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Building a Risk Control Index with Drawdown Protection (Part 1)

July 9, 2019

Introduction

Both trend-following and absolute momentum are well established methods for managing risk. Another method for managing risk is to use volatility targeting. The former are superior for reducing large drawdowns in bear markets while the latter tends to reduce kurtosis by normalizing the daily bet size. The combination of the two tends to increase the sharpe ratio while generally reducing both kurtosis and skew. For a great review of the subject check out Rob Carver’s post. One of the concepts Rob brings up is that part of the challenge of trend-following and absolute momentum is that they are binary in nature– you are either “all-in” or “all-out” and this is suboptimal.

There are no magical numbers in finance- if the 1 year excess return of the stock market is 1% does this mean that you should have the same conviction as if it is up 10% or more? Clearly the slope has some relationship with forward risk. Is a -1% excess return that much worse than a 1% excess return? These levels are more arbitrary than you think. Exiting or reducing a position can be done profitably at a wide range of levels.

Another disadvantage of binary trend/momentum systems from a variance or luck standpoint is that by going all-in or all-out you can be hurt a lot more by the arbitrary execution timing of any one trade. (One way to reduce this problem is to use multiple lookbacks for a good review see this post by Newfound Research. This is also used within our “Trend Strength” indicator within Investor IQ) In contrast a strategy that employs a continuous position size has the benefit of scaling exposure as a function of conviction and is less susceptible to timing risk.

Lastly, the biggest challenge to trend/momentum systems is that they are not tied directly to any financial or risk-based objective. There is no limit on how much you can lose in any given time frame given either repeated whipsaws or large short-term corrections that occur before your signals trigger. In high momentum markets or situations like 1987, this added tail-risk can be significant as the binary trend/momentum signals will often still be 100% invested.

Risk Control

The concept of risk control is used more frequently in the annuity market or in various programs run by insurance companies to manage equity risk. Typically these are exactly the same as using volatility targeting (see this example here). However, there are more exotic strategies that add a type of dynamic overlay in order to further reduce risk. Regardless of the exact method used, this second layer is designed to be a form of drawdown protection. This feature is important given that a traditional risk control/vol targeting with a moderate risk profile will still have plenty of equity exposure through bear markets.

To build a risk control index with drawdown protection, I propose that investors use a drawdown target or “floor” that has some time frame attached to it. For example, many investors have a risk preference for not losing more than -20% on their portfolio in one year (this choice of floor and lookback is optional). You can directly control for this risk by scaling the size of your positions as a function of the current drawdown of your portfolio’s equity curve. This method roughly mimics a synthetic put option designed to insure losses below -20%. Here are the steps to building a risk control index with drawdown protection. For this example we can call this the “Risk Control 20/20 Index” (20% risk target, 20% drawdown target):

STEP 1: Risk Exposure (RE): Develop a volatility targeting method with a chosen volatility forecast or realized volatility forecast window (I chose 20-day realized historical in this example). Scale positions by target volatility (20% in this case) divided by current volatility whereby there is some maximum leverage permitted (no leverage in this case). Track the equity curve of this strategy for step #2

STEP 2: Drawdown Exposure (DE): Choosing some target drawdown (I chose 20% in this example) the equity “floor” (F) is equal to 1 minus the target drawdown. The current equity level (CE) is the value of yesterday’s risk control/vol target equity curve divided by the maximum price over the past n-days (I chose 1-year for this example). The formula for drawdown exposure (DE) is: MAX((1/(1-F)) x (CE-F)),0)

STEP 3: Total Exposure (TE): The final portfolio exposure that gets applied for the following day is calculated as: TE= RE x DE

The advantage of this approach is that you respond in a continuous manner to market drawdowns while scaling by volatility to improve risk-adjusted returns. Keep in mind that a 20% risk target and a 20% floor is fairly generous, so we can readily compare this Risk Control 20/20 index to standard absolute momentum (1-year return minus t-bills). The results of this comparison applied to the S&P500 index can be seen in the table below using daily execution to avoid bias (the choice of index price data allows for observing action across a wider array of different market regimes):

Both methods have nearly equal performance, but the Risk Control 20/20 index has better risk statistics with lower volatility, higher sharpe ratio and a much lower maximum drawdown. It is hard to see the difference between the two equity curves, but the rolling drawdown analysis is far more revealing:

In this chart you can clearly see that the Risk Control 20/20 Index does a much better job of controlling large drawdowns. In fact, the largest drawdown for absolute momentum occurred in 1987, when momentum was high and the signal failed to change in time for the crash. In contrast, the risk control index gradually shifted to a lower level of equity exposure. There are several other large drawdowns in the last thirty years where the risk control index with drawdown protection was superior owing to its ability to continuously size positions. Of course nothing can prevent against jump risk or large one day declines, but for most cases in theory the risk control index with drawdown protection should provide more explicit protection for investors. In the next post we will look at various methods to improve upon this original method along with some heuristics to make it more practical for real trading.

