Asset pricing models go a step further than Markowitz did, without which any portfolio management technique is a lot less useful. Asset pricers ask what happens in equilibrium if all investors choose their portfolios using such a technique. Equilibrium is defined as a situation in which prices are set in the market so that there is no surplus or shortage of assets in the market (i.e., the market clears). The outcome of these models is the structure of expected returns, that is, which risk factors F are compensated and which mispricings α may persist in equilibrium. The structure of expected returns provides a roadmap to the investor for the optimal composition of his portfolio. Note the vicious circle: an asset pricing model shows how assets are priced and what the composition of your portfolio should be, but these models are derived from assumptions about investors’ optimal portfolio allocation. Fortunately, we will not explore this issue further.

Hence we need some asset pricing models to understand what our return equation looks like in real life; this results in our optimal portfolio. The next section begins with a case that will lead to our first source of performance: diversification of unrewarded risk.

Diversification of Unrewarded Risk

Let’s consider a case in which all stocks have the same expected return Ε[R]. When we combine these stocks in a portfolio, we necessarily get a portfolio that has the same expected return as any of its underlying stocks. However, the risk in our portfolio is a lot lower than the average risk of these stocks. We get the same level of reward Ε[R] but lower risk Var[R] because the idiosyncratic terms are diversified away; positive and negative asset-specific return shocks average out. Figure 5.1 illustrates this. Each month, we form a portfolio by randomly selecting among all U.S. stocks and computing the realized volatility from 1962 to 2012. By repeating this exercise numerously, say 100,000 times, we compute the average realized volatility of these portfolios. Figure 5.1 reports this average volatility on the vertical axis as a function of the number of stocks selected in the portfolios on the horizontal axis (from one to one hundred stocks). The black line compares the risk of value-weighted random portfolios to the value-weighted portfolio containing all stocks (dashed black line). Similarly, the gray line compares the risk of equally weighted random portfolios to the risk of the equally weighted portfolio of all stocks (dashed gray line).

Figure 5.1 shows the power of diversification in lowering our portfolio risk. But why should we care about risk if we get the same expected return? The simplest way to show the importance of diversifying unrewarded risk is through the effect of compounding returns.

FIGURE 5.1 Average portfolio volatility of random portfolios of U.S. stocks held from 1962 to 2012

Let’s consider the following scenarios. You invest $100 for twenty years and the average return of your portfolio is zero. If returns are certain, then twenty years gives you only the initial $100. However, what if the volatility of your portfolio returns was 1 percent? Or what if it was 5 percent? These are all scenarios in which the average return is 0 percent, but your final wealth would be drastically different in each case. Table 5.1 shows the expected growth rate of your portfolio in each scenario.

The average annual return is also called the arithmetic mean, while the effective annual return is called the geometric mean or compounded return. This very simple example illustrates how volatility amputates your portfolio growth rate and does so in a nonlinear way. Twice as much volatility will amputate performance by a factor of four and four times as much volatility by a factor of sixteen. Here is another example in which the average annual return is not 0 percent but the compounded return in nil. Let’s assume you have a 50 percent loss followed by a 100 percent return. The average mean is 25 percent [(−50 percent + 100 percent) / 2], but your final wealth will be zero because a 50 percent loss on your portfolio must be compensated by a 100 percent gain simply to get back to the initial level of wealth. Risk really does matter!

TABLE 5.1 Expected geometric return over twenty years according to volatility scenarios

The geometric mean is always less than the average mean unless there is no risk (i.e., returns are identical in all periods). Bad risks (such as volatility and negative asymmetry—the fact that extreme negative returns may be more likely to be observed than positive extreme returns) amputate geometric returns. However, if we limit our concerns solely to volatility, the performance drain attributed to volatility alone is equal to one-half of the variance. The relation between the periodic expected returns (arithmetic mean) and geometric mean is the following:

Geometric Mean = Ε[R] – Bad Risk ≅ Ε[R] – ½ Var[R].

This is not a forecast but a structural consequence of the impact of volatility on geometric returns. Hence we should diversify risks not associated with higher average (arithmetic) returns. Doing so is relatively easy. There exist portfolio solutions in the markets that aim to minimize risk and maximize diversification, some of which we will examine in the next chapter.

