Manfred Frühwirth

The Jarrow/Turnbull default risk model—Evidence from the German market

Abstract This article estimates default intensities within the continuous-time Jarrow and Turnbull model for German bank and corporate bond prices. It is shown that a joint implicit estimation of the default intensity and the recovery rate is numerically unstable. In addition to cross-sectional estimations, separate estimations (for each bond individually) are performed. Results strongly support separate estimation over the building of any cross-sections. In contrast to preceeding literature, the optimum volume of data required to provide reasonable estimates of the default intensity is also investigated. It is shown that calibration based on daily data as a rule does not minimize the ex ante mean squared pricing errors. Finally, it is shown that the constant default intensity assumption is not sound with the underlying data and the determinants of the default intensity are investigated. Regressions show that the lagged default intensity estimate, the level of the default-free term structure and liquidity proxies affect the estimated default intensity via joint parameters.

The Risk Microstructure of Corporate Bonds: A Case Study from the German Corporate Bond Market

This article presents joint econometric analysis of interest rate risk, issuer-specific risk (credit risk) and bond-specific risk (liquidity risk) in a reduced-form framework. We estimate issuer-specific and bond-specific risk from corporate bond data in the German market. We find that bond-specific risk plays a crucial role in the pricing of corporate bonds. We observe substantial differences between different bonds with respect to the relative influence of issuer-specific vs. bond-specific spread on the level and the volatility of the total spread. Issuer-specific risk exhibits strong autocorrelation and a strong impact of weekday effects, the level of the risk-free term structure and the debt to value ratio. Moreover, we can observe some impact of the stock market volatility, the respective stocks return and the distance to default. For the bond-specific risk we find strong autocorrelation, some impact of the stock market index, the stock market volatility, weekday effects and monthly effects as well as a very weak impact of the risk-free term structure and the specific stocks return. Altogether, the determinants of the spread components vary strongly between different bonds/issuers.

Die optimale Kapitalstruktur österreichischer Kapitalgesellschaften nach der Steuerreform 2000 unter besonderer Berücksichtigung der Eigenkapitalzuwachsverzinsung

SummaryFollowing the methodology of Zechner/Swoboda (1986), Swoboda (1991) and Swoboda/Zechner (1995) the optimal capital structure was analysed for a corporation under uncertainty in the Austrian tax system after the tax reform 2000.In spite of the innovative provisions as regards deductibility of equity (cumulation) interest charge, maximum debt finance is optimal. This is due on the one hand to the bankruptcy effect, on the other hand to the tradeoff effect. Irrelevance of capital structure would require a fictitious equity interest rate which was linked to the corporations default risk.A multiperiod extension of the model aggravates the fiscal inequality of equity and debt, as for equity only interest on the cumulation of equity can be deducted from tax, whereas for debt the whole amount of debt is deductible (see Bogner/Frühwirth/Höger (1999)).

The Optimal Design of Savings Plans for Prospect Theory Investors

In this paper we compare static and dynamic savings plans with lump sum investments from the perspective of a prospect theory investor. To evaluate these strategies we use an ex ante approach taking recourse to Monte Carlo Simulation and parameters from Tversky and Kahneman (1992) and check the stability of our results by using results from other literature. Process parameter values are derived from historical data in various countries. In a first step we calculate the optimal growth rate of dynamic savings plans. We find that the optimal growth rate is an increasing function of volatility, risk-free rate, sensitivity to losses and loss aversion coefficient and a decreasing function of drift rate and sensitivity to gains. Restricting to parameter values found in empirical literature, we observe that the optimal growth rate is highly negative. As static savings plans correspond to a dollar cost averaging strategy, our study also adds to the literature on dollar cost averaging, extending the settings of Leggio and Lien (2001) and Dichtl and Drobetz (2011) in several ways.

Bayesian Versus Maximum Likelihood Estimation of Term Structure Models Driven by Latent Diffusions

This paper provides an econometric analysis of parameter estimation for continuous-time affine term structure models that are driven by latent diffusions. Simulating an affine two factor short rate model where one process is Gaussian and the other factor is square root we perform a comparison between Markov Chain Monte Carlo (MCMC) and maximum likelihood (ML) estimation. To cope with the discrepancy between a continuous-time formulation and data only available in discrete time, we use closed-form expansions of the transition densities. In order to find reasonable starting values for both MCMC and ML estimation we employ genetic algorithms with penalty functions for the parameter restrictions. For ML estimation we employ both simplex and gradient based solvers. We find that with only a few exceptions the MCMC estimates reveal the true parameters and are in general more consistent within different estimation procedures than maximum likelihood estimation. For both estimation methodologies we observe negative correlation between the estimates of the factor loadings and the estimates of the unconditional mean of the square root process. Finally we find that both methodologies identify time series of latent state variables that are more likely than the data generating process itself.