Investor IQ New Analytics

June 24, 2019

We have added some new analytics to the Investor IQ report. The signals are generated using a composite of 28 different momentum and trend-following signals over time frames ranging from 1-12 months. The number of buy signals determines whether the overall signal is “buy”, “hold” or “sell.” The “Trend Strength” is a new feature which shows the percentage of buy signals across the 28 different momentum and trend systems. This allows users to differentiate between the strength of the trend across ETFs or stocks. The “Volatility Score” is also a new feature which shows the relative volatility ranking (low ranking=lower volatility) from 0-100 across all ETFs or stocks. This can provide insight into relative risk and also allow users to form lower volatility portfolios with relative ease. A visual of the new output can be seen below:

Current S&P 500 Economic Prediction

June 10, 2019

The following is the composite point-in-time prediction for the S&P500 economic forecasting model. Currently the direction has changed from a flat prediction to an up prediction which indicates a resumption of the bullish trend. On the technical side check out our Investor IQ to look at the US Market Summary:

New Feature on Investor IQ: Asset Class Breadth and Relative Strength Summary Statistics

May 28, 2019

One of the new features introduced yesterday on Investor IQ is a summary of the breadth and relative strength of various asset class categories. This helps provide another layer of information for investors to determine which asset classes to focus on and which to avoid. We compile the % of buy signals using a matrix of trend and momentum signals as well as the average RS or Relative Strength using momentum within the asset class category. The best combination is obviously high % of buy signals and high RS. However a high RS with a low% of buy signals indicates caution as not all areas are participating as they would typically in a healthy market. The RS Spread is the difference between the strongest and weakest performer in the category and indicates the degree of opportunity for long/short portfolios within the same asset class. A visual of the current output can be seen below:

The asset class categories are listed in order of average RS. We can see that domestic equity and style,sector and factor components have the strongest relative strength. Traditional equity factors have the highest % buys within the domestic equity category. On the international front things are looking challenging – likely the result of the trade war. The % buys across countries is only 40% which suggests that markets across the globe are broadly struggling right now. This also correlates with the weakness in both breadth and relative strength in the Currency category which only has 14% buys and has the weakest asset class category average RS of only 7. The strongest asset class categories in terms of breadth are bonds and credit which is a trend worth watching. Commodities are the worst performing category in terms of breadth with 0% buys and also are relatively weak with an average RS of 28. The RS Spread of Commodities is the highest across asset class categories which indicates a good opportunity to go long a strong market such as Oil (USO) and short a weak market such as Gas (UNG).

This summary is a good way to keep on top of the market and spot new opportunities to overweight/underweight certain asset class categories.

Current S&P500 Economic Forecasting Model Prediction

May 27, 2019

We introduced our machine-learning economic forecasting model as a neat new way to compress a ton of economic data to gauge the health of the economy in order to predict cyclical (not sentiment driven) drawdowns in the stock market. The current prediction uses two different models:

1) Composite Point-in-time– this model only creates a forecast when all data required by the model is available at the point-in-time that it was available. If the model is waiting on data it will simply carry forward the last prediction made when all data was available. The historical prediction table was generated using this model.

2) Preliminary – this model is trained using the data available and is capable of making forecasts when there is missing data that the Composite model is waiting for. It does this by interpolating the missing data. Currently given that there are three missing pieces of data we can only make a preliminary forecast through the end of June.

Current Prediction- Preliminary

For the prediction period Apr 2019 – Jun 2019, the model predicts the following results based on economic data as of Mar 31, 2019:

  • Is there a reasonable chance of a large correction happening between Apr 2019 – Jun 2019? Not Expected
  • What is the predicted direction of returns between Apr 2019 – Jun 2019? Flat

Investor IQ: Focus List

May 22, 2019

Our Investor IQ weekly publication which is updated every Monday morning (on the top right hand corner of this blog) provides basic trend-following and relative strength (RS) signals for both US and Canadian ETFs and individual stocks. We recently added a “Focus List” at the request of some of our readers which highlights both long and short positions to focus on. The focus list long positions have a relative strength>90% and are either a buy or a hold position based on a composite of trend-following and momentum signals. The focus list short positions have a relative strength<10% and are either a sell or a hold position. An example can be seen in the picture below:

We also recently added signals for the Dow 30 stocks and also the S&P/TSX 60 stocks in Canada. We plan to expand the universe of both ETFs and Stocks over time. As a result of the trade war, we have included the Chinese Yuan (CYB) to the currency section for US ETFs as being one ticker worth watching as it has been an early warning for the stock market in recent times.

