Leading Economic Indicators and a Probabilistic Approach to Estimating Market Tail Risk Sonu Vanrghese, Ph.D. Director of Research Angshuman Gooptu Senior Economist The shifting trends observed in leading economic indicators should be able to lead swings in the business cycle since they provide information about shifts in individual market demand and supply trends that translate to shifts in aggregate demand and aggregate supply. For instance, an uptick in the demand for labor or a sudden increase in the hourly wages offered in the economy signals a surge in the aggregate consumption. Or, a rise in the demand for durable goods or for housing signals more disposable income available for expenditure and a potential expansion in the business cycle. However, we emphasize that markets are not always efficient and may have externalities involved at the micro-level.. Our team at Convex Capital Management develops and utilizes a proprietary leading economic indicator, the Convex Proprietary Leading Economic Index (CPLEI), to create a fundamental macroeconomic rating for individual countries that can further be aggregated to a regional and global level. These country-specific economic ratings are subsequently combined with other analyses, including probabilistic tail-risk forecasting (described in this paper), yield curve shifts and Markov regime switching, to develop market risk-ratings for each country. These risk-ratings govern the overall allocation of the portfolio to any particular country and region. In this paper, we start by describing our approach to creating a proprietary composite leading indicator of the economy. Next we describe the Conference Board s Leading Economic Index for the United States (LEI), which is then used to analyze the relation between composite leading indicators and market returns. We turn to the LEI, as opposed to our proprietary index, since it has been validated and is widely used to predict turning points in the business cycle. Finally, we develop a probabilistic approach that utilizes the LEI to warn us about tail-risks in the market. 1
Convex Proprietary Leading Economic Index Our approach to creating the Convex Proprietary Leading Economic Index (CPLEI) combines indicators that capture information from five categories that tend to lead business cycles in most developed economies. These categories lead expansions or contractions in the business cycle by either incrementally affecting the aggregate demand or supply in the overall economy. Labor Market Conditions Monthly unemployment claims, Hours of work in manufacturing and industrial sector; Demand for Manufacturing and Industrial Sector Manufacturing orders, Industrial orders, Manufacturing and industrial Inventory; Demand for Durable Goods - New housing upstarts, Purchase of newly registered vehicles; Consumer and Business Sentiment Consumer confidence indicator, Business outlook by manufacturing and industrial sector, stock prices; Price trends in the economy - Consumer Price Index; Monetary Policy Stance & Availability of Credit Money Supply; Loans to households and businesses, Short-term and long-term interest rates. In addition, since underlying economic trends and structural differences exist between developed and emerging economies, Flow of Funds and Fiscal Situation Capital Accounts, Current Accounts, Balance of Payments, and Fiscal debt. In order to capitalize and ensure that we are capturing inflection points in the economic cycles, we have prioritized our mix of variables to be heavily based on variables updated on a monthly basis relative to variables updated on a quarterly basis. We categorize components in each country s leading economic index since they provide adequate information about sudden shifts in the demand and supply of goods and services and thereby predict potential movements in economic conditions of a country. We emphasize that these shifts are not accounting for exogenous and unforeseen events such as sudden geopolitical shifts that require a more in-depth sophisticated research and analysis prior to a decision on investment allocations. 2
Conference Board Leading Economic Index The Conference Board Leading Economic Index (LEI) for the United States is a composite average of several individual leading economic indicators. It is a commonly used forecasting tool that attempts to predict changes in the direction of aggregate economic activity and business cycle turning points (Levanon et al, 2011a). Cyclical movements in the economy may depend on multiple factors whose contributions may change over time. Hence a composite indicator like the LEI tracks economic movements better than individual indicators. The LEI is also attractive as a tool to smooth out the volatility of the individual indicators. The ten specific components of The Conference Board Leading Economic Index for the U.S. include: 1. Average weekly hours, manufacturing 2. Average weekly initial claims for unemployment insurance 3. Manufacturers new orders, consumer goods and materials 4. ISM new order index 5. Manufacturers new orders, nondefense capital goods excluding aircraft orders 6. Building permits, new private housing units 7. Stock prices, 500 common stocks 8. Leading Credit Index 9. Interest rate spread, 10-year Treasury bonds less federal funds 10. Average consumer expectations for business conditions Each of the components contributes a different aspect of economic activity to the LEI, including labor market conditions (initial claims, weekly hours), contractual relationships (orders, permits, etc.) and consumer expectations or sentiment (stock market prices, consumer expectations, etc.). The monthly change in LEI is the sum of contributions from each component, forming a summary