## Information Ratio Analysis of Time-Series Momentum Strategy Thursday, 16 June, 2016

**A related paper has been added to:**

#118 - Time Series Momentum Effect

**Authors: **Ferreira, Silva, Yen

**Title: **Information ratio analysis of momentum strategies

**Link:** http://arxiv.org/abs/1402.3030

**Abstract:**

In the past 20 years, momentum or trend following strategies have become an established part of the investor toolbox. We introduce a new way of analyzing momentum strategies by looking at the information ratio (IR, average return divided by standard deviation). We calculate the theoretical IR of a momentum strategy, and show that if momentum is mainly due to the positive autocorrelation in returns, IR as a function of the portfolio formation period (look-back) is very different from momentum due to the drift (average return). The IR shows that for look-back periods of a few months, the investor is more likely to tap into autocorrelation. However, for look-back periods closer to 1 year, the investor is more likely to tap into the drift. We compare the historical data to the theoretical IR by constructing stationary periods. The empirical study finds that there are periods/regimes where the autocorrelation is more important than the drift in explaining the IR (particularly pre-1975) and others where the drift is more important (mostly after 1975). We conclude our study by applying our momentum strategy to 100 plus years of the Dow-Jones Industrial Average. We report damped oscillations on the IR for look-back periods of several years and model such oscilations as a reversal to the mean growth rate.

**Notable quotations from the academic research paper:**

"Similar to Moskowitz, Ooi and Pedersen, we focus on the momentum of individual assets. We study the technical rule (moving average of past returns) for one asset, therefore avoiding the portfolio effect that is important for cross-section momentum. This work adds to the paper of [ Moskowitz, T. J., Ooi, Y. H., Pedersen, L. H.. Time series momentum.] by looking at the information ratio of the time series momentum strategy. Our work also contributes to the literature of linking momentum to cycles/regimes. However, contrary to the previous studies, we do not associate economical episodes to the regimes. Our approach is to divide and transform the data in a way such that the final asset returns are as close as possible to stationary. We believe that our work is new in this respect.

We study momentum by looking at the risk adjusted performance measured by the information ratio (IR) as a function of the look-back lag used to construct the portfolio. Our main new contribution from a mathematical point of view, is to present in close form the risk associated with the momentum strategy. Previous works calculate the same expression for the average return as given here, however they do not calculate the standard deviation of the strategy. Furthermore, we analyze the stability of the results across time as non-stationary effects become important in explaining the results. We find that both autocorrelation and mean drift of the random process are important in the final performance of the strategy. In particular, for look-back periods up to 4 months, the most important effect is the autocorrelation; and for look-back periods larger than 4 months to 1 year, the drift. However, in contrast with previous studies, we find that the mean drift is the most important factor after 1975.

In case I, all the autocorrelations are zero, performance comes from the drift. In case II all performance comes from autocorrelation. Lag is in weeks.

"

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## Trend Model via Difference Between Long- and Short-Term Variance Wednesday, 8 June, 2016

**Related to CTA/trendfollowing strategies:
Authors: **Bouchaud, Dao, Deremble, Lemperiere, Nguyen, Potters

**Title: **Tail Protection for Long Investors: Convexity at Work

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2777657

**Abstract:**

We relate the performance of trend following strategy to the difference between a long-term and a short-term variance. We show that this result is rather general, and holds for various definitions of the trend. We use this result to explain the positive convexity property of CTA performance and show that it is a much stronger effect than initially thought. This result also enable us to highlight interesting connections with Risk Parity portfolio. Finally, we propose a new portfolio of options that gives us a pure exposure to the variance of the underlying, shedding some light on the link between trend and volatility, and also helping us understanding the exact role of hedging.

