A Study of Short Term Mean Reversion in Equities

A Study of Short Term Mean Reversion in Equities Written by Aditya Bhave & Nick Libertini September 2013 Introduction Mean reversion in equities has been consistently documented as a source of positive alternative investment returns over the last nine decades. Mean reversion investing attempts to capitalize on the tendency for an asset s price to move from extreme levels towards long term averages and it can be conducted on an absolute or relative basis. In an absolute mean reversion model a stock s attractiveness is determined solely by the relationship of its current price to its long term average. The downside to this is that the model will persistently flag stocks as undervalued in a declining market and overvalued in a rising market. Alternatively, in a relative mean reversion model a stock s attractiveness is judged relative to the movements of other stocks. The benefit of using a relative measure of mean reversion is that the underlying drift of the equity market is removed allowing each stock s attractiveness to be determined from the merits of its idiosyncratic movements relative to the group. In a rising market, a relative mean reversion portfolio will concentrate its long positions in stocks that have appreciated in price the least, while focusing its short positions in stocks that have appreciated in price the most. Conversely, in a falling market the portfolio will concentrate its long positions in stocks that have depreciated in value the most, while focusing its short positions in stocks that have depreciated the least. In this way, the model is indifferent to the absolute return of any of its holdings because it derives return from the relative movement of its long and short positions. This paper examines possible explanations for the persistence of the mean reversion anomaly, evidence of short term mean reversion in U.S. stocks, and factor exposures associated with a market neutral mean reversion portfolio. Ultimately, the paper shows that short term mean reversion is a consistently profitable strategy that has marginal correlation to other risk factors. Possible Explanations for Mean Reversion Substantial research has revealed that investors do not act rationally when making decisions. 1 This irrational behavior leads to several exploitable market phenomena, one of which is mean reversion. Specifically, mean reversion is the byproduct of the availability bias, the aversion to losses, and the affinity for lower prices. Kanhneman and Tversky (1977) illustrate that humans bias their choices towards information that is easily recallable from memory. The consequence of this availability bias is that new information is given too much weight when making decisions because of the cognitive ease with which it can be recalled. Kanhneman and Tversky s finding explains why stock prices are predisposed to overreaction; investors overweight new data, such as news events, while ignoring other pertinent information that is less cognitively available. After the initial overreaction to a negative news event occurs investors who still hold the stock become loss averse, unwilling to sell their position. Conversely, other investors become enticed by the lower price. As all investors finish digesting the new information, prices revert from the extremes causing a previously underperforming stock to outperform. Overreaction to new information is accentuated when the decision making environment is complex and many variables have to be analyzed. Therefore, investors are given many opportunities to overweight new information because of the multitude of complex factors that drive stock prices. Another factor that contributes to mean reversion in stocks is the attractiveness of lower prices. Psychologically, it is satisfying to purchase an item at a discount and it is painful to purchase an item at a premium. 2 This is one reason why portfolio managers periodically increase their exposure to underperforming positions and trim their exposure to outperforming positions. These psychological biases naturally inflate buying pressure for underperforming stocks and selling pressure for outperforming stocks, leading to a cycle of mean reversion in equities that has been evident for at least the last 86 years. 3 1 Kanhneman and Tversky, De Bondt and Thaler, and De Bondt all provide considerable evidence of the overreaction bias in humans. 2 Thinking, Fast and Slow, pages 278-289. 3 The combination of De Bondt and Thaler s, Poterba and Summers, Balvers and Wu s, and this paper s study of mean reversion encompassed the time period from 1926 to 2012, all reporting statistically significant evidence of mean reversion in equities. 361 CAPITAL (866) 361-1720 Page 1

Evidence of Short Term Mean Reversion in Stocks Many academic and industry studies have shown that equities consistently mean revert from price extremes. However, much of the research has focused on long term mean reversion of stock prices (24 36 months), ignoring short term anomalies ( 1 month). De Bondt and Thaler (1984) concluded that mean reversion in NYSE equities mostly occurs during the second and third year. However, a close examination of their research shows evidence of 1 month mean reversion. Figure 1 depicts a reproduction of De Bondt and Thaler s findings, illustrating that mean reversion in NYSE equities persisted for 36 months after portfolio formation, with the previously underperforming stocks returning an average of 19.60% and the outperforming stocks returning an average of -5.00%. Interestingly, 41.06% of the observed outperformance came in the first month with the underperforming stocks returning an average of 8.00% and the outperforming stocks returning an average of -2.10%. 