DCF Valuation and Imputed Interest on Equity Increase - Implications of the Austrian Tax System in a Model with Stochastic Profitability

As early as the 1980s, several European countries implemented tax systems with imputed equity interest provisions. Since its tax reform in 2000, Austria has also allowed the deduction of (fictitious) imputed equity interest from the tax base. This paper integrates the resulting equity-related tax benefits into the valuation of corporations. Using the equity method with special attention to the deductibility of imputed equity interest, we calculate the value of a business in a multi-period model. We find that a market-to-book ratio endogenous to the model results. We then demonstrate how to apply the APV method in a model with imputed equity interest. For each business — and thus also for an unlevered company — an adjustment is necessary to account for the tax shield resulting from equity financing. Therefore, an unlevered company that does not use equity tax shields has to be chosen as a common denominator in the application of the APV method, in which a closed-form solution is presented for the value of this tax benefit. Finally, we derive a weighted average cost of capital that considers the deductibility of imputed equity interest. We show that an additional term correcting for equity tax shields is necessary.

DCF Business Valuation with Imputed Interest on the Stock of Equity

In the last two decades several European countries implemented tax systems allowing for the deduction of imputed equity interest from a companys tax base. This paper integrates the tax benefits resulting from imputed interest on the stock of equity into business valuation. Three discounted cash flow valuation methods are used to this end: the equity method, the APV method and the entity method. Intertemporal differences in risk require the use of various risk-adjusted term structures of interest rates in the equity method as well as the APV method. Using the equity method we show that the well-known market-to-book ratio of the constant growth dividend discount model holds in a risk-adjusted form. When applying the APV method with imputed equity interest an adjustment is necessary for each business, also for an unlevered company, to account for the tax shield resulting from equity financing. A closed-form solution is presented for the value of this tax benefit. We furthermore derive the WACC under imputed interest on the stock of equity and the adjustment of the cost of equity which is necessary to derive the WACC as a weighted average of cost of equity and debt.

The optimal timing of the transfer of hidden reserves in the German and Austrian tax systems: OPTIMAL TIMING OF THE TRANSFER OF HIDDEN RESERVES

In this paper, the optimal timing of hidden reserves transfers is derived with special attention to the term structure of interest rates and interest rate risk, and using well-known concepts from the field of finance. The paper presents one model under certainty and, as a generalization of this model, another model under interest rate risk. In both models, the criterion used for decision-making is the value of the right to transfer, which can be interpreted as the initial cost of a replicating/hedging strategy for tax payments incurred/saved. In the model under certainty, the net present value concept is used to derive the value of the right to transfer. The procedure used in the model under interest rate risk is a combination of flexible planning and the no-arbitrage approach common in derivatives pricing. It is shown that the right to transfer hidden reserves with flexible timing is equivalent to an American-style conversion option. In addition, the impact of term-structure volatility on the value of the right to transfer is analyzed. The technique presented in this paper can also be used to solve other timing problems resulting from trade-offs between early and late tax payments/tax benefits.

A pricing model for secondary market yield based floating rate notes subject to default risk

Abstract The purpose of this article is to price secondary market yield based floating rate notes (SMY-FRNs) subject to default risk. SMY-FRNs are derivatives on the default-free term structure of interest rates, on the term structures for default-risky credit classes, and on the structure of a determined pool of bonds. The main problem in SMY-FRN pricing (as compared to the pricing of standard interest rate or credit derivatives) is market incompleteness, which makes traditional no-arbitrage pricing by replication fail. In general, SMY-FRNs are subject to two types of default risk. First, the SMY-FRN issuer may go bankrupt (direct default risk). Second, the possibility of the bankruptcy of the issuers in the underlying pool has an influence on the SMY-FRN coupons (indirect default risk). This article is the first one which provides a no-arbitrage pricing model for SMY-FRNs with direct and indirect default risks. It is also the first article applying incomplete market pricing methodology to SMY-FRNs.