A common misconception is that diversification has a cost, that is, we get lower risk, but also lower returns. Diversification is all about having lower risk for a given average periodic return. When we diversify unrewarded risk, we remove the impact of the idiosyncratic terms’ variance Var[ε] on our portfolio variance (see the second equation in this chapter), which reduces the performance drag in the geometric mean expression. Diversification might not be a sexy issue, but it pays.

Commodities illustrate well the impact of more efficient diversification on the geometric mean. In 2006, two articles on the benefits of investing in commodities were published side by side in the same issue of the Financial Analysts Journal. Both articles analyzed the performance of investing in commodities between 1959 and 2004, yet their conclusions differed greatly. The first study concluded the geometric excess return on commodity futures was −0.5 percent on average, while the second study reported an average of +5.23 percent.

The answer to this puzzling fact can partly be found in how these averages are computed and how each methodology impacted volatility. The first study computed the geometric excess return of individual commodities and then calculated the average across all commodities.² Average geometric excess performance was −0.5 percent and the average volatility of each commodity was about 30 percent.

The second study created an equally weighted index of thirty-six commodities rebalanced monthly.³ The portfolio volatility was only about 12.5 percent. Not only did the excess performance of commodities nearly match that of equity (5.65 percent), but risk was lower. In their opinion, commodities are an appealing asset class.

The average arithmetic return of all commodities and the average arithmetic return of an equally weighted portfolio of the same commodities are mathematically the same. Yet the spread in compounded returns between the two studies is nearly 5.75 percent. However, the previous equation states that volatility drains performance by half the variance. Assuming that the volatility of the average commodity is 30 percent and no rebalancing occurs, the performance drain from volatility would be as high as 4.5 percent (30%² / 2). However, if a portfolio has no more than 12.5 percent volatility, the performance drain is only 0.78 percent (12.5%² / 2). This factor alone explains nearly 3.75 percent of differential compounded return.

An equally weighted portfolio of commodities rebalanced monthly has much lower volatility than the average volatility of single commodities. This lower portfolio volatility is a result of their low cross-correlations, a measure of how much they co-move together, and of a portfolio assembly process that efficiently exploits these low correlations. Cross-correlations are as low as 15 to 20 percent on average, while they are more than three times as much for equities. Thus, the commodity asset class is incredibly heterogeneous and a perfect candidate for efficient diversification. Unlike equities that are subject to a dominant risk factor (the market), commodities related to energy, grains, livestock, metals, and precious metals have much less in common, which allows for the construction of portfolios having volatility as low as the 12.5 percent reported previously despite the high volatility of single commodities.

This example also conveys another message. When these articles were published, several investment advisors favored the study with the optimistic conclusion and recommended investing in commodities because they concluded that commodities offered a significant risk premium. However, the first study showed that these results were largely explained by the diversification benefits resulting from investing in an equally weighted portfolio, not necessarily by the extraction of risk premiums. Therefore these results could not be used to justify investing in commodities using a product that was not similarly diversified. For example, the S&P GSCI Index, with its heavy concentration in energy commodities, does not offer the same diversification benefits.

We are not saying, however, that maximizing geometric mean should be your objective. Rather, we are using it to illustrate the importance of reducing unrewarded risk in a portfolio. Investor preferences can lead to very different portfolios than that which maximizes the geometric mean. For example, the average annualized monthly excess returns and volatility of the U.S. stock market since 1971 are 6.47 percent and 15.79 percent, respectively. The allocation that maximizes the geometric mean is given by the ratio of the expected excess return divided by its variance.⁴ In the case of our U.S. equity example, this ratio is 259 percent (6.47 percent over 15.79 percent squared). An investor would have to borrow 159 percent against his wealth. Clearly few of us would be comfortable with such leveraged investment. Furthermore, this conclusion assumes that volatility is stable. When volatility explodes in crisis time, the level of tolerable leverage usually is much less.

To ensure that we do not negatively impact the expected return of our portfolio, we must better understand what determines expected returns. Hence we are back to our emphasis on asset pricing, which is discussed in detail in the following section.

