Can robust optimization offer improved portfolio performance?: An empirical study of Indian market

Mohammed Bilal Girach; Shashank Oberoi; Siddhartha P. Chakrabarty

REVIEW 4 major objections 6 minor 17 references

Can robust optimization offer improved portfolio performance?: An empirical study of Indian market

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Robust portfolio optimization matches or beats Markowitz on Indian index data.

desk verdict The math is fine but the performance claim is built on in-sample Sharpe ratios, so the Indian-market evidence doesn't support the conclusion. read the letter →

arxiv 1908.04962 v1 pith:DJ2RKCCL submitted 2019-08-14 q-fin.PM

Shashank Oberoi , Mohammed Bilal Girach , Siddhartha P. Chakrabarty This is my paper · ORCID

classification q-fin.PM

keywords robustportfoliooptimizationworst-casescenariouncertaintysetsS&PBSE30100MarkowitzmodelSharperatioIndianstockmarket

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

This paper asks whether robust portfolio optimization, which builds uncertainty about estimated returns and covariances directly into the portfolio choice, can stand in for the classical Markowitz mean-variance model in practice. Using daily log-returns from the Indian S&P BSE 30 (31 stocks) and S&P BSE 100 (98 stocks) indices, plus simulated returns matched to those stocks, it compares Markowitz with three robust formulations based on box, ellipsoidal, and separable uncertainty sets. The paper argues that the answer is yes: in the risk-aversion range $\lambda \in [2,4]$, the ellipsoidal and separable models deliver average Sharpe ratios equal to or higher than Markowitz's, on market data as well as simulated data. The box model, by contrast, mostly tracks Markowitz. If the comparison holds, Indian practitioners have a straightforward, risk-aware alternative to mean-variance optimization that does not sacrifice risk-adjusted return.

What carries the argument

The argument turns on replacing the Markowitz objective with a worst-case (max-min) counterpart in which the expected-return vector $\mu$ and possibly the covariance matrix $\Sigma$ are allowed to vary inside uncertainty sets. For a general set $\mathcal{U}$, the robust problem maximizes $\min_{(\mu,\Sigma)\in\mathcal{U}} \mu^\top x - \lambda x^\top \Sigma x$ subject to $x^\top 1 = 1$ and $x \ge 0$. A box uncertainty set around the expected return produces the penalty $-\delta^\top |x|$ (the Box model); an ellipsoidal set produces $-\delta \sqrt{x^\top \Sigma_\mu x}$ (the Ellip model); and a separable set treats lower and upper bounds on every entry of $\mu$ and $\Sigma$ independently, yielding a tractable maximization (the Sep model). These three formulations are the machinery: they convert parameter estimation error into an explicit penalty or constraint, and the paper's empirical comparison of their Sharpe ratios is what carries the conclusion.

What would settle it

A reader could refute the central claim by recomputing the six comparisons with a train/test split or a rolling window: estimate means, covariances, and uncertainty sets on data through September 2018, then evaluate realized Sharpe ratios on 2019–2020 returns for S&P BSE 30 and S&P BSE 100. If the ellipsoidal and separable models no longer meet or beat Markowitz on average, the central claim is falsified.

Watch

Extended reading notes

Core claim

The paper's central claim, stated in the abstract and supported by Tables 1–6, is that robust approaches are a viable alternative to the Markowitz model in a real market setup, not only in simulated data. Concretely, for S&P BSE 30 data (193 daily log-returns, December 2017 to September 2018) and S&P BSE 100 data (442 daily log-returns, December 2016 to September 2018), the ellipsoidal and separable uncertainty-set formulations produce average Sharpe ratios that are greater than or equal to the Markowitz benchmark over the risk-aversion interval $\lambda \in [2,4]$. On the 31-stock market data the separable model has the highest average Sharpe ratio (0.200 versus 0.189 for Markowitz), while on the 98-stock market data the ellipsoidal model is marginally ahead (0.194 versus 0.182). The paper also reports that these two models outperform Markowitz on simulated data in the same risk-aversion range, and it treats the lower-lying efficient frontiers of the robust models as evidence against the over-optimism of the Markowitz frontier.

Load-bearing premise

The paper's conclusion assumes that a portfolio's Sharpe ratio calculated on the same data used to build the portfolio tells you how it will perform in the future.

