Often interesting ideas pop up when we look at same data but with different lenses. Many readers of the blog probably might be aware of Low Volatility Anomaly in markets. If you are not familiar with it and interested on that topic, then do a Google search for "Low Volatility Anomaly". You will find many articles, academic journal papers and explanations on that anomaly.
The low-volatility anomaly basically says portfolios of low-volatility stocks have produced higher risk-adjusted returns than portfolios with high-volatility stocks in most markets studied. Now often most of these low-volatility anomaly studies take one of the following two approaches -
Ranking-Based Approach:
In rankings based approach, the market or target segment (like large cap, small cap, emerging etc) is divided into deciles/quintiles based on a volatility measure. The division is such that securities in the lowest decile/quintile will be of low volatility. The portfolio is then invested in these low volatility deciles (or weighted heavier) and re-balanced monthly.
Minimum Variance Approach:
Another scheme is constructing minimum variance portfolios with the understanding minimum variance portfolios will have lowest risk. Then a weighting algorithm is used to determine the weights and limits for the selected securities & sectors belonging to that minimum variance portfolio. Then the portfolio is re-balanced monthly.
While the idea is good, I am not sure either of the above approaches are practical for individual traders unless one has large account and time. Also my personal preference when it comes to academic papers on trading is to generally pick the concept, understand the authors viewpoints, discard rest and figure my own way to incorporate those concepts for profitable outcome.
Capturing Volatility Premium:
IMO often good ideas come from simple rearrangement of concepts picked in various contexts over time. Applying that here, what do we know when it comes to volatility and these approaches -
- Volatility in markets is mean reverting i.e., low volatility begets high volatility and vice-versa.
- A big part of low volatility portfolio returns is due to periodic re-balancing of the portfolio.
Most would probably know above. Now combining the above two, it seems to me basically low volatility portfolio profits are more to do with volatility harvesting then the actual volatility level. In other words, following low-volatility anomaly, one buys low volatility stocks for portfolio and then sell those stocks when their volatility is high. The latter happens indirectly because of the periodic re-balancing of the portfolio.
If that is true, then why not simply pick few broad market (liquid) ETFs, buy when their volatility is low and sell when their volatility is high?
Let's put above hypothesis to test. The broad market ETFs chosen for the test are - Emerging Markets (EEM, Europe (EFA), Asia & Pacific (EPP), US Small cap (IJH) and US Mid cap (MDY).
Some Notes:
- Average True Range is used to measure volatility here. There are other ways to measure volatility. The choice of ATR as volatility measure is mostly a matter of convenience.
- The test results are frictionless i.e., no slippage and commissions.
- The test is done on weekly charts. Duration: 2000 - Current.
- The portfolio is weighted equally across the 5 major markets.
Results:
Following annotated images provides various performance stats. One can glean several insights both at individual market level as well as at portfolio level. Some highlights:
In the below image, notice the horizontal areas in the equity curve (black line) and the behavior of benchmark (red line) in those periods. The system goes into sidelines or has position only for a short time when the volatility is high in the benchmark. That is what we want.
The following image provides various performance stats and ratios both for individual markets and for portfolio. The pie-chart provides the color notation. Notice anything of interest in "Annualized Sharpe", "Sortino Ratio" and "Rolling Correlation" bar plots?
The below scatter plot shows where individual markets and equal weighted portfolio fall in annualized Risk-Return spectrum.
The last image provides detailed performance stats, calendar returns and draw downs etc. Looks like US Small cap has better returns of all whereas on risk-adjusted basis, the account seems to do better.
Now one idea doesn't make a system. The purpose of the test is basically to check for myself whether the hypothesis (i.e., buying and selling based on volatility level and price action )has legs and worth investigating further. The results are better than I expected for first round. The hypothesis seems to be worth investigating further. Thoughts?
I have not seen any low volatility anomaly studies on net that approach it this way. If you know of any studies/articles that discuss low volatility anomaly using approaches (besides ranking into deciles or using minimum variance) then please let me know.
Side Note: Like other tests on the blog, formulation of test rules, back-testing, analysis and visualizations are done using a proprietary software I developed over time. The software was built using R language and C#.