of the cyclical movements of each of them (Levanon et al, 2011a). Financial market expectations in the form of stock prices, interest rate spreads and the Leading Credit Index (LCI) are a core part of the LEI. The LCI, also published by The Conference Board, consists of six additional financial indicators: 1) 2-years Swap Spread, 2) LIBOR 3 month less 3 month Treasury-Bill yield spread, 3) Debit balances at margin account at broker dealer, 4) AAII Investors Sentiment Bullish (%) less Bearish (%) - a contrarian indicator, 5) Senior Loan Officers C&I loan survey - Bank tightening Credit to Large and Medium Firms, and 6) Total Finance: Liabilities - Security Repurchase. The LCI replaced the real money supply component (real M2) in the LEI in January 2012, and retroactive to 1990, to improve its coverage of financial and credit market activity. The relationship between real M2 and business cycles has weakened and become unstable since the late 1980s, deteriorating its ability to act as a leading indicator (Levanon et al, 2011a, 2011b). 3
Conference Board Leading Economic Index (contd.) It would seem obvious that there are important linkages between the actual economy and the financial sector, especially given the nature of the most recent recession. One may even intuit that economic conditions should lead the market over the long run. Given that, and the fact that an explicit goal of the LEI is to predict turning points in the U.S. economy, we want to explore whether it contains any information on future movements of the U.S. stock market. Particularly whether significant changes in the LEI contain any information on tail risks in the market. In the following sections, we investigate the relationship between monthly changes in the LEI and market returns, and develop a probabilistic framework for estimating market tail risks. The Data A prior study by CXO Advisory Group, LLC analyzed the relationship between the Economic Cycle Research Institute s (ECRI) Weekly Leading Index (WLI) and the stock market (S&P 500). They found that the WLI has no predictive power and that WLI movements lag stock market behavior, offering no guidance to future market returns. We replicate the above study with the LEI, which is a monthly index, and market returns obtained from the Fama-French (FF) Data Library to see if there is a relationship between the two. The market return used here is the value-weight return of all firms in the Center for Research in Security Prices (CRSP) database and listed on the NYSE, AMEX and NASDAQ. The chart compares a market index, created using the FF return series, with LEI, between January 1960 and November 2013. The market index starts at a Figure 1. Market index (created using the Fama-French monthly return series) and LEI between 1960 and 2013. value of 1 in January 1960. The two series appear to track one another over time, with both series falling and recovering from troughs seemingly at the same time. However it is not obvious as to which series leads and which one lags. 4
An important issue we had to deal with was the lag between the month for which the LEI value was reported and the actual month in which it was reported. Typically, this lag is about 2-3 weeks. For example, the LEI for January may be available only after the second or third week of February. As a result, market return predictions for March can only use LEI data up to January. We have used a one-month lag for the all the results reported from here on. Exploring the relation between changes in LEI and future market returns Since both the LEI and the market index are non-stationary, we consider the monthly changes in both. We calculated the 1-month change in LEI as well as an average of the 1, 3, 6 and 12-month LEI changes to see how these relate to the market return the following month. The following scatter plots show the relation between monthly changes in LEI and the future market return. Figure 2. Scatter plot of market returns (1-month ahead) and monthly changes in LEI. Figure 3. Scatter plot of market returns (1-month ahead) and average (1, 3, 6, 12 months) changes in LEI. 5
The scatter plots, and the blue regression lines, indicate that there is no discernible relation between LEI changes (whether 1-month or the average over 1, 3, 6 and 12 months) and market returns in the month ahead. The correlation coefficients are almost 0 in both cases, and so is the coefficient of determination (R 2 ), confirming that changes in the LEI do not explain market returns. As in the study by CXO Advisory Group, LLC, we also looked at whether LEI changes can predict market returns further than one month. At the same time we also explore the converse: whether market returns explain some of the variation in LEI. The following chart plots correlation coefficients between the change in LEI (both 1-month and average change) and market returns for various lead-lag time periods. We move from the correlation when the market leads LEI by 10 months (x-axis value of -10) to when the LEI leads the market by 10 months (x-axis value of10). The chart indicates no relation between LEI changes and Figure 4. Correlations between LEI changes and market returns for different lead/lag periods. market returns in the future. The correlations between LEI changes and future market returns are close to 0, ranging between -0.05 and 0.05 for x-values 1 through 10. Interestingly, the correlations are significantly higher when the. Market changes are most highly correlated to 1-month LEI changes (red line) that are 1-2 months in the future (x-values of -1 and -2, respectively). Market changes also lead average LEI changes (blue line) by several months, with the highest correlations occurring when the market leads by 6-7 months. Figure 5. Scatter plot of market returns and changes in LEI (in the following month). It appears that The Conference Board s LEI has a fairly significant component made up of recent market returns, which may explain why market returns lead the LEI. This effect is more apparent in the following scatter plot (Figure 5), relating market returns to the monthly change in LEI one month into the future. For example, the market return in January is related to the monthly change in LEI in February. 6
