## Invited Session Fri.2.H 3021

#### Friday, 13:15 - 14:45 h, Room: H 3021

**Cluster 7: Finance & economics** [...]

### Risk management under probability model misspecification

**Chair: Apostolos Fertis and Victor Demiguel**

**Friday, 13:15 - 13:40 h, Room: H 3021, Talk 1**

**David Wozabal**

Robustifying convex risk measures: A non-parametric approach

**Abstract:**

We introduce a framework for robustifying portfolio selection problems with respect to ambiguity in the distribution of the random asset losses. In particular, we are interested in convex, version independent risk measures. We use an ambiguity set which is defined as a neighborhood around a reference probability measure which represents the investors beliefs about the distribution of asset losses. The robustified risk measures are defined as the worst case portfolio risk over the ambiguity set of loss distributions. We demonstrate that under mild conditions, the infinite dimensional optimization problem of finding the worst case risk can be solved analytically and consequently closed form expressions for the robust risk measures are obtained. We use these results to derive robustified version for several examples of risk measures. The resulting robust policies are computationally of the same complexity as their non-robust counterparts. We conclude with a numerical study that shows that in most instances the robustified risk measures perform significantly better out-of-sample than their non-robust variants in terms of risk, expected losses as well as turnover.

**Friday, 13:45 - 14:10 h, Room: H 3021, Talk 2**

**Victor Demiguel**

Stock return serial dependence and out-of-sample portfolio performance

**Coauthors: Francisco J. Nogales, Raman Uppal**

**Abstract:**

We study whether investors can exploit stock return serial dependence to improve the out-of-sample performance of their portfolios. To do this, we first show that a vector autoregressive (VAR) model captures daily stock return serial dependence in a statistically significant manner. Second, we characterize (analytically and empirically) the expected return of an arbitrage (zero-cost) portfolio based on the VAR model, and show that it compares favorably to that of other arbitrage portfolios in the literature. Third, we evaluate the performance of three investment (positive-cost) portfolios: a conditional mean-variance myopic portfolio obtained using the linear VAR model; a conditional mean-variance portfolio using a nonparametric autoregressive (NAR) model; and, a portfolio that is dynamic rather than myopic in its use of the VAR model. We show that, subject to a suitable norm constraint, all three investment portfolios substantially outperform the traditional (unconditional) portfolios, even in the presence of transaction costs of up to 10 basis points.