**Notable quotations from the academic research paper:**

"In this paper, we have shown that a single-asset trend has a built-in convexity if we aggregate its returns over the right time-scale. This becomes apparent if we rewrite the performance of the trend as a swap between the variance defined over long-term returns (typically the time scale of the trending filter) and the one defined over short-term returns (the rebalancing of our portfolio). This feature appears to hold for various filters and saturation levels.

**The importance of these 2 time-scales has been underlined, and it is clear that the convexity (and the hedging properties) are only present over long-term time scales (as defined by the trending filter itself): it is wrong to expect a 6-month trending system rebalanced every week to hedge against a market crash that lasted only a few days.**

We also turned our attention to CTA indices, and particularly the SG CTA Index. We have proposed a simple replication index, using a very natural un-saturated trend on a pool of very liquid assets. Assuming realistic fees, and fitting only the time-scale of the lter, we get a very good correlation (above 80%), and capture the drift completely. This shows again that CTAs are simply following a long-term trending signal, and there is little added value in their idiosyncrasies.

However, this also shows us that a CTA does not provide the same hedge a single-asset trend provides: some of the convexity is lost because of diversication. We however have found that CTAs do offer an interesting hedge to Risk-Parity products, which we approximated with a very good precision by long positions on the main asset classes.A ll in all, these results prove that a trending system does offer protection to long-term large moves of the market.

We then turned our attention to the link between trend and volatility. We found that a simple trending toy-model shares an exposure to the long-term variance with a naked straddle. The difference is the fact that the entry price for the straddle is fixed by the at-the-money volatility, while the trend pays the realized short-term variance. We then propose a very clean way to get exposure to this short term variance by using the trending toy-model as a hedging strategy for a portfolio of strangles. This is a simple, model-free portfolio that offers the same pay-off than traditional variance swaps."

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## Factor Attribution of Jim Cramer's ‘Mad Money’ Charitable Trust Performance Friday, 3 June, 2016

**Weekend reading, on a lighter note:
Authors: **Hartley, Olson

**Title: **Jim Cramer's ‘Mad Money’ Charitable Trust Performance and Factor Attribution

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2778724

**Abstract:**

This study analyzes the complete historical performance of Jim Cramer’s Action Alerts PLUS portfolio from 2001 to 2016 which includes many of the stock recommendations made on Cramer’s TV show “Mad Money”. Both since inception of the portfolio and since the start of “Mad Money” in 2005 (when it was converted into a charitable trust), Cramer’s portfolio has underperformed the S&P 500 total return index and a basket of S&P 500 stocks that does not reinvest dividends (both on an overall returns basis and in Sharpe ratio). These findings contrast with previous studies which analyzed Cramer’s outperformance in short windows before the 2008 financial crisis. Using factor analysis, we find that Cramer’s portfolio returns are primarily driven by underlevered exposure to market returns and in some specifications tilting toward small cap stocks, growth stocks and stocks with low quality of earnings. These results have broad implications for market efficiency, the usefulness of single name stock recommendations made on television, financial education, and the implementation of academic factors thematic in Cramer’s portfolio.

**Notable quotations from the academic research paper:**

"The usefulness of the financial advice from CNBC financial markets commentator Jim Cramer and other television finance personalities has historically been one of controversy.

Returns data from the Action Alerts Portfolio PLUS are provided by TheStreet.com which are also made available to the public (See Table 1, Figure 1). Subscribers are also given access to portfolio holdings data which we use to confirm some the findings of our risk factor analysis.

The results of the regressions are reported in Table 2. Analyzing the entire history of the portfolio, our CAPM specification finds a CAPM Beta of approximately 0.95 (statistically significant at the 1% level) and a negative alpha of -2.38% that is statistically significant (at the 10% level). Being underleveraged (underinvesting in the market portfolio) in part may be a result of the portfolio’s policy of not reinvesting cash dividends.

Across almost all of our specifications, the results demonstrate that underleverage explains most of the portfolios relative underperformance given the S&P 500’s positive absolute performance over the period. This is also confirmed by the portfolio holdings data which indicates that the AAP portfolio often holds a significant cash position, largely to make its annual cash distribution in March to make charitable contributions.