Editorial extensions

If this is right

The paper implies that an Indian large-cap investor can adopt the ellipsoidal or separable robust formulation instead of Markowitz and expect at least the same average Sharpe ratio in the $\lambda \in [2,4]$ risk-aversion range.
The box uncertainty model is not a useful upgrade on this evidence: its average Sharpe ratios hover at or just above Markowitz, and its Sharpe-ratio behavior is inconsistent across the data sets.
Increasing the number of stocks helps the robust models in simulated data: the maximum average Sharpe ratio rises from 0.200 at 31 stocks to 0.244 at 98 stocks when 1000 samples are used, a gain the paper attributes to diversification.
Because the robust models' efficient frontiers lie below Markowitz's, the paper reads their performance as consistent with the known over-estimation of the Markowitz frontier, meaning the robust portfolios achieve comparable risk-adjusted return with less optimistic inputs.
The paper's conclusion that robust optimization is practically useful across numbers of stocks, sample sizes, and data types flows from these Sharpe comparisons rather than from a separate out-of-sample test.

Reading between the lines

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

Editorial extension: because all Sharpe ratios are computed in-sample, the paper does not itself establish that the robust advantage persists out-of-sample; a rolling-window replication would turn its central claim into a testable trading rule.
Editorial extension: the persistent edge of the ellipsoidal and separable models over the box model suggests that the geometry of the uncertainty set, not the mere act of adding robustness, is the active ingredient in the improvement.
Editorial extension: the paper leaves unexplained why, for 31 stocks, fewer simulated samples produce better performance than 1000 samples; identifying that mechanism would sharpen the practical guidance.
Editorial extension: re-running the comparison with a different assumed risk-free rate or with data after September 2018 would reveal how sensitive the model ranking is to these calibration choices.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 clearly written application of three standard robust portfolio formulations to Indian index data, but the evidence for the headline claim is an in-sample comparison and that is not enough.

What's actually new: applying box, ellipsoidal and separable uncertainty-set models to S&P BSE 30 and S&P BSE 100, and comparing simulated data against market data. The formulations are textbook but they are stated correctly, and the authors make a genuine effort to discuss practical dimensions like number of stocks and sample size. The non-parametric bootstrap construction for the separable set is a reasonable choice.

Where it falls short: the central comparison is average Sharpe ratios computed on the same sample used to estimate means, covariances, uncertainty-set radii, and the risk-free rate. There is no train/test split, no rolling window, no out-of-sample evaluation, and no measure of sampling uncertainty. That is not a minor gap; it is the whole argument. The Markowitz portfolio is optimised for that same data, so its in-sample Sharpe is biased upward, and the robust portfolios are solving a different in-sample problem — comparing the two on the training data tells you about estimation bias, not about which would do better going forward. The simulated-data experiments could have avoided this by testing against the known true mean and covariance, but they also report in-sample Sharpe on the generated samples. The paper itself flags unstable or unexplained trends in Section 4 (the sample-size effect for 31 stocks, and the Box model's inconsistency), which underscores the fragility. I also note the risk-aversion window λ∈[2,4] is fixed after seeing the results, with no sensitivity analysis on α or β.

It is not a bad paper in conception. The Indian-market angle is a legitimate extension of work by Tütüncü-Koenig and Santos, and it is well written enough that the method is reproducible. But the abstract's claim that robust approaches are a 'viable alternative' in real markets is not supported by the evidence as presented.

Bottom line: I would not desk-reject this outright — with an out-of-sample evaluation protocol it could be a useful empirical note — but it needs major revision before it makes any claim about practical viability. If I were handling it, I'd send it to a referee with instructions to focus on the evaluation protocol, and I'd expect the paper to come back either with rolling-window results or with a much more modest conclusion.

Referee Report

4 major / 6 minor

Summary. The paper empirically compares the Markowitz mean-variance model with three robust portfolio optimization models (box, ellipsoidal, and separable uncertainty sets) on simulated data and on daily returns of stocks in the S&P BSE 30 and S&P BSE 100 indices. The authors report average Sharpe ratios over a risk-aversion range λ∈[2,4] and conclude that the ellipsoidal and separable robust models are viable alternatives to the Markowitz model in practice. Sections 2 and 3 present the model formulations and the computational results; Section 4 discusses the influence of the number of stocks, sample size, and data type; Section 5 concludes.

