Portfolio Optimization Under Solvency II: Implicit Constraints Imposed by the Market Risk Standard Formula

• Published date: 01 March 2017
• Author: Florian Schreiber,Alexander Braun,Hato Schmeiser
• DOI: http://doi.org/10.1111/jori.12077
• Date: 01 March 2017

©2015 The Journal of Risk and Insurance. Vol.84, No. 1, 177–207 (2017).

DOI: 10.1111/jori.12077

Portfolio Optimization Under Solvency II:

Implicit Constraints Imposed by the Market Risk

Standard Formula

Alexander Braun

Hato Schmeiser

Florian Schreiber

Abstract

We optimize a life insurance company’s asset allocation in the context of

classical portfolio theory when the firm needs to adhere to the market risk

capital requirements of Solvency II. The discussion starts with a brief review

of the standard formula and the introduction of a parsimonious partial in-

ternal model. Subsequently, we estimate empirical risk–return profiles for

the main asset classes held by European insurers and run a quadratic opti-

mization program to derive nondominated frontiers with budget, short-sale,

and investment constraints. Wethen compute the capital charges under both

solvency models and identify those efficient portfolio compositions that are

permitted for an exogenously given amount of equity. Finally, we consider

a systematically selected set of inefficient portfolios and check their admis-

sibility, too. Our resultsshow that the standard formula suffers from severe

shortcomings that interfere with economically sensible asset management

decisions. Therefore, the introduction of Solvency II in its current form is

likely to have an adverse impact on certain parts of the European insurance

sector.

Introduction

The new risk-based capital standards Solvency II, which are currently scheduled for

implementation in 2016, aim to modernize and harmonize the regulation of insurance

companies in the member states of the European Union (EU). Particularly for smaller

firms with less sophisticated risk management and modeling capacities, the regulator

provides standard formulae that allow the calculation of solvency capital require-

ments with regard to all kinds of differentrisk types. Although Solvency II is regarded

as one of the most innovative regulatory frameworks, its market risk module is a quite

basic stress factor approach. In this article, we examine the impact of the respective

Alexander Braun, Hato Schmeiser, and Florian Schreiber are at the Institute of Insurance

Economics, University of St. Gallen, Tannenstrasse 19, CH-9000 St. Gallen, Switzerland. The

authors can be contacted via e-mail: alexander.braun@unisg.ch, hato.schmeiser@unisg.ch,

florian.schreiber@unisg.ch

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capital charges on a life insurer’s strategic portfolio choice. Potential implications are

far-reaching since inadequate constraints may give rise to asset allocations that are

disadvantageous for both policyholders and shareholders. Apart from that, insurance

companies are among the largest institutional investors in Europe, together holding

some EUR 6.7 trillion of assets. Hence, major changes in their asset management

practices could entail substantial consequences for the demand situation and pricing

of asset classes in European capital markets (see, e.g., Fitch Ratings, 2011).

Despite the tremendous amount of literature on differentaspects of Solvency II, only a

few authors deal with the relationship of the market risk standard formula and an in-

surer’s investment policy. Rudschuck et al. (2010) argue that the new framework will

prompt insurance companies to reduce their equity holdings, thus rendering it more

difficult to earn required returns in the current low interest rate environment. Bragt,

Steehouwer, and Waalwijk (2010) show that portfolio structure and asset duration

of an insurer have a considerable influence on its capital charges. Moreover, in their

report on the impact of Solvency II on insurance companies’ asset allocations, Fitch

Ratings (2011) anticipates strong effects on European debt markets. Further practi-

tioner studies published by Ernst & Young (2011, 2012) address opportunities for

portfolio construction that will be brought about by the regulatory changes. Gatzert

and Martin (2012) demonstrate that the asset allocation strongly influences the sol-

vency capital requirements and point out that model risk may be an important issue.

In addition, Hoering (2013) investigates whether the investment portfolios of insur-

ance companies will be reshaped under the new framework. As the rating model of

Standard & Poor’s (S&P) seems to be more conservative than the Solvency II standard

formula, Hoering does not expect a binding constraint for the asset management of

insurance companies. Similarly, Fischer and Schl¨

utter (2015) examine how the cali-

bration of the equity risk module affects the regulatory capital and the investment

strategy of an insurer that maximizes its shareholder value. Their findings indicate

situations in which a more conservative stress factor leads to a reduction in both

the firm’s equity portfolio and capital buffer. Finally, Braun, Schmeiser, and Siegel

(2014) compare the capital charges for private equity under the market risk standard

approaches of Solvency II and the Swiss Solvency Test with results for an internal

model and find that the former excessively penalize the asset class.

A rigorous examination of constraints to portfolio optimization under Solvency II has

been conducted by Eling, Gatzert, and Schmeiser,(2009).1They propose an alternative

standard model that determines firm-specific lower limits for investment perfor-

mance, employing the ruin probability, the expected policyholder deficit, and the tail

value at risk (VaR). Our work differs from the aforementioned study in at least three

important aspects. First, in their empirical analysis, Eling, Gatzert, and Schmeiser

provide for a skewed claims distribution but assume stochastic independence of

assets and liabilities. Their results are therefore particularly insightful for nonlife

insurers. In contrast, we consider a life insurance company where the duration gap

1Beyond the insurance literature, Kocagil and Klein (2013) of the investment manager PIMCO

calculate mean-tail risk-efficient portfolios for the banking sector,taking into account the risk-

weighted asset charges of Basel III.