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2019 | OriginalPaper | Chapter

6. Extension of the Model to Uncertainty

Authors : Thorsten Hens, Sabine Elmiger

Published in: Economic Foundations for Finance

Publisher: Springer International Publishing

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Abstract

This chapter extends the model to uncertainty in order to explain the crucial difference between equity and debt. When households hold equity, they face future returns that tend to be high in good times and low in bad times. Thus, they demand a return on equity that is higher than the return on debt as a compensation for the pro-cyclical returns. When firms are maximizing their profits, they will use debt only if the future profits by the use of debt are larger than the costs in terms of interest payments on debt on average.

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previous chapter Extension of the Model to an Infinite Horizon

next chapter Extension of the Model to Exhaustible Resources

The return on equity is on average higher than the risk-free interest rate.

\(\mathbb {E} _t\left [\ldots \right ]\) denotes the expectation conditional on z ^t.

In case of a Cobb–Douglas production function, multiplying the production function with the state of the world can be interpreted as labor-augmenting technological progress under uncertainty: zF(L, K) = (z ^1∕a L)^a K ^1−a = F(z ^1∕a L, K).

Note that \(\mathbb E_t\left [\text{SDF}_{t+1}\right ]=\frac {1}{1+r_{t+1}}\). This follows from the definition of the stochastic discount factor (6.9) and from the fact that \(\Delta _{t+1}^*\) is a probability measure.

We see immediately that \(U(\mathbb E[C])=\mathbb E[U(C)]\).

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Title: Extension of the Model to Uncertainty
Authors: Thorsten Hens
Sabine Elmiger
Publisher: Springer International Publishing
Book: Economic Foundations for Finance
Print ISBN: 978-3-030-05425-0

Electronic ISBN: 978-3-030-05427-4

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-05427-4_6