Continuous put protection this effective should cost more than 41 basis points a year. The paper rolls a three-month put struck 10% below spot across three index markets for six years, while portfolio volatility falls from 19.35% to 8.76%. An implementer first has to reconcile those figures.
We could not trade the contracts used in the paper. The run discussed later is our adaptation.
Two overlays, four limits
The paper contrasts the hedging logic of futures and options, then identifies the theoretical boundaries at which each instrument ceases to work. Futures address directional, systematic risk with a linear payoff. They offset moves in either direction, surrendering the upside with the downside. Options have a nonlinear payoff. A put preserves spot upside while charging premium for tail protection, and it adds volatility exposure.
Four boundaries follow. The first is the Black-Scholes assumptions: constant volatility, no transaction costs, constant rates. Market efficiency and liquidity come next, since the futures leg depends on orderly basis behavior. Risk factor coverage concerns the factors each instrument can reach. Transaction costs form the last boundary.
A third of the paper is prescriptive, and none of it is tested in the empirical section. It offers a framework for matching instruments to risk types and investors, adapting strategies to market conditions, and coordinating regulation through margin rules, position limits and cross-market information sharing.
Daily data run from 1 January 2019 to 31 December 2024. The sample covers the S&P 500, the CSI 300 and the Euro Stoxx 50, together with their futures and options, using data from Wind and Bloomberg. The futures overlay applies a minimum-variance hedge ratio, recalculated and rebalanced every month. The option overlay buys a put with three months to maturity at 90% of spot, then rolls monthly. The paper scores hedging efficiency, Sharpe and maximum drawdown, both in aggregate and by market environment. Environments are classified "according to the rise and fall range and volatility of the stock index": bull means an annualized move of +10% or above, bear means -10% or below, and volatile covers the range between them.
All three columns in the overall table matter. The unhedged portfolio records 8.72% return, 19.35% volatility, Sharpe 0.35 and drawdown 28.64%. The futures-hedged portfolio delivers 7.95%, 10.28%, hedging efficiency 46.87%, Sharpe 0.58 and drawdown 15.32%. For the option-hedged portfolio, the corresponding figures are 8.31%, 8.76%, hedging efficiency 54.73%, Sharpe 0.72 and drawdown 12.78%. Both overlays sacrifice return relative to the unhedged book. The paper acknowledges the shortfall and attributes it to hedging costs. Its conclusion relies on Sharpe and risk control: options lead every risk measure in every market environment. In bull markets, option hedging efficiency reaches 46.83%, versus futures at 36.17%.
What hedging efficiency measures
The overall table reveals the calculation exactly. Subtracting 10.28/19.35 from 1 gives 46.87%; subtracting 8.76/19.35 from 1 gives 54.73%. The paper defines the measure only as "the proportion of portfolio risk reduction after hedging". A variance-reduction reading would put 79.5% in the option row. The operative definition of risk is standard deviation, a distinction required when comparing these results with the futures-hedging literature. This reconstruction works only for the overall table. Because the regime tables omit unhedged volatility, their figures cannot be checked the same way.
The futures cost formula combines the margin ratio multiplied by the risk-free rate, a 10-year Treasury average of 2.8% over 2019-2024, cost of carry, and 0.015% per transaction. Elsewhere, the paper cites margin ratios from 8% to 12%. Applying those inputs ourselves gives an annual margin opportunity-cost leg of 22 to 34 basis points. The paper does not report that range. Its regime thresholds are numeric, as are the option leg's roll frequency, tenor and strike.
The missing premium
The portfolio itself presents the first gap. Three indexes appear in the data, while the results describe one "portfolio". We did not find weights or a currency treatment for the non-USD legs. Two implementers using the same data and stated rules could therefore construct different books.
Position size creates the second gap. The paper specifies strike and tenor without giving notional coverage. It first calls the trade the "call put option strategy", then specifies a put. At inception, a put with three months remaining and a strike 10% below spot is far out of the money. A 46.83% reduction in realized standard deviation during bull markets requires a notional or sizing rule that the paper never supplies.
The money is the third gap.
Futures receive an explicit cost formula: margin ratio multiplied by 2.8%, cost of carry, and 0.015% per trade. Options receive no numerical charge for premium, service charge or slippage, although all three appear in the transaction-cost boundary section. In the authors' own comparison table, options are the expensive instrument, with hedging cost described as "premium needs to be paid, relatively high cost". The futures entry requires margin only. The empirical conclusion repeats that option hedging cost mainly comes from premium.