Significance. If the central claim were supported, the paper would provide practical guidance for Indian equity portfolio construction and contribute to the ongoing debate on whether robust optimization improves on Markowitz in real markets. The manuscript has several strengths: the robust formulations (box, ellipsoidal, separable) are standard and correctly derived; the computational experiments cover two index sizes and simulated data with two sample sizes; and the tabulated results allow easy comparison across models and settings. However, the significance of the conclusion is undermined by the evaluation methodology: all Sharpe ratios are computed in-sample, without any out-of-sample validation, statistical significance testing, or adjustment for the look-ahead bias inherent in comparing models on the data used to estimate their inputs.

major comments (4)

[Section 3, Tables 1-6] The central claim that robust models are 'a viable alternative to the Markowitz model' in a real market setup is not supported by the evidence because all reported Sharpe ratios are computed on the same sample used to estimate means, covariances, uncertainty-set parameters, and portfolio weights. Section 3 describes no train/test split, rolling window, or any other out-of-sample procedure. The Markowitz weights are chosen to optimize the in-sample mean-variance objective, so its in-sample Sharpe ratio is optimistically biased; the robust models solve a different in-sample objective, so their higher tabulated Sharpe ratios may reflect a different in-sample bias rather than better realized performance. To substantiate the practical-viability claim, the authors should evaluate portfolios on a holdout sample or with rolling-window re-estimation, and for the simulated data they should compare portfolios against the known population mean and covariance or on an independently generated test sample.
[Section 4.1, Table 7] The general statement that 'larger the number of stocks, better is the performance of the portfolios constructed using robust optimization' is contradicted by the authors' own market-data results: Table 7 reports a maximum average Sharpe ratio of 0.2 for N=31 versus 0.194 for N=98. The subsequent paragraph acknowledges this opposite behavior for market data and attributes it to limited data and estimation error, but the paragraph's opening claim is still stated without qualification. This internal inconsistency weakens the discussion section and should be corrected by either revising the general claim or explicitly conditioning it on data type.
[Section 3, simulated data description] The paper states that simulated samples are generated using 'the true mean and covariance matrix' of the historical log-returns, but the text in Section 3 says these are the mean and covariance 'obtained from' or 'set to those' of the historical data. These are sample estimates, not population truths. This imprecision matters because the subsequent in-sample evaluation on simulated data is then not a test against known parameters; it is a test on a finite sample drawn from an estimated distribution. The authors should use the phrase 'estimated mean and covariance' or, better, generate a test sample from the same estimated parameters and evaluate the portfolios on that independent sample, which would provide a genuine out-of-sample check.
[Tables 1-6] No statistical significance is reported for the differences in average Sharpe ratios. For example, in Table 1 the Markowitz average is 0.181 and the separable model average is 0.182; in Table 6 the ellipsoidal model is 0.194 versus 0.182 for Markowitz. Given that these are in-sample averages over only five λ values, the differences may be within sampling noise. The authors should provide standard errors, confidence intervals, bootstrap tests, or paired tests across the λ grid (and ideally across replications for the simulated data) before concluding that one model outperforms another.

minor comments (6)

[Title] The title contains a typo: 'PERFORMAN CE' should be 'PERFORMANCE'.
[Section 2.2] There is a typo: 'condidence' should be 'confidence'.
[Section 3, Sharpe ratio calculation] The paper assumes a 6% annualized risk-free rate but does not state how daily log-returns are annualized for the Sharpe ratio. Clarify the annualization convention (e.g., multiply daily Sharpe by sqrt(252) and adjust for log vs. simple returns).
[Tables 7-9] The description of the entries as 'maximum possible Sharpe Ratio' is ambiguous. It appears the entries are the maximum, across the four models, of the average Sharpe ratio over λ∈[2,4]; please state this explicitly in the table captions or the text.
[References] Reference [15] contains a long tracking parameter (fbclid) and a broken URL format; the reference should be cleaned up or replaced with a stable citation.
[Section 4.2] The observation that the cross-over in performance with sample size is 'not obvious' for the smaller-stock case is honest, but the discussion would benefit from a hypothesis (e.g., estimation error in the covariance matrix) rather than leaving the trend unexplained.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the robust formulations are standard and the performance metric is not an input to the optimization.

full rationale

The paper's derivation chain is not circular. The robust portfolio models (Box, Ellip, Sep) are standard worst-case reformulations of the Markowitz objective, obtained by substituting explicit uncertainty sets into the max-min problem (2.2) and simplifying to (2.5), (2.7), and (2.11). These formulations are not defined in terms of the Sharpe ratio, nor is any parameter fitted to the reported Sharpe values. The empirical conclusion that robust models are a 'viable alternative' is based on comparing in-sample Sharpe ratios across models for λ ∈ [2,4]. This comparison is a statistical-validity concern because the same data are used to estimate means, covariances, and uncertainty-set parameters and to compute performance; however, that is not circularity under the definition used here, since the models are not constructed to reproduce the Sharpe ratios and no output quantity is equivalent to an input by construction. There are no self-citations, no imported uniqueness theorems, and no ansatz smuggled in by citation. The paper even flags unexplained trends (e.g., 'the reason behind such a pattern ... is not obvious'), further indicating that the results are empirical findings rather than manufactured identities. Thus the central claim has independent content, even if its out-of-sample generalizability is not established.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