In our Fama-French (1993) three factor specification, we do find that the portfolio has some exposure to small caps given that the SMB factor is statistically significant at the 10% level, something confirmed by the portfolio holdings data. We do not find such a statistical significance when only looking at the entire history of Mad Money from 2005.

Also, when controlling for momentum factors in our Carhart (1997) four factor specification, statistical significance of the size factor also disappears nor do we find evidence of statistically significant exposure to momentum stocks.

However, we do find that when analyzing the March 2005 to March 2016 time period, when adding the extra size, value and momentum factors in the Fama-French (1993) and Carhart (1997) 4 Factor regressions that the statistical significance of the negative alpha of -3.06%, found in the CAPM for the same period, disappears.

When we include the Frazzini and Pedersen (2014) Betting-Against-Beta factor and the Asness, Frazzini and Pedersen (2013) Quality Minus Junk (QMJ) factor, we find some evidence that Cramer tilts toward growth stocks and away from stocks with high quality of earnings.

Using the factor analysis results obtained above, we also construct a “robo-Cramer” portfolio that uses the same factor loadings as estimated from the regressions. The systematic Cramer-style portfolio is constructed from the same regressions of monthly excess returns, namely the Carhart Four Factor regression using data over the entire time period (August 2001 to March 2016). The portfolio is rebalanced annually at year-end to keep constant weights. The explanatory variables are the monthly returns of the standard size, value, and momentum factors. Note that such a synthetic portfolio outperforms Cramer’s actual cumulative returns for the entire period.

"

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## Forecasting the VIX to Improve VIX-Derivatives Trading Wednesday, 25 May, 2016

**A related paper has been added to:**

#198 - Exploiting Term Structure of VIX Futures

**Authors: **Donninger

**Title: **Forecasting the VIX to Improve VIX-Derivatives Trading

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2771019

**Abstract:**

Konstantinidi et. al. state in their broad survey of Volatility-Index forecasting: "The question whether the dynamics of implied volatility indices can be predicted has received little attention". The overall result of this and the quoted papers is: The VIX is too a very limited extend (R2 is typically 0.01) predictable, but the effect is economically not significant. This paper confirms this finding if (and only if) the forecast horizon is limited to one day. But there is no practical need to do so. One can - and usually does - hold a VIX Future or Option several trading days. It is shown that a simple model has a highly significant predictive power over a longer time horizon. The forecasts improve realistic trading strategies.

**Notable quotations from the academic research paper:**

"Konstantinidi et. al. investigate in [E. Konstantinidi., G. Skiadopoulos, E. Tzagkaraki: Can the Evolution of Implied Volatility be Forecasted? Evidence from European and U.S. Implied Volatility Indices. Draft from 18/12/2007] different models for forecasting several volatility indexes one day ahead. There is no practical need to restrict the forecast to one day. The one day convention is for trading purposes unusual. One either trades intraday or over a longer time horizon. It is well known that the VIX has a mean-reverting behavior. Mean-reversion is swamped in the short run by the high volatility of the index. But it should be possible to exploit mean-reversion in the long run. The best – and most practical – model I have found is:

VIXret(h) = a0 + a1*VIX(t) + a2*VXV(t) + a3*IVTS(t)

VIXret(h) is log(VIX(t+h)) – log(VIX(t)) where h is the forecast horizon in trade days.

VIX(t) is the current VIX-value.

VXV(t) is the 3-months volatility index.

IVTS(t) is the implied-volatility-term-structure defined as VIX(t)/VXV(t).

The model uses the current VIX level, VXV can be interpreted as a smoothed version of the VIX. The IVTS is a measure of the current term-structure.

Campasano & Simon proposed in [J. Campasano, D. Simon: The VIX Futures Basis: Evidence and Trading Strategies. June 27, 2012] a simple VIX Futures strategy to exploit the positive bias.

