Equal weight beat long-only minimum-CVaR on median Sharpe and median STARR. Minimum-CVaR also posted negative median STARR across most specifications. Those are the traded results a reader should keep in view when looking at the paper's SMH-heavy allocation. That allocation belongs to a full-sample tangent portfolio, while the realized-performance figures (Figures 10 to 14) cover only the rolling minimum-CVaR books, C95 and C99, whose objective has no mean term. The paper nevertheless says the CVaR portfolios "exhibited substantial shifts toward SMH during the post-COVID period". Without a weight plot, a reader cannot tell whether that sentence describes C95 and C99 or the tangent portfolio.
Thirty ETFs and two CVaR objectives
Lee, Shirvani, Afroz, Rachev and Fabozzi compare mean-variance and CVaR optimization across 30 Taiwan-exposed ETFs. Their starting concern is concentration. Taiwan's foundries underpin most leading-edge chip production, leaving U.S.-listed funds with Taiwan exposure subject to semiconductor cycles, export-control shocks and cross-strait risk. Returns are negatively skewed and fat-tailed. Variance treats upside and downside moves alike; CVaR measures the expected loss beyond the VaR threshold and should produce different allocations. The approach makes no excess-return forecast. Its value would have to come from smaller left-tail losses.
The authors use daily Bloomberg prices for 30 ETFs from February 20, 2015 to February 20, 2025, alongside the DJIA and S&P 500. Their tests include historical VaR and CVaR at 95% and 99%, Hill tail-index plots, GJR-GARCH(1,1)-t and rolling FIGARCH. They construct two CVaR portfolios with different jobs. A full-sample tangent portfolio maximizes STARR, mean excess return divided by CVaR. Rolling minimum-CVaR portfolios use the Rockafellar-Uryasev linear program at 95% and 99%; these are C95 and C99. The rolling books are re-estimated on a 1,008-day window and rebalanced daily. The authors run them long-only and long-short, with weights bounded between -0.3 and 1.3, then compare them with global minimum variance (MVP) and 1/N (EWP) over 2019 to 2025.
Four findings carry the argument. Semiconductor funds have the largest tail losses, attributed to scale rather than tail shape. Long memory in squared returns vanishes after GJR filtering: EWP's GPH d moves from 0.187 to -0.019. The CVaR tangent portfolio lies "very close to SMH". Sharpe and STARR favor EWP, while the Rachev ratio favors CVaR.
Why does SMH dominate the 2015-2025 tangent portfolio?
SMH returned 21.317% annualized with 30.286% volatility and a Sharpe near 0.62. Its 95% CVaR was about 4.5%, compared with 2.5% to 3.0% for diversified international funds. Those funds earned roughly 2% a year: ACWX returned 2.109% and VEU 2.116%. SMH brought perhaps 1.5 to 1.8 times their tail loss and about ten times their return. An excess-return-over-CVaR objective has an obvious reason to choose it.
Table 1 lends some support to the authors' scale explanation. Excess kurtosis for SMH and SOXX was 4.998 and 4.747, among the sample's lowest, versus 17.279 for EWT. Their moves were large, even though their tails looked relatively thin against their own scale. The Hill evidence offered for "broadly similar asymptotic tail-decay behavior across the ETF universe" is narrower: it covers EWP, EWT, DJIA and the S&P 500. We did not find Hill plots for SMH or SOXX. The paper's stable k region, between 500 and 1,500, also leaves an implementer with a choice. Against roughly 2,500 daily observations, it uses a large share of the sample, awkwardly close to the k/m going to zero condition the authors state. There is a smaller arithmetic wrinkle in the long-memory bandwidth. The paper describes m = n^0.5 as about 40 ordinates; for roughly 2,500 observations, n^0.5 is about 50.
Which CVaR book was actually held?
The tangent portfolio takes its sample means from the whole decade. SMH's weight incorporates returns realized through February 2025, making the allocation in-sample by construction. The authors acknowledge that dependence: SMH's prominence "may partly reflect sample-specific conditions rather than a persistent structural feature of semiconductor ETFs". Their 2020 to 2025 subsample tangent portfolio also lies closer to SMH than the 2015 to 2019 version. They deserve credit for saying so.