Diversification of Priced Sources of Risk

In the decade following Harry Markowitz’s groundbreaking work, financial economists found the results should everyone follow his portfolio choice technique. In such a simple setup, called the capital asset pricing model (CAPM), the market portfolio F_m, in which all assets are weighted by their market value, arises naturally as the only source of positive average returns. According to this model, the market is the only risk factor and only the differences in exposure to risk factor β_m explains the difference in expected returns across portfolios or securities, such as Amazon having a greater market β_m than Walmart. This is an important theoretical finding with long-lasting impact. We have become accustomed to think in terms of this market portfolio. When we ask, “Did a fund manager beat the market?” we implicitly compare it to what should be done under the CAPM, that is, holding the market portfolio, and not to any other benchmark such as the equally weighted performance of all stocks. From our discussion in chapter 2 on the economics of active management, we remember that the market portfolio is the only portfolio that every investor can hold.

However, more than three decades’ worth of academic research has shown that we live in a multifactor world. Financial assets’ average returns are related to more than just the market factor. In the stock market, we have decades of evidence showing how value stocks, stocks that have a low price compared to their accounting value, tend to outperform growth stocks on average. In the currency market, forward contracts on currencies of countries with high interest rates tend to have higher returns than currencies with low national interest rates. Some factors are important in multiple markets, like momentum, the tendency of assets that have been recently trending up to have higher returns than those that have dropped. This factor appears to generate excess returns in all asset classes (equity, commodities, and currencies) and geographic regions. We will discuss this evidence later.

If average asset returns are related to several risk factors, we know that our portfolio should combine them in some way. By having a mix of all available risk factors, we will have less variable portfolio returns (the first component of variance in the second equation in this chapter is lower): when one factor is down, another might be up. For example, when small capitalization firms perform badly, value firms may perform well. Risk factors bring sources of average returns beyond the market risk premium, and bundling them up lowers total portfolio risk. Hence we should diversify these priced sources of systematic risk.

Let’s first examine how traditional portfolios stand in terms of risk factor exposures. A typical balanced allocation puts 60 percent of a portfolio into the stock market and 40 percent in safe government bonds. Figure 5.2 shows the contribution to total portfolio risk of the stock allocation (black line), which is invested in the S&P 500 Index of U.S. stocks, and of the bond allocation (black dashed line), which is invested in a ten-year U.S. government bond. The portfolio risk (gray line) is measured here by the annualized volatility of the portfolio and is reported on the right-hand side axis as a reference.⁵ Despite a 60 percent portfolio allocation, the contribution to total portfolio risk of the equity component is almost always higher than 80 percent, even higher than 100 percent during most years after 2000. The fact that the contribution of equity risk is always greater than 80 percent is attributed to the much greater volatility of equity versus that of fixed income, even in normal times. But the observation that this contribution can be greater than 100 percent is attributed to specific periods in which equity risk is significant and correlation between equity and fixed income is negative. Several aspects contributed to this negative correlation. Fixed income acted as a safe haven, monetary policy favored fixed income assets in turbulent periods, and many large players, specifically pension funds, increased the duration of their fixed-income portfolio component. Hence the total portfolio risk is overwhelmingly driven by the equity allocation.

FIGURE 5.2 Contribution of the stock market and government bonds to a 60/40 portfolio’s risk

But this is an analysis based on asset classes (stocks versus bonds). Asset pricing models generally provide optimal portfolios based on risk factors, not asset classes. Asset classes are bundles of factors. Ang has an intuitive explanation for risk factors: risk factors are to asset classes what nutrients are to different foods—a balanced diet seeks to offer the appropriate mix of nutrients and should be tailored to individual needs. His argument is that investors should determine how much exposure their portfolio should have to specific risk factors and what appropriate mix of assets will deliver that exposure. This approach has the advantage of ensuring that the investor’s portfolio diversification reflects the investor’s desired risk exposures and may reduce the exposure to dominant risk factors, like the market. For example, many investors may not realize that some asset components (like emerging market bonds) are very sensitive to equity market risk and may have more exposure to equity risk than they believe.

Therefore let’s analyze our 60/40 portfolio in terms of risk factor exposures. A total of five risk factors will be considered. First, we use the market factor defined as the excess return (above the risk-free rate) on the market portfolio of all U.S. stocks (the risk factor F_m should be the value-weighted portfolio of all available stocks, not an index of large capitalization stocks like the S&P 500). Then we use three other risk factors that are supported by tremendous empirical evidence: a size factor that buys small capitalization companies and sells large capitalization companies, a value factor that buys value stocks and sells growth stocks, and a momentum factor that buys stocks with high previous annual return and sells stocks with low previous annual returns. Finally, we include a risk factor used for government bonds, which is the return on a long-term bond minus the return on a short-term bond. Hence all factors are defined as long-short portfolios, even the market factor that is short the risk-free rate. We limit our analyses to these primary factors for simplicity.