This admission makes the headline figures harder to accept. The option-hedged portfolio returns 8.31%, compared with 8.72% unhedged. Across six years of continuously rolled protection, the entire net shortfall is 0.41 percentage points a year. The authors explain that gap as "mainly due to the existence of hedging costs", placing premium within the reported 8.31%. Forty-one basis points cannot plausibly represent the whole charge. A three-month put struck at 90% and rolled monthly is purchased roughly twelve times a year across three option markets and three currencies. The sample also includes 2020, when S&P 500 daily kurtosis reached 6.8 and this protection should have been most expensive. The standard variance-risk-premium result makes systematic long-put programs costly. Here, the same program appears nearly free while cutting volatility almost in half. Without the premium calculation, those facts cannot be reconciled.
Every performance result is a point estimate. Statistical testing is confined to the K-S test and the kurtosis diagnostic for 2020, when S&P 500 daily kurtosis was 6.8, compared with 3.2 to 4.1 in the other five years. The authors describe 2020 as abnormal and requiring separate treatment. We did not find a headline table excluding it. Regime labels use annualized move and volatility, though the paper does not state the data frequency. It also gives no counts for index-years in each bucket. Across six years and three indexes, the bear column may contain very few independent observations. That column reports a -0.14 futures Sharpe and a 0.01 option Sharpe.
Basis adjustment changes the ranking
With basis adjustment, futures hedging efficiency rises from 46.87% to 55.17% over 2019-2024. The largest improvement is 12.5% during the 2020 pandemic stretch. The paper reports this gain for hedging efficiency alone.
The resulting 55.17% exceeds the option overlay's 54.73%. The paper's own modification to the futures hedge therefore reverses the risk-reduction ranking behind its conclusion. Yet the adjusted version appears only in prose, without a Sharpe or a definition of the adjustment rule. The printed evidence cannot complete the comparison. I would most like the authors to write that sentence next.
Our substitute
We could not trade the paper's instruments. CSI 300 and Euro Stoxx 50 derivatives are unavailable to us, while our options data is end-of-day only. Futures margin mechanics and basis risk therefore remain untestable here. We used a short SPY position in place of the index futures leg and listed SPY puts for the index options leg. The long portfolio held 20 equal-weighted US mega-caps. This preserves the linear-versus-convex mechanism, while our run evaluates only the substitute rather than the paper's method.
Our sample covers 2020-01-02 to 2024-07-01. Annualized return was 14.42%, with 25.02% volatility, a -47.82% maximum drawdown and beta of 1.02 to SPY. Sharpe was 0.74. The paper's option-hedged portfolio reports Sharpe 0.72, 8.76% volatility and a 12.78% drawdown. Our 0.74 came with 25.02% volatility and a -47.82% drawdown. The Sharpes are nearly identical, though the underlying books are incomparable, leaving the match uninformative about the overlay.
Our 14.42% return exceeds the paper's 7.95% futures-hedged result and its 8.31% option-hedged result. Full market exposure during a strong mega-cap tape can produce that outcome. It is consistent with a hedge that accomplished very little. Different universes and instruments leave it without evidentiary value.
Beta of 1.02 shows how little overlay exposure remained. Our own rules created two mechanical problems. A 10% per-position cap truncates a minimum-variance short requiring roughly 100% notional. The option rule also required exactly 0.9000 moneyness and exactly 90 days to expiry, without a fallback. Whenever no matching contract printed, the roll was skipped. The window begins during the COVID crash, the fat-tail outlier isolated by the paper, and omits calm 2019. Our long portfolio contains 20 concentrated names, creating idiosyncratic risk beyond the reach of an index hedge. We charged zero slippage and no option service charges as well. Those assumptions flatter return and cannot account for the risk gap.
The -47.82% drawdown is worse than the paper's unhedged 28.64%. The capped hedge and concentrated portfolio do not fully explain the difference, and we cannot account for the entire gap from the information available. Our single automated pass failed to show the overlay working. It reaches no conclusion about the paper's method, which we could not run.
A per-index table would change my view of the headline if it charged option premium, bid-ask and roll slippage explicitly, then showed the option overlay retaining its Sharpe lead after the basis-adjusted futures hedge was evaluated on the same three metrics.
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.