A Basket and Risk Approach to Portfolio Management

December 7, 2016


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How are baskets used in financial markets?

Baskets of equities held together provide an understand of statistical profiles for the underlying companies, such as hedging or trading, that cannot be by looking at individual components. By analyzing the tendencies of similarly behaving securities, we can generate alpha over traditional buy and sell strategies. Our basket trading uses market behavior to determine the factors that drive equity basket performance, and then spreads exposure equally over the constituents. 


We describe our methodology used to create baskets, how we account for changes in market regimes, and then present the results of our strategy vs. an equally long short portfolio from our quantitative model. 



Portfolio managers build strategies that translate their views on financial markets into long and short positions, while hedging exposure to risks they have no view on.  In this research, we use outputs from our quantitative research group to represent our view on specific securities in the short-term. Our goal is to use the broad market’s behavior to select a market neutral portfolio that maximizes alpha. 


Our input from the quantitative research team is a list of historical stock predictions generated from out of sample tests. In this methodology, we focus on the outputs from a model created using 2010 and 2011 data as in sample. In order to include the events of the financial crisis, we use 2008, 2009, and 2012 to build our strategy. 


A proprietary signal is used in predicting short-term price movement for each security. We normalize this data point from 0 to 1 for simplicity. Furthermore, we organize our data into two separate groups: stocks to long, and stocks to short, based on our signal each period. This list is subject to change during in-sample testing.


Below is a sample of input data starting February 2, 2008 for 0018300 company:


We divide data into 50% for training baskets, and the other 50% for testing.


Creating Trading Baskets

We use distribution curves to fit US equities into baskets for long companies and baskets for short companies. Volatility of recent periods’ returns and trading signal classify each constituent’s basket.


Two distribution fittings are performed to capture different aspects of volatility on groups of stocks. Firstly, t-distribution is applied to the trading signals for all stocks (Figure 1) then F and lognormal distribution are fitted on the volatility values for long and short companies (Figures 2 and 3). The better distribution is chosen based on sum of squared errors. For both long and short stocks 10 decile values are found, and 100 baskets are created (200 in total).



We used Fitter Package in Python to fit 80 different distributions. The parameters are optimized each time a distribution is fitted by minimizing sum of squared errors. By fitting the distributions for trading signal and volatility we can more accurately create baskets with similar characteristics and equal amount of stocks in each.


Accounting For Market Regimes

Now that our process is in place for calculating the constituents for our trading baskets, it is important to consider changing market regimes. Regime switching models match the tendency of financial markets to abruptly change their behavior for potentially several periods. These periods often correspond to different cycles of regulation, policy, and other secular changes. The regime switching often means volatility, auto correlations, and cross variances of stock returns change, which allow the strategy to capture behavior of financial series including fat tails, skewness, and time varying correlations. 


Two methods are implemented for calculating basket constituents, a regime shifting case that uses a moving window, and a stationary case. Stationary case uses the full period’s time series data and tends to have a wider spectrum of trends, as it accounts for outliers in all markets. Regime shifting uses recent factors to calculate next period baskets, and should perform better in periods of increased volatility. A third method, dynamic regime shifting method, will be introduced in future research. 


Portfolio Construction

The portfolio construction stage begins by analyzing the results of each basket using the above mentioned methods. We focus on investment metrics that tell a story about the collective portfolio from multiple angles: returns, volatility, and risk. The list of metrics used in our analysis can be found in Figure 4. 


Accuracy of prediction holds the greatest factor in determining basket performance. Accuracy is metric between 0 and 1, creating unbiased results when accounting for outliers. Our initial goal is to understand the trend of baskets relative to volatility and trading signal. Figures 5 and 7 show heat maps of performance for long and short baskets assuming a stationary window. Figures 6 and 8 show heat maps of basket and neighbor scores (explained in more detail next page). 


Performance Metrics

Neighborhood Method To Analyze Basket Performance

We apply a neighborhood method to see a more clear pattern between signal and volatility. In Figures 5 and 7, accuracy metric is used to identify the best performing baskets. This process does not fully explain the underlying basket trends. In Figures 6 and 8 we introduce the neighborhood concept, which takes the averages of each basket and its surrounding basket’s accuracy. This neighborhood average score clearly identifies the underlying trend of the baskets.


Basket Accuracy For Long Positions

Figure 5 below shows long stock prediction accuracy by baskets. X-axis shows trading signals 
(Signal10=strongest signal). Y-axis shows recent volatility, Vol10 = most volatile). Numbers in percentage. 

Figure 6 below shows the neighborhood score for each long basket (i.e.: the average performance for the specific basket and the baskets it is next to). All numbers in percentage. 

