I summarize below how my different research papers tie in together. My primary research interest is investment management. Investment management is inherently a question of asset pricing, and I therefore also conduct research in asset pricing.
We first examined the behavior of the market, size, value, and momentum portfolios in the US stock market. Combinations of these portfolios are referred to as risk factors by academics and are used to explain the differences in average returns across stocks. For example, stocks with value characteristics (e.g. high accounting value compared to its market value) have had higher returns on average over the past century. A value factor, or more precisely a value-minus-growth factor, captures this source of performance.
These portfolios, which involve long and short positions in stocks, are also the basic elements of strategies used by some hedge funds. For example, hedge funds such as AQR Capital Management follow, among other strategies, a combination of value and momentum. Risk factor investing is also common in mutual funds. Firms such as Dimensional Fund Advisors were early small cap investors and Warren Buffet is probably the best-known value investor. More recently, the practice of combining risk factors, or more simply tilting a diversified portfolio towards stocks with certain attributes, has become known as smart beta investing.
An investor combining these sources of performance should be concerned with how they co-move together. If they all move in the same direction at the same time, then your portfolio is risky because you can simultaneously lose money on all fronts. Part of what makes them attractive is the fact that these long-short portfolios have low correlations between themselves, meaning that their returns do not usually go in the same direction. These low cross-correlations are not surprising: these factors are generally constructed to behave this way. Given these low cross-correlations, an investor can gain large diversification benefits by combining these long-short strategies in a portfolio.
But here the word usually is key; we show in Christoffersen and Langlois (2013) that these cross-correlations vary wildly over time and they hide striking dependence between extreme events. For example, we find extreme dependence despite close-to-zero cross-correlations, which means that when one risk factor is having its worst day in history there is a chance that another risk factor is also having its worst day in history. This may remind some of the Quant meltdown in August 2007 during which the returns of many long-short strategies favored by hedge funds tanked despite the overall market barely moving.
What is problematic is that the standard statistical measures of risk—volatility and correlation—do not allow for this possibility. Even worse, when we conducted that research few flexible econometric methodologies could model both close-to-zero cross-correlations and extreme dependence.
In Christoffersen and Langlois (2013), we propose a flexible econometric methodology that can account for multiple facets of risk in the data. Our methodology better captures how risk factor returns actually behave. We show that funds combining long-short strategies based on these risk factors can increase their risk-adjusted returns by more than 1% per year when using our methodology. This added value is impressive given that it comes from simply using a better risk model, not better forecasting the profitability of these strategies.
Then, we went beyond risk factors in the US equity market and turned our attention to international equity markets. The structure of international financial markets has changed over the past few decades; barriers to international investment have fallen and financial markets have become more integrated. We show in Christoffersen, Errunza, Jacobs, and Langlois (2012) that measures of dependence between national equity markets have at the same time greatly increased. Higher correlations and higher occurrence of joint extreme events (e.g. crises) imply that the benefit for an investor of diversifying his portfolio internationally has decreased over time. For example, a US investor allocating a part of his wealth in Germany and Japan would have improved his portfolio risk-return profile a lot in the 1980s. Nowadays, these gains are lower.
To model these patterns we generalize the econometric methodology of Christoffersen and Langlois (2013) in two different ways. First, we introduce a trend in long-run correlation. Correlations of short-term returns (i.e. weekly or monthly) depend on current market conditions, but in addition, they fluctuate around a long-run value that slowly increases over time, a feature robustly supported by the data. Second, we adopt an estimation methodology that allows estimating our model on a wide set of countries. This large set of countries makes it possible to capture the time trend in average dependence measures.
We show that correlations, but also dependence among extreme events, have increased between developed country equity markets (e.g. between the US and UK), between emerging country equity markets (e.g. between Brazil and India), and between developed and emerging country equity markets (e.g. between Japan and Russia). While a large proportion of the benefits from diversifying across developed countries has disappeared, larger gains remain in diversifying across emerging markets. The intuition is that while crises may be more frequent in emerging markets, they are more country-specific than in developed markets.
To better illustrate how these diversification benefits in international equity markets have gone down, I developed a new measure of conditional diversification benefit. The objective was to find one measure that could summarize several risk measures (volatility, correlations, downside risk, tail risk, etc.) into one meaningful measure of portfolio diversification.
We start with a well-known and widely used risk measure: the expected shortfall. In a nutshell, the expected shortfall is the average portfolio loss one can expect given that the loss on the portfolio is equal to or larger than a pre-chosen level. If you determine that you are in trouble if you lose 5% or more on your portfolio, then the expected shortfall tells you how much you should expect to lose in this scenario (is it closer to 5% or to 20%?). We use this risk measure because it respects a set of nice mathematical properties that a risk measure should have.