As the upward sloping trend line in the figure makes clear, positive market returns are correlated with positive changes in LEI one month in the future. Similarly, negative market returns are correlated to negative changes in LEI one month ahead. The R 2 statistic indicates that changes in market returns explain about 11% of the variation in LEI changes one month ahead. It seems like The Conference Board attunes its LEI quite significantly to recent market data. On the face of it, and based on the above analysis, changes in LEI appear to be a rather poor choice as an explanatory variable of future market returns. In fact, our results indicate the opposite effect. The question remains though as to whether the information present in a composite economic indicator such as the LEI can be used in any form to discern future returns. A Probabilistic Approach Since the explicit goal of the LEI is to forecast turning points in the U.S. economy, we explore the forecasting capability of the tails of the LEI distribution. Essentially, we investigate whether large negative changes in LEI can effectively inform us about the tail risks in the market. To do this, we consider a probabilistic approach to utilizing the information present in the LEI (or rather, within the economic variables that constitute the LEI) to forecast market risks. To ensure that our study is not completely in-sample, and to actually test predictive ability, we separate our dataset into two groups. A training set is created with the data from year 1960 to 1999 and a test set with the data from 2000 to 2013. The training set is used to analyze the potential relationship between the LEI and market returns and build a predictive model. The idea is to build a model as if we were analyzing this at the beginning of year 2000, using data from 1960 through 1999. We start with summary statistics of our training set, for changes in the LEI as well as market returns. Both 1-month changes in LEI and the average change over 1, 3, 6 and 12-months are considered here. As we discussed earlier, due to the 2-3 week lag in reporting of the LEI we use a one-month lag between the LEI and market data. So the LEI change in month is related to the market return in month +2. The data for LEI changes run from January 1960 through October 1999, and the forecast period for market returns from March 1960 through December 1999. Table 1 reports the mean and standard deviation of each of our three variables, as well as the skewness and kurtosis of each. Skewness measures the symmetry of a distribution (or its deviation from symmetry) while kurtosis measures how peaked (positive values) or flat (negative values) a distribution is. A perfect normal distribution, with a symmetric bell-curve, has a skewness value of 0 and a kurtosis of 3. 7
The skewness and kurtosis values for all three variables indicate that the distributions skew left and are markedly more peaked than would be expected in a normal distribution. This is readily apparent in the figures below (Figures 6, 7, 8), which show the distribution of market returns and changes in LEI. An overlay of a normal curve that has the same mean and standard deviation is also shown (in red) to highlight the deviation from normality. Figure 6: Histogram of market returns between 1960 and 1999. The red line represents a normal curve with the same mean and standard deviation. Figure 7. Histogram of 1-month change in LEI between 1960 and 1999. Figure 8. Histogram of average monthly change (1, 3, 6, 12 months) in LEI between 1960 and 1999. While the distribution of market returns and LEI changes are clearly left-skewed, our focus is primarily on whether the left tails of LEI changes have any information regarding the tails of market returns in the future. 8
We define our tails of market returns as the area outside of 1.25 standard deviations from the mean. Table 2 (below) shows the estimated empirical probability that market returns are more than 1.25 standard deviations away from the mean, based on the period March 1960 to December 1999. Next, we separate the LEI changes into deciles: with decile 1 consisting of months with the lowest (or most negative) changes and decile 10 containing months with the largest (positive) changes. We then estimate the conditional probability that market returns, two months in the future, are more than 1.25 standard deviations away from the mean when LEI changes are in decile 1. These estimated conditional probabilities are in Tables 3 and 4. 9