Figures 6 selects lower volatility and higher trading signal baskets as best neighbor accuracy. Low volatility and high trading signal perform best. Figure 5 shows the best neighbor accuracies, each with over 50% accuracy in prediction. From these baskets, we select the 3 best baskets to long in future steps (Signal9-Vol1, Signal8-Vol1, Signal7-Vol1).


Figure 7 below shows short stocks prediction accuracy by individual baskets. All numbers in percentage. 

Figure 8 below shows the neighborhood score for each short basket. All numbers in percentage. 


Figures 8 selects higher volatility and higher trading signal baskets as best neighbor accuracy. High volatility and high trading signal perform best. Figure  7 shows the best neighbor accuracies, each with over 50% accuracy in prediction. From these baskets, we select the three best baskets to short in future steps (Signal9-Vol9, Signal10-Vol10, Signal9-Vol10).


Security Selection

There are two methods we use to select specific stocks to select from our basket strategy each period. Method 1: Choosing top three baskets for long and top three baskets for short in the best neighborhood, invest in each constituent.
Method 2: Invest into a minimum of ten stocks of buy, and ten stocks to short, every period. This method is more diversified. 


Asset Allocation

We adopt 2 methods to construct portfolio asset allocations: Method 1: Equal weights for each stock.
Method 2: Equal risk contribution (described below). 


Equal Risk Contribution Method (ERC)

Equal risk contribution is an asset allocation method where contribution-to-risk (CtR) for each constituent is equal, defined as: 


Where ω is weight for stock i and V is the covariance matrix for the trading basket calculated based on historical returns. 

We use a minimization function to minimize the following target functions to generate the equal risk contribution weightings:

When the target function is minimized at zero, the contribution to risk for all stocks is equal to 1/n, thus we arrive at the ERC weights for each constituent. 


Three Step Process

Three processes, and two methods, are used to calculated performance. This key classifies each method:


Three digit code refers to each method:



Performance Metrics For Each Method

Combinations of each method in cases of a long portfolio, short portfolio, and long short portfolio. Benchmark is an equally weighted portfolio of ten positions long, short, and ten long and short. 




Net Performance For Each Method

Summary of Results

Figures 9, 10, and 11 show that method 1-0-0 has higher returns than the benchmark in all three portfolios, while maintaining lower volatility and drawdown. Applying a basket method, determining allocation weight based on equal risk, applying a stationary window, and forcing enough baskets to buy or sell ten stocks results in the best risk-adjusted returns. 


Long only portfolio following these three criteria outperforms the benchmark Sharpe Ratio by 1.30, and outperforms the S&P 500 Sharpe Ratio during the same period by 0.68.


Future Work

Hyper-parameters in each method need to be optimized. Periods of volatility, moving window, and stocks selected can be run through historical back tests to analyze if any parameters generate additional alpha.


The boundaries of baskets vary in this model, but are in the same location relative to other baskets. In the future, a dynamic basket trading model will be introduced to allow for changing basket locations. 


A more detailed factor model will be applied to measure basket performance to make the result most relevant. This result will be tested on additional out of sample data then implemented in real-time trading.  


Important Disclaimer and Disclosure Information

Algo Depth makes no representations of any kind regarding this report. This includes, without limitation, warranties of title, merchantability, fitness for a particular purpose, non-infringement, absence of latent or other defects, accuracy, or the absence of errors, whether or not known or discoverable. In no event shall the author(s), Algo Depth or any of its officers, employees, or representatives, be liable to you on any legal theory (including, without limitation, negligence) or otherwise for any claims, losses, costs or damages of any kind, including direct, special, indirect, incidental, consequential, punitive, exemplary, or other losses, costs, expenses, or damages, arising out of the use of the report, including the information contained herein. 


This report is prepared for informational and educational purposes only, and is not an offer to sell or the solicitation of an offer to buy any securities. The recipient is reminded that an investment in any security is subject to many risks, including the complete loss of capital, and other risks that this report does not contain. As always, past performance is no indication of future results. This report does not constitute any form of invitation or inducement by Algo Depth to engage in investment activity. 


Algo Depth has not independently verified the information provided by the author(s) and provides no assurance to its accuracy, reliability, suitability, or completeness. Algo Depth may have opinions that materially differ from those discussed, and may have significant financial interest in the positions mentioned in the report. 


This report may contain certain projections and statements regarding anticipated future performance of securities. These statements are subject to significant uncertainties that are not in our control and are subject to change. 


Algo Depth makes no representations, express or implied, regarding the accuracy or completeness of this information, and the recipient accepts all risks in relying on this report for any purpose whatsoever. This report shall remain the property of Algo Depth and Algo Depth reserves the right to require the return of this report at any time.

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