The expected shortfall of a portfolio has two natural bounds. It cannot be lower than the pre-chosen threshold (e.g., 5%), a situation in which all portfolio losses equal to or larger than this level actually are equal to this threshold. Think of buying an insurance contract on the value of your portfolio that would pay you the extra loss in such case. At the other end of the spectrum, the expected portfolio shortfall cannot be higher than the average of the expected shortfalls of each asset weighted by their weight in your portfolio. This situation corresponds to the case in which combining these assets in a portfolio does not bring any diversification benefits.
The Conditional Diversification Benefit measure, CDB, is the distance of our portfolio’s expected shortfall, ES, to its upper bound, max(ES), standardized by the distance between the two bounds: ( max(ES) – ES ) / ( max(ES) – min(ES) ).
The conditional diversification benefit measure is extremely useful and has intuitive properties: it does not depend on the asset expected returns, which are notoriously hard to measure, and it varies between zero (no diversification benefits) and one (perfect diversification). By measuring its value at different points in time, we can describe the evolution of diversification benefits obtained from a portfolio.
Using this measure, we show that diversification benefits have been halved since the 1970s for developed countries. In contrast, diversification benefits among emerging markets have decreased by around 25% during the two decades up to the end of the 2000s.
What about diversification in other asset classes? In Christoffersen, Jacobs, Jin, and Langlois (2018) we show how to measure time variations in risk of a large portfolio of corporate bonds. Whereas we considered up to 33 equity markets in the previous paper, here we show how we can handle credit securities of more than 200 U.S. firms. Our methodology is useful when allocating a portfolio, assessing the risk of a portfolio, or even pricing a structured product on a large set of bonds.
We find that the dependence between the prices of default insurance (i.e. credit spreads) on large US companies’ debt has spiked during the financial crisis of 2007-2009 and has remained elevated since. In comparison, the correlation between the stocks of these same companies has spiked later in the crisis but has since come back down. When measuring the Conditional Diversification Benefit measure for an equal-weighted portfolio of investment grade corporate bonds, we find that it has decreased by more than one third during the 2000s.
We further find evidence that our dependence measure affects the level of credit spreads for these US corporations; higher dependence between a firm’s credit spread and the average credit spread in the market is associated with a higher credit spread level. We explore further pricing effects in the next section where we focus on the determinants of expected investment returns.
Measuring Expected Returns
While my papers described above mainly focused on modelling risk over time and across a large number of assets, I discuss in this section my research dedicated to measuring a crucial input in asset management: the expected return on an investment.
In Langlois (2020), I revisit an old question in finance using a new empirical methodology: How does the risk of extreme returns affect stock prices? If I hold a stock that is susceptible to a drastic fall in value (think of a stock price that crashes following bad news), I would like to be compensated with higher returns on average. Conversely, if I hold a stock that has a small chance of shooting up in price—think of a company discovering a breakthrough technology—I am willing to accept lower returns on average.
While many studies have shown that extreme return risk affects stock prices, determining what kind of extreme return risk matters has remained difficult. Do investors care about crashes that happen during bad economic times (i.e., when we are in a bear market, during a recession, etc.)? Or do investors only care about companies experiencing large negative or positive returns because news just broke out about its prospects, regardless of market conditions?
By definition, we observe few extreme events. Therefore, identifying how stocks differ in their exposures to downside risk or upside potential is difficult. I propose a new empirical methodology to better measure the differences in extreme return risk across stocks. Based on this methodology, I show that it is the possibility of a large negative return during bad market environments that has a strong and robust impact on stock prices.
How do I get a better sense of the impact of extreme return risk? There are two main elements in my methodology. The first element is straightforward: I use a large number of predictors at the stock level to forecast its future risk. For example, I use how risky a stock has been in the past and stock characteristics such as value ratios, the profitability and investment intensity of a company, its payout yield, etc.
Most importantly, it is the second element of my methodology that is the key to unlocking its predictive power. At each point in time, I transform all variables into their percentile ranks in the cross-section of stocks. For example, a stock with the smallest market capitalization in the market would have a percentile rank of zero and a stock with the highest past volatility would have a volatility percentile rank of one. Then, I estimate a predictive model using percentile ranks of predictors and of extreme return risk measures instead of their original values.
For example, I measure whether being one of the smallest company in the market predicts having one of the highest skewness, not whether having a market capitalization of five billion dollars predicts having a skewness of, say, -1.5. Using variables transformed into percentile ranks produces better forecasts of the future differences in risk across stocks.
While the paper offers econometric arguments to explain why this methodology better performs, its intuition is simple. We want to know whether differences in risk explain differences in average returns across stocks. Consequently, we forecast the differences in stocks’ exposures to extreme return risk, not their own individual exposures. Forecasting the former is easier than predicting the latter.
 We model time-varying volatilities and cross-correlations, and univariate and multivariate fat tails and asymmetries.
 See Artzner, Delbaen, Eber, and Heath (1999) for a thorough discussion of coherent risk measures, and Basak and Shapiro (2001).
 They cancel out when computing the ratio.