Figure 5.3 shows the factor exposures through time of the 60/40 portfolio.⁶ First, the exposure to the whole stock market hovers around 60 percent and the exposure to the size factor is around −10 percent, which indicates that the portfolio has negative sensitivity to smaller capitalization stocks. The negative sensitivity to the size factor is not surprising. The market factor is built from all available U.S. stocks, while our portfolio is only invested in large capitalization U.S. stocks, those within the S&P 500. The S&P 500 has a large capitalization bias when compared to the overall equity market. Therefore to explain the performance of the S&P 500 Index, we need to buy the whole stock market (go long our market factor) and sell short small capitalization stocks (our size factor). Similarly, the bond allocation is captured by a 40 percent allocation to the bond risk factor. None of these results are unexpected.

FIGURE 5.3 Exposures to risk factors of a 60/40 stock/bond portfolio

Less appealing are the very low allocations to the value and momentum factors. If these are genuine risk factors for which investors receive compensation in the form of a risk premium, an investor interested in maximizing the risk/return profile of his portfolio should allocate to these risk factors. However, a standard 60/40 allocation based on the S&P 500 Index and the ten-year government bond is simply not designed to deliver a balanced exposure to all factors.

Figure 5.4 shows the comparative performance of our 60/40 portfolio and a portfolio in which we adopt an equal allocation to each of the above five factors (20 percent each), a very naïve but often efficient allocation implementation. Because factors are represented by long-short portfolios, the performance also incorporates the return of risk-free security.

The cumulative performance underlines the importance of factor diversification: for very similar average returns (9.57 percent versus 9.53 percent), we get a much lower risk (annual volatility of 9.96 percent versus 4.77 percent). Hence the terminal value of the equally weighted factor portfolio is greater, implying a greater geometric return despite a similar average return. Remember our first source of performance: lower volatility for the same level of expected returns results in higher long-term compounded returns.

FIGURE 5.4 Cumulative performance of a 60/40 portfolio and an equally weighted portfolio of risk factors

Two caveats are worth noting at this point. First, we assume that investors can invest directly into these risk factors. However, in real life, these involve many stock positions, both long and short, and potentially high transaction costs. Chapter 6 deals with how to implement such improved portfolios in practice, either using portfolios of single securities or factor replicating exchange-traded funds. Second, we assume a prior knowledge of an equally weighted allocation providing good results. Equal weights are used for simplicity here, and a closer look at optimal allocations in practice will be explored in chapter 6.

Must we simply better balance risk factors in our portfolio for optimal performance? Of course not. Investors have heterogeneous preferences. Risk factors exist because some investors have a reason to avoid the systematic risk to which these factors are exposed. For example, risk-averse investors avoid stocks with high exposure to the market β_m as these stocks are more likely to fall with the market. Stocks with higher β_m should theoretically have higher average returns to compensate investors for bearing this risk. What about the economic explanation for other risk factors? The jury is still out. It is not that we do not know what causes these effects. Rather, we have too many competing economic stories. For example, value stocks fall a lot at the onset of economic recessions,⁷ value firms face higher cost when disinvesting assets in place during recessions,⁸ are more exposed to labor income risk,⁹ may not have the flexibility to adjust to competitive changes without facing significant cost commitments and losses on outdated infrastructure, etc. A potential explanation for momentum is the fact that it is exposed to severe downside risk; the momentum factor in the U.S. stock market lost more than 70 percent between July and August 1932 and more than 55 percent from February to September 2009!

Hence common risk factors exist because they expose you to some form of systematic risk that cannot be diversified away. In figure 5.4, we obtained a better performance only because we examined the problem through the lens of an investor who wants to optimize average returns and reduce volatility. Keep in mind that we collectively own the market. If, for example, we adopt an allocation different from the market portfolio by overweighting value stocks, it means that somebody else is willing to take the opposite bet. Of course, some of these risk premiums could also be due to irrational mistakes investors make, but we will cover that possibility in a later section.

Because of the many risk factors proposed by academics and practitioners, a proper understanding of the economic forces at work is crucial. To ensure that you include a genuine risk factor in your portfolio that will give you sustainable excess performance, it should have a valid economic basis for existence, should be easily measurable (impact from a once-in-a-century natural disaster, for example, would be hard to properly analyze), and should be supported by strong out-of-sample empirical results. We come back to this point later in the chapter.

A Closer Look at Empirically Motivated Risk Factors

Empirically motivated factors are factors that are supported by strong out-of-sample empirical results but were not necessarily derived from a well-defined economic model. Size, value, and momentum are examples of such factors.

The fact that small stocks or value stocks that look underpriced compared to their accounting value subsequently have high returns might seem like a tautology. Of course cheap stocks would have higher returns! But the surprising fact is not that small or value stocks tend to have higher average returns, rather it is that their average return is not explained by their exposure β_m to the market portfolio. In fact, none of this should be surprising at all. It simply shows that average returns are related to more risk factors than only the market.

As in the case of value, it is not the metric usually used to express value (the book value-to-market price ratio) per se that is priced. If all one had to do was to look up a stock’s price on Yahoo Finance and its book value in the company’s latest financial statement, compute the ratio, and invest in companies with a high book-to-price ratio, everyone would do it. This in turn would bid up the prices of value stocks and put downward pressure on the prices of growth stocks until the anomalously high average returns would disappear. The fact that this does not happen indicates that value is a proxy for a source of systematic risk (i.e., is exposed to this risk) that asset pricers have not yet fully understood. Hence investors expect to be compensated to support this risk.

To get a better sense of empirically motivated factors such as size and value, remember that according to basic finance theory the price of an asset should equal expected discounted cash-flows:

Price = Σ (Expected cash flow at time t) / (1 + Ε[R])^t.

In this equation, which we will call our price equation, the left side is the price observed in the market and the right side is the sum of all the cash flows received in future periods discounted to the present time. Following basic finance intuition, we discount future cash flow (the numerator) because cash in the future is less valuable than the same amount today. Because these cash flows are uncertain, we discount them using a higher or lower expected return (the denominator) depending on their riskiness.

Is this a new model compared to our return equation? Not really. Imagine you are planning on selling a stock in the next period. In this case, the only expected cash flow that matters for you is the expected market price and possible dividend payout at the time you are going to sell. The expected return in the denominator is the same as in our return equation at the beginning of this chapter. We are simply expressing the relation in terms of cash flows instead of returns. Once you consider all future cash flows, the denominator becomes a measure of the long-term average expected return. Put simply, buying an asset at $100 and expecting to sell it for $105 is the same as having an expected return of 5 percent. This price equation is a general representation of market prices, just as the return equation was a representation of realized return. Both are generic and do not rely on any model.

Now consider two companies with the same expected cash flows for all future periods (the same numerator on the right side of our price equation). If one has a smaller price, expected returns (the denominator on the right side) must be higher. Similarly, if both companies also have the same accounting book value and we divide both sides of our price equation by their book value, a lower price-to-book ratio on the left side implies a higher expected return in the denominator on the right side.

In this example, the size and price-to-book value ratios of these companies become signals or proxies for expected returns required by investors. But if we could truly control for factors that explain expected return, this relation would disappear. In other words, expected return should be entirely explained by the true risk factors, not characteristics like size or price-to-book. The fact that we still find a relation empirically and that this relation is persistent simply means that we have yet to find the right model for expected returns Ε[R]. This intuition is not surprising for academics and has been understood for more than twenty years.¹⁰

Hence many empirically motivated variables, such as value and momentum, find much more empirical success than theoretically motivated factors, such as downside risk and liquidity risk. This is also not surprising. For example, downside risk has the ability to explain momentum profits, and liquidity risk has the ability to explain the size effect. Both measures are motivated by an economic model, that is, we understand why they should be the right risk factors in real life. But they are not completely successful at explaining the momentum and size effects because downside risk and liquidity risk are hard to measure empirically. Readily available measures such as the size of a company or its return over the last year do not suffer from such measurement issues and can therefore perform better empirically.

Diversification of Mispricing Risk

Let’s now discuss our third and final form of diversification. At its peak in the summer of 2000, Nortel Network, the former Canadian electronic and communication giant, traded at 125 times earnings and represented more than 30 percent of the Canadian equity index. To put this figure into perspective, its market capitalization was 40 percent of Canada’s GDP! But by the end of 2009, Nortel had filed for bankruptcy.