No new entities are introduced. The central claim rests on standard models plus several data-driven choices, most importantly the in-sample evaluation, which makes the empirical comparison non-predictive.

free parameters (6)

Box uncertainty radius δ_i = σ_i z_{0.025} / sqrt(n), with α=0.05 and n=193 or 442
Chosen from the same sample that is later used to compute Sharpe ratios; the confidence level is a modeling choice.
Ellipsoidal uncertainty radius δ = sqrt(chi-square_N(0.05))
Set by degrees of freedom N and confidence level α=0.05; uses the same data and is not validated out-of-sample.
Risk-aversion window λ∈[2,4] = 2, 2.5, 3, 3.5, 4
Called the 'ideal range' citing Fabozzi et al.; conclusions are averaged over this window, so the choice affects which model appears superior.
Risk-free rate = 6% annualized
Assumed from observed T-bill range in India 2016-2018; used in Sharpe ratio calculation.
Bootstrap simulations β = 8000
Used to construct the separable uncertainty set; no convergence or sensitivity analysis is provided.
Large simulated sample size = 1000
Arbitrary large sample count used for the second simulation scenario; the choice affects the reported trends.

assumptions (6)

domain assumption Asset returns follow a multivariate normal distribution
Used to define δ_i for the box model and to generate simulated data; if returns are not normal, the uncertainty-set calibration is not valid.
domain assumption Historical sample mean and covariance are the true parameters for simulation
Simulated data are generated by sampling from a multivariate normal with mean and covariance set to historical estimates, implicitly treating history as truth.
ad hoc to paper In-sample Sharpe ratio measures portfolio performance
The paper uses the same data to estimate parameters and evaluate portfolios; no holdout or rolling-window check is performed.
domain assumption The range λ∈[2,4] is the ideal risk-aversion range
Cited to Fabozzi et al., but the choice determines which model is declared superior in the average-Sharpe comparisons.
domain assumption Yahoo Finance adjusted closing prices reflect investable daily returns
Data source; no discussion of corporate actions, survivorship bias, or data-cleaning procedures.
domain assumption Separable uncertainty set built via 8000 bootstrap replications is a valid confidence set
Details of the bootstrap construction are not given, and the number of replications is chosen by hand without sensitivity analysis.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Can robust optimization offer improved portfolio performance?: An empirical study of Indian market." pith.science (2026). https://pith.science/paper/DJ2RKCCL

@misc{pith2026190804962,
  author       = {Pith},
  title        = {Pith review of: Can robust optimization offer improved portfolio performance?: An empirical study of Indian market},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DJ2RKCCL}},
  note         = {Machine review of arXiv:1908.04962}
}

read the original abstract

The emergence of robust optimization has been driven primarily by the necessity to address the demerits of the Markowitz model. There has been a noteworthy debate regarding consideration of robust approaches as superior or at par with the Markowitz model, in terms of portfolio performance. In order to address this skepticism, we perform empirical analysis of three robust optimization models, namely the ones based on box, ellipsoidal and separable uncertainty sets. We conclude that robust approaches can be considered as a viable alternative to the Markowitz model, not only in simulated data but also in a real market setup, involving the Indian indices of S&P BSE 30 and S&P BSE 100. Finally, we offer qualitative and quantitative justification regarding the practical usefulness of robust optimization approaches from the point of view of number of stocks, sample size and types of data.

Figures

Figures reproduced from arXiv: 1908.04962 by the authors.

**Figure 2.** Efficient Frontier plot and Sharpe Ratio plot for di [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Efficient Frontier plot and Sharpe Ratio plot for di [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Efficient Frontier plot and Sharpe Ratio plot for di [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: Efficient Frontier plot and Sharpe Ratio plot for di [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: Efficient Frontier plot and Sharpe ratio plot for di [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages

[1]

and Grauer, R.R

Best, M.J. and Grauer, R.R. (1991). On the sensitivity of mean-variance-efﬁcient portfolios to changes in asset means: some analytical and computational results, Th e Review of Financial Studies, 4(2): 315–342

work page 1991
[2]