Wish you all good health and happy holidays!
This study is about bull and bear markets (S&P 500) performance by VIX regime. For the test, I used SPY etf as the proxy for S&P 500.
Definitions:
- Bull Market Phase - Market is above 200 day simple moving average.
- Bear Market Phase - Market is below 200 day simple moving average.
- VIX Regimes: 0-15 (low volatility), 15-30, 30-45, 45-60 (high volatility)
Bull Market Test
- Market is in Bull Market phase.
- Go long when market transitions from previous VIX regime to new regime.
- Exit long when market transitions from current VIX regime to next regime.
Bear Market Test
- Market is in Bear Market phase.
- Go short when market transitions from previous VIX regime to new regime.
- Exit short when market transitions from current VIX regime to next regime.
Misc
- Test Duration: 1996 t0 Current
- Friction less results i.e., no commissions, no slippage.
- Long only trades.
Results Analysis - Bull Markets:
- Profitable in all 3 VIX regimes. The Trades category provides an idea of how many times the market entered into a particular volatility range.
- The Win% is highest in VIX range 30-45. But the number of time market entered into that VIX range is relatively less.
- Average Win/Loss Ratio and Average trade returns are highest in VIX range 0-15. I wonder if it is because of low volatility anomaly in markets?
Results Analysis - Bear Markets:
- As expected, results show bear markets are more volatile than bull markets. Unlike bull markets, bear markets entered VIX 45-60 range multiple times.
- Long trades are profitable in the volatility regime 30-45. Not sure Why?
- Another is high average win/loss ratio in volatility regime 0-15. Why?
Feel free to let me know if your conclusions from results is different from above. Also I am curious to hear your thoughts on above 3 questions.
Note: The above is not a system nor it is a recommendation. Just a study of one of the market characteristics.
Today while scanning through WallStreetCurrents site, I came across a post on new Volatility ETF (VIXH). What caught my attention in that ETF prospectus was its rules based on VIX levels for buying VIX options. Thought will check out how those VIX rules would fare if I apply it on SPY.
Now rather than blindly buying SPY at each VIX level, thought I will combine with another study I am checking currently i.e., week of the day effect on SPY. (Note: If any readers are interested in pure VIX level based entries test then please let me know. I will do in one of the future posts).
Test:
- Divide VIX range into 4 levels : 0-15, 15-30, 30-45, 45-60. (Note: My levels are slightly different from ETF but that shouldn't make much difference).
- Buy @ market next day open and sell after 2 days. Note: Only one position at a time. Next position is opened after the current position is closed. I think this condition is more realistic.
- Finally tabulate the performance metrics categorized by VIX level and Week of the day.
- Test Duration - 1995 to 2012 Current. Caveats - Results are frictionless i.e., no slippage & no commission.
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| SPY ETF - Week of the day profile by VIX regime |
Results:
Some takeaways
- Poor performance of longs when VIX level is above 45.
- Low performance of longs when VIX level is below 15. But draw downs are also low. So may be risk parity approach to increase the returns.
- The sweet spot seems to be to go long on SPY only when VIX level is between 15-45.
In the ETF prospectus, rules related to VIX level are as follows:
- VIX futures less than or equal to 15, no VIX calls are purchased
- VIX futures above 15 and less than or equal to 30, 1% of portfolio in VIX calls
- VIX futures above 30 and less than or equal to 50, 0.50% of portfolio in VIX calls
- VIX futures above 50, no VIX calls are purchased
Your thoughts?
Continuing the series, this part examines the calendar day of month returns by volatility regime. You can find the prior two posts here and here. Now classifying volatility regimes into various levels is bit tricky. Often the approach taken is to measure and divide the volatility of market into static levels to classify as high/low/medium etc. Example: VIX level below 15 as low etc or historical volatility ratio above 30 as high etc. My preference is to use dynamic metrics that both adapt with market character and are also relevant to the cycle length of the strategy being evaluated.
Volatility Regime:
For this test, my definition of volatility regime and classification is as follows - Calculate the 50 day historical volatility of the underlying market. Then calculate the percentile rank of historical volatility for today in relation to last 20 days volatility. Then place current day volatility rank into one of the four buckets - (0-25), (25-50), (50-75) and (75-100).
