Ho, ho, ho.... it's that time of year again! Will Santa come to town bearing gifts in the form of a rally in equites in the final week of the year? If you are not familiar with the Santa Claus rally, as this has come to be known as, it's the tendency for equities to rally during the final week of the year. Several factors have been ascribed to this phenomenon, some of which include the anticipation of the broadly known January effect, trades executed for tax and accounting reasons and portfolio managers window dressing their holdings with stocks that have performed well during the year. Regardless of the cause, up until the end of 2014 the propensity for this rally to unfold has been remarkable to say the least. I documented the performance of the Santa rally back in December 2014, so I'm interested to know how things have looked for Santa's good tidings since the last time I ran these numbers.
The Test Rules
The rules are simple, buy equites at the close in December on the first trade day that has a day of month value greater than 24. Exit all trades at the close on the first trade day of the New Year. I also included a liquidity filter to ensure we're transacting in liquid stocks, but other than that, there are no other rules to speak of. So, did Santa's generosity continue?
It appears Santa has been a little tight fisted of late. Although the rally continued during the 2014/2015 transition, they slowed somewhat relative to the recent past. The 2015/2016 rally was however strongly negative, which is no real surprise really given that 2016 saw the worst start to a year of trade in 18 years. Whether Santa will resume his run this year is yet to be seen, but I suspect that may well be the case.
Small sampled edges, such as Santa's, are much more likely to be negatively surprised (as in Nassim Taleb's turkey's surprise on Thanksgiving Day) than large sampled edges that have broad and deep confirmation. Therefore, one would never trade something like this in isolation, if at all. Moreover, the reason for the tendency, although intuitive, is very easily changed - managers catch on and stop window dressing at this time etc. – relative to say for instance an edge that exploits market participant's irrationality - it's much less likely that all market participants start to behave rationally.
Until next year, have a happy, safe and relaxing break through the festive season. I wish you everything of the best for the New Year. Thanks for your support and I look forward to another year together.
PJ Sutherland BSc, CMT
CEO QuantLab (Pty) Ltd
I was recently asked to be interviewed by Andrew Swanscott who runs bettersystemtrader.com. If you haven't heard of this site before, it's well worth a visit. Many of the trading legends that I have studied during the past ten years have shared their insights with Andrew during a Podcast. I wouldn't be where I am today without the generous sharing of knowledge by the countless individuals I've studied to date, so it was a great honour to have the opportunity to give back to the trading community with Andrew.
In the Podcast I discuss mean reversion in detail as well as some of the powerful ideas that we use within our platforms. If you're looking to gain a better understanding of our approach, or simply to broaden your trading knowledge, then this Podcast is well worth listening to. Hope you enjoy, and if you have any questions I'd be happy to answer them.
PJ Sutherland, BSc, CMT
CEO of QuantLab
The Sharpe Ratio
A well-known and often quoted measure of risk is the Sharpe ratio. Developed in 1966 by Stanford Finance Professor William F. Sharpe, it measures the desirability of an investment by dividing the average period return in excess of the risk-free rate by the standard deviation of the return generating process. In simple terms, it provides us with the number of additional units of return above the risk-free rate achieved for each additional unit of risk (as measured by volatility). This characteristic makes the Sharpe ratio an easy and commonly used statistic to measure the skill of a manager and can be interpreted as follows: SR >1 = lots of skill, SR 0.5-1= skilled, SR 0-0.5 = low skilled, SR = 0 = no skill and conversely for negative numbers. Although the Sharpe ratio can be an effective means of analysing investment performance, it has several shortcomings that one needs to be aware of and which I'll discuss below. But before I do, here is the formula for calculating the Sharpe ratio:
(Mean Portfolio Return – Risk-Free Rate) / Standard Deviation of Portfolio Return
The most obvious and glaring flaw is the fact that the Sharpe ratio does not differentiate between upside (good) and downside (bad) volatility. Thus, a performance stream that experiences more positive outliers (a good thing for investors) will simultaneously experience elevated levels of volatility which will decrease the Sharpe ratio. This means that one can improve the Sharpe ratio for strategies that exhibit a positive skew in their return distribution (many small losses with large infrequent gains), for instance trend following strategies, by simply removing some of the positive returns, which is nonsensical because investors generally welcome large positive returns.
On the flipside, strategies with a negative skew in their return distribution (many small gains with large infrequent losses), for instance option selling strategies, are much riskier than the Sharpe ratio would have us believe. They often exhibit very high Sharpe ratios while they are "working" because they tend to produce consistent small returns that are punctuated by rare but painful negative returns.
The reason for the shortcomings discussed above can be attributed to the fact that the Sharpe ratio assumes a normal distribution in returns. Although strategy and market returns can resemble that of a normal distribution, they generally are not; if they were then we would expect some of the market moves we've experienced within the last decade to occur once in a blue moon, but they evidently do not. This is the result of the phenomena referred to as "fat tails", or the market's higher probability of realising more extreme returns than one would expect from a normal distribution. This, in and of itself, is reason enough to be dubious of blindly evaluating a manager or strategy's performance based on a Sharpe ratio without an understanding of exactly how the returns are made.