4 This suggests that there was significant 1 month mean reversion in NYSE stocks from 1933 to 1980. Poterba and Summers (1987) highlight that returns of NYSE stocks showed significant signs of mean reversion at long [time] horizons. Their findings also provide evidence that stocks exhibit short term mean reversion. Specifically, the 1 month holding period had the highest level of statistical significance of any of the holding periods under 60 months in their study of mean reversion from 1926 to 1985. 5 Finally, Jegadeesh (1990) reports that, monthly returns on individual stocks exhibit significantly negative first-order serial correlation. 6 The findings below indicate that short term mean reversion is a compelling source of consistent returns. However, short term mean reversion did not become feasible to implement for many investors until recently. Implementation barriers such as high transaction costs, high portfolio turnover, and high data costs 7 made short term mean reversion unapproachable for everyone, except the academic community and sophisticated institutional investors. Starting in the mid 1990 s, the transformation of the investment industry from brickand-mortar to electronic centric allowed for a precipitous decline in transaction and data costs, as well as an increase in implementation flexibility. These changes were instrumental, allowing short term trading strategies to become viable to a much broader investor base. 20.00% Persistance of Mean Reversion in Underperforming and Outperforming NYSE Stocks January 1933 - December 1980 19.60% Cumulative Excess Return 15.00% 10.00% 5.00% 0.00% -5.00% -10.00% 1 Month Mean Reversion 8.00% -2.10% -5.00% 0 5 10 15 20 25 30 35 40 Months After Portfolio Formation Outperforming Stocks Underperforming Stocks 4 The estimated spread of cumulative excess return between the underperforming stocks and the outperforming stocks 10.10% one month after portfolio formation from Figure 1 in Does the Stock Market Overreact? De Bondt and Thaler documented that the final return spread was 24.60%, thirty-six months after portfolio formation. 10.10% / 24.60% equates to 41.06% of the total outperformance in the first month. 5 Observing the values in Table 2 of Mean Reversion in Stock Prices: Evidence and Implications it is clear that confidence intervals on the 1 month variance ratios were smaller than any other holding period under 60 months. For example, looking at the Equal-Weighted Excess Returns data series, the 1 month holding period s variance ratio had a 95% confidence interval of 0.504 1.092 while the 24 and 36 month holding periods had 95% CI of 0.853 1.143 and 0.665 1.139, respectively. 6 Negative first-order serial correlation of monthly returns implies that monthly returns tend to mean revert opposed to following a random or momentum time series path. 7 In The Only Three Questions that Still Count, Ken Fisher describes how he paid Goldman Sachs $20,000 in 1981 for a one-time screen of the NYSE on price to sales (page 101). Figure 1: Cumulative excess returns for outperforming and underperforming portfolios of 35 NYSE stocks from January 1933 to December 1980. 41.06% of the outperformance is observed in the first month after portfolio formation. Outperforming and underperforming portfolios were formed by ranking stocks on their previous 36 month performance. (Reproduced from De Bondt and Thaler s paper, Does the Stock Market Overreact? ). 361 CAPITAL (866) 361-1720 Page 2

Analysis of Short Term Mean Reversion Portfolio This paper examines the existence of short term mean reversion in S&P 500, S&P 400, and S&P 600 stocks from 1/1/1995 to 12/31/2012 using a 1 month relative mean reversion model. A systematic ranking process was followed at the end of every month over the analysis period in order to identify the best mean reversion candidates. Mean Reversion Ranking: 1. Rank the index s stocks on their prior one month return from worst performing to best performing. 2. Group ranked stocks into quintiles. The first quintile (quintile 1) contains the worst performing stocks in the index, which are considered the most likely to outperform next month. Conversely, the last quintile (quintile 5) contains the best performing stocks, which are considered the least likely to outperform next month. 3. Perform steps 1 & 2 on the S&P 500, S&P 400, and S&P 600. 4. Average the S&P 500, S&P 400, and S&P 600 quintile breakdowns into a single combined quintile breakdown. 8 Specifically, 1/3 of the combined quintile 1 is the S&P 500 s first quintile, 1/3 is the S&P 400 s first quintile, and 1/3 is the S&P 600 s first quintile. 9 To test the hypothesis that short term mean reversion exists in stocks, the returns of quintile 1 (Q1) and quintile 5 (Q5) were compared and the monthly returns of the mean reversion portfolio were analyzed. If mean reversion is truly a positive return driver, quintile 1 s returns should consistently outperform quintile 5 s returns over the simulation history, creating a statistically significant positive return series for the mean reversion portfolio. Figure 2 depicts the annualized performance of the combined quintiles over the analysis period. Quintile 1 outperformed quintile 5 by 6.64% annually. The annualized returns for each quintile were also monotonically decreasing from quintile 1 to quintile 5. This illustrates that there was consistent information transfer from the mean reversion ranking methodology to each quintile s long term performance; a sign of a statistically robust model. Specifically, there was a positive return spread between quintile 1 and quintile 2, quintile 2 and quintile 3, and so on. If there was only a positive return spread between quintile 1 and quintile 5, then the ranking methodology might have been picking up on a spurious relationship. Instead, the monotonically decreasing quintile returns indicate a strong relationship between a stock s recent underperformance and its ensuing outperformance for the next month. Annualized Combined Quintile Returns 1/1/1995-12/31/2012 18% 15% 14.43% 14.09% Annualized Return 12% 9% 6% 12.21% 10.80% 7.79% 3% 0% Q1 Q2 Q3 Q4 Q5 Quintile Figure 2: Annualized combined quintile returns from the mean reversion ranking from 1/1/1995 to 12/31/2012, gross of transaction costs. Quintile 1 outperformed quintile 5 by 6.64% annually. 