Current and Historical S&P500 Economic Forecasting Model Predictions

May 15, 2019

In the last post we introduced the S&P500 Economic Forecasting Model which seeks to predict the chances of a moderate or large drawdown over the next 90 days. The model considers a large range of different macroeconomic variables and their derivatives to assess the likelihood of a given event. What the model can do is identify when there are signs of economic weakness that may or may not be reflected in the current market price. What the model cannot do is identify sentiment, liquidity, or news driven corrections (ie the Donald Trump effect). Currently the model is waiting on several new pieces of data before making a new prediction. The table below shows the model predictions using “point-in-time” data as of the first day of the respective month. Here is the current and historical output:

The most recent prediction which was made as of the beginning of March shows that the model does not expect a moderate to large correction through the end of May. The direction of the market is expected to be sideways or flat. So from a macroeconomic perspective it seems as if the economy is healthy for the time being. Absent any major news events or tweets and the economy is likely to keep chugging along and the stock market will probably remain in a trading range before climbing higher. If you look at the historical predictions they have been fairly accurate in recent times and provide some guidance of when it might be worthwhile buying on weakness (during December 2018) by looking at both the chance of a drawdown and the predicted market direction. While the model was created without running backtests, we will show some applications of using the signals for timing the S&P500.

Shiny New Toys

May 14, 2019

Its been a long time folks, but we have some shiny new toys in the works. Current trends in the industry and working with data scientists has made me a believer in the benefits of using a machine learning approach. I have always been a proponent of “theory-free” approaches on this blog as long as they are designed with robust architecture. In contrast, strict adherence to overly simplistic theories and rules is not optimal for complex systems like the stock market. After experiencing many years of getting whipsawed by traditional indicators, I have recently become convinced a la Philosophical Economics (see this great piece) that you need to have a model(s) that can provide insight into market returns/risk without strictly using price-based indicators. A true macroeconomic model helps to gauge risk that may not be present in current prices and also helps to de-emphasize the reliance price movements that are false alarms. Predicting recessions is not necessarily the most useful for macro models because 1) you can have a bear market without a recession and 2) you can have a recession without a bear market. Furthermore you can have large and damaging corrections that are neither. As a result predicting drawdowns is potentially a more interesting and practical exercise.

S&P 500 Indicator Series

Economics Report

The S&P500 Indicator Series are machine learning forecasting models that use either 1) Macroeconomic 2) Sentiment 3) Technical or 4) Seasonality data with a very wide range of indicators/inputs to make investing decisions.

S&P 500 Economic Forecasting Model Introduction

The S&P 500 Economic Forecasting Model employs a Gradient Boosting Model (GBM) to predict the future distribution of S&P500 returns over the next 90 days based on economic data. GBM is a machine learning methodology which can be used for either regression or classification.

The S&P500 Economic Forecasting Model is a classifier model that predicts the likelihood of equity market drawdowns (moderate or large corrections) and the direction of returns (positive, negative or flat) over a 90-day period. The input variables are derivatives of monthly aggregated macroeconomic data, and does not include price-based or technical data. The choice of a classifier model is due to the fact that equity markets are driven by a wide variety of variables that are often nonlinear by nature. Furthermore, it is important to note that macroeconomic variables are just one component that explains the variation in equity market returns and by using a classifier we avoid many of the issues that regression models have with unobserved features.

The model itself is based on an ensemble of GBM style models (specifically using the XGBoost library. A large number of input macroeconomic data series are selected (see Model Importances for the list) and transformed to create derivative time series. Given that monthly economic data is still relatively sparse (60 years of backdata x 12 months/year), we wanted to choose a model technique that doesn’t required huge amounts of data, but is still very flexible. We excluded alternative models such as logistic regression and neural networks for this reason.

In a GBM model that is attempting to match similar periods together, it is important to make the input values ‘comparable’ in some sense, so the raw values are not appropriate in most cases. Otherwise, it is possible for the model to use the values to simply use the values to memorize where it is in time, which does not generalize well. Instead, values are transformed to make them relative (i.e. percentage change Year over Year, or lognormal differences). It is not necessary to make the inputs stationary in a strict sense, but this is useful to maximize the generality of the model.

The models are trained using a k-fold training algorithm, using a Bayesian optimization routine to select the hyperparameters (tree depth, learning rate, etc). Again, this is done to maximize accuracy and generality while avoiding overfitting.

The output of the model is a score, which is then optimized to maximize theMatthews Correlation Coefficient, which can be considered to be a robust accuracy measure for unbalanced classification sets (which the training data in face is).

The model results over time are shown in the chart below. The blue and red bars show the periods where we expect a drawdown of 10%+ (Moderate Correction) or 15%+(Large Correction) respectively from the end of that period onwards.

More on this model to follow very soon along with weekly model updates on the predicted output.

