Orpheus Risk Management Indices

Mean Reversion

Regression to the mean was discovered in the nineteenth century by Francis Galton, a half cousin of Charles Darwin and a renowned polymath. What is truly noteworthy is that he was surprised by a statistical regularity that is as common as the air we breathe. Regression effects can be found wherever we look, but we do not recognize them for what they are.

Mean Reversion Failures and End of Behavioral Finance

Mean Reversion concept has been extensively used by behavioral finance experts to challenge conventional economics, which considers markets totally random. Behavioral finance has now proved that extreme groups regress to the mean over time. Findings of reversion in stock prices towards some fundamental values remain in literature for a decade. [ DeBondt and Thaler -1985 using overreaction showcased that a stock experiencing a poor performance over a 3-5 year of period subsequently tend to outperform that had previously performed relatively well. This implies that, on average, stocks which are ’losers’ in terms of returns subsequently become ’winners’ and vice versa.

Researchers in finance have long been interested in the long-run time-series properties of equity prices, with particular attention to whether stock prices can be characterized as random walk (unit root) or mean reverting (trend stationary) processes. If stock price follows a mean reverting process, then there exists a tendency for the price level to return to its trend path over time. If stocks which are losers become winners that means they are showing the property of mean reversion. Fama and French (1988) also report mean reversion in U.S. equity market using long-horizon regressions, and Poterba and Summers (1988) document evidence of mean reversion using the variance ratio test.

On one side behavioural finance usesmean reversion to suggest that markets are not all random, but on other side fails to acknowledge that understanding mean reversion failure is a bigger science than highlighting behavioural anomalies. The five aspects Thaler points out in his paper (a term he confidently used to suggest that behavioural finance will be the only form of finance left) are 1) The equity premium puzzle, 2) Predictability, 3) Dividends, 4) Volatility and 5) Volume myth. All of these five aspects can be explained as mean reversion failures.

Redefining Mean Reversion; Extreme Reversion

Mean reversion phenomenon is not specific to stock market data, but data from any natural system. We proved this by using rankings derived from price performance data. A test for random walk hypothesis can be done by Dickey and Fuller [1979, 1981] and the Philips and Perron [1988, PP] method. ADF and PP tests are not so strong to test stationarity (mean reversion) because the test fails to detect slow-speed mean reversion in small samples. Hence the failure to reject the null hypothesis may not be interpreted as decisive evidence against mean reversion. Because of this inherent problem, researchers have advocated pooling data (testing various time series simultaneously) and testing the hypothesis in a panel framework to gain test power. Choudhuri and Wu [2002] showed the presence of mean reversion in emerging market using panel based test. We have applied the panel based tests on outliers from our performance ranking data.

In our academic submission to (Social Science Research Network)] we tested a database of composite group of assets from 2005 to 2011. We created various groups of assets and ranked them on a scale of 0.1% to 100% based on their performances over various holding peridsin last 1.5 years. The ranking data was a weekly time series of 1000 assets.

The worst performers, negative outliers are chosen based on the 81 week performance (1.5 years) i.e. rankings < 20 %. We tested this list of assets for change in ranking percentile. Positive change in ranking percentile suggests an outperformance and vice versa. Then the respective assets are tracked till 2011. All the assets which have reached the 50% rankings limit are tabulated. The assets that changed in rankings from below 20% to above 50% witnessed mean reversion (earlier losers to current winners). A test was made on 20 asset outliers (ranking < 20%), which moved from sub 20% ranking to above 50 % ranking limit during 2008 till 2011 period. Outlier Performance in last 5-6 years suggested that 44% to 25% of these negative outliers witnessed mean reversion tendency. The percentage number of reverting stocks increased to 60% as we reduced the reversion limit up till 50% ranking for different groups. This way we redefined ’Mean Reversion’ to ’Extreme Reversion’

Momentum; Reversion and Risk Preference

Active and Passive are two different risk preferences. It’s like the school of thought which says value is better than growth. We all have a risk preference, what if my risk preference is not about holding value (reversion) for the long term, but playing with growth (momentum) for a shorter term. It’s this risk preference the investing community has muddled up. The fruit market is for everybody, somebody needs apples, somebody needs oranges, and somebody grapes. If we don’t sell Beer to the Wine drinker, why do we undersell the Active as Stone Age to sell the glorious Passive and vice versa. There is no customer surprise, delight, satisfaction in the financial industry today. “This is the only solution”. We disagree. Our framework marries momemntum with reversion, value with growth according to a preferred risk preference.

Methodology; Styles and Universe

The Index can select, allocate, across any respective group components (Example SandP 500, DOW 30, BSE500, Sensex 30, FTSE 100, ETFS, Commodities etc.). RMI uses rankings, Jiseki performance cycles and other variables and allocates based on various risk preferences and investing styles among the filtered assets or group.

ACTIVE STYLE is a periodical entry and exit signals like the RMI Active US, RMI Active Toronto, RMI Active India. The difference between them is the underlying universe. RMI Active US and RMI Active Toronto selects components from the respective Universe. Active styles are cash conserving, absolute return Indexed models. They actively enter and exit a position and go cash if needed.

THEWORST 20 STYLE is about selecting the worst components from top 100 Universe (USA, Canada, UK, India etc.). This is a quarterly rebalanced portfolio and is more about relative performance vs. the underlying top 100. This style is not a cash conserving absolute return model, but about beating its respective peer universe. Because of the idea of negative outliers outperfrming, the worst 20 style outperforms the universe. So it’s portfolio basket easier to create and hold.

THE EXTREME REVERSION STYLE recreates the top benchmarks and sector indices. It’s an all invested strategy. For
example the Dow 30, TSX 60, Sensex 30 or various regional sector indices like Banking, Auto, Energy, Health Care etc. Why do we need to recreate the top benchmarks? There is a section of market that is not active and wants to outperform or assume exposure to top blue chip components and sector indices like Energy.

THE RELATIVE PERFORMANCE STYLE recreates the top benchmarks and sector indices using relative performance. It’s an all invested strategy. For example the Dow 30, TSX 60, Sensex 30 components, or the GSPTSE 50, or various regional sector indices like Banking, Auto, Technology, Pharma etc.

THE BEST 20 STYLE is about selecting the best components from top 100 Universe (USA, Canada, UK, India etc.). This is a periodically rebalanced portfolio vs. the underlying top 100. This style is not a cash conserving absolute return model, but about beating its respective peer universe. It’s a portfolio basket easier to create and hold.