8 The three universes were ranked separately and then combined into an all-capitalization mean reversion portfolio in order to remove significant market capitalization biases in quintiles that might occur if the universes were ranked together. If the entire S&P 1500 universe was ranked together, any given month could result in quintile 1 having a significant capitalization bias relative to quintile 5 solely due to the underperformance of one market capitalization style relative to another. 9 Each of the combined quintiles contains 100 S&P 500 stocks, 80 S&P 400 stocks, and 120 S&P 600 stocks for a total of 300 stocks per quintile. Because each of the index quintiles comprises 1/3 of the combined quintile, the 100 S&P 500 stocks are each weighted 0.33%, the 80 S&P 400 stocks are each weighted 0.42%, and the 120 S&P 600 stocks are each weighted 0.28%. 361 CAPITAL (866) 361-1720 Page 3

The outperformance of quintile 1 over quintile 5 is further exemplified by the growth of a $10,000 investment in each of the two quintiles from 1/1/1995 to 12/31/2012. Investing $10,000 in quintile 1 at the start of 1995 would have yielded a final portfolio value of $113,224 at the end of 2012 while investing in quintile 5 would only have yielded a portfolio value of $38,604; a difference of 193%. Quintile 1 also outperformed the Combined Quintile Average 10 by 45.57% over the time period. The results presented thus far demonstrate that quintile 1 substantially outperformed quintile 5. A profitable investment strategy can be formulated to exploit this mean reversion phenomenon by buying quintile 1 stocks and shorting quintile 5 stocks, which captures the performance spread between the two quintiles while remaining market neutral. Growth of $10,000 invested in Quintile 1, Quintile 5, and the Combined Quintile Average $120,000 $100,000 $80,000 $113,224 $77,782 $60,000 $40,000 $38,604 $20,000 $- Quintile 1 Quintile 5 Combined Quintile Average Figure 3: Growth of $10,000 invested in quintile 1, quintile 5, and the Combined Quintile Average from 1/1/1995 to 12/31/2012. Growth does not account for transaction costs. Long/Short Mean Reversion Portfolio Construction: 1. Go long quintile 1 and short quintile 5 from the combined quintile breakdown to create a market neutral, long/short portfolio. 2. Hold long and short positions until the end of next month. 3. Rebalance portfolio at end of next month. The above ranking and portfolio construction methodologies were simulated over the analysis period using Bloomberg s Factor Backtester 11 with an assumption of 0.15% per month in transaction costs. 12 The resulting mean reversion portfolio produced an annualized net return of 4.68% over the analysis period with a correlation to the S&P 500 of only 36.53%. To measure the statistical validity of the mean reversion portfolio s performance, a comparison was done to a randomly constructed market neutral portfolio (long a random quintile and short a random quintile). Although the mean reversion portfolio was profitable, if a portfolio constructed in a random fashion outperforms it over the analysis period, then the short term mean reversion anomaly is likely a statistical artifact 13 observed only by chance. To determine if the performance of the mean reversion portfolio was an artifact, the portfolio s returns were bootstrapped 14 to create multiple unique return series. The annualized return was calculated for each return series in the bootstrap and aggregated to form a distribution of expected annualized returns for the mean reversion portfolio. Additionally, a random portfolio was built for each bootstrap sample by investing long in a random quintile and short in a different random quintile for every month in the return series. The distribution of the mean reversion s samples was then compared to the distribution of the random samples to test if they were statistically different. 10 The Combined Quintile Average is calculated by averaging the five quintiles from the combined quintile breakdown and rebalancing at the end of every month. 11 Bloomberg s Factor Backtester was used to conduct the historical simulations so that this paper s results can be reproduced by other researchers. For exact methodology on using Bloomberg s Factor Backtester, please see the Bloomberg Factor BackTesting Methodology Guide. 12 Similar mean reversion models were backtested on 361 Capital s proprietary software and transaction costs were consistently estimated to be between 0.05% and 0.15% per month. 13 A statistical artifact is a spurious finding that has no expectation to persist in future data sets. 14 Bootstrapping is a method of resampling a set of returns many times to create alternate return histories. This allows for estimation of distribution characteristics that are not directly observable from a single return set s history. 361 CAPITAL (866) 361-1720 Page 4