One also needs to place the reason for the Sharpe ratio's initial development into perspective. It was conceived as a measure for comparing mutual funds, not as a comprehensive risk/reward measure. Mutual funds are a very specific type of investment vehicle that represent an unleveraged investment in a portfolio of stocks. Thus, a comparison of mutual funds in the 60's, when the Sharpe ratio was developed, was one between investments in the same markets and with the same basic investment style. Moreover, mutual funds at the time held long-term positions in a portfolio of stocks. They did not have a significant timing or trading component and differed from each other only in their portfolio selection and diversification strategies. The Sharpe ratio therefore was an effective measure to compare mutual funds when it was first developed. It is however not a sufficient measure for comparing alternative investments such as many hedge funds because they differ from unleveraged portfolios in material ways. For one thing, many hedge funds employ short-term trading strategies and leverage to enhance returns, which means when things go wrong money can be lost at a far greater rate. Moreover, they often do not provide the same level of internal diversification nor have lengthy track records.
Investors that do not understand the difference between long-term buy-and-hold investing and trading, often incorrectly measure risk as smoothness in returns with the Sharpe ratio. Smoothness does not equal risk. In fact, there is often an inverse relationship between smoothness and risk - very risky investments can offer smooth returns for a limited period. One need only consider the implosion of Long-Term Capital Management which provided very smooth and consistent returns (excellent Sharpe ratio) before being caught in the Russian default on bonds which created a financial crisis.
The strategies that we employ in QuantLab would be categorised as alternative in nature and do not mimic typical mutual funds. Therefore, the Sharpe ratio is not the most suitable measure to assess our performance. So, let's examine a couple of alternatives to the Sharpe ratio.
The Sortino Ratio
The Sortino ratio is like the Sharpe ratio but differs in that it takes account of the downside deviation of the investment as opposed to the standard deviation – i.e., only those returns falling below a specific target, for instance a benchmark. Formula:
(Mean Portfolio Return – Risk-Free Rate) / Standard Deviation of Negative Portfolio Returns
The Sortino ratio in effect removes the Sharpe ratio's penalty on positive returns and focuses instead on the risk that concerns investors the most, which is volatility associated with negative returns. It is interesting to note that even Nobel laureate Harry Markowitz, when he developed Modern Portfolio Theory (MPT) in 1959, recognized that because only downside deviation is relevant to investors, using it to measure risk would be more appropriate than using standard deviation.
We can see the effects of removing the penalty on positive outliers with the Sortino ratio by examining our live performance in QuantLab, which to date exhibits a strong positive skew - we've enjoyed several large positive outliers – so the Sharpe ratio unfairly penalises our performance. In fact, if we remove the effect of positive volatility (good for investors), QuantLab's risk-adjusted performance improves from 1.11 (Sharpe) to 1.85 (Sortino). However, since the return stream of QuantLab is asymmetric, that is it displays skew and is not symmetric around the mean, the standard deviation is not an adequate risk measure (as discussed above). Although the Sortino ratio improves on the Sharpe ratio for performance profiles that exhibit positive skew, it still suffers from the flawed assumption that returns are normally distributed, which is required when using the standard deviation to measure risk.
There is however an alternative risk/reward measure free of the shortcomings discussed above which I personally prefer to use when evaluating performance. I'll explore this measure next.
The MAR Ratio
In an absolute sense, the most critical risk measure from an investors perspective is maximum drawdown because it measures the worst losing run during a strategy's performance. A pragmatic approach then to measuring risk/reward is to determine how well we're compensated for assuming the risk associated with drawdown. This is precisely what the MAR ratio achieves. It was developed by Managed Accounts Reports (LLC), which aptly reports on the performance of hedge funds. The ratio is simply the compounded return divided by the maximum drawdown. Provided we have a large enough sample, the MAR ratio is a quick and easy to use direct measure of risk/reward; It tells you how well you're being compensated for having to risk your capital though the worst losses. The formula follows:
CAGR / Max DD
l find this ratio immensely useful. It's simple, does not rely on flawed assumptions about market return distributions such as standard deviation, which is used in both the Sharpe and Sortino ratios, and it measures what's important to investors: the number of units of return delivered for every unit of direct risk (maximum drawdown) assumed. When we use this metric to measure our live performance to date we find that QuantLab has delievered three units of return for every unit of risk, that is, our live MAR ratio is currently 3.
The MAR ratio is a transparent and direct measure of risk and reward that is impossible to manipulate (the Sharpe and Sortino ratios can be manipulated higher in several devious ways) and is thus my preferred measure of risk-adjusted performance when evaluating strategies.
We all have unique return expectations and tolerance for pain. For this reason, there is no single measure that appeals universally to everyone. In my personal trading, I analyse the MAR ratio, maximum drawdown, overall return and like to keep an eye on the smoothness in which returns are generated by examining the Coefficient of Variation, Sharpe and Sortino ratios. Keep in mind that regardless of the statistic you use, they are good estimates at best. Therefore, one can never be too conservative when analysing past performance. Given a long enough timeline, every strategy will exceed its maximum drawdown. This is a harsh reality that we as traders need to accept and prepare for, so it's a good idea to be suspicious of any statistic and ensure we have buffers built into our expectations to handle new extremes that will likely be posted in the future.
