Abstract
In Chap. 3, risk management was restricted to one of two alternatives: Either leave the asset in question without insurance protection or buy a certain amount of insurance coverage. This narrow view may be appropriate for the decision situation of a household who owns just one marketable asset (e.g. a house). Closer inspection shows that even in this case, two more assets should be considered, namely health and human capital (wisdom). This gives rise to the question of whether the existence of these other assets might influence the decision to buy insurance coverage for the home. Consider a household whose human capital and hence labor income depends heavily on regional economic development. To a certain degree, it can diversify its assets by buying an apartment in a neighboring region that however has different economic prospects. In this way, it can reasonably expect that its marketable asset does not lose value at the same moment when its wage income goes down. Obviously, risk can be reduced or mitigated through diversification, an additional means of risk management.
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Notes
- 1.
Let d t + 1 denote the dividend and P t + 1 the share price in period t + 1. With P t the share price in period t, the share’s rate of return is given by \({r}_{t} = \frac{{d}_{t+1}+({P}_{t+1}-{P}_{t})} {{P}_{t}}\). The expected rate of return amounts to Er t  =  ∑ π i r it , with π i symbolizing the probability of different values of r it occurring. Its standard deviation is given by \(\sigma ({r}_{t}) = {[E{({r}_{it} - E{r}_{t})}^{2}]}^{1/2}\). In Table 4.2, covariances and correlation coefficients are calculated using formulas (4.1) to (4.5), with \({\pi }_{i} = 1/10\) for simple averaging, using past observations to estimate (future) expected values.
- 2.
A critique of the CAPM will be provided in Sect. 6.2.2, where it is applied to insurance. It also has been subjected to empirical testing, with mixed results [see e.g. Roll (1977)].
- 3.
Since the variance of capital market returns cannot be influenced, β i can only be lowered by lowering Cov(r i , r M ) according to equation (4.15). The covariance formula of equation (4.9) shows that this can be achieved by reducing the deviations of r i from its expected value in a symmetric way (i.e. a reduction of its variance). However, volatility could also be diminished in an asymmetric way such that small values of r i increasingly coincide with small values of r M , causing covariance in fact to increase. Therefore, a reduction in the volatility of firm-specific returns can (but need not) result in a decrease of β i .
- 4.
The distinction between risk underwriting and capital investment as the two core activities of an IC will be taken up in Sect. 6.2.1 below.
- 5.
This beta is the same as the β u appearing in the insurance CAPM of Sect. 6.2.2 [see equation (6.23)].
- 6.
The purchase of reinsurance coverage by the IC constitutes an application of option pricing theory to the insurance industry itself (see Sect. 5.7).
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© 2012 Springer-Verlag Berlin Heidelberg
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Zweifel, P., Eisen, R. (2012). Insurance Demand II: Decisions Under Risk with Diversification Possibilities. In: Insurance Economics. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20548-4_4
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DOI: https://doi.org/10.1007/978-3-642-20548-4_4
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