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  • Writer's pictureRenexe Project

Long/short portfolio optimization for the market crash of late 2018, Sharpe ratio 1.82, Return 35.4%

Updated: Dec 11, 2019

In this report, we present the backtesting results for the year 2018. We collect stocks with the market cap between USD 500mn and USD 2bn and stock history from the year 2012. This time we apply a shortlisting strategy dividing stocks into two baskets based on the two criteria: credit rating and the relative value to peers based on PEG ratio. The credit rating metric is used to divide companies into groups based on their financial health and the default probability. Hereby, in the “long” basket are stocks with high credit rating but the low relative PEG ratio in comparison to peers, which we deem to have the potential for increased valuation in the medium/long term. In the “short” basket, we select stocks with relatively higher default probabilities and higher PEG ratios in comparison to peers in the corresponding sector. We consider these stocks to be relatively overpriced and to have downside potential. The resulting short-list will contain 157 stocks in the “long” basket and 161 stocks in the “short” basket.

We conduct the data processing and specify models for Monte Carlo simulation as described in the previous report. This time we link the behavior of stocks to the SP&500 and obtain 10000 return scenarios for individual stocks’ returns and SP&500 after 100 trading days.

Based on the output of the simulation model we construct tail risk minimization model. Leverage is 3, and exposure is 0 with 1.5 units to buy and 1.5 units to sell. The maximum investment into a single stock is limited to 0.1 units. For the first testing, we make no assumptions about the current macroeconomic cycle and accept the market to be moving on average as in the last 6 years (from historical data). The model produces over 20 solutions as presented in Figure 1.

Backtestng CVaR optimization for market crash of late 2018. Efficient frontier. Diversification.
Figure 1. Efficient frontier. Backtesting for market crash 2018.

The marginal return from the increased risk is quickly decreasing. One way to choose the optimal risk-return combination is to use derivative at different points of the frontier. As we move along the frontier to the right, the slope of the tangent to the frontier will get flatter. The decision-maker, therefore, can decide on the acceptable slope of the tangent as a proxy of risk-return combination e.g. no more than 1. In this case, the software will choose such a last solution point on the frontier for which the slope of the tangent is still less than 1. The backtesting results are presented in Figure 2. Again for simplicity no rebalancing was applied and investing was made only at one point in the end of January 2018 and held until February 2019 .

Backtesting CVaR portfolio optimization for market crash of late 2018. Long/short equiy strategy. Leverage 3. Exposure 0. Shapre ratio 1.82 acheved.
Figure 2. Financial portfolio backtesting for 2018. Sharpe ratio 1.82. Return 35.4%.

Before the late 2018 crash, the model achieved an impressive 30%+ return. However, the months following the market crash the results were inconclusive and there was a large drawdown right before the stock market fall. We do the backtesting again but with the starting point in October 2018 just days before the crash. With the default macroeconomic scenario, the model fails to provide any returns. Intrinsic market neutral long/short hedging makes the portfolio return fluctuating just below 0 (Figure 3).

Backtesting CVaR portfolio optimization for the late 2018 market crash. Long/short equiy portfolio optimization. Leverage 3. Exposure 0. Shapre ratio 1.82 acheved.
Figure 3. Backtestng long/short portfolio optimization for the late 2018 market crash.

We can observe that the model performance is also strongly linked to the general macroeconomic environment at the investment time point. For this purpose, we apply an enhanced portfolio modeling procedure to find the best performing portfolios for different business cycles. As a starting point, we analyze the Treasury yield spread and other leading macroeconomic indicators to determine the prevalent business and market cycle. In particular, we see from the FRED data in Figure 4 that the spread is decreasing with persisting upbeat macroeconomic numbers for the US economy. Taking into account that current US economic expansion is one the longest in history, we can make a conclusion that the markets are in the late (peak) growth stage entering the year 2018.

Historical treasury yield spread. Stock market cycle. Recessions.
Figure 4. Treasury yield spread. Stock market cycle.

Based on our analysis, we take a conservative approach assuming that the SP&500 index will not increase in the coming hundred days. Therefore, we only use those scenarios from the Monte Carlo simulation model when SP&500 does not increase over the considered period 100 days. We build again long/short market neutral model with zero exposure and leverage 3. The model return improves immediately to 10-15% over the ~100 trading days period. The model is performing just as well during the crash itself and the following recovery period.

Treasury yield spread. Conservative macroeconomic scenario. Late stage growth market cycle. CVaR long/short equity portfolio optimization.
Figure 7. Backtesting for the late 2018 market crash. Conservative macroeconomic scenario.

Hereby, we confirm the strong positive effect of macroeconomic scenario modeling. In the enhanced portfolio optimization setup, the model behavior is modified for different business cycles: fast growth (early-stage), late-stage growth, and recession. Other macroeconomic parameters can be included in the model. For example, energy prices or even currencies exchange rates. Using combinations of those global indicators we can implement more complex modeling. For instance, we can optimize equity portfolios for the combination of factors:

1) GDP will NOT increase in the coming 6 months

2) Oil price will increase in the coming 6 months

3) USD/EUR exchange rate will decrease by at least 5% in the coming 6 months.

Various model modifications can be tested by modeling independently macroeconomic proxies. This way we can achieve unique portfolio characteristics for any markets.

In this section, we demonstrate the portfolio optimization efficiency minimizing the tail risk. The same data is used as for the year 2018 backtesting (Figure 1). Firstly, we build a basic heuristic long/short equity strategy based on the output of Monte Carlo simulation model. We choose 30 best-performing stocks from the conducted Monte Carlo simulation and take equal long positions in those, 0.075 investment units each. Similarly, we choose 30 worst performing stocks from the Monte Carlo and take short positions in those, -0.075 investment units each with total leverage 3 and exposure 0.

Here we demonstrate CVaR optimization efficiency for long/short equity investment strategies. Tail risk of the portfolio is significantly reduced.
Figure 6. Portfolio return distribution. Optimization efficiency.

The blue line represents the fitted probability density function (PDF) for the resulting portfolio return distribution. The yellow line is a return distribution for basic long/short strategy. The red line is the resulting PDF for the optimal risk-return strategy which is chosen as the solution from the frontier where the tangent slope equals 1. We can observe that the tail risk is significantly higher for the basic strategy. For a given VaR, expected tail loss for the basic heuristic strategy consists of an area filled by all three colors. The area is several times larger for the basic strategy than for the lowest risk strategy the area filled with the blue color.

The optimal risk-return strategy provides higher returns as the distribution is shifted noticeably to the right with significantly lower risk in the lower tail. The corresponding expected tail loss of the optimal portfolio is ~2x lower than for the basic strategy. Another observation is that the variance of the lowest risk portfolio is significantly lower than the variance of the other two strategies. Hereby, the optimization algorithm changes considerably the risk-return characteristics of the portfolios as demonstrated in Figure 6. Most importantly, it allows for effective macroeconomic modeling and can be used to build multiple variations of investment strategies.

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