Welcome to Investor IQ

May 13, 2019

There is some interesting new content on the CSSA blog that will be very useful for readers. Investor IQ is currently a free tool that shows basic trend signals (Buy, Hold or Sell) for a wide range of US and Canadian ETFs as well as a relative strength ranking. The signals will be updated as of the close of Friday and posted on Monday morning. This feature is currently in Beta and will be expanded to include individual stocks and other analytics. It can be found on the blog under the tab “CSSA” as a dropdown menu. A sample of some of the output can be seen below. More details to follow……

“2D Asset Allocation” using PCA (Part 2)

August 21, 2018

In the last post we showed how to use PCA to create Offense and Defense portfolios by focusing on the first principal component or “PC1.” After rotation has been completed it is possible to derive weights or portfolios for each principal component. Another good primer on using PCA for asset allocation is written by a reader of the blog- Dr. Rufus Rankin. The link for this book is here. We can separate the PC1 portfolio which represents broad systematic risk by dividing it into two dimensions- Offense (Risk On) and Defense (Risk Off)- by isolating positive versus negative weights. To form each portfolio you would simply take the absolute value of each weight and divide it by the sum of absolute values of weights for each of the Offense and Defense portfolio. In this example we will use 8 core asset classes for the sake of simplicity- Domestic Equity, Emerging Market Equity, International Equity, Commodities, High Yield Bonds, Gold, Intermediate Treasurys, Long-Term Treasurys. Here is the PC1 Offense Portfolio using the in sample period from 1995-2018 on various ETFs with extensions using indices:

This portfolio shows that some of the more aggressive asset classes such as emerging markets have the highest weighting, while international and domestic equity have nearly equal weightings. Equity overall has the highest weighting in the offense portfolio which is logical. Commodities take second spot while assets such as high yield bonds and gold have smaller weightings. In general this portfolio makes sense: for the most part when the market goes down and systematic risk is very high, all of these asset classes have a tendency to fall. However, during a bull market, these asset classes tend to do very well. In contrast when we look at the PC1 Defense Portfolio and it looks predictably like the opposite of the offense portfolio:

The PC1 Defense Portfolio has a high duration portfolio tilted toward long-term treasurys that has historically performed quite well during recessionary periods or other periods when systematic risk is high. The performance of both the PC 1 Offense and Defense Portfolios over time is plotted in the graph below.

In the graph we can clearly see the inverse correlation between the PC1 Offense and Defense Portfolios. Both obviously perform well at different times as we would expect. A simple tactical model would be to hold the PC1 Offense portfolio when systematic risk is low and to hold the PC1 Defense portfolio when risk is high. To do this we can simply use the 200-day simple moving average strategy on the PC1 Offense portfolio on a daily basis (generating an equity curve by using the weights of PC1 and rebalancing this portfolio monthly) and holding the PC1 Offense portfolio when risk is on- the equity curve is above its 200-day sma- and holding the PC1 Defense portfolio when risk is off- the equity curve of PC1 Offense is below its 200-day sma. We can give this simple strategy a name- “2D Asset Allocation”- which represents the two dimensions that we have separated the asset class universe into: Offense and Defense. The performance of this strategy is shown below:

The performance of this simple strategy is quite good, and manages to perform well even during the 2015 period which was difficult for traditional momentum/trend-following strategies. Below is a table showing the summary statistics. A good tactical strategy will ideally perform better than the buy and hold version of its underlying offense/defensive components over a full market cycle. Clearly the 2D Asset Allocation does substantially better than either component in isolation.

The best part about this strategy is that it was by no means “curve-fit” since the 200sma is a well-established strategy and is not the optimal strategy on the PC1 Offense portfolio. Using PCA to reduce dimensionality and derive this portfolio is a well-established statistical practice. The only caveat is that this portfolio was derived “in sample” which is less than ideal but no different than the starting place from which traditional system developers create trading strategies via backtests. Perhaps a better way to do this would be to using a rolling or anchored PCA analysis to derive the two portfolios instead on a walk forward basis. The choice of asset class universe in this case was designed to capture major asset classes, but the good thing about PCA is that you can use just about any asset class universe you want without introducing undue bias by choosing an arbitrary subset. In either case, this is a good example of how tactical asset allocation can be greatly simplified. Refinements to the strategy could include holding a minimum allocation to PC1 Defense for diversification purposes or potentially using momentum within the PC1 Offense and Defense portfolios to overweight/underweight different holdings. The possibilities are endless.

 

This material is for informational purposes only. It is not intended to serve as a substitute for personalized investment advice or as a recommendation or solicitation of any particular security, strategy or investment product. Opinions expressed are based on economic or market conditions at the time this material was written. Economies and markets fluctuate. Actual economic or market events may turn out differently than anticipated. Facts presented have been obtained from sources believed to be reliable, however, cannot guarantee the accuracy or completeness of such information, and certain information presented here may have been condensed or summarized from its original source.