The daily roll of a VIX-Future is defined as:

R(t) = (VXF(t) – VIX(t))/TTS(t)

VXF is the VIX Futures Price.

TTS are the Trade-days Till Settle (expiry).

One enters a short VIX Future position if R(t) is above a given threshold and sells the Futures back if the basis is either below a lower threshold or one is close to the expiry. One can replace the current VIX value with the VIX forecast at expiry. The strategy with the plain VIX has a P&L of 110.2% with a Sharpe-Ratio of 0.93 and a maximum relative drawdown of 18.2%. The forecast improves this to a P&L of 156.2%, a Sharpe-Ratio of 1.12 and a drawdown of 16.8%.

"

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## A Global Macroeconomic Risk Explanation for Momentum and Value Thursday, 19 May, 2016

**A related paper has been added to:**

#28 - Value and Momentum across Asset Classes

**Authors: **Cooper, Mitrache, Priestley

**Title: **A Global Macroeconomic Risk Explanation for Momentum and Value

**Link:** http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2768040

**Abstract:**

Value and momentum returns and combinations of them are explained by their loadings on global macroeconomic risk factors across both countries and asset classes. These loadings describe why value and momentum have positive return premia and why they are negatively correlated. The global macroeconomic risk factor model also performs well in summarizing the cross section of various additional asset classes. The findings identify the source of the common variation in expected returns across asset classes and countries suggesting that markets are integrated.

**Notable quotations from the academic research paper:**

"U.S. macreconomic risk factors can successfully describe the return premia on both value and momentum strategies, and combinations of them across both countries and asset classes. In addition, it can explain the negative correlation between these two return premia. We present three main results.

First, the positive return premia on value and momentum, across both asset classes and countries, can be explained by the estimated prices of risk and loadings on the global risk factors. For example, the value, momentum, and combination return premia that are aggregated across all asset classes and all countries are 0.29%, 0.34%, and 0.32% per month, respectively, and they are statistically significant. The global macroeconomic factor model produces expected returns that are 87%, 109%, and 103% of the actual return premia, respectively, with small and statistically insignificant pricing errors. We find similar results for separate asset classes and across different countries, thus, offering a unified macroeconomic risk explanation of value and momentum return premia.

The second result is that the negative correlation between the return premia can be explained by their differing factor loadings. For example, for the aggregated value, momentum, and combination return premia, the factor loadings on the global industrial production factor are -0.34 for value, 1.77 for momentum, and 0.80 for the combination. For global unexpected inflation they are -2.20, 7.81, and 3.16. For the change in expected inflation they are -1.69, 3.92, and 1.31. For global term structure they are 0.35, -0.01, and 0.17, and for global default risk they are -0.04, 0.17, and 0.07. Based on these loadings, we calculate the expected returns of the return premia and compare the expected

return correlations with the correlations of the return premia. For example, remaining with aggregated value and momentum across all asset classes and markets, the actual correlation between the value and momentum strategies is -0.48, whereas the implied correlation of the two strategies from their expected returns is -0.47. We also observe differing factor loadings within each asset class and country. These differences in the factor loadings allow us to match the actual negative correlation between value and momentum return premia with a negative correlation between the expected returns of value and momentum strategies across asset classes and countries.

The third result shows that the global macroeconomic factor model does a good job in explaining the return premia on the combinations of the value and momentum strategies both in the time series and cross section. This is interesting since Asness, Moskowitz, and Pedersen (2013) note that because of the opposite sign exposure of value and momentum to liquidity risk, the equal-weighted (50/50) combination is neutral to liquidity risk. However, we show that this 50/50 combination is not neutral to global macroeconomic risk even if the value and momentum return premia have opposite sign exposures with respect to the global macroeconomic factors. These exposures have different magnitudes and this is clearly seen when we examine the loadings of the combination strategies."

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