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  • Writer's pictureRenexe Project

Long only optimization for the stock market boom of 2017. Leverage - 1, 50% return vs 30% benchmark.

Updated: Nov 5, 2019

Previous reports demonstrate that the leveraged long/short models do very well in flat or falling stock markets especially with the enhanced negative macro-scenario modelling. However, we find that long/short models with zero exposure do not perform as well in fast-growing stock markets.

Therefore, in this report we present out-of-sample backtesting results for long only models for booming stock market of 2017. SP&500% gained impressive +25% over the year. Our goal is to build a medium/long term highly diversified portfolios which would outperform the market with the lower/same risk. By that we take a neutral macro-scenario approach without constructing any special scenarios for market performance, volatility or autocorrelation. We assume that the market will behave on average similarly to what it did in the last 4-5 years (1200 trading observations) before 2017. Additionally, we do not use any short-listing, alpha/beta, ratios information dividing stocks into buy/sell baskets. We use the same data on random 300+ stocks from the US, Europe, and Asia as in previous reports.

Efficient frontier. Long only portfolio. CVaR optimization.
Figure 1. Efficient frontier. Long only broad optimization.

The Monte Carlo simulation is conducted for 220 stocks with obtained 10000 scenarios of 100 days stock returns. Out 220 stocks the model would choose 28 stocks for the investment without leverage. The highly convex curvature of the frontier gives ground to foresee big potential for risk optimization. The model chooses the first solution from the frontier for which the tangent angle is < 2. Hereby, we can expect high optimization efficiency in this (red) point because we achieve a significant return increment with only very little increase in tail risk.

CVaR optimization. Expected shortfall.
Figure 2. Asymmetric portfolio return distribution.

We plot the resulting (smoothed) return distribution based on the simulated data. We can visually observe that the distribution is not symmetric and the right tail of the distribution (excess returns) is noticeably large than the the left tail (losses).

Long only out-of-sample optimization. CVaR minimization. Tail risk.
Figure 3. Out-of-sample backtesting. Long only strategy.

The resulting portfolio easily outperforms the benchmark in the bull market without any significant drawdowns. The benchmark represents the average return of 300+ stocks in the original list with a return similar to that of SP&500 of the same period. Interesting to note that the portfolio return is significantly lower than that of the benchmark in the first 50 days before the long term optimization logic kicks in. In order to check the riskiness we check the performance of the same portfolio without any rebalancing for the next year 2018. By that we significantly overstate the risk of the portfolio because it is not optimized for over 500 days after the initial investment data. Normally, we would rebalance portfolio at much shorter periods, e.g. 100 days.

Unrebalanced portfolio outperforms benchmark. CVaR optimization.
Figure 4. Unrebalanced portfolio behavior in 2018

We can see in Figure 4 that the drawdown of the optimized portfolio is larger then that of the benchmark but not significantly ~-21% vs ~-17%. Herewith, the unrebalanced "old" portfolio still markedly outperforms the benchmark recording ~8% return for the year whereas the benchmark was still down ~-5%. Figure 4 confirms the long term optimization efficiency of the model. The portfolio continues outperform the benchmark for years following the investment date even without rebalancing.

In the end of this report we demonstrate that long/short models without meaningful categorization of stocks do not perform just as well for strongly bullish markets. We build a portfolio with leverage 3, exposure 0 without any short-listing, macro-scenario modelling/assumptions and with risk preferences similar to the long only part above. The model still achieves out-of-sample returns similar to benchmark but with large drawdowns and higher volatility. Nonetheless, considering that it is a market-neutral, zero exposure strategy without any short-listing, the optimization algorithm can be still characterized as very efficient.

long/short portfolio for bullish markets. CVaR optimization.
Figure 5. Out-of-sample return for long/short portfolio

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