Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark?

Austin Pollok

REVIEW 4 major objections 4 minor 60 references

Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark?

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that volatility forecasts which do not clearly beat the HAR benchmark on standard error metrics can still produce economically large gains in daily straddle-portfolio returns, with a nested PCA-HAR model reaching a daily…

desk verdict A large empirical study with a novel evaluation angle, but the headline economic claim is not yet supported by the tables, inference, or a transaction-cost analysis. read the letter →

arxiv 2506.07928 v1 pith:REP22CJ2 submitted 2025-06-09 q-fin.ST

Austin Pollok This is my paper

classification q-fin.ST

keywords realizedvariancevolatilityforecastingout-of-sampleevaluationHARmodelprincipalcomponentsoptionportfoliosstraddlereturnsriskpremium

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether any forecasting model can beat the HAR benchmark when predicting daily firm-level realized variance across S&P 500 firms from 1993 to 2019. On standard error measures (RMSE, MAE, QLIKE, Mincer–Zarnowitz R2), no model wins unanimously; HAR and LASSO lead on loss functions while a nested PCA-HAR model and an equal-weighted ensemble lead on regression R2. The paper then evaluates the same forecasts through the eyes of an options trader, forming daily long-short portfolios of at-the-money straddles sorted on the spread between forecast realized variance and implied volatility. It reports that PCA-HAR delivers a daily Sharpe ratio of 0.80 and average daily return of 2.06%, versus 0.63 and 1.39% for HAR. The paper's central message is that marginal forecast-error improvements can translate into economically significant portfolio gains, making the case for training and evaluating volatility models with end-user objectives in mind.

What carries the argument

The load-bearing object is the daily, firm-level volatility-risk-premium sorting variable $\ln(\hat{RV}_{i,t+1}/IV_{i,t})$, the log gap between a model's forecast of next-day realized variance and the market's at-the-money implied variance. Portfolios are formed each day by ranking S&P 500 straddles into quintiles on this variable and taking the long-short high-minus-low portfolio, with all variables measured before 3:55pm and trades placed before the close to avoid look-ahead bias. The model that carries the result is the nested PCA-HAR specification, which uses a rolling one-year eigendecomposition of the firm-level realized-variance panel to extract common factors, forecasts factor levels with daily/weekly/monthly lags, forecasts the residual with the same HAR structure, and adds the firm's own HAR predictors. The walk-forward pseudo out-of-sample protocol with a 250-day rolling window, nested cross-validation for hyperparameters, and reconstruction of forecasts each day for every firm is what gives the portfolio returns their claim to being out-of-sample.

What would settle it

Lock the PCA-HAR specification (number of factors, inclusion of residual forecasts, estimation window) before any analysis of the option sample, then evaluate it on a genuinely untouched later period such as 2020–2024; if the long-short straddle Sharpe ratio no longer beats HAR's, the paper's economic-significance claim collapses.

Watch

Extended reading notes

Core claim

The central discovery is that the ranking of volatility forecasts changes when they are judged by the returns of portfolios built from the forecasts rather than by forecast-error statistics, and that a model combining common factors with firm-specific predictors can exploit this. The PCA-HAR model extracts principal components from the cross-section of firm-level realized variances over a rolling year, forecasts those factors with HAR-style daily, weekly, and monthly lags, and adds the firm's own HAR predictors; it nests both the HAR model and a pure factor model. On pooled and cross-sectional error measures the model does not consistently beat HAR, yet the long-short at-the-money straddle portfolio sorted on $\ln(\hat{RV}/IV)$ earns 2.06% per day with a Sharpe ratio of 0.80, against 1.39% and 0.63 for the HAR-based portfolio. The paper interprets this as evidence that standard forecast evaluation is an incomplete guide to economic value, and that the realized-minus-implied volatility spread remains a strong daily predictor of option returns when the realized side is forecast more effectively.

Load-bearing premise

The headline improvement rests on the assumption that the PCA-HAR model was chosen before peeking at the 1996–2019 option-return sample, rather than selected after trying many forecasting variants on that same sample; if that assumption fails, the measured Sharpe and return gains could be luck.