An interesting consequence of securities that are apparently overvalued is that they will also have among the biggest weighting in a capitalization-weighted index. Because the price of a security influences the total market value of a firm, if the security is relatively overpriced (compared to other securities in the index), it will have more weight than it deserves in the index. The reverse is also true. At its peak, Nortel accounted for a significant portion of the Canadian market index simply because the stock was expensive. When the price of Nortel collapsed, indexed investors lost significantly, not only because of the substantial price decline, but also because it had the highest weighting in the index. Investors lost significantly on a large portfolio allocation.

Prices are not always equal to their fundamental values. The holy grail of investing consists of identifying which securities are undervalued and which are overpriced. We want to overweight the former and underweight or simply avoid the latter. However, when buying a security, the only information we know with certainty is its market price.

Think back to our discussion in chapter 2: markets should be inefficient (assets should offer a non-zero α) to entice active investors to look for them and make prices more efficient. We can capture this intuition by adding a mispricing on the right side of our price equation:

Price = Σ [(Expected cash flow at time t) / (1 + Ε[R])^t] + Mispricing.

Of course, the mispricing comes from the presence of a non-zero α in the expected return in the denominator, but we write it as a separate term for expositional simplicity. Why is α referred to as a mispricing? Consider two stocks that have the same exposures βs to all risk factors F. If their αs are not equal, they must be relatively mispriced because we could buy the one with the highest α, short sell the other, and obtain a positive average return without any systematic risk. At first sight, picking stocks with high α appears to be a very profitable endeavor.

Just as understanding why some investors shun some source of systematic risk and give rise to the existence of risk premiums, it is crucial to understand the origin of a mispricing. Conceptually, mispricing is literally free money; an appropriately diversified portfolio with a positive α provides positive returns every period with no risk! Simply to exist implies that other investors behave irrationally and do not pick up this free money. For such mispricing to disappear, all we need is one rational investor in the market who is not constrained in taking advantage of these arbitrage opportunities. He could buy positive α assets, hedge away the risk factor exposures by short selling negative α assets, and obtain positive average returns free of systematic risk. Such trading should put pressure on prices until these αs disappear, effectively arbitraging away mispricings.

However, there are plenty of reasons why these mispricings persist in financial markets. We have already discussed the need for the existence of α to entice active investors to invest in research. Another important reason is limits to arbitrage, which are all those frictions that prevent smart investors from picking up this free return (difficulty in shorting stocks or sustaining a significant short position over a long period, leverage constraints, limited liquidity, policies that restrict large investors from holding specific assets such as lower grade bonds or sectors linked to higher carbon emissions, etc.). Thus, even if we believed in 2014 or early 2015 that the Shanghai Shenzhen CSI 300 Index was grossly overvalued, and even if it were easy to implement a short position, it would have required significant staying power and courage to bet against a horde of retail investors in a country where the middle class numbers over 300 million and is growing by the millions, creating new demand for equity. Similarly, much courage was required in 1999 to significantly underweight technology stocks.

A quick look at the expressions at the beginning of the chapter for average return and variance reveals a key fact: maximizing the average return on a portfolio can be done by investing in high α assets, but doing so exposes your portfolio to more concentrated asset-specific risk Var[ε], which increases the overall risk of your portfolio. For example, at one extreme, if you believe you can pick high α stocks, you should keep in mind that you still face a tradeoff between this source of return and the negative impact of the higher portfolio variance on your geometric return. Put simply, if you determine that Apple Inc. has a positive α, you shouldn’t bet it all on Apple. There is a combination of Apple shares and risk factors that has both the same average return and lower risk.

At the other extreme, if you believe you have absolutely no expertise in identifying high α stocks, there are no reasons to hold anything else than a combination of risk factors. Any other portfolio exposed to single stocks would have higher risk without higher average return.

There is a middle ground. If you instead form a well-diversified portfolio that tends to overweight high α assets (i.e., undervalued assets) or underweight low α assets (i.e., overvalued assets) or both, you are letting diversification eliminate the impact of asset-specific random shocks while still taking advantage of mispricings. The trick is to identify variables that could be correlated with underpricing, or at least not correlated with mispricing, and form a portfolio based on these measures.

