Publication: Capital requirements: Are they the best solution?
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2008-12
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Abstract
General risk functions are becoming very important in finance and insurance. Many risk functions
are interpreted as initial capital requirements that a manager must add and invest in a risk-free
security in order to protect his clients wealth. Nevertheless, until now it has not been proved that
an alternative investment will be outperformed by the riskless asset.
This paper deals with a complete arbitrage free market and a general expectation bounded risk
measure and analyzes whether the investment in the riskless asset of the capital requirements is
optimal. It is shown that it is not optimal in many important cases. For instance, if the risk measure
is the CVaR and we consider the assumptions of the CAPM or the Black and Scholes model.
Furthermore, the Black and Scholes model the explicit expression of the optimal strategy is
provided, and it is composed of several put options. If the confidence level of the CVaR is close to
100% then the optimal strategy becomes a classical portfolio insurance strategy. This may be a
surprising and important finding for both researchers and practitioners. In particular, managers can
discover how to reduce the level of initial capital requirements by trading options.
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Risk measure, Capital requirement, Optimal strategy, Portfolio insurance