A Theory of Asset Pricing and Performance Evaluation for Minority Banks with Implications for Bank Failure Prediction, Compensating Risk, and CAMELS Rating

Abstract

This paper introduces a comprehensive theory of performance evaluation and asset pricing for minority (type-m) banks incuding, but not limited to, CAMELS rating, bank failure prediction, compensating risks, and risk adjusted internal rates of returns in a complete market. Our theory predicts and explains several empirical regularities of minority banks. First, we provide a novel mechanism for generating a synthetic cash flow stream in Hilbert space, by comparing NPV projects selected by minority and nonminority (type-n) peer banks. Thus, laying a foundation for security design for sound type-m banks. Second, even when internal rates of return and managerial ability are equal for type-m and type-n banks, the expected cash flows for type-n banks uniformly dominate that for type-m banks by a factor greater than 2. Third, a behavioral mean-variance analysis of liquidity preference explains type-m banks‘ seeming zero covariance frontier portfolio, and asset pricing anomalies like concavity of their internal rates of return in project risk. Such anomalies affect computation of unlevered betas, imply undercapitalization and inefficiency that crowds out positive NPV projects, and suggest that type-m banks overinvest in residual [second best] projects eschewed by type-n banks. See e.g., Ruback (2002); Jensen and Meckling (1976); Myers (1977); and Williams-Stanton (1998). Even so, the returns on minority banks‘ portfolios are viable provided that the risk free rate is less than that for the minimum variance [frontier] portfolio. Fourth, we introduce a compensating risk factor for type-m banks–priced by a two-factor asset pricing model induced by Vasicek (2002) for loan portfolio value, i.e. return on assets (ROA). Our theory predicts that that compensating transfer scheme is tantamount to a put option on type-m bank assets in accord with Merton (1977). And we use Deelstra et al. (2010) model to identify the optimal strike price for that option. According to Merton (1992) and Glazer and Kondo (2010), to mitigate moral hazard in such schemes either (1) type-m banks must bear the associated costs, or (2) the costs must not be bourne by other banks. Arguably, our put option prices type-m banks under FIRREA § 308 (1989). Fifth, on the fixed income side, Vasicek (1977) interest rate model predicts that the term structure of bonds issued by type-m banks is a floor for the term structure of bonds issued by type-n peer banks. Moreover, if risky cash flows follow a Markov process, then under Rothschild and Stiglitz (1970) type mean preserving spread analysis, type-m bank bonds are riskier, provide lower yield, and need to be issued over shorter duration–according to Barclay and Smith (1995) empirical findings on asymmetric information and the “contracting-cost hypothesis”. Sixth, we extend Vasicek (2002) to an independently important conditional probit representation for bank failure prediction–more granular than Cole and Gunther (1998) ad hoc probit model. Seventh, we establish a nexus between random utility analysis, the conditional probit, and a simple bivariate CAMELS rating function that (1) predict bank examiners attitudes towards type-m banks, and (2) identifies root causes of their bias towards high CAMELS scores for type-m banks. In particular, we show how bank examiners‘ CAMELS scores for return on assets risk is predicted by bank specific variables.