A UDmax of 354.30 against a 5% cutoff of 8.88 owes much to the repetition built into a 36-month rolling window. That arithmetic supports the paper's headline figures and limits how much a trader should infer from them.
The result still matters.
What the loadings tell you
The Fama-French three-factor model prices returns through three exposures: the market, size (SMB) and value (HML). Its original specification keeps those exposures constant over the estimation sample. In practice, the loadings feed risk models, factor limits and return attribution. This paper reports no strategy, no portfolio return, no Sharpe, no alpha and no return forecast. It asks a tighter question: do the coefficients remain stable?
Çobanoğlu's answer is clear.
He forms six value-weighted portfolios from Borsa İstanbul firms, sorting them independently each month by lagged market equity and lagged book-to-market. Three-factor regressions use a fixed 36-month rolling window and advance one month at a time. The process produces 144 beta estimates for each factor and portfolio from July 2013 through June 2025. Bai-Perron rejects constancy in 17 of the 18 beta series. Each rejected series has two to five breaks, concentrated around 2015, 2018, 2021 and 2023.
We cannot trade Borsa İstanbul equities. An implementable version would estimate the same changing market, size and value loadings on US equities. The Turkish universe and this particular window determine the reported break dates, so those dates do not carry over. The broad pattern could.
How Çobanoğlu constructs the test
Each monthly sort uses the median market equity breakpoint to create two groups. The 33rd and 66th book-to-market percentiles create three groups. SMB equals the average return of the three small portfolios minus the average of the three big portfolios. HML takes the average of the two high-BE/ME portfolios and subtracts the average of the two low portfolios.
The market factor is the BIST All Shares excess return over the BIST overnight repo rate. Çobanoğlu uses the previous month-end annualized rate divided by twelve. Financial firms and observations with negative equity are excluded. Returns are winsorized at the 0.5th percentile in both tails, and the portfolios are rebalanced monthly.
A rolling regression at t draws on data from t-36 through t*-1, with the estimate indexed one period ahead. Çobanoğlu then models each beta series as a segmented constant-mean process, a flat average that can jump to another average at dates the model must find. Bai-Perron searches for those jumps. HAC errors use a quadratic spectral kernel with Andrews AR(1) automatic bandwidth. Trimming is 15%, the maximum number of breaks is five, and UDmax chooses the break count.
Only the HML beta for the Small/Low portfolio survives. Its UDmax is 8.53 against the 8.88 cutoff, a gap of 0.35.
Where is the cross-sectional information?
The paper's most useful figure is absent from the abstract. Across the six portfolios, mean rolling market betas range from 0.81 to 0.89. Small value and big growth sit within eight hundredths of each other, with everything below one against a market factor defined by the BIST All Shares index.
Those market betas still vary through time. Their standard deviations range from 0.08 to 0.21. In mid-2013, all six portfolios were between roughly 0.47 and 0.64. By April 2017, the B/M market beta had moved above 1.10 while B/L remained near 0.55.
Yet the market loading barely separates the portfolios. Almost all cross-sectional dispersion appears in SMB and HML. The small portfolios have average SMB loadings from +0.51 to +0.61, versus -0.35 to -0.53 for the big portfolios. For HML, S/H is +0.63 and B/H is +0.56, while S/L is -0.40 and B/L is -0.41.
HML undergoes the clearest regime change. Before 2018, both high book-to-market portfolios carry HML betas near 0.8. After 2021, they settle near 0.3. B/L drops from roughly 0.0 in early 2018 to about -0.8 by end-2021, while S/L falls from about -0.2 to -0.6.
The loadings on the portfolios used to construct the value factor collapse by more than half. That says something direct about the underlying sort. During the same period, the SMB premium averages 0.07% a month. Average portfolio excess returns range from 1.57% to 2.63% a month, compared with a market factor mean of 0.73%.
The asymmetry travels better than the dates. Mean market betas span 0.08 across the six portfolios. SMB spans roughly 1.14, from B/H at -0.53 to S/H at +0.61. A reader can see that difference without running any break test.
The estimator leaves fingerprints
Adjacent 36-month windows share 35 observations. Heavy autocorrelation and smoothing are therefore built into the beta series.
