United Tractors' PBV result shares its price with the return

The PBV coefficient of 49.014, with p = 0.013, tells a trader nothing about what to buy next year. It is the paper's strongest result, yet the same-year share price appears on both sides of the regression. That leaves little to say about value investing.

What went into the regression

Agustin and Marthadinata examine PT United Tractors Tbk, the Indonesian heavy-equipment, mining and energy group, over 2015 to 2025. Their question is whether four ratios track annual changes in this company's share price. Debt to Equity Ratio (DER) and Earnings Per Share (EPS) form their "fundamental analysis" pair. Price Earnings Ratio (PER) and Price to Book Value (PBV) represent "value investing". They calculate all four by hand from annual reports. Shares outstanding remain constant at 3,730,135,136 throughout.

PHS is their name for the dependent variable: the year-over-year percentage change in share price. It averages 7.77%, with a standard deviation of 26.75 points. Its extremes are 66.588% in 2017 and -22.740% in 2018. The authors use OLS in SPSS 26 to regress PHS on the same year's four ratios, giving them 11 observations. Their explanation concerns contemporaneous prices. Investors judge whether a stock is undervalued or overvalued using PBV; changes in PBV alter their assessment of the company's prospects and thereby move its price. The paper reports associations. It develops no strategy.

DER has a significant negative coefficient (B = -0.939, t = -2.478, p = 0.048). PBV has a significant positive one (B = 49.014, t = 3.499, p = 0.013). Neither EPS (p = 0.069) nor PER (p = 0.505) is significant. The joint F statistic is 5.985 (p = 0.027), with (4, 6) degrees of freedom. Adjusted R² is 0.666.

We could not reproduce the regression. Doing so requires United Tractors' IDX price history and Indonesian financial statements; our data covers US equities only. Substituting a US company would ask whether another firm's ratios move with its own price. That would test a different proposition.

Does PBV say anything beyond the price?

PBV divides this year's price by this year's book value. PHS divides this year's price by last year's and subtracts one. Book value per share rose fairly steadily from Rp10,522 to Rp27,649. Most of PBV's annual movement therefore comes from the numerator it shares with price growth.

The peaks coincide. The highest PBV, 2.778x in 2017, accompanies the highest growth, 66.588%, and a price of 35,400. Even the worst year, 2018 (-22.740%), had a PBV of 1.788, above the mean of 1.477.

The value thesis calls for the opposite sign, measured with a lag. A stock cheap on book or earnings should eventually rerate: low PBV today should precede higher returns tomorrow. A positive contemporaneous coefficient says that years ending expensive were good years. That comes close to arithmetic.

PER also has price in its numerator. Multiply EPS by PER and, allowing for rounding, you recover the price itself (Table 3). Two of the four regressors directly contain the same-year price; including EPS alongside PER also lets the regression reconstruct the price level. That price becomes known only after the year's return has occurred.

Five parameters, eleven years, six residual degrees of freedom

Fitting five parameters to 11 points leaves 6 residual degrees of freedom. DER just clears 5%, at p = 0.048. Its bivariate correlation is -0.393 with p = 0.231. Significance arrives only when the other three regressors enter the model.

Those regressors are heavily entangled. EPS and PER have a correlation of -0.898, with VIFs of 5.288 and 7.329. EPS alone correlates with growth at -0.170. Put it into the regression and its coefficient changes sign to +13.177, with a standardized beta of 0.928. PBV's standardized beta is 0.979. Near-one betas on collinear inputs, alongside a sign reversal across 11 points, leave the individual coefficients unstable.

Accounting for the number of regressors reduces R² from 0.800 to an adjusted R² of 0.666. The estimate's standard error is 15.46 points; the standard deviation of growth is 26.75.

Little power in residual tests at n = 11

Every residual check passes. The Kolmogorov-Smirnov p-value is 0.170. Shapiro-Wilk gives p = 0.080, three hundredths above the 0.05 cut-off. Testing heteroscedasticity through an absolute-residual regression produces p-values from 0.139 to 0.662. The runs test records 6 runs, Z = 0.000.

These tests have little power to reject anything with 11 residuals. Passing offers weak evidence. The authors call the Durbin-Watson statistic of 1.323 "an initial indicator" and draw no conclusion from it. They then use the runs test to give the residuals clearance.

There is also the choice of dependent variable: raw price change. We found no adjustment for the Jakarta index or the coal cycle, and dividends are excluded. To their credit, the authors identify coal prices and mining conditions as omitted drivers.

Keep the 2018 and 2023 earnings-price split, drop the PBV coefficient

The authors acknowledge both the small sample and the absence of a causal claim. They write that "given the limited number of observations and the single-company setting, these findings should be interpreted cautiously and do not establish causal relationships." They describe the gap as "empirical and contextual, rather than a claim of developing a new financial theory."

The next sentence in the abstract says the results "highlight the individual statistical relevance of DER and PBV." PBV owes that statistical relevance to a same-year price term shared with growth. The paper never acknowledges the overlap. Its caution addresses sample size and causality alone. DER's relevance depends on p = 0.048 with six residual degrees of freedom, despite an insignificant bivariate correlation.

The discussion moves from that caution to "significant effect" and hypotheses "accepted". Investors, the conclusion says, "can consider DER and PBV as part of their investment analysis." There is no lagged regression supporting that advice. We found no out-of-sample year or cost figure behind it either.

The descriptive observations survive. The authors single out 2018 and 2023, two of eleven years when EPS and price diverged. In 2022 they moved together: EPS more than doubled and the stock gained 17.720%. In 2018, EPS increased from Rp2,057 to Rp3,083 as the stock lost 22.740%. In 2023, EPS reached Rp5,933 and the stock declined 13.231%.

The PBV coefficient tells a trader nothing about next year's return.

A regression of year t+1 growth on year t ratios would change our view. Even with ten observations, a negative PBV coefficient in that regression would at least have the direction predicted by the value thesis.