Bootstrapped Annualized Return Distribution Annualized Return (net of transaction costs) Mean Reversion Portfolio Random Portfolio Figure 4: Bootstrapped annualized net return distribution for the mean reversion portfolio and the random portfolio. Figure 4 demonstrates that the mean reversion portfolio s bootstrapped return distribution was distinctly different than the random portfolio s distribution. The mean reversion portfolio had a bootstrapped average annualized return of 4.78%, net of transaction costs. The random portfolio had a bootstrapped average annualized return of -1.93%. These results yielded a t-score 15 of 8.60 and a KS-score 16 of 3.65, both indicating that the mean reversion portfolio s average return was statistically better than the random portfolio s average return at the 99% confidence level. Because the mean reversion portfolio s returns were significantly better than a random portfolio s returns, it is unlikely that the phenomenon of short term mean reversion is a statistical aberration. Avoiding Falling Knives One possible solution to negate this trapping effect is to filter out companies with questionable financial fitness. A filter for financially healthy companies should remove stocks that become falling knives due to financial duress, reducing their detrimental impact on the first quintile. To test this hypothesis, a simple fundamental filter designed to identify companies with stable cash burn rates was applied to the historical simulation every month. Specifically, the filter compared a company s cash flow from operations (CF) to its working capital (WC) in an effort to screen out companies that either do not have sufficient working capital to support their cash burn rate or companies that do not have sufficient cash flow to support their working capital deficit. The rules of the filter are detailed in Table 1 and the improved performance of the filtered universe is highlighted in Figure 5. Runaway declining stocks, typically labeled falling knives, are a concern in a mean reversion portfolio. Because the portfolio is always long stocks that have underperformed, it is at risk of constantly trying to catch these falling knives. A potential reason for why this occurs is stocks in a precipitous selloff flow through the second quintile and get trapped in the first quintile of a mean reversion ranking. These stocks then stay in the first quintile until they either revert or become delisted. The longer they sit in the first quintile, the more potential damage they can do. 15 A two sample t-score measures the statistical significance between the two means of the samples. The higher the absolute value of the score, the more statistically significant the difference is. A value of 1.96 would indicate statistical significance at the 95% confidence level. 16 The Kolmogorov Smirnov score is a non-parametric measure of the difference between two samples. Where the t-score only identifies differences between the sample means, the KS-score considers differences between the means, deviations, skew, and kurtosis. The KS-score tends to be a more robust measure when the assumption of normality is violated. Like the t-score, the higher the absolute value of the KS-score, the more statistically significant the difference is. A value of 1.36 would indicate statistical significance at the 95% confidence level. 361 CAPITAL (866) 361-1720 Page 5

Table 1: Cash Burn Rate Screen Working Capital 0 Working Capital < 0 Cash Flow 0 PASS If CF > ABS(WC) then PASS else FAIL Cash Flow < 0 If WC > 2*ABS(CF) then PASS else FAIL FAIL Annualized Return 18% 15% 12% 9% 6% 3% 14.43% Annualized Combined Quintile Returns: Unfiltered v. Filtered 1/1/1995-12/31/2012 16.45% 0% Q1 Q2 Q3 Q4 Q5 Quintile Unfiltered Filtered Figure 5: Mean reversion portfolio annualized quintile returns (unfiltered and filtered) from 1/1/1995 to 12/31/2012, gross of transaction costs. Filtered quintile 1 outperforms unfiltered quintile 1 by 2.02% annually. The filtered mean reversion portfolio was also compared to the unfiltered portfolio via bootstrapping to assess the statistical significance of the increased performance. The filtered portfolio had a bootstrapped average three year annualized return of 6.84%, net of transaction costs. The unfiltered portfolio had a bootstrapped average three year annualized return of 4.78%. These results yielded a t-score of 2.21 (significant at the 99% confidence level) and a KS-score of 1.10, indicating that financially distressed companies are likely a drag on the performance of mean reversion strategies. Although simplistic, this systematic method for identifying financial quality is one step that could be taken to improve risk and returns of a mean reversion portfolio. Table 2: Summary of Unfiltered Mean Reversion Portfolio and Filtered Mean Reversion Portfolio Unfiltered Filtered Avg. Net Month Return 0.48% 0.65% Annualized Net Return 4.68% 6.85% Standard Deviation 15.99% 15.86% Return/Deviation 0.29 0.43 t-score 8.60 11.53 KS-score 3.65 4.70 361 CAPITAL (866) 361-1720 Page 6

