Companies that invest more or grow their total assets more are likely to experience a strange result: lower risk-adjusted returns. This outcome is called the investment or asset growth anomaly and it has attracted interest from researchers seeking an explanation.

Two different schools of thought have emerged, one behavioral and the other rational. The behavioral argument is that investors are too slow to incorporate information from firm investment into stock prices, which causes the mispricing. The rational view is that firms invest more when expected returns are lower, and less when expected returns are higher, which induces the negative relation between investment and subsequent stock returns.

So which theory is right? Or are they both right? The latter possibility attracted the attention of F.Y. Eric C. Lam and K.C. John Wei, whose study helps to close the gap between the two theories.

They focus on limits-to-arbitrage to represent the behavioral theory and investment frictions for the rational theory.

Limits-to-arbitrage argues that arbitrage is risky, costly and limited, so if the asset growth anomaly is due to mispricing, it will be more pronounced for stocks that are difficult to arbitrage.

With investment frictions, such as firm age, firms become less responsive to changes in their expected returns. So for a given change in the cost of capital, the change in their investment is smaller when investment frictions are higher, resulting in a stronger asset growth anomaly.

"As the proxies for both limits-to-arbitrage and investment frictions are highly correlated, these two explanations should make similar predictions about the anomaly. If that is the case, the supporting evidence for one explanation should support the other," the authors say. It is therefore only by testing both hypotheses jointly that one might sort out their relative importance in understanding the anomaly.

They test the relative importance of the two hypotheses by conducting cross-sectional regressions of returns on asset growth on subsmaples split by a given measure of limits-to-arbitrage or investment frictions. They use four measures of limits-to-arbitrage (arbitrage risk, information uncertainty, shareholder sophistication and potential transaction costs) and four for investment frictions (firm age, asset size, payout ratio and credit rating) on a sample of US firms from July 1971-December 2009. They also test both value-weighted and equal-weighted returns.

The results are remarkably strong and similar support for both hypotheses when each hypothesis is tested separately. In direction comparisons between the two competing hypotheses, each hypothesis is supported by a fair and similar amount of evidence. The results for the equal-weighted tests are much stronger than those for value-weighted tests. In addition, the evidence against either hypothesis is very small, representing no more than one percent of the cases.

"There is indeed a similar amount of evidence supporting each explanation," the authors say. "In addition the two explanations appear to complement each other in explaining the asset growth anomaly when small and large firms are given equal weight."

However, they add that the evidence is substantially weakened when firm characteristics are controlled for, or when larger firms are given more weight. In particular, the idiosyncratic return volatility appears to be the only measure of limits-to-arbitrage that has a reliable effect on the asset growth anomaly, while firm age seems to be the only measure of investment frictions with a reliable effect.