Editorial extensions

If this is right

If the paper's claim is right, forecast-error rankings by RMSE, MAE, or QLIKE are not reliable proxies for the economic value of a volatility forecast, and models that tie or lose on those metrics can still win in portfolio construction.
The realized-minus-implied volatility spread, already documented at the monthly horizon, appears to work at the daily frequency for individual equity options when the realized-volatility forecast is improved.
The nested PCA-HAR model's success suggests common-factor information in the cross-section of firm variances contains predictive content for option returns that firm-specific HAR dynamics alone miss.
Portfolio-based evaluation could become a standard complement to statistical loss functions for comparing volatility forecasts, and model training could be re-targeted at portfolio objectives rather than squared error.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension would be to train the volatility model directly on the sorting signal or on option-portfolio returns, rather than on squared forecast error; the paper's own evidence implies this could sharpen the spread further, but it does not test this.
The Sharpe improvement could be checked against multiple-testing corrections, since the paper concedes that pseudo-out-of-sample evaluation can still be mined; applying a correction for the number of model variants tried may shrink the gap between PCA-HAR and HAR.
The same forecast-to-portfolio pipeline could be transferred to other asset classes or to volatility products such as VIX futures, where the realized-minus-implied spread is also observable; this is an extension the paper leaves implicit.
Transaction costs are deliberately set aside; with realistic bid-ask costs and margin on short straddles, the 2.06% daily gross return would shrink, and the ranking across models could change.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a large, carefully assembled daily firm-level realized variance forecasting exercise, and the idea of evaluating forecasts through option portfolios is a good one. But the paper's central claim as stated in the abstract—that marginal forecast-error improvements lead to economically significant portfolio gains—is not what the tables show. The forecast-error rankings actually favor HAR; the portfolio rankings favor PCA-HAR, and the Sharpe difference (0.80 vs 0.63) is reported without any standard errors. Add the fact that returns are midpoint-based and ignore transaction costs, and the economic significance claim is unproven, though the direction is suggestive.

What is actually new: the scale is genuinely new. 1,078 S&P 500 firms, daily, 1993–2019, with HAR, LASSO, PCA-HAR, and ensemble forecasts compared out of sample and then evaluated through one-day straddle portfolios. The result that portfolio-based rankings diverge from forecast-error rankings is worth taking seriously, and the author is transparent about the data-mining risk (Section 3.1) and the transaction-cost caveat (Section 6.2). The literature coverage is solid, and the implementation of the walk-forward scheme is careful.

Soft spots, in proportion: three real ones. First, the abstract overstates. Table 2 shows HAR beats PCA-HAR on RMSE, MAE, and QLIKE in the panels the author says are most relevant, and PCA-HAR only wins on MZ-R2. So the 'marginal improvements' story is not supported; it is a divergence, not an improvement. Second, Table 4 has no inference. With daily return kurtosis above 18, the Sharpe difference is plausibly noise. The author should provide standard errors or a HAC test. Third, the transaction-cost issue is load-bearing. The long-short straddle portfolio rebalances daily, and the 0.67%/day advantage could be eaten by bid-ask spreads. The author acknowledges this but does not quantify it. There are also minor implementation inconsistencies: footnote 20 says LASSO is retrained monthly, while Section 3.1 says every day; and the predictor RV is measured before 3:55pm while Section 5.1 describes full-day RV.

Who this is for: people working on volatility forecasting, option returns, or forecast evaluation. It deserves a serious referee, but the referee should ask for a revised version that fixes the abstract, adds inference, addresses transaction costs, and clarifies implementation. If that happens, the divergence result could be a solid contribution.

Referee Report

4 major / 4 minor

Summary. The paper forecasts daily realized variance for a large panel of S&P 500 firms from 1993 to 2019 using several models: the HAR benchmark, LASSO regressions on a high-dimensional cross-section, a nested PCA-HAR factor model, and equal-weighted forecast ensembles. Forecasts are evaluated both by standard loss functions (RMSE, MAE, QLIKE, MZ-R2) and by the returns of daily at-the-money delta-neutral straddle portfolios sorted on the forecast-minus-implied volatility spread. The paper reports that, while no model unambiguously beats HAR on forecast-error metrics, the PCA-HAR model and the ensemble produce long-short straddle portfolios with higher average returns and Sharpe ratios than HAR (e.g., 2.06% per day and Sharpe 0.80 for PCA-HAR versus 1.39% and 0.63 for HAR, Table 4), and interprets this as evidence that portfolio-based evaluation can reveal value not captured by standard forecast-loss rankings.

