Abstract
We present various notions of risk adjusted performance and show their applicability and their limits. These measures include the economic value added, return on capital, risk adjusted return on capital, and return on risk-adjusted capital. The concept of a “hurdle rate” gives a quantitative criterion as to whether a certain endeavor is worth undertaking. We also discuss value based performance concepts. Key performance indicators are introduced to provide practical performance measures that are tailored to the company at hand.
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Notes
- 1.
In contrast, risk capital is not linear, see Chap. 5.
- 2.
EVA is a registered trademark of the firm Stern Stewart & Co. The notion that a risk-appropriate interest rate is decisive as to whether one should invest in a company is however much older and is present, for example, in the work of Eugen Schmalenbach [5, pp. 49–50].
- 3.
In Germany there is a principle of equal treatment that forbids a reduction in the surplus to policy holders, if it applies only to existing business and not to new business.
- 4.
In Sect. 6.6.4 we will define another “risk neutral” probability measure which does not describe the “real world” directly.
- 5.
For \(a,b\in\mathbb{R}^{k}\) the inequality a≤b means that the inequality holds in every component.
- 6.
Personal computers that are commercially available in 2013.
- 7.
Presently (2013) market consistent methods (and Solvency II too) enjoy only limited acceptance in the USA.
- 8.
In jurisdictions where such a regulatory minimum is not prescribed, one could use the confidence level prescribed by Solvency II as a proxy.
- 9.
Since we obviously have a binomial distribution at our disposal one may wonder why we have not explicitly computed the capital. This is because it makes no sense to calculate the risk capital for an individual personal risk: either the policy holder dies and the full amount of the claim must be paid, or he lives and no loss occurs. The value of risk would thus be either the full sum insured or nothing (depending on the confidence level). The concept of capital only makes sense at the portfolio level. We assume here that our policy holder is a member of a larger insurance portfolio, and that the amount \(C_{\mathrm {norm}}^{\mathrm {Mort, Reg}}\) is just the portion of the total capital for the mortality risk that is assigned to him. That we have chosen capital to be constant in time is a further simplification.
- 10.
This stochastic process is not to be confused with the value for the cost-of-capital-based valuation as defined in Sect. 6.6.3, since that is not an adapted stochastic process. Also the value process defined in that chapter is not identical to the notion used here, since there we explicitly used the cash flow structure and the cost of capital method. The economic interpretation of both value processes is the same.
References
CFO Forum, Market consistent embedded value — basis for conclusions. www.cfoforum.nl, October 2009
CFO Forum, Market consistent embedded value — principles. www.cfoforum.nl, October 2009
R.J. Elliott, P.E. Kopp, Mathematics of Financial Markets (Springer, New York, 1999)
M. Kriele, J. Wolf, On market value margins and cost of capital. Blätter DGVFM 28(2), 195–219 (2007)
E. Schmalenbach, Finanzierungen, 3rd edn. (Gloeckner, Leipzig, 1922)
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Kriele, M., Wolf, J. (2014). Performance Measurement. In: Value-Oriented Risk Management of Insurance Companies. EAA Series. Springer, London. https://doi.org/10.1007/978-1-4471-6305-3_6
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