Covariance Principle for Capital Allocation: A Time-Varying Approach

Jilber Urbina,Miguel Santolino,Montserrat Guillen

doi:10.3390/math9162005

Abstract

The covariance allocation principle is one of the most widely used capital allocation principles in practice. Risks change over time, so capital risk allocations should be time-dependent. In this paper, we propose a dynamic covariance capital allocation principle based on the variance-covariance of risks that change over time. The conditional correlation of risks is modeled by means of a dynamic conditional correlation (DCC) model. Unlike the static approach, we show that in our dynamic capital allocation setting, the distribution of risk capital allocations can be estimated, and the expected future allocations of capital can be predicted, providing a deeper understanding of the stochastic multivariate behavior of risks. The methodology presented in the paper is illustrated with an example involving the investment risk in a stock portfolio.

Highlights

Risk in financial and actuarial applications is often defined as a random variable associated with losses [1,2]
We propose a dynamic capital allocation principle based on the variance-covariance of risks that change over time
Taking the capital allocation from Equation (7), i.e., daily losses are considered individual observations and no time-varying approach is followed, and using statistics shown in Table 1, the following capital assignment scheme based on covariance allocation principle is obtained: S&P 500 (SP500) 25.68%, DAX 37.93% and CAC40 36.39%

Summary

Introduction

Risk in financial and actuarial applications is often defined as a random variable associated with losses [1,2]. Examples of capital allocation problems can be found in many areas of finance, where agents attempt to define investment risks [5,6,7,8,9,10,11], and in insurance, where they involve the allocation of the total solvency capital requirement across the business lines or the total costs or expenses across the coverage of an insurance policy, among other areas [12,13,14]. Capital allocation principles are defined by a capital allocation criterion and a given risk measure. The combination of an allocation criterion and a risk measure will usually give different capital allocation solutions. A recent review and comparison of techniques can be found in [21]

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