Portfolio diversification and asset pricing are central aspects of risk management. Together, they constitute the focus of the latest issue of The Journal of Risk. While the classical mean-variance approach is well understood theoretically, its actual implementation continues to present a challenge. On the other hand, credit risk contracts have a significantly shorter history and their pricing and hedging has directed the debate surrounding the financial crisis of late.
Asset allocations based on the mean-variance trade-off have been shown to be very sensitive to their inputs. The latter, which include the mean asset returns and their covariance matrix, must be estimated based only on finite samples. In the first paper, "Sample tangency portfolio, representativeness and ambiguity: impact of the law of small numbers", Ghislain Yanou develops a framework to assess the impact of the degree to which the small-sample effect is ignored. In this context, investors are profiled in a range depending on their ambiguity relative to the underlying mean- variance model. Following this classification, the author shows that the most ambiguous investors perform best according to a certain deviation criterion.
Diversification based on the mean-variance trade-off is the bedrock for the ubiquitous capital asset pricing model (CAPM). Despite its long-established popularity, it has been criticized for using volatility (standard deviation) as a risk measure, since this only captures movements around their averages. However, tail events and their overwhelming impact were on full display during the recent financial crisis. The second paper in this issue, "Calibrating risk preferences with the generalized capital asset pricing model based on mixed conditional value-at-risk deviation" by Konstantin Kalinchenko, Stan Uryasev and R. Tyrrell Rockafellar, develops a technique that makes use of market data to elicit parameters identifying alternative downside risk measures. As a result, they derive new CAPM-like betas that measure systematic risk in a way that accounts for tail losses.
Credit risk instigated and then amplified the recent financial crisis. During the crisis, the largest losses occurred when both obligor and guarantor defaulted (the socalled "double default"). Our third paper, "Failure of the saddlepoint method in the presence of double defaults" by Eva Lütkebohmert, focuses on evaluating the effect of undiversified idiosyncratic risk (due to name concentration) on credit portfolio risk in the presence of double default. Two evaluation alternatives to the computationally onerous Monte Carlo simulation are compared: namely, the granularity approach and the saddlepoint approximation. Based on this study, the former accounts better for the salient features of a standard credit risk model and for the internal-ratings-based approach of Basel II.
The counterintuitive profitability resulting from credit deterioration is a peculiar phenomenon that the financial crisis has brought to the fore. In the final paper of this issue, "Pricing to acceptability: with applications to valuation of one's own credit risk", Ernst Eberlein, Thomas Gehrig and Dilip B. Madan show that the theory of pricing to acceptability, developed for incomplete markets, leads to valuing assets and liabilities differently and, in turn, mitigates the counterintuitive profitability.
Calibrating risk preferences with the generalized capital asset pricing model based on mixed conditional value-at-risk deviation