Çobanoğlu uses the appropriate defence. HAC standard errors, calculated with a quadratic spectral kernel and Andrews AR(1) bandwidth, adjust inference for autocorrelated residuals in the mean-shift regression. The beta series itself remains mechanically smoothed. Month-to-month variation shrinks, allowing adjacent segment means to separate more cleanly.
Our reading is that this mechanism inflates the significance figures. Across the 18 series, UDmax ranges from 8.53 to 354.30 against a 5% critical value of 8.88. The concern is greatest for the five extreme series, at 126.19, 167.03, 178.81, 270.30 and 354.30. With adjacent windows sharing 35 of 36 observations, those series show very little month-to-month movement and sharply divided segment means.
Several results are far closer to the boundary. The S/M size beta records 15.49, B/M value 19.31, B/H market 25.38 and S/L size 26.21. All are under 30.
Çobanoğlu reports diagnostics that support the same reading. ADF rejects a unit root at the 1% level for all nine return series, including SMB at -12.64 and HML at -11.14. It fails to reject for 15 of the 18 beta series. Only the S/L and B/H market betas and the B/M value beta reject, at the 10% and 5% levels.
Kurtosis is frequently below three for the beta series. The paper interprets that result as evidence of distributions flatter than normal. We see regime-like plateaus in it. A trending or unit-root beta process could produce the same appearance under a segmented constant-mean test and generate exactly these breaks. In the paper's own language, the loadings may not simply fluctuate randomly around a constant mean but may exhibit persistent movements over time. A mean-shift specification cannot distinguish persistent movement from stepwise regimes.
Additional checks use three window lengths, 24, 36 and 48 months, then add E-Divisive. This change-point search requires no regression model and examines all 18 series jointly. The settings are alpha=1, 199 permutations, a 5% level and a minimum cluster of 22 observations.
Instability appears throughout, although the dates move. The 24- and 48-month runs favour 2020 and 2022 where the baseline identifies 2021 and 2023. The 48-month run places a break in 2016 instead of 2015. Çobanoğlu reports the movement directly and attributes it to the dating effects of the smoothing horizon.
That dependence weakens the year-by-year macro interpretation. The paper associates 2015 with political uncertainty, 2018 with the currency crisis, then cites COVID and the post-2023 policy shift. Those stories are attached to dates that change with the specification. The paper explicitly establishes no causal link.
Dating and future information
A break labelled 2018M03 belongs to a beta estimate built from returns extending back to 2015. A trader could not have observed that break at the time or traded on its reported date. The paper makes no such claim, but the timing constrains any practical use of the dates.
Winsorization creates a quieter problem. The paper says the trim comes from the pooled return distribution and does not describe a trailing-window calculation. As written, the bounds appear to use the whole sample. Every rolling regression, including the first in mid-2013, would then use returns whose extremes had been bounded with later information.
The paper provides no sensitivity check for the winsorization choice. A live risk process would need trailing-window bounds. Otherwise, the estimator has seen the future.
No delisting or survivorship treatment is described, and the paper states no universe size. Its stated exclusions cover financial firms and negative equity. There is no liquidity screen either. The reported betas come from value-weighted, monthly rebalanced portfolios containing Turkish small caps.
What remains useful
We have written before about the distance between a well-fitted regime model and one that can be used. In our review of NEPSE volatility, a full-sample estimate described neither of the two regimes it covered (/articles/adding-egarch-asymmetry-buys-no-forecasting-edge-over-plain-garch). The same structure appears here. The instability is genuine. The dates lack enough reliability for trading decisions, and we think the smoothing left untouched by the HAC correction inflates the significance figures.
Çobanoğlu's narrower result is more useful than the paper's broader framing. Value loadings experience the largest regime shift. Market betas also break. Bai-Perron identifies two to three breaks in every one of the six market series, and the paper plainly shows that market risk exposure is far from constant.
The cross-sectional information, however, resides in HML and SMB. HML on the extreme portfolios halves. A factor-risk limit on value exposure therefore needs re-estimation over a much shorter horizon than a limit on market exposure. Size falls between them: the SMB max-min range exceeds 0.75 for every portfolio and exceeds 1.20 for B/H. Refreshing value limits more frequently than market limits does not require any reported break date to be correct.
A run using non-overlapping windows would change our view, as would testing the breaks against a fitted unit-root beta process instead of a constant. If the 17-of-18 rejection survives either test, the finding would be much stronger than the current statistics can establish.