This paper proposes a methodology to analyse the risk and return of large loan portfolios in a joint setting. I propose a tractable model to obtain the distribution of loan returns from observed interest rates and default frequencies. I follow a sectoral approach that captures the heterogeneous cyclical features of different kinds of loans and yields moments in closed form. I investigate the validity of mean–variance analysis with a value at risk constraint and study its relationship with utility maximisation. Finally, I study the efficiency of corporate and household loan portfolios in an empirical application to the Spanish banking system.

We conduct an extensive empirical analysis of VIX derivative valuation models before, during, and after the 2008–2009 financial crisis. Since the restrictive mean-reversion and heteroskedasticity features of existing models yield large distortions during the crisis, we propose generalisations with a time-varying central tendency, jumps, and stochastic volatility, analyse their pricing performance, and implications for term structures of VIX futures and volatility “skews.” We find that a process for the log of the observed VIX combining central tendency and stochastic volatility reliably prices VIX derivatives. We also uncover a significant risk premium that shifts the long-run volatility level.

We derive Lagrange multiplier and likelihood ratio specification tests for the null hypotheses of multivariate normal and Student-t innovations using the generalized hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange multiplier-type tests into skewness and kurtosis components. We also obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the likelihood ratio test, whose asymptotic distribution we provide. Finally, we conduct detailed Monte Carlo exercises to study the size and power properties of our proposed tests in finite samples.

We propose a new method for analysing multi-period stress scenarios for portfolio credit risk more systematically than in current macro stress tests. The plausibility of a scenario is quantified by its distance from an average scenario. For a given level of plausibility, we search systematically for the most adverse scenario. This ensures that no plausible scenario will be missed. We show how this method can be applied to some models already in use by practitioners. While worst case search requires numerical optimisation we show that we can work with reasonably good linear approximations to the portfolio loss function. This makes systematic multi-period stress testing computationally efficient and easy to implement. Applying our approach to data from the Spanish loan register we show that, compared to standard stress test procedures, our method identifies more harmful scenarios that are equally plausible.