A 5% daily rise in crude implies a loss of about 0.6% for Ryanair's ADR and about 0.3% for Delta in Moschos's estimates. Each figure is an elasticity multiplied by five. Ryanair's elasticities are -0.1183 against WTI and -0.1272 against Brent; Delta's are -0.0573 and -0.0494. These are all same-day regression slopes fitted over the full sample. The paper describes its 5% scenario analysis as presenting the evidence "in a more accessible form rather than providing independent evidence."

Anyone attempting a reproduction faces a more basic question: do the slopes and the statistics alongside them describe a coherent set of daily returns?

The paper's own arithmetic says they cannot. Its correlations and R² cannot come from the same daily returns as its slopes.

Fuel costs, hedges and the sample

The economic case is familiar and sound. Fuel accounts for roughly 20 to 30% of airline operating costs, while fares respond slowly. Higher crude prices should reduce expected cash flow and hit the share price that day. Hedging should cushion the effect. Moschos chooses three carriers with different approaches:

Yahoo Finance supplies daily closing prices for RYAAY, DAL and LHA.DE, alongside continuous front-month WTI (CL=F), Brent (BZ=F) and the S&P 500. The prices become log returns, matched by trading date. The paper then runs five analyses. These comprise a correlation matrix, a two-oil regression for Delta used only for R², the 5% scenario, market betas, and six single-factor elasticity regressions covering each airline and benchmark.

The study builds no trading strategy. Its two research questions concern how strongly oil enters each carrier's returns and whether hedging, business model and listing explain the differences.

The written specification is precise about the return formula and regression equations. We found no start date, end date or observation count anywhere in the text. This omission matters: the paper says the sample includes COVID-19 and the 2022 energy shock, yet gives neither boundary of the window.

Can Delta's -0.33 correlation and 0.308 R² come from daily returns?

Moschos identifies three problems himself. Credit is due for that. He says Figure 1 "is labelled as computed on closing prices rather than returns," and requests confirmation using returns. He also calls Delta's joint R² of 0.308 inconsistent with the weak elasticities and says it requires re-estimation. The Lufthansa series, meanwhile, is broken.

Arithmetic strongly supports the first two warnings. A return correlation is the slope multiplied by the ratio of the two volatilities. Delta's WTI slope of -0.0573 could produce a -0.33 correlation only if crude's daily volatility were about 5.8 times Delta's. That ratio is hard to credit for an airline with a market beta of 1.4435.

The R² encounters another obstacle. A -0.33 correlation limits the one-benchmark R² to around 0.11. Suppose daily WTI and Brent returns were as closely correlated as the 0.99 level correlation shown in Figure 1. Adding a nearly identical regressor would still be unlikely to raise the R² to 0.308.

Both statistics resemble output calculated on price levels.

The paper nevertheless continues to use them. Its summary table places -0.49/-0.50 for Ryanair and -0.33 for Delta alongside the elasticities. The conclusion states that "for the two carriers with reliable data, the different methods give a consistent picture." Section 4.6 describes their agreement as "a consistency check rather than independent confirmation." That weaker formulation still asserts agreement between measures that cannot all be correct on the arithmetic above. The hedging advice also uses the same -0.33 to -0.50 range to assess hedge effectiveness. Numbers disclaimed in one passage thus carry the argument in two others.

There is a separate difficulty with the p-values. A bracketed choice between White (1980) and Newey-West (1987) standard errors remains unresolved in the paper. Ryanair's p of 1.05e-11 would survive any reasonable choice. Delta's Brent p of 0.0207 might not; the author himself describes it as borderline. Anyone implementing the regression must choose a lag length and make Delta's significance conditional on that choice.

The implementer inherits two further decisions. Continuous front-month futures move between contracts, and the paper says roll jumps "should be checked" without reporting whether that happened. It also mentions that WTI futures settled below zero during COVID-19. If that day falls within the sample, its log return is undefined. We found no account of how the study dealt with it.

Lufthansa leaves the comparison short

For Lufthansa, the output consists of n/a correlations, a beta of exactly 0.0000 and elasticities of -0.0002 (p = 0.9915 against WTI, 0.9917 against Brent). Moschos correctly treats this as faulty data. As he writes, a zero beta "is not economically plausible for a large listed airline."

Only two carriers remain to answer the hedging question. Two data points cannot distinguish hedging from business model. And the available comparison cuts against the simple hedging argument: Ryanair hedges forward yet has the larger slope. Delta's is less than half as large.

The author acknowledges the problem. His three possible explanations are finite hedge horizons, the greater fuel cost share of a low-cost carrier, and EUR/USD movements within a dollar ADR. Distinguishing among them, he says, would require hedge-ratio data and an augmented model. Neither enters the paper.

Before sizing a hedge

Moschos acknowledges the omitted factor directly. The single-factor regressions "do not control for market returns," he writes, and some apparent oil exposure "may in fact reflect market exposure." Including the market could change the ranking itself. Crude's betas against the S&P 500 are 0.1784 for WTI and 0.1658 for Brent, showing positive co-movement between oil and equities. Regressing airline returns on oil alone therefore captures some market exposure too. This pulls the oil slope toward zero. The size of that pull grows roughly with the airline's market beta.

Delta's beta is 1.4435, compared with Ryanair's 0.9453. Adjusting for the market should therefore move Delta's exposure further from zero than Ryanair's. Yet the paper recommends underweighting Ryanair relative to Delta when oil is expected to rise. It bases that advice on the unadjusted -0.1183 versus -0.0573 gap. The attached qualification says "the estimates are averages over the sample period and may change over time," addressing time variation while leaving the market factor out of the discussion.

The elasticities are also offered as a guide to the hedge ratio. We found no out-of-sample test of how that hedge would have performed.

We did not attempt to reproduce the study. Our futures data lack Brent, one of its two benchmarks, and Frankfurt-listed LHA.DE falls outside our US-listed universe. Running Delta against WTI would have produced a narrower study. We therefore did not substitute that regression.

Pending a market-controlled regression and an out-of-sample hedge test, the paper supports a sign and an ordering. Ryanair's ADR has a same-day oil slope of about -0.12; Delta's is about half as large. Both estimates omit a market control, a limitation the author explicitly acknowledges.