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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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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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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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 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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Cliff Asness (AQR Capital Management) on Factor Timing:

Authors: Asness

Title: The Siren Song of Factor Timing

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2763956

Abstract:

Everyone seems to want to time factors. Often the first question after an initial discussion of factors is “ok, what’s the current outlook?” And the common answer, “the same as usual,” is often unsatisfying. There is powerful incentive to oversell timing ability. Factor investing is often done at fees in between active management and cap-weighted indexing and these fees have been falling over time. Factor timing has the potential of reintroducing a type of skill-based “active management” (as timing is generally thought of this way) back into the equation. I think that siren song should be resisted, even if that verdict is disappointing to some. At least when using the simple “value” of the factors themselves, I find such timing strategies to be very weak historically, and some tests of their long-term power to be exaggerated and/or inapplicable.

Notable quotations from the academic research paper:

"Finding a factor with high average returns is not the only way to make money. Another possibility is to “time” the factor. To own more of it when its conditional expected return is higher than normal, and less when lower than normal (even short it if its conditional expected return is negative). An extreme form of factor timing is to declare a previously useful factor now forever gone. For instance, if a factor worked in the past because it exploited inefficiencies and either those making the exploited error wised up or far too many try to exploit the error (factor crowding) one could imagine the good times are over and possibly not coming back. I think of these as the “supply and demand” for investor error!7 Factor efficacy could go away either because supply went away or demand became too great.

Why do I call factor timing a “siren song” in my title? Well, factor timing is very tempting and, unfortunately, very difficult to do well. Nary a presentation about factors, practitioner or academic, does not include some version of “can you time these?” or “is now a good time to invest in the factor?” I believe the accurate answer to the first question is “mostly no.” However, my answer is usually met with at least mild disappointment and even disbelief. Tempting indeed.

I argue that factor timing is highly analogous to timing the stock market. Stock market timing is difficult and should be done in very small doses, if at all. For instance, Asness, Ilmanen, and Maloney (2015) call market timing a “sin” and recommend, using basic value and trend indicators, to only “sin a little.” The decision of how much average passive stock market exposure to own is far more important than any plausibly reasonable amount of market timing. Given my belief in the main factors described above – that is I do not think they’re the result of data mining or will disappear in the future – the implication is to maintain passive exposures to them with small if any variance through time. Good factors and diversification easily, in my view, trump the potential of factor timing.

While I believe that aggressive factor timing is generally a bad idea, there is one possible exception. Perhaps the only thing of interest in these value spreads would be if and when we see things unprecedented in past experience. The 1999-2000 tech bubble episode focused on by AFKL was indeed such a time. If timing were ever to be useful it would be at such extremes. Factors being “arbitraged away” or an extreme version of “factor crowding” would likely entail observing such extremes. In the extreme crowding case we’d see spreads in the opposite direction of what value experienced in 1999-2000 when the value factor looked much cheaper than any time in history. So, an “arbitraging away” would lead to a factor looking much more expensive than any time in history. To date, the evidence that this has already occurred is weak and mixed. For example, if you look at the “value spread” of the factors through time to judge them as cheap or expensive, you get very different answers depending on whether you use, say, book-to-price or sales-to-price. For instance, if you use book-to-price you’d find the value factors currently look cheap versus history (though nowhere near the levels of 1999-2000) and the non-value factors (things like momentum, profitability, low beta) look expensive. However, if instead you use sales-to-price to make this judgment you find current levels are far closer to historical norms.

In sum, here’s what I would suggest. Focus most on what factors you believe in over the very long haul based on both evidence (particularly out-of-sample evidence including that in other asset classes) and economic theory. Diversify across these factors and harvest/access them cost-effectively. Realize that these factors, like the stock market itself, are now well-known and will likely “crash” at some point again. So, invest in them if you believe in them for the long-term and be prepared to survive, not miraculously time, these events sticking with your long term plan. If you time the factors, and I don’t rule it out completely, make sure you only “sin a little.” Continue to monitor such things as the value spreads for signs these strategies have been arbitraged away – like value spreads across a diversified set of value measures being much less attractive and outside the historical reasonable range – signs that, as of now, really don’t exist."

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