Short Term Mean Reversion Factors and Correlations Based on the vast amount of historical evidence it is clear that mean reversion is a persistent anomaly that can be exploited by going long underperforming stocks and short outperforming stocks. However, the relationship between mean reversion and other market factors is also of interest. For instance, it is useful to understand if the portfolio had a bias towards value stocks, or if it tended to favor stocks with low quality earnings growth, or stocks with low quality balance sheets. Multi-factor linear regressions were run against the mean reversion portfolio s monthly returns to estimate linear relationships between the portfolio and explanatory factors. Table 3: Style/Strategy Factor Monthly Correlations Factors with statistically significant regression coefficients indicate a material relationship between short term mean reversion and that factor. Two factor models were analyzed: one focusing on investment style factors and the other on market environment factors. Style/Strategy Factor Model Seven unique investment styles/strategies were regressed on the monthly returns of the mean reversion portfolio: market capitalization i, balance sheet quality (BSQ) ii, earnings variability (EV) iii, value iv, growth v, 12 month momentum vi, and 1 month sector mean reversion vii. Beta xi was excluded from the factor model because of its high absolute correlation (77.78%) with earnings variability. MR Port Mkt Cap Beta BSQ EV Value Growth Momentum Sector MR MR Port 100.00% Mkt Cap 15.65% 100.00% Beta 31.20% 14.42% BSQ 2.28% -51.23% EV -31.68% -11.04% Value 18.78% 15.96% Growth 1.68% -44.63% Momentum -36.07% -45.42% Sector MR 80.96% 4.01% 100.00% 40.21% 100.00% -77.78% -35.98% 100.00% -49.24% -57.60% 37.88% 100.00% 3.28% 48.35% -11.47% -22.13% 100.00% -47.27% 24.03% 39.64% -24.21% 15.08% 100.00% 1.93% -1.49% -5.89% 18.25% 16.99% -12.31% 100.00% Table 4: Style/Strategy Factor Model Coefficients t-score P-value Lower 95% Upper 95% Intercept (alpha) 0.55% 3.61 0.0004 0.25% 0.86% Mkt Cap 3.73% 0.58 0.5602-8.88% 16.34% BSQ 27.78% 3.17 0.0017 10.51% 45.04% EV -38.14% -5.28 0.0000-52.38% -23.90% Value 16.20% 3.48 0.0006 7.02% 25.39% Growth -24.16% -3.93 0.0001-36.28% -12.05% Momentum -9.72% -3.25 0.0013-15.60% -3.83% Sector MR 83.47% 23.01 0.0000 76.32% 90.62% The seven factor model (Table 4) explained 78.03% 17 of the variance in the monthly returns of the mean reversion portfolio over the history of the simulation. Even considering the explanatory power of the factor model, the mean reversion portfolio still exhibited a statistically significant alpha of 0.55% per month 18, net of transaction costs. The most significant factor in the regression was the sector mean reversion factor. This factor had a high correlation to the mean reversion portfolio (80.96%), explaining the majority of the variation in the portfolio s returns. This positive relationship is to be expected because both the mean reversion portfolio and the sector mean reversion factor were designed to capitalize on 1 month mean reversion in equities. However, the positive relationship suggests that a portion of the mean reversion portfolio s returns were attributable to sector bets. For example, quintile 1 might have more exposure to the technology sector than quintile 5 in any given month, creating a positive sector bet on technology for the portfolio that month. 17 The regression had an adjusted R 2 of 78.03%. 18 The mean reversion portfolio and all seven explanatory factors were examined on a market neutral basis; therefore, the risk free rate over the simulation period was not taken into account because the cash generated from short sales could have been invested at the risk free rate. 361 CAPITAL (866) 361-1720 Page 7

Monthly Return of Mean Reversion Portfolio 30% 20% 10% 0% -10% -20% Sensitivity of Mean Reversion Portfolio to Sector Mean Reversion Factor y = 0.6648x + 0.0022 R² = 38.83% y = 1.1802x - 0.0019 R² = 61.75% -30% -30% -20% -10% 0% 10% 20% 30% Monthly Return of Sector Mean Reversion Factor Linear (Sector MR Negative) Linear (Sector MR Positive) Figure 6: Historical scatter plot of mean reversion portfolio returns v. sector mean reversion factor returns. Figure 6 illustrates the relationship between the mean reversion portfolio and the sector mean reversion factor. An interesting feature of this relationship is that the magnitude of the relationship increases when the sector mean reversion factor is positive (green line) and decreases when the factor is negative (red line). Explicitly, the slope of the green line is 77.52% larger than the slope of the red line and the R 2 of the positive linear relationship is 59.02% larger than the negative linear relationship. This implies that mean reversion gets a larger tail wind when sector mean reversion is working and a smaller head wind when sector mean reversion is not working. Finally, the portfolio also had a mild negative correlation to momentum (-36.07%). Although the momentum factor exhibited a statistically significant t-score, its effect size was also fairly low implying that the strength of momentum in stock movements could change substantially without significantly impacting the performance of the mean reversion portfolio. The value factor and earnings variability factor both showed a statistically meaningful relationship to the mean reversion portfolio. The portfolio had a positive bias towards value stocks (18.78% correlation) and a negative bias towards stocks with higher earnings variability (-31.68% correlation). However, the absolute correlations of these factors to the portfolio were relatively low, indicating that the effect size 19 of these style biases are small enough that they do not substantially impact the performance of the strategy over time. 19 Effect size measures the strength of the relationship between two variables without reflecting the statistical significance of the relationship. 361 CAPITAL (866) 361-1720 Page 8