Significance. If the results hold, the paper makes a useful empirical contribution by scaling up daily firm-level realized-variance forecasting to the full S&P 500 cross-section and by drawing attention to the disconnect between standard forecast-error rankings and end-user portfolio performance. The design has notable strengths: a walk-forward out-of-sample procedure, a clear timing convention that uses information only up to 3:55pm to allow trades before the close, careful filtering of option data, and explicit discussion of look-ahead bias and data-snooping concerns. However, the economic-significance conclusion currently rests on gross midpoint-based returns with no transaction costs, on differences in Sharpe ratios without any inference, and on a model that was selected after trying several variants on the same sample. The significance of the paper is therefore conditional on these load-bearing issues being addressed.

major comments (4)

[Section 6.2, Table 4; Section 5.2] The headline economic-significance claim is computed from OptionMetrics end-of-day bid-ask midpoints, with no transaction costs or margin requirements, as the paper itself concedes in Section 6.2. Because the long-short portfolios are rebalanced daily and equal-weighted, each rebalance crosses the bid-ask spread on both legs of each straddle; the PCA-HAR advantage over HAR is 0.67% per day (0.0206 vs 0.0139), which is within a plausible one-way ATM-straddle round-trip cost. The manuscript should either report returns net of realistic transaction costs or compute the break-even cost per rebalance that would erase the advantage; without this, the 'economically significant' conclusion is not established.
[Table 4 and Table 5] No standard errors, confidence intervals, or significance tests are reported for the differences in mean returns or Sharpe ratios across forecasts. Given the daily long-short portfolio return kurtosis of 18.64 for PCA-HAR (Table 5), the difference between the PCA-HAR Sharpe (0.8044) and the HAR Sharpe (0.6317) may be within sampling noise. Please provide HAC or bootstrap inference for the average return and Sharpe difference, and ideally a test of equal performance across the two portfolios.
[Section 3.1, Section 4.3, footnotes 20 and 24] The paper's main model, PCA-HAR, is presented in Section 4.3 only after describing several alternatives, and footnotes 20 and 24 report that various other specifications were tried with little difference. Section 3.1 explicitly concedes that pseudo-OOS tests can still suffer from p-hacking, multiple testing, and data mining, yet no correction (e.g., a multiple-testing adjustment) or a true holdout period is applied. Since the central claim is that PCA-HAR improves option-portfolio performance, the possibility of selection on the same sample is load-bearing; a pre-specified specification, a final holdout, or a multiple-testing assessment is needed.
[Abstract, Section 6.1, Table 2] The abstract's claim that 'marginal improvements to standard forecast error measurements can lead to economically significant gains' is not supported by Table 2: PCA-HAR has larger RMSE, MAE, and QLIKE than HAR in Panels A and B, and only in the pooled MZ-R2 (Panel C) does it beat HAR. If anything, the model looks worse on most loss functions, so the paper should either identify which specific forecast-error improvement drives the portfolio gains, or reframe the conclusion to say that forecast-error rankings are ambiguous and do not predict portfolio performance. The current phrasing mischaracterizes the evidence in the paper's own tables.

minor comments (4)

[Table 1] Table 1 reports kurtosis values without stating whether they are excess kurtosis; Section 6.2 later refers to excess kurtosis, so define this consistently in the table note.
[Throughout] There are numerous typographical and encoding issues, such as 'A ¨ ıt-Sahalia' in references, 'varainces' in Section 4.3, 'for for' in Section 2.3, and 'of of' in Section 4.2, which should be corrected.
[Equations (9) and (10)] Equations (9) and (10) use notation like 'Et [Rstocks t+1 ]' and 'Et [Roptions t+1 ]' without definitions; clarify what these expectations represent.
[Section 6.2] The paper states that the results 'confirm the so-called volatility risk premium is large and economically significant' in daily option returns, but Table 3 Panel A shows unconditional ATM straddle excess returns are slightly negative; the confirmation pertains to long-short sorted portfolios, so the wording should be qualified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the option-portfolio results are genuine out-of-sample outcomes and the PCA-HAR advantage is not forced by construction.

