The one number here worth carrying away is the spread in daily open-to-close volatility. Alkem Laboratories sits at 1.584%, Torrent Power at 2.335%. A Brown-Forsythe F of 22.7482 (df 9 and 12,380, p < 0.001) rejects equal variances across the ten names. The means test, the consistency ranking and the correlations all rest on ten observations per name.
Ten price series and three tests
Deepika and Pavan Kumar assemble daily bars from the BSE for ten companies over five financial years, 01-04-2021 to 30-03-2026: 1,239 trading days each, 12,390 rows in total, with no gaps across names. The ten are Alkem Laboratories, Apollo Tyres, Ashok Leyland, Bank of India, Canara Bank, Exide Industries, TVS Motor, Astral, Federal Bank and Torrent Power, chosen by purposive sampling.
From that panel they build a half-year closing-price index (base 100), a matrix of half-year closing-price returns, and a linear trend slope and R-squared on closing prices. Table 5 then reports descriptive statistics of the daily open-to-close return for each company: mean, median, standard deviation, mean absolute deviation, min and max. A return-to-risk ratio follows, mean open-to-close return divided by its standard deviation with no risk-free rate. Alongside it sit historical 95% VaR (2.45% to 3.53% across names) and 95% expected shortfall (3.48% to 4.93%). Three tests close it out. Kruskal-Wallis on the ten half-year average intraday returns per company. Brown-Forsythe on equality of daily intraday variances. Pearson correlation of half-year closing-price returns across all 45 pairs.
What they report on the closing-price side: TVS Motor up 471.3% (589.10 to 3,365.80, trend slope 340.92, R-squared 0.96), Federal Bank up 228.9%, Torrent Power up 205.4%. Two names went the other way. Canara Bank fell 20.9% on a trend R-squared of 0.06, and Astral fell 5.10%.
The abstract's central claim, that no company achieved a positive average intraday return, sits on Table 5, where the means run from -0.003% (Alkem) to -0.167% (Bank of India). Table 6 carries the companion figure: positive open-to-close days run 48.6% down to 44.3%, below half for every name. The abstract then answers itself in the next breath, concluding that "volatility and downside risk differentiate securities more clearly than average intraday returns." That answer is the one thing in the paper the tests do not establish, for reasons of power I come back to below.
Where did the mutual funds go?
No scheme, NAV, expense ratio or benchmark appears anywhere in the ten tables. The authors' own abstract and conclusion drop the mutual-fund frame: the abstract describes "selected companies suitable for mutual-fund and equity investment analysis," and the conclusion says the study examined "ten BSE-listed companies over the five financial years." That concession sharpens the title question rather than answering it. The single introductory paragraph opens on what a mutual fund is and then sets out SEBI's scheme classification (ranks 1-100 large-cap, 101-250 mid, 251 onward small). We did not find the ten names assigned to any of those buckets. The literature review, covering 50 articles published 2015 to 2026, says seven measures were widely used to compare risk-adjusted returns in that body of work: standard deviation, beta, Sharpe, Treynor, Jensen's alpha, CAPM and the dividend discount model. None of the four risk-adjusted measures in that list is computed here.
This study substitutes ten price series for the funds and drops the risk-adjusted machinery with them, against a review of 50 papers that mostly used it.
Every mean is negative, including the 471.3% winner
The authors put the gap in their own recommendations: a strong long-term price rise should not be read as evidence of profitable intraday performance. Open-to-close returns exclude the overnight gap, so the two series can diverge. The return/risk column makes the point in one line, running from -0.0017 (Alkem) to -0.0735 (Bank of India), negative for all ten.
But look at the size of what they are asking us to accept. TVS Motor averaged -0.078% open-to-close per day across 1,239 sessions, the close beat the open on 47.1% of them, and the stock still compounded to +471.3%. My own inference from that arithmetic: the overnight gap is the only place the gain can have come from, for the eight names that rose, and Canara Bank and Astral fell outright. That regularity is either a real feature of BSE microstructure over this period or an artifact of unadjusted opening prices. The data source is given as the BSE website with Excel files compiled by the researcher, and we did not find a statement of how splits and bonus issues were handled. Canara Bank posted a -81.0% half-year in 24-25 H1, in a name whose five-year change was -20.9% and whose fitted trend explains 6% of the variation. A single half-year move of that size has the shape an unadjusted corporate action leaves behind.
One test on 100 numbers, one on 12,390
The headline contrast is between an insignificant Kruskal-Wallis (H = 3.9764, df 9, critical chi-square 16.9190, p = 0.9130) and a strongly significant Brown-Forsythe (F = 22.7482, p < 0.001).
Same underlying data.
The means test runs on ten half-year aggregates per company, 100 numbers in total; the variance test runs on all 1,239 daily observations per company. A power gap of that size will produce this pattern whether or not the mean returns differ, so the comparison does not establish that risk is the more discriminating dimension.
The volatility spread does most of the work the abstract wants: 1.584% for Alkem against 2.335% for Torrent Power, a factor of 1.47. VaR runs from 2.45% (Alkem) to 3.53% (Canara Bank), broadly following the volatility ranking, though Torrent Power's 3.46% sits below Canara's despite the higher standard deviation. We did not find a post-hoc breakdown identifying which variances differ from which, which is what you would need to use the ranking. Second moments carrying the information while first moments do not is familiar ground; we made a related point reviewing a NEPSE GARCH study where the model ranking itself flipped with the loss function (/articles/adding-egarch-asymmetry-buys-no-forecasting-edge-over-plain-garch).
Eight degrees of freedom carry the diversification advice
Two of 45 pairs clear p < 0.05: Alkem with Torrent Power at r = 0.670 (p = 0.0339) and Apollo Tyres with TVS Motor at r = 0.859 (p = 0.0015). On my own arithmetic, ten half-year observations per pair puts the two-tailed 5% critical r on 8 degrees of freedom near 0.63. Three near-misses fall just under it: Exide-Apollo at 0.599, Ashok-Federal at 0.576 and Canara-Federal at -0.51. The recommendation that diversification is advisable because most pairs showed no significant co-movement is therefore built on failures to reject at 8 df. A 0.599 estimate between Exide and Apollo Tyres is co-movement worth sizing around; ten observations per pair just cannot certify it.
One table is worth a second look. Federal Bank is ranked most consistent, on the lowest dispersion of half-year mean intraday returns (0.14%), while the same row records positive intraday half-year means in 1 of 10 periods. The paper prints a general caveat under that table, that stability in the mean should be assessed together with the level of return and downside exposure, and never flags the rank-1 conflict itself. A consistency rank that rewards tight losses needs that caveat printed next to it.
We could not test any of this.
The universe is BSE-listed Indian equities and we have no Indian price coverage. A US-equity version would test a different universe and would not reproduce the BSE-company findings. There is also no selection or exit rule in the paper to evaluate.
The volatility and downside-risk ordering across these ten names is the usable output, and it is the part the authors say is the usable output. What would change my reading of the rest is a documented adjustment procedure for the open prices, and a Kruskal-Wallis run on daily returns rather than half-year averages. If the means test still comes back at p = 0.91 on 12,390 observations, the paper has a result.