The trading question remains. The realized-performance sections assess C95 and C99, which minimize CVaR without a mean term. They cannot pursue SMH's 21% return through their stated objective; a minimizer should tend to shed a fund with 30% volatility and 4.5% CVaR. Yet the descriptions of the held weights vary. Section 5.2.1 says "MVP and CVaR optimization systematically underweighted high-volatility holdings". Section 6.2 says the CVaR portfolios "retain meaningful exposure to semiconductor-related ETFs". Section 7.2 says they "exhibited substantial shifts toward SMH during the post-COVID period". We did not find a plot of the rolling weights. An implementer cannot tell which description is right.
Equal weight wins the mean-return measures
EWP ended with the highest cumulative value in both long-only and long-short panels. At 1/30 each, it holds SMH, SOXX and IXN at 10% combined. It also holds EWT and Asia funds that own TSMC (Taiwan Semiconductor Manufacturing). EWP had the highest long-only median Sharpe in the boxplots; MVP's median was slightly negative, and C99 was weakest. EWP led long-only STARR at both confidence levels, while the minimum-CVaR books fell below zero in most panels. Long-short C99 had the most negative median STARR. The Rachev ratio gave C99 the highest median, most clearly in the long-short panel.
The Rachev ratio divides right-tail CVaR by left-tail CVaR. Mean return does not enter. A minimum-CVaR book is designed to shrink its denominator and can therefore lead that ranking with median excess return below the risk-free rate. Sharpe and STARR, both of which put mean return in the numerator, favored EWP. The Rachev ratio favored CVaR.
Section 6.3 recognizes part of this distinction. It says "the Rachev ratio emphasizes tail asymmetry, and STARR emphasizes downside-risk-adjusted efficiency", then concludes that CVaR portfolios do better "under measures that explicitly account for tail asymmetry". The broader framing still misplaces the divide. The Section 6 introduction says "tail-sensitive measures tended to favor CVaR-based allocations", and the paper describes "variance-based and tail-sensitive performance measures" as favoring different portfolios. STARR has CVaR in its denominator and sided with Sharpe. The authors' explanation, that tail-minimizing books "reduced the STARR numerator proportionally more than they reduced the CVaR denominator", better matches a divide based on whether mean return enters the numerator.
These rankings come from boxplot medians. The authors acknowledge that Jobson-Korkie, Memmel or bootstrap tests would be needed to establish significance.
Our monthly rebuild: 28.88% from 2020 to mid-2024
We built a long-only minimum-95%-CVaR book from the paper's description. On the first session of each month, it rebalances at the close using 1,008 joint daily return scenarios ending on the prior session. Three choices differ from the paper: monthly rather than daily rebalancing, a 10% cap per fund, and a 23-fund universe. EEMV and six other names were unavailable; we made no substitutions for them. Our window covers January 1, 2020 to July 1, 2024. Every fill incurs a commission of $0.004 a share.
Net of commissions, our book returned 28.88%, with a Sharpe of 0.37, volatility of 17.26% and a maximum drawdown of -34.25%. The paper gives no numeric Sharpe for C95. Its boxplots show only that long-only C95's median sits below EWP's. Any comparison is therefore qualitative, across daily and monthly rebalancing, uncapped and capped weights, and 30 funds and 23.
The 17.26% volatility helps explain what we obtained. In the paper's table, full-sample volatility is 17.360% for ACWX and 17.130% for VEU. The windows differ, so that resemblance is only a rough marker. Our cap requires at least ten holdings, most of the 23 funds move together, and our book's beta to SPY was 0.69. The optimizer had little scope to escape common exposure. The -34.25% drawdown includes March 2020; with a January 2020 opening, the first scenarios were drawn from 2016 to 2019 and contained no crash of that size. This was one automated pass rather than a verdict on the authors' work. We also ran equal weight and minimum variance but do not report them here, so we have not tested the ranking reversal.
An allocation rule remains unproven
The authors acknowledge that their reported returns omit transaction costs and turnover, a particular concern with daily re-optimization. They say about 1,000 observations estimate the 30-fund covariance matrix "with reasonable precision". By our count of the paper's ETF list, 26 of the 30 funds, including ACWI, are broad international, emerging-market or Asia funds that move together. Requiring full histories through February 2025 also excludes funds that closed or launched late. The 2019 to 2025 test covers a single historical stretch: the COVID crash followed by an AI-driven semiconductor expansion that favored holders of SMH.
Minimum-CVaR reduced volatility and drawdowns against EWP (Section 5.2.1), at the expense of mean return. A rolling, cost-adjusted backtest of the STARR tangent portfolio that retained an edge outside 2020 to 2025 would change that reading.
Our backtest stops at 2024-07-01, and everything after that date is deliberately left untouched so the same strategy can be checked out of sample later.