Broadie, M. (1993). Computing efﬁcient frontiers using estimated parameters. Annals of Operations Re- search, 45(1): 21–58

work page 1993
[3]

and Stubbs, R.A

Ceria, S. and Stubbs, R.A. (2006). Incorporating estima tion errors into portfolio selection: Robust portfo- lio construction. Journal of Asset Management, 7(2): 109–1 27

work page 2006
[4]

and Nogales, F.J

DeMiguel, V . and Nogales, F.J. (2009). Portfolio select ion with robust estimation. Operations Research, 57(3): 560–577

work page 2009
[5]

and Focardi, S.M

Fabozzi, F.J., Kolm, P .N., Pachamanova, D. and Focardi, S.M. (2007). Robust Portfolio Optimization and Management, Wiley

work page 2007
[6]

and T¨ ut¨ unc¨ u, R.H

Halldorsson, B.V . and T¨ ut¨ unc¨ u, R.H. (2003). An interior-point method for a class of saddle-point prob- lems. Journal of Optimization Theory and Applications, 116 (3): 559–590

work page 2003
[7]

and Fabozzi, F.J

Kim, J.H., Kim, W.C. and Fabozzi, F.J. (2014). Recent dev elopments in robust rortfolios with a worst-case approach. Journal of Optimization Theory and Applications , 161(1): 103–121

work page 2014
[8]

Lu, Z. (2006). A new cone programming approach for robust portfolio selection. Technical report, De- partment of Mathematics, Simon Fraser University, Burnaby , BC

work page 2006

Show all 17 references

[9]

Markowitz, H.M. (1952). Portfolio selection. The Journ al of Finance, 7(1): 77–91

1952
[10]

Markowitz, H.M. (1959). Portfolio selection: Efﬁcien t diversiﬁcation of investments, Y ale University Press

1959
[11]

Michaud, R.O. (1989). The Markowitz Optimization Enig ma: Is ’Optimized’ Optimal?. Financial Ana- lysts Journal, 45(1): 31–42

1989
[12]

Santos, A.A.P . (2010). The out-of-sample performance of robust portfolio optimization. Brazilian Review of Finance, 8(2): 141–166

2010
[13]

Scherer, B. (2007). Can robust portfolio optimization help to build better portfolios?. Journal of Asset Management, 7(6): 374–387

2007
[14]

and Koenig, M

T¨ ut¨ unc¨ u, R.H. and Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1-4): 157–187

2004
[15]

Portfolios: Do number of stocks matter?, V alue Researc h Online, https://www.valueresearchonline.com/story/h2_storyView.asp?str=200396&fbclid=IwAR3YkUaNLCY3keZGXfooehh0WU90zkZ5s94h0Uazj1-rzOFSy5bw6R1E-MY
[16]

Reserve Bank of India – Weekly Statistical Supplement, https://www.rbi.org.in/scripts/WSSViewDetail.aspx?TYPE=Section&PARAM1=4%0A
[17]

Y ahoo Finance, https://in.finance.yahoo.com/ 8 6 6.5 7 7.5 8 8.5 9 9.5 10 Standard Deviation 10 -3 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95Return 10 -3 Vanilla Markowitz With Box uncertainty With Ellipsoid uncertainty With Separable uncertainty 2 2.5 3 3.5 4 Risk Ave...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

and Grauer, R.R

Best, M.J. and Grauer, R.R. (1991). On the sensitivity of mean-variance-efﬁcient portfolios to changes in asset means: some analytical and computational results, Th e Review of Financial Studies, 4(2): 315–342

work page 1991

[2] [2]

Broadie, M. (1993). Computing efﬁcient frontiers using estimated parameters. Annals of Operations Re- search, 45(1): 21–58

work page 1993

[3] [3]

and Stubbs, R.A

Ceria, S. and Stubbs, R.A. (2006). Incorporating estima tion errors into portfolio selection: Robust portfo- lio construction. Journal of Asset Management, 7(2): 109–1 27

work page 2006

[4] [4]

and Nogales, F.J

DeMiguel, V . and Nogales, F.J. (2009). Portfolio select ion with robust estimation. Operations Research, 57(3): 560–577

work page 2009

[5] [5]

and Focardi, S.M

Fabozzi, F.J., Kolm, P .N., Pachamanova, D. and Focardi, S.M. (2007). Robust Portfolio Optimization and Management, Wiley

work page 2007

[6] [6]

and T¨ ut¨ unc¨ u, R.H

Halldorsson, B.V . and T¨ ut¨ unc¨ u, R.H. (2003). An interior-point method for a class of saddle-point prob- lems. Journal of Optimization Theory and Applications, 116 (3): 559–590

work page 2003

[7] [7]

and Fabozzi, F.J

Kim, J.H., Kim, W.C. and Fabozzi, F.J. (2014). Recent dev elopments in robust rortfolios with a worst-case approach. Journal of Optimization Theory and Applications , 161(1): 103–121

work page 2014

[8] [8]

Lu, Z. (2006). A new cone programming approach for robust portfolio selection. Technical report, De- partment of Mathematics, Simon Fraser University, Burnaby , BC

work page 2006