As always, I welcome your thoughts and suggestions.
PJ Sutherland BSc, CMT
CEO QuantLab (Pty) Ltd
In my last post we contrasted the effects of data integrity and sample size on the backtested performance of mean reversion and trend following models. In today's post we'll explore which markets are most suited to each approach, but before we do that, let's quickly take a look at why I believe that every strategy can be categorised as either mean reversion or trend following, regardless of the underlying logic.
Over the years I've tested and analysed the performance of countless trading strategies. Through the process I've learned that the performance profile of any strategy falls within either of the following:
- Moderate to high activity, high win rates, low average gains and consequently low risk/reward ratios and fat left tails.
- Low activity, low win rates, high average returns and consequently high risk/reward ratios and fat right tails.
The first profile is typical of mean reversions strategies, while the second trend following strategies. It doesn't matter whether you're employing fundamental, technical, economic or any of form of data to drive the decision making, the performance profile will resemble one of the above. This essentially has to do with the way trades are closed – if the exit strategy capitalises on long pronounced trends, then you're going to see a performance profile that resembles that of trend following. On the other hand, if a strategy seeks to lock in small and frequent gains, the performance profile will more closely resemble that of mean reversion.
The stark differences in performance statistics across each of these approaches leads to a unique set of risks, which in turn provide some insight into the suitability of each approach with a given set of markets. Next we'll explore these risks and then look for markets that are more conducive to reducing these risks, providing each approach with the best set of market conditions for success.
Mean reversion strategies do not let profits run since the target exit point is the mean. Essentially, they cut profits short which results in many small gains but infrequent and large losses - make small gains every month and then loose a fortune in a single month. Therefore, the single most significant risk to mean reversion lies in the left tail, or the probability that the market will trend severely against us (price shocks).
Trend following strategies let profits run, but since trends are rare, they experience many small losses and few large gains. Although losses are small, their frequency can result in large overall losses to a portfolio. Therefore, the primary risk to trend following is the cumulative effect of many consecutive losses, or said differently, the market's inability to trend.
We can then conclude that mean reversion is better suited to markets that are less susceptible to powerful trends, while trend following is better suited to markets that tend to display powerful trends. As a result, we tend to find that either mean reversion or trend following work at any given moment, but not at the same time, that is, they're mutually exclusive.
I'm now specifically examining the equity markets. Let's see if we can uncover segments of the market that are better suited to each approach.
Which market segment is more prone to trend? What about large cap stocks? Well, for one thing these stocks are broadly followed, have already disrupted their respective markets and are well established. Therefore, the ability of large cap stocks to continually deliver products or services with massive market impact deteriorates, reducing the probability of significant future price trends.
What about small cap and mid cap stocks? These companies are still in the process of establishing themselves, are not as broadly followed and may provide technologies or services with the potential to significantly disrupt markets resulting in massive growth and powerful price trends.
The above premises are intuitive and make economic sense. Moreover, they bear themselves out in the data. I've quantified this extensively and found this to universally hold, not matter which exchange from the global markets we consider. With this knowledge we can now assign the most suitable approach to each market segment thereby boosting our chances of success.
Trend following strategies are far more effective in the mid cap and small cap market segment (long only – shorting the equity market to capture trends is exceedingly difficult due to the strong upward bias that equities display). These market segments provide the best hope of capturing extended price trends that can easily offset the many small losses that result from high losing rates and are consequently perfectly suited to trend following.
On the other hand, mean reversion strategies work much better on large cap stocks. These stocks have reduced price shock risk and their strong following means professionals actively support stocks during sell-offs (institutions love buying dips) and often engage in profit taking during short-term bursts to the upside, which results in precisely the behaviour we're after for successful mean reversion.
Trends take time to mature, which is why trend following approaches are better suited to longer time frames or longer holds. In fact, using weekly or monthly data yields better results than daily data. Because mean reversion is actively seeking to avoid long powerful trends, they tend to work better in shorter time frames. Therefore, daily data is more appropriate, and unless you have access to fundamental data that you can use as an overlay to gauge the health of a stock, mean reversion does not work well on weekly or monthly data because price is given too much room to mature into a powerful trend against us.
The unique performance characteristics of mean reversion and trend following make them ideal complements within a single portfolio. Mean reversion works well to bring some consistency to a portfolio, while trend following keeps the door open for the rare but significant right tail trends that can lead to fantastic outsized returns. Blending the two approaches in a single portfolio yields very desirable trade return distributions that enjoy both higher win rates and right skew. As a result, it's my view that a blended approach is as close to holy grail as we can get. And the exciting news is that you can expect to see a multitude of powerful trend following strategies added to QuantLab within the next twelve months. Including trend following in our diverse offering will greatly improve our diversification abilities and further empower clients to build truly powerful and robust portfolios that enjoy exceptional trade return distributions.
PJ Sutherland BSc, CMT
CEO QuantLab (Pty) Ltd