Is it possible to reliably estimate the cost of capital with CAPM (or any other factor model)?

In a previous post I discussed why the cost of debt has little influence on investments. What about the cost of equity? Firms typically use (much) more equity than debt to finance their investments. So the cost of equity should matter more. In a recent study, Murray Frank and Tao Shen investigate how the cost of equity and the weighted average cost of capital (WACC) influence investments of US firms.  Remarkably, they find that the cost of equity and the WACC are positively related to corporate investments. Firms with a higher estimated cost of equity and WACC tend to invest significantly more. That is a very strange result. We would expect firms with a high cost of capital to invest less, not more.

Perhaps something is wrong with the model that Frank and Shen use to estimate the cost of equity? They focus on the Capital Asset Pricing Model (CAPM) which is still the most commonly used model for determining the cost of capital. In a recent survey of finance professionals, Lilia Mukhlynina and Kjell Nyborg find that 76% of these professionals use CAPM. Nevertheless, CAPM has been criticized a lot. The model assumes that the expected return on investments is determined by their systematic risk, i.e. the extent to which the return to the investment is correlated with overall market return. Researchers including Nobel price winner Eugene Fama argue that other factors such as market capitalization and the market-to-book ratio also affect the expected return of investments, up and above systematic risk. These factors should therefore be included in any empirical model that estimates the cost of equity. However, the findings of Frank and Shen not only hold for CAPM but also for the two most commonly used alternative factor models: the Fama and French three factor model and the Carhart version with four factors. Frank and Shen additionally check whether their results hold for different time periods, they take into account differences in firm size and leverage, add additional price factors, consider the possibility of autocorrelation which may affect their findings and use different estimation periods to determine the cost of equity. Whatever they do, the positive relation between the equity cost of capital and corporate investments remains significant. 

However, when they try a different approach to estimate the equity cost of capital, the implied cost of equity capital, the relation between cost of capital and corporate investments becomes negative. This is what we would expect: a lower cost of equity capital makes it cheaper to finance investments and hence induces firms to invest more. Calculation of the implied cost of equity capital is based on valuation models such as the Gordon growth model and the residual income model, which value equity by discounting expecting future cash flows or earnings. If you have estimates of equity value (based on the stock market price) and expected future cash flows or earnings (based on analyst forecasts), you can 'back out' the implied cost of equity capital. This is the cost of equity that stock market investors use to value the stocks (assuming that their expectations about future cash flows / earnings tend to be in line with those of analysts).

Why then is there a positive relation between factor model estimates of the cost of equity and corporate investments? From an economic point of view this does not make sense, and Frank and Shen are not able to explain the positive relation. Anyway, their findings raise serious doubts about the validity of factor models for determining the cost of capital. This is troubling, since these models still are the most common approach to estimate the cost of equity and WACC. The findings of Frank and Shen suggest that the implied cost of equity is a better approach. Unfortunately there are limits to this approach. Estimation requires not only the availability of stock market prices but also reliable estimates of expected future cash flows or earnings, which are often not available. A major advantage of CAPM is that it is a fairly easy model to estimate, which explains why it is still so popular with finance professionals.