For example, Research Affiliates’ Fundamental Indexes (RAFI) avoid using market capitalizations as a weighting mechanism because of their sensitivity to mispricings. Their intuition is simple: an overpriced stock is more likely to be overweighted in a market capitalization–weighted index because the stock price itself is a component used to determine its weight in the index. Instead, they use accounting variables that are less sensitive to mispricing to weight their portfolio solutions, variables such as cash flows, sales, book value, and dividends paid. For example, the amount of sales of GM and Apple tell us very little about the mispricing of these two securities, and so the correlation of sales to mispricing should be low. Other weighting methodologies also lead to a lower correlation between portfolio weights and overpricing, such as using equal weights or simply using a moving average over time of market capitalizations.

Nevertheless, the intuition that mispricing imposes a performance drag on market capitalization–weighted portfolios crucially depends on the correlation between market prices and mispricings and the very existence of this performance drag is contested.¹¹ Also, if prices are on average equal to their fundamental values, a fact on which fundamental indexes rely to declare that prices eventually revert to fundamental values, returns of securities that tend to be more dramatically mispriced will offer a mispricing risk premium.¹² Overall, we need to understand that things are not as simple as just using metrics other than prices to form a portfolio. Fortunately, the methodologies that emphasize risk factors and the ones that focus on the effect of mispricings in the market are not drastically different. The next section discusses this point further.

Risk Premium, Mispricing…Why Do We Even Care?

It is hard for most of us to precisely identify mispricings, so taking advantage of mispricings boils down to forming a portfolio based on a variable that we hope is correlated with underpricing or at least is uncorrelated with it. This sounds suspiciously like the way we constructed risk factors in a previous section. So what is the real difference between a risk premium and a mispricing-immune portfolio?

They differ greatly in terms of economics, but not drastically in practice. A risk premium is a rational compensation for exposing yourself to a systematic risk. Investors on the other side of the trade have other constraints and preferences and are happy to lose this risk premium. Mispricing is the result of irrationality in markets and can create average returns with no associated risk. These mispricings may persist because investor psychology does not correct itself, but most importantly because some financial frictions prevent it from being fully arbitraged away.

This economic difference underlies their potential sustainability. If you believe you are exposing yourself to a risk factor, you should understand the economic motive for investors to take the opposite bet and give you some average returns. If you believe you are taking advantage of a mispricing, you should understand the friction in the market that prevents it from being arbitraged away.

Most importantly for investors, the solutions offered to attenuate the impact of mispricings on market indexes are aligned with the objective of including risk factors other than the market portfolio. As specified earlier, RAFI uses weights based on accounting variables’ relative values across companies, another approach uses moving averages of market capitalizations to form weights, and an extreme solution consists of forming an equally weighted portfolio. In each case, we implicitly diminish the role of the market capitalization–weighted portfolio and load up on other factors. As such, forming a portfolio whose weights are correlated with underpricings is in line with the objective of building factor-replicating portfolios. In one case, we wish to attenuate the impact of behavioral biases on the performance of market capitalization–weighted indexes. In the other, we want to deviate from a pure market index–based portfolio and include other risk factors. The question of whether one variable is related to risk or not is of lesser importance for investors who are well-diversified across mispricing- and factor-replicating portfolios. Although the underlying philosophies of factor-building portfolios and mispricing-neutral portfolios are different, the impact on portfolio structure can be similar.

Mispricings only appear as mispricings within the current financial paradigm. As finance academics develop a better understanding of investor preferences and the inner workings of financial markets, it is possible that sources of returns once perceived as being created by irrationality in financial markets will no longer appear as mispricings. John Cochrane, an economist and professor at the University of Chicago Booth School of Business, points out that “the line between recent ‘exotic preferences’ and ‘behavioral finance’ is so blurred that it describes academic politics better than anything substantive.”¹³

Let’s Go Fishing for Factors!

So we can bundle up different risk factors to get a better portfolio. We examined U.S. stock risk factors in a previous section, but evidence is also available for other asset classes: value and momentum are profitable in U.S. and international stocks, international equity indices, government bonds, commodity futures, and currency forwards,¹⁴ the interest rate–based factor in currency market,¹⁵ or the term structure slope factors in the bond and commodity markets.