Mean Reversion Return 10% 8% 6% 4% 2% 0% -2% -4% -6% -8% Sensitivity of Mean Reversion Portfolio to Momentum Factor y = -0.2502x + 0.0051 R² = 13.01% -10% -10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10% Momentum Return Figure 7: Historical scatter plot of mean reversion returns v. momentum returns. Line represents linear sensitivity of mean reversion to momentum. Table 5: Percentage Breakdown of Monthly Returns of Mean Reversion Portfolio v. Momentum Factor Negative Momentum Positive Momentum Positive Mean Reversion 27.31% 24.54% Negative Mean Reversion 17.59% 30.56% Figure 7 demonstrates the insensitivity of the mean reversion portfolio to shifts in momentum. Using a single factor linear model between momentum and the mean reversion portfolio (black line), the average expected return for the mean reversion portfolio, assuming the momentum strategy returned 10% in a month, would be -1.99%. Alternatively, if the momentum strategy returned -10% in a month, the average expected return for the mean reversion portfolio would be +3.01%. The wide spread of observations in Figure 7 highlights that there was a large degree of deviation from these averages. Table 5 also shows that, despite the negative correlation between the mean reversion portfolio and the momentum factor, 24.54% of the time both strategies had positive returns. These findings articulate the complementary relationship between mean reversion and momentum, confirming Balvers and Wu s (2004) findings that the two strategies can profitably coexist. 361 CAPITAL (866) 361-1720 Page 9

Environment Factor Model Seven unique market environment factors were regressed on the monthly returns of the mean reversion portfolio: volatility x, volatility change xi, average earnings yield xii, average volume ratio xiii, correlation xiv, dispersion xv, and noise xvi. The seven factors only explained 1.37% of the variance in the monthly returns, indicating that the portfolio s profitability was insensitive to many different market environments. Table 6: Market Environment Factor Model Coefficients t-score P-value Lower 95% Upper 95% Intercept -1.69% -0.23 0.8154-15.93% 12.56% Volatility -1.18% -0.20 0.8446-13.00% 10.65% Volatility Change -0.83% -0.97 0.3343-2.51% 0.86% Avg. Earnings Yield 6.44% 0.38 0.7069-27.27% 40.14% Avg. Volume Ratio 0.22% 0.08 0.9374-5.25% 5.69% Correlation -3.67% -1.07 0.2837-10.40% 3.06% Dispersion 19.24% 1.38 0.1705-8.34% 46.83% Noise 1.90% 0.21 0.8346-16.05% 19.85% The statistically insignificant relationship between the mean reversion portfolio and the intra-market correlation and dispersion factors is worth noting. It is widely believed that spread strategies (strategies that derive their return from a combination of long and short positions) are sensitive to intramarket correlations and dispersion. The assumption is that the higher the correlation between stocks and the lower the dispersion between returns, the less opportunity there is for a spread strategy to capture profits. However, the negligible relationship of the correlation and dispersion factors imply that profitable mean reversion opportunities can exist in highly correlated, low dispersion environments. Even still, the magnitude of the mean reversion portfolio s return were sensitive to market dispersion. Figure 8 reveals that as dispersion increased so did the absolute return and risk of the portfolio. The residuals of the linear regression between market dispersion and absolute return of the mean reversion portfolio were heteroscedastic, 20 showing a significant increase in variance as dispersion increased. These findings reveal that the volatility of a market neutral mean reversion portfolio will likely increase as market dispersion increases, but the profitability of the portfolio should not materially change. Absolute Monthly Return 30% 25% 20% 15% 10% 5% Mean Reversion Portfolio Absolute Monthly Return v. Average Monthly Dispersion 1/1/1995-12/31/2012 y = 0.4968x - 0.0241 R² = 28.97% 0% 0% 5% 10% 15% 20% 25% 30% Average Monthly Dispersion Negative Month Positive Month Linear (Abs. Mean Reversion Return) Figure 8: Scatter plot of the mean reversion portfolio s absolute monthly return and the dispersion factor from 1/1/1995 to 12/31/2012. Green and red dots differentiate between positive and negative return months for the mean reversion portfolio. 20 Heteroscedasticity describes the existence of non-normality in the residuals of an explanatory model, suggesting that there is an unexplained pattern in the data. 361 CAPITAL (866) 361-1720 Page 10

Unfavorable Market Environments for Short Term Mean Reversion The previous two factor analyses of the mean reversion portfolio highlighted that a short term, market neutral mean reversion strategy has low exposure to other investment styles and is relatively insensitive to market environments. However, short term mean reversion is still susceptible to periodic underperformance. Rolling Return 80% 60% 40% 20% 0% -20% -40% -60% -80% Rolling 12 Month Return of Mean Reversion Por olio and Momentum Factor MR worst rolling return: -28.45% @ 15.28% avg. dispersion MR best rolling return: 60.91% @ 14.91% avg. dispersion 20% 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% Rolling Dispersion MR Port Momentum Dispersion (rolling 12m avg.) Figure 9: Rolling 12 month returns of the mean reversion portfolio and the momentum factor from 12/31/1995 to 12/31/2012. The 12 month average of the dispersion factor is plotted on the right axis. Figure 9 displays that the mean reversion portfolio experienced periods of negative rolling 12 month returns over the simulation, the worst of which lasted 33 months (Feb. 2007 to Oct. 2009) with a max negative rolling 12 month return of -28.45%. A runs test for non-randomness indicated the portfolio s monthly returns were streaky, 21 leading to extended periods of both positive and negative rolling 12 month returns. Also from Figure 9, it is clear that the portfolio had its best and worst rolling 12 month returns in environments where there was high dispersion. As previously mentioned, periods of high dispersion increase both the expected return and the expected risk of spread strategies which can create streaks of outperformance and underperformance. Even though momentum is only mildly inversely correlated to mean reversion (-36.07%), Figure 9 portrays that the two strategies complement each other well, especially in time of stress. 