Range 0-25 is the lowest volatility bucket, 75-100 is the highest volatility bucket and rest in between. There is nothing special about dividing the volatility range into 4 quarters. We could have as well classified into 3 parts or as 5 parts.
Test:
The test details are same as described in the first post except for one extra condition i.e., take trade only if today's volatility rank is in (0-25) bucket (for calendar strategy test in low volatility regime). Same for others volatility ranges. Same caveats as in prior posts apply here.
Results discussion:
I have intentionally left discussion of results in this and prior posts. My thinking was it is more fruitful for everyone to see the raw data, derive own conclusions and share with me & other readers your thoughts in either comments/LinkedIn discussion threads of this blog. That way I also gain new insights and learn something from you on these studies/concepts strength and weaknesses.
Thoughts on Max Drawdown..
On surface, the drawdown numbers of these studies appear quite high. So it is natural to write off and move on to something else. Unlike other studies, I am developing this strategy as I go along. So I don't know yet the direction this series takes or what the final numbers look like. But I think pursuing the concept is still promising for following reasons.
The strategy shows consistently positive edge (see this and last 2 studies) during certain days of the month for last 40 years. And the positive edge shows up on days different from conventional wisdom regarding End of Month strategies. For things related to market, I generally like stuff that either majority ignores or goes against their understanding.
Also at this stage we are just assessing whether the concept has positive edge or not with a dumb entry & exit tactic. There are several things one can do to reduce max drawdown significantly by the time strategy reaches final stages like fine tuning of entry tactics based on price action/stop losses/dynamic exit tactics/equity curve based money management/position sizing based on regime/volatility etc.
Third reason is the correlation of this to other methods. I have not yet done study but conceptually it appears to me this strategy results will likely have low correlation to other timing approaches and to SP500 returns. That makes the strategy pretty potent.For an idea, see the strategy diversification study (posted on blog couple weeks back) and the performance graphs (cumulative returns, max DD etc) of individual systems and combined portfolio. See also time diversification study.
Readers
I look forward to hear your thoughts and suggestions. We learn most when our views differ. So feel free to share your thoughts and more so if your views are opposite to above or on aspects not covered by above post.
Wish you all good health and good trading!
(Correction: Sept-04-2012...Updated the post with correct results image)
Recently I read an interesting journal paper on Volatility. Many people typically equate volatility with risk and view it as something to avoid/unavoidable. On other hand, there are ways one can systematically harvest and profit from volatility. I am not talking about gains from timing skill or choosing right stock etc. This topic is more about systematically harvesting the volatility of the underlying stock/asset to make additional profits.
Different market regimes favor different types of strategies. Some regimes favor trend following strategies while other regimes favor mean reversion strategies. Similarly some market regimes favor growth strategies whereas other regimes favor value based strategies. Similarly some regimes favor following crowd while other regimes favor going against crowd.
Also within each regime the performance of strategies varies.
I think knowing systematically what kind of market regime we are in and what type of strategies will be favored and by how much will be extremely helpful on several fronts.
Following tables has the results of a mean reversion strategy categorized by different levels (deciles) of market volatility for 3 markets - SPY, QQQ, DIA. (1990 - July 2012).
Markets can be relatively stable at some points in time and explosively volatile at others. This means that the risk associated with a traditional (fixed-weight) strategic asset allocation policy can be highly variable over time. This paper explores the possibility of a dynamic asset allocation policy that varies as market volatility changes. The conclusion of the paper is that a volatility responsive asset allocation policy can lead to a more consistent outcome and a better trade-off between risk and return.
One thought I had from this paper that I felt would be interesting to traders is - How about overweighting mean reversion setups when market volatility is high and breakout methods when volatility is low? Mean reversion works better when market has good swings (i.e., high volatility). Now many traders use volatility or ATR in bet sizing for valid reasons. But this makes the position size for MR methods small when volatility is high i.e., exactly when environment is conducive to the method.
Feel free to let me know any corrections to above or your thoughts.
We're quite volatile as individuals, but that doesn't work exponentially when we are together. Relationships are about eating humble pie ~ Unknown