full rationale

The paper's derivation chain is linear and data-driven. Realized variances are measured from TAQ intraday prices; each forecast model (HAR, LASSO, PCA-HAR, equal-weighted ensemble) is re-estimated on rolling 250-day windows ending before 3:55pm ET; the sorting variable is VRP_{t-1} = ln(RV_hat_t / IV_{t-1}) (Eqs. 16-17 and 40), using only information available when portfolios are formed; and straddle returns are computed from OptionMetrics midpoints over the subsequent day. Option returns never enter the estimation of any volatility model or the selection of hyperparameters, and the portfolio weights are equal weights, so no parameter is fitted to the outcome being predicted. The paper's own warning that pseudo-OOS tests may suffer from p-hacking and multiple testing (Section 3.1) is a model-selection and data-mining caveat, not a circular reduction: no equation in the paper equates the reported Sharpe ratios or average returns to a fitted input, and the PCA-HAR specification is not defined in terms of the option returns it is used to predict. Citations to Jones et al. (2021a, 2021b) and Jones (2001, 2006) are supporting references for data construction, option-return properties, and factor extraction; they do not function as a uniqueness theorem or as the sole justification for the central claim. The central economic-significance finding is therefore an independent out-of-sample empirical result, subject to the usual robustness concerns about multiple testing and midpoint pricing, but not circular.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on several hand-chosen hyperparameters and on measurement conventions that are not fully specified. No new entities are introduced; the volatility risk premium signal comes from prior literature.

free parameters (4)

LASSO penalty lambda = not reported
Selected by nested cross-validation per rolling window (Section 4.2, Eq. 25); value not reported.
Number of PCA factors K = 3
Chosen by hand; Section 4.3 uses the top three principal components.
Rolling window length W = 250 days
Chosen by hand; Section 3.1 sets W = 250 days.
Ensemble weights = equal weights
Equal-weighted average of forecasts, chosen as a simple default (Section 4.4).

assumptions (5)

standard math Realized variance converges to integrated variance as sampling frequency increases (RV to IV under a continuous-time semimartingale)
Invoked in Section 2.1, Eq. 7, to justify the realized variance proxy.
domain assumption Returns evolve as a continuous-time semimartingale with finite quadratic variation
Underpins the realized variance estimator (Section 2.1).
ad hoc to paper The 3:55pm partial-day realized variance is a valid, consistently scaled predictor for next-day full-day realized variance
The paper uses predictors measured before 3:55pm (Section 3.1) but does not specify how the partial-day RV is computed or scaled relative to the full-day RV used as the target.
domain assumption At-the-money straddle returns computed from bid-ask midpoints approximate realizable returns
Used throughout Section 6.2; the paper acknowledges transaction costs and midpoint bias as limitations but still bases economic significance on these returns.
domain assumption The realized-minus-implied volatility spread predicts the cross-section of option returns
Borrowed from Goyal and Saretto (2009) and used as the sorting variable (Sections 2.4 and 3.3).

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Cite this review

Pith. "Pith review of Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark?." pith.science (2026). https://pith.science/paper/REP22CJ2

@misc{pith2026250607928,
  author       = {Pith},
  title        = {Pith review of: Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/REP22CJ2}},
  note         = {Machine review of arXiv:2506.07928}
}

read the original abstract

The discrepancy between realized volatility and the market's view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast's ability to predict firm-level volatility. We consider this phenomenon at the daily frequency using high-dimensional machine learning models, as well as low-dimensional factor models. We find that marginal improvements to standard forecast error measurements can lead to economically significant gains in portfolio performance. This makes a case for re-imagining the way we train models that are used to construct portfolios.

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Figures reproduced from arXiv: 2506.07928 by the authors.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

A\"it-Sahalia and J

Y. A\"it-Sahalia and J. Jacod. High F requency F inancial E conometrics . Princeton University Press, first edition, 2014

work page 2014

[2] [2]

A\"it-Sahalia, Y

Y. A\"it-Sahalia, Y. Wang, and F. Yared. Do Option Markets Correctly Price the Probabilities of Movement of the Underlying Asset? Journal of Econometrics, 102 0 (1): 0 67--110, 2001

work page 2001

[3] [3]

A\"it-Sahalia, C

Y. A\"it-Sahalia, C. Li, and C. X. Li. Implied Stochastic Volatility Models . The Review of Financial Studies, 34 0 (1): 0 394--450, 03 2020

work page 2020

[4] [4]

Ammann and M

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