But here’s the tricky part. The risk factors that we can find by solving an economic model of the world are usually harder to measure and don’t perform as well. We can instead go fishing for factors, analyze the data, and find what looks like priced risk factors. But finding such empirically motivated factors boils down to data mining and does not necessarily guarantee future average returns (spoiler alert: calling it smart beta does not change a thing). A recent study headed by Duke University’s Campbell Harvey lists more than three hundred risk factors that have been studied in the literature.¹⁶ They propose statistical means of dealing with different issues; for instance, the fact that the same datasets (such as U.S. stocks) have been tortured in multiple studies and that only good results are published and unsuccessful ones are not. Many risk factors do not pass a sufficiently high statistical hurdle.

Consider the lifecycle of an academic publication that discovers a new risk factor. The authors of a paper run their empirical analysis on a sample period that ends as recently as data availability permits. They present their results in conferences and submit their paper for peer review at a journal. This second step may take several years, during which anonymous experts critique the paper and ask for further analysis or changes. The paper may even go through the rounds at several journals until an editor decides to publish it. Investors become aware of the paper’s findings either before or after publication. A recent Journal of Finance paper studies the effect of publication on newly discovered factors.¹⁷ They study ninety-seven variables that have been shown to forecast stock returns in academic publications. One possibility is that results are pure data mining, which means that average returns after the publication’s sample period are no more likely to be positive than negative. They find that average returns fall on average by 26 percent, which suggests that some data mining may be at work. The overall average decline after publication is 58 percent, indicating that a newly discovered factor’s average return is halved once results are published. Return predictability is far from disappearing completely, but we need to be careful in selecting factors and in adjusting our expectations of future average return. In our professional careers, we have witnessed this phenomenon many times. A few years ago, an institutional investor asked us why we did not incorporate a new but debated factor in our portfolio management process. We replied that at the time there was insufficient empirical and conceptual evidence of its validity, but this did not deter their insistence that we should incorporate it.

In chapter 6, we’ll look at case studies involving different portfolio solutions, focusing on widely used and empirically supported factors such as market, value, momentum, and carry. Readers interested in knowing more about factors should consider the excellent textbook treatment in Antti Ilmanen’s Expected Returns.

Concluding Remarks

We simply do not know what the market will throw at us in the future. Therefore it makes sense to adopt an approach that integrates all sources of long-term excess performance. The critical issue is to determine what comprises expected returns and to focus on proper risk management. The three forms of diversification cover each aspect of the return equation: the appropriate exposure β to risk factors F, the efficient diversification of idiosyncratic risks ε, and mispricings α. Explicit return forecasts, such as whether stocks would outperform bonds in a given year, were not needed in this framework.

It is also very useful that our blueprint to long-term performance is not asset class specific. The three forms of diversification are not equity-centric, but can theoretically be applied to all public market asset classes, whether equity, commodities, currencies, or fixed income. They can also be implemented within the allocation process of a balanced portfolio. It does not mean that each form of diversification will have the same beneficial impact on all portfolios and in all regions. The potential for diversification of mispricings, factors, or unrewarded risks will vary depending on the structural nature of asset classes and markets and their efficiency and also on the portfolio constraints imposed by investors, but the principles remain valid in all situations. They form the basis for general investment principles and can be used to explain the expected long-term return structure of almost any portfolio. This framework helps us isolate which products and/or managers are more likely to be part of the winning group.

There is also another aspect that requires further clarification. The framework we have discussed applies to traditional managers and alternative managers alike. The same portfolio structural qualities that can be used to explain much of the performance of traditional managers can also be used to explain that of a large segment of the hedge fund industry. The fact that hedge funds operate with very permissive investment policies does not change this conclusion. Hence it makes little sense to pay five times as much in fees for a hedge fund manager than for a benchmark agnostic factor-based long-only manager. Investors can obtain much of the factor exposure provided by hedge funds through their traditional mandates at a lower cost.

Now that we have whetted our appetite, we turn in the next chapter to the practical implementation of better portfolios. We have not yet discussed the impact of investment policy decisions. It is obvious that these decisions, such as choosing whether or not leverage, shorting, and derivatives should be allowed, do impact the potential for superior risk-adjusted returns and our ability to implement them. But they do not impact our understanding of the sources of this potential. The next chapter discusses how these investments and constraints impact portfolio selection in practice.