Based on the data between 1960 and 1999, the probability that market returns are in the left and right tails of the returns distribution are 9% and 8%, respectively. However, the probability that returns fall within the tails increases significantly when we condition it on the event that LEI changes are in the first decile (i.e. when LEI changes are most negative.) The conditional probability that market returns are in the left tail of the distribution is almost 19% when 1-Month LEI changes fall in the first decile, more than twice the unconditional probability of 9%. The probability that market returns are in the right tail is close to 15% when we condition it on the first decile of 1-Month LEI changes, whereas the unconditional probability of returns in the right tail is only about 8%. The story does not change even when we use average changes in LEI. We now validate the results from our training set using the data in our test set If the results hold, we should find that the probability of market returns being in the tails of the returns distribution increases when the LEI shifts significantly downward during the period between 2000 and 2013. To do this we create real-time vignettes of LEI changes and market returns between the test period of November 1999 and September 2013 (167 total months). Since the LEI change in month is related to the market return in month +2, the forecast period for market returns in our test set runs from January 2000 to November 2013. In our training set, the first decile of 1-month LEI changes and average LEI changes consisted of changes that were less than -0.55% and -2.5% respectively. We estimate the probability that future market fall in the tails of the returns distribution when LEI changes during our test period are below these same cut-off points. This is to ensure that no data from the future is used in any month and the tails of the returns distribution are defined using only data that would be available at that time. As in our training set, we define our tails of market returns as the area outside of 1.25 standard deviations from the mean. Table 5 shows the estimated empirical probability that market returns are more than 1.25 standard deviations away from the mean between January 2000 and November 2013. 10
Comparing the results in Table 2 and Table 5 we see that the estimated probability of market returns falling in the left tail, i.e. large negative returns, rises from 9% in the 1960-1999 period to more than 14% between 2000 and 2013. This is only to be expected since we have had two significant bear markets during the latter period. We subsequently estimate the conditional probability that market returns, two months in the future, are more than 1.25 standard deviations away from the mean when LEI changes are below the cut-off points obtained from the training set. These estimated conditional probabilities are presented in Table 6 and 7. The results from our test period closely follow those observed in our training period. Between 2000 and 2013, the probability that market returns are in the left and right tails of the returns distribution is about 14% and 7%, respectively. However, these probabilities almost double when we condition it on 1-month LEI changes being less than the cut-off points obtained from our training set. When average LEI changes are used as the conditioning variable, the probability that market returns are in the left tail rises to 31%, and within the right tail to almost 16%. 11
Conclusion A prior research paper by Convex Capital Management ( Volatility Clustering, How to Avoid the Tails ; Chattopadhyay and Varghese, 2013), discussed how volatility tends to cluster. Large positive and negative changes in price are followed by large changes, and small price changes tend to be followed by more small changes. As the authors note, the real benefit of effective risk management comes from setting the risk posture of the portfolio in low or high volatility clustered regimes, and re-adjusting as the cluster changes. Portfolios can be highly vulnerable to tail risks when in a high volatility cluster. A safer risk-managed investment strategy tends to outperform in the long run by eliminating the tails. As we saw in the prior section, the probability of market returns within both the left and right tails increases significantly when conditioned on large (negative) changes in LEI. This information, that large shifts in leading economic indicators increases the probability of tail returns, could potentially be used to avoid upcoming bouts of high volatility and create a smoother ride for a portfolio. The team at Convex Capital employs proprietary composite of leading economic indicators using macroeconomic variables from five categories indicated in page 2 within a probabilistic framework, as discussed in the previous section. This composite (the CPLEI) is used to develop proprietary risk ratings for individual countries (e.g. Buy Risk, Sell Risk ) and avoid periods of high volatility in order to achieve higher risk-adjusted returns for a portfolio. Both and information are used for investment allocations. An example of information may be a large shift in economic indicators that results in the team altering it s allocation.. Future returns may not exhibit the same probability as in the past. This is especially true in the tails, which are evident in our study (compare left and right tail returns in Tables 2 and 5). Our approach allows us to invalidate the assumption that market returns follow any particular distribution and thus avoids the pitfalls of fitting several parameters to a historical record, especially those that may be non-recurrent. References: Chattopadhyay, S., Varghese, S. S. (2013) Volatility Clustering, How to avoid the tails?, Convex Concept Paper: Volatility Series, Convex Capital Management LLC Levanon, G., Manini, J-C, Ozyildirim, A., Schaitkin, B., Tanchua, J., (2011a) Using a Leading Credit Index to Predict Turning Points in the U.S. Business Cycle, Economic Program Working Paper Series #11-05, The Conference Board Levanon, G., Ozyildirim, A, Schaitkin, B., Zabinska, J. (2011b) Comprehensive Benchmark Revisions for The Conference Board Leading Economic Index for the United States, Economic Program Working Paper Series #11-06, The Conference Board ECRI s Weekly Leading Index and the Stock Market, CXO Advisory Group, LLC Fama French Data Library available online at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 12