The Application of Turning Tail Risks into Tailwinds (中文)

本文主要目標為扭轉投資之尾部風險，使其成為我們投資策略提升績效之方法。於投資前，投資人經常考量其投資之商品，其風險大小是否於可承受範圍內。於此研究過程中，採用不同種類之風險衡量方法，達到精準評估投資組合風險之目的，並獲得穩定優於大盤之績效。

There must be risks to investing. However, we always want to eliminate it as much as possible. How to trasform the tail risks into our return is this report want to solve. We test different risk measures mentioned in Turning Tail Risks into Tailwinds to control the tail risks of our portfolios. We can avoid unreasonable risk and ensure expected return. In the experiments, their maximum Sharpe can reach almost one stably.

We use Equally Risk Contribution and spectral risk measures to construct portfolios. First, each asset has the same level of risk rather than the same amount of capital. Second, estimated volatility through the cumulative volatility of the tail risks and spectral risk measures.

The assets we used in the experimental process are sector ETFs, including XLE, XLF, XLK, XLV, XLI, XLY, XLP, XLU, and XLB. The data source is from Dec, 26th, 1998 to Dec, 23th, 2022. We construct portfolios by naive measures and correlated measures. Also, we examine that the latter has better performance than the former. Table 1 and Table 2 display the performances. There are eight different risk measures for naive and correlated, respectively. Vol is the abbreviation of volatility; D.Vol is the abbreviation of downside volatility; CVaR is the cumulative value at risk; PSM is the power spectral measure. MB means moment-based, including both kurtosis and skewness. ER means extreme risks, using simulation data to estimate risks.

Naive Portfolio	Vol	D.Vol	CVaR	PSM	MB-CVaR	MB-PSM	ER-CVaR	ER-PSM
Sharpe	0.63	0.64	0.63	0.63	0.64	0.64	0.64	0.64

Correlated Portfolio	Vol	D.Vol	CVaR	PSM	MB-CVaR	MB-PSM	ER-CVaR	ER-PSM
Sharpe	0.63	0.79	0.74	0.67	0.68	0.69	0.6	0.68

We tested different timeframes for our portfolio. The best and most intuitive one is rolling one year. We can observe the performance in Figure 1 to Figure 3. Figure 1 shows that correlated D.Vol performs better than SPY on cumulative return. Figure 2 describes the difference of rolling 252 days Sharpe Ratio between D.Vol and SPY. The mean of the difference is more significant than zero, implying that the Sharpe of D.Vol is greater than SPY on average. Figure 3 shows the rolling 252 days return of D.Vol and SPY, and D.Vol trim the extreme gain and loss to robust gain.

In this report, there are some critical points we have examined. First, the correlated portfolios can reach
better performances than the naive ones. Second, we can change the original setting of the paper into 3-year and 1-year rolling data; correlated portfolios still could work excellently. Third, even when we split the backtesting timeframe, the D.Vol correlated portfolio could maintain a high standard. Thus, we affirm that the D.Vol correlated portfolio is an excellent method for constructing a portfolio under sector assets. Taking more different-market assets into account will be future research direction.

Contact us at info@gammaparadigm.com for the full report.

Ya-Qi, Lin
Quantitative Research Intern, Quantitative Finance, Gamma Paradigm
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