21 Conducting a runs test for non-randomness on the mean reversion portfolio s monthly returns produced a z-score of -2.03. This z-score is statistically significant at the 95% confidence level, suggesting that the strategy s monthly returns exhibit more streaks than would be expected if a random process generated the data. 361 CAPITAL (866) 361-1720 Page 11

Conclusion Numerous academic studies have demonstrated the existence of long term mean reversion in equities over the last nine decades. However, there is substantial evidence that short term mean reversion is an equally prevalent phenomenon. The recent decline in implementation barriers for short term trading has allowed short term mean reversion to become a viable alternative investment strategy. The mean reversion portfolio presented in this paper outperformed a random portfolio by 6.71% annually, confirming that short term mean reversion is a consistent source of robust returns. The portfolio did exhibit sensitivity to sector mean reversion, but the exposure was asymmetrically beneficial to the portfolio. The mean reversion portfolio also had a low correlation to momentum, indicating that the two strategies are complementary and can profitably coexist. Furthermore, it was shown that systematically filtering out companies with questionable financial fitness improves the risk adjusted returns of a market neutral mean reversion portfolio. However, there are times when short term mean reversion investing will struggle. In periods of high price momentum or when growth and earnings variability factors are heavily in favor, this strategy has the potential to underperform. High dispersion environments and the strategy s tendency to exhibit streaky returns also present increased risk for a mean reversion portfolio. Nonetheless, short term mean reversion is a systematic method for gaining exposure to recently underperforming stocks. Because of their underperformance, these stocks reward mean reversion investors with a unique return factor that is not a material component of other investment styles and therefore typically overlooked. Ultimately, mean reversion is the byproduct of behavioral biases in investors. These biases are imbedded in human nature and will continue to impact equities over future market cycles. About the Authors Aditya Bhave is an analyst at 361 Capital. He is responsible for performance reporting, trading strategy development and testing, risk analysis, proprietary software development, database design, equity and futures trading and quantitative research. Mr. Bhave has experience working with a variety of programming languages and database structures. Prior to joining 361 Capital, Mr. Bhave was a Data Analyst for a local marketing firm. He has also held multiple leadership positions at Franklin & Marshall College. Mr. Bhave graduated from University of Denver s Daniels College of Business with a Master of Science in Finance. He received his Bachelor of Arts degree in Finance and Economics from Franklin & Marshall College. Nick Libertini is an analyst at 361 Capital. He focuses on trading strategy development and testing, risk analysis, proprietary software development and quantitative research. Mr. Libertini has experience working with a variety of programming and statistical languages. His research interests include machine learning methodologies, advanced statistical analysis and stochastic modeling. Mr. Libertini graduated from the University of Denver s Daniels College of Business with a Master of Science in Finance where he was awarded Outstanding M.S.F. Student 2011. He also holds a Bachelor of Science in Mechanical Engineering with a minor in Economics from the Colorado School of Mines. 361 CAPITAL (866) 361-1720 Page 12

References Balvers, Ronald J. and Wu, Yangru, 2004, Momentum and Mean Reversion Across National Equity Markets. Hong Kong Institute for Monetary Research and Singapore Management University. Berger, Adam L., Israel, Ronen and Moskowitz, Tobias J, 2009, The Case for Momentum Investing. AQR Capital Management. De Bondt, Werner F. M., Does the Stock Market Overreact to New Information? Unpublished Ph.D. dissertation, Cornell University 1985. De Bondt, Werner F. M. and Thaler, Richard, 1984, Does the Stock Market Overreact? The Journal of Finance 40 (December 28-30, 1984), 793-805. Jegadeesh, Narasimhan, 1990, Evidence of Predictable Behavior of Security Returns. The Journal of Finance 45 (July, 1990), 881-898. Kanhneman, Daniel. Thinking, Fast and Slow. Farrar, Straus and Giroux, 2011. Kanhneman, Daniel and Tversky, Amos, 1977, Intuitive Prediction: Biases and Corrective Procedures. Defense Advanced Research Projects Agency. Kolmogorov-Smirnov test, Wikipedia, accessed on February 27, 2013. Molinari, Gioel, 2012, Bloomberg Factor BackTesting Methodology Guide, Bloomberg Financial, January, 2012 Version 1.1. Poterba, James M. and Summers, Lawrence H, 1987, Mean Reversion in Stock Prices: Evidence and Implications. National Bureau of Economic Research. Student s t-test, Wikipedia, accessed on February 27, 2013. i Market capitalization style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked on market capitalization from smallest to largest and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. ii Balance sheet quality style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked separately on current ratio, cash flow per share, and financial leverage ratio (total assets / total equity). Better ranks were given for larger current ratios, larger cash flow per share, and smaller leverage ratios. The universe was then ranked by the average of the three sub-ranks from best average (highest balance sheet quality) to worst average (lowest balance sheet quality) and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. iii Earnings variability style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked separately on two ratios. Earnings volatility ratio: (standard deviation of EPS over the last 12 quarters) / (average of EPS over the last 12 quarters). Cash flow volatility ratio: (standard deviation of cash flow per share over the last 12 quarters) / (average of cash flow per share over the last 12 quarters). Better ranks were given for smaller earnings volatility and smaller cash flow volatility. The universe was then ranked by the average of the two sub-ranks from best average (lowest earnings variability) to worst average (highest earnings variability) and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. iv Value style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked on trailing twelve month earnings yield from largest to smallest and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. v Growth style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked separately on 5 year free cash flow growth and 5 year sales growth. Better ranks were given for larger free cash flow growth and larger sales growth. The universe was then ranked by the average of the two sub-ranks from best average (highest growth) to worst average (lowest growth) and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. 361 CAPITAL (866) 361-1720 Page 13

vi Momentum style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked on momentum from largest to smallest and bucketed into quintiles. Momentum is defined as the total return of a stock over the past year excluding the most recent month. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. vii Sector mean reversion style factor: Nine sector monthly returns were calculated for each of the S&P 500, S&P 400, and S&P 600 every month. A sector s return was calculated by equally weighting the returns of each stock in the sector. Then, a long basket was created from the previous month s worst three performing sectors and a short basket from the best three sectors. The factor s monthly return was an average of the return spread between the long and short baskets for each of the 3 indices. viii Volatility style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked on 260 day return volatility from largest to smallest and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. ix Beta style factor: The constituents of the S&P 500, S&P 400, and S&P 600 were each ranked on 1 year betas, to the S&P 500, from largest to smallest and bucketed into quintiles. The return spread between Q1 and Q5 was averaged across the 3 indices and rebalanced monthly to create the factor. x Volatility environment factor: The rolling 20 day annualized volatility of the S&P 1500. xi Volatility change environment factor: The monthly percentage change of the rolling 20 day annualized volatility of the S&P 1500. xii Average earnings yield environment factor: The rolling 20 day average earnings yield of the S&P 1500. xiii Average volume ratio environment factor: The rolling 20 day average of the volume ratio for the S&P 1500. The volume ratio is defined as the 20 day average volume divided by the 252 day average volume. xiv Correlation environment factor: For the S&P 500, S&P 400, and S&P 600, the average correlation between each constituent s returns and its index s returns over the course of a month was found and then all the correlations for an index s constituents were averaged together. The index correlation levels were then averaged every month to create the factor. xv Dispersion environment factor: For the S&P 500, S&P 400, and S&P 600, the standard deviation of monthly returns of the constituents was calculated. The three standard deviations were then averaged every month to create the factor. xvi Noise environment factor: For the S&P 500, S&P 400, and S&P 600, the intra-month noise level of each constituent was calculated and then all the noises levels for an index s constituents were averaged together. The index noise levels were then averaged every month to create the factor. Noise level is defined as: 1 ABS(SUM(daily returns)) / SUM(ABS(daily returns)). The opinions are those of the 361 Capital Investment Team as of September 2013 and are subject to change at any time due to changes in market or economic conditions. The comments should not be construed as a recommendation of individual holdings or market sectors, but as an illustration of broader themes. 361 Capital makes no representation as to whether any illustration/ example mentioned in this document is now or was ever held in any products advised by 361 Capital. Past performance is not indicative of future results. Illustrations are only for the limited purpose of analyzing general market or economic conditions and demonstrating 361 Capital s research process. In preparing this document, 361 Capital has relied upon and assumed, without independent verification, the accuracy and completeness of all information available from public sources. 361 CAPITAL (866) 361-1720 Page 14