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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.

Introduction

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: