Finance and Insurance Seminar SS 2012
12. April Prof. Dr. Michael Kötter, University of Groningen, Netherlands
“Credit risk connectivity in the financial industry and stabilization effects of government bailouts?”
We identify the connections between financial institutions based on joint extreme movements in credit default swap spreads. Estimated pairwise co-crash probabilities identify significant connections among 193 financial institutions. We calculate network centrality measures to identify systemically important financial institutions and test if bailouts stabilized network neighbors. Financial firms from the same sector and country are most likely significantly connected. Inter-sector and intra-sector connectivity across countries also increase the likelihood of significant links. Network centrality indicators identify many institutions that failed during the 2007/2008 crisis. Excess equity returns in response to bank bailouts are negative and significantly lower for connected banks.
Prof. David Hobson, University of Warwick, UK
“Robust hedging of variance swaps”
The twin assumptions of continuous monitoring and a price process which is continuous, Dupire and Neuberger separately showed how the variance swap can be replicated perfectly with an investment in the underlying and the puchase of -2 (minus two) log contracts. The log contracts can be replicated with vanilla options so that if calls and puts are liquidly traded then the variance swap has a unique model independent price. But what if the price process is not continuous, or if, as is always the case in practice, the payoff of the variance swap is based on price changes over a finite number of dates? We show how to construct best possible sub- and super-hedges for the variance swaps, and describe the worst case models. A perhaps suprising corollary is that the effects of jumps depends crucially on the precise formulation of the kernel of the variance swap.
Prof. Dr. Holger Kraft, Goethe Universität Frankfurt am Main
“Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies”
Utility-maximizing consumption and investment strategies in closed form are unknown for realistic settings involving portfolio constraints, incomplete markets, and potentially a high number of state variables. Standard numerical methods are hard to implement in such cases. We propose a numerical procedure that combines the abstract idea of artificial, unconstrained complete markets, well-known closed-form solutions in affine or quadratic return models, straightforward Monte Carlo simulation, and a standard iterative optimization routine. Our method provides an upper bound on the wealth-equivalent loss compared to the unknown optimal strategy, and it facilitates our understanding of the economic forces at play by building on closedform expressions for the strategies considered. We illustrate and test our method on the life-cycle problem of an individual who receives unspanned labor income and cannot borrow or short-sell. The upper loss bound is small and our method performs well in comparison with two existing methods.
Markus Pelger, UC Berkley
“Contingent Convertible Bonds: Pricing, Dilution Costs and Efficient Regulation”
Contingent convertible bonds (CCBs) are new debt instruments that automatically convert to equity when the issuing firm or bank reaches a specified level of financial distress. This paper presents a formal model of CCBs with finite maturity and where the firm's value process is driven by a jump diffusion process. We are able to derive closedform solutions for the value of the CCBs. In this paper we can completely characterize two different types of CCBs: In the ?rst case the number of shares granted at conversion is fixed a priori. In the second specification the number of shares granted at conversion is chosen a posteriori such that the value of the shares equals a specified value. Incorporating jumps into the dynamics of the firm's value process is important for two reasons. First it can solve the predictability problem of the conversion and default event, i.e. including jumps into the firm's value process creates non zero credit spreads for short maturities. Second, the evaluation of CCBs depends on the capital structure. Without jumps the evaluation of contingent convertible bonds can be independent of the amount of straight debt. In a model with jumps the valuation of straight debt and contingent convertible debt is interlinked as jumps could be large enough to trigger conversion and default simultaneously. Furthermore, it is observed that short-term debt has very different features than long-term debt. Our model can capture the effect of the maturity on the debt contracts. In order to apply CCBs in practice it is desirable to base the conversion on observable market prices that can constantly adjust to new information in contrast to accounting triggers. We can show how to use credit spreads and the risk premium of credit default swaps to construct the conversion trigger and to evaluate the contracts under this specification. CCBs are intended to avoid bank bailouts of the type that occurred during the subprime mortgage crisis when banks were in trouble to recapitalize themselves and regulators feared the consequences of default contagion. Hence, the second focus of this paper is to analyze whether CCBs can be used as a regulation instrument. It is crucial to require that the parameters of the CCBs are chosen such that they satisfy a no-early-default condition. In this case a regulation that combines a restriction on the maximal leverage ratio and the requirement of issuing a certain fraction of CCBs as part of the whole debt, can efficiently lower the default probability without reducing the total value of the firm. However, if this condition is violated, CCBs can increase the default risk of a bank.
Ivo Welch, UCLA
“Asset-Class Based Capital Budgeting”
Fama and French (1997) show that the CAPM and FFM (Fama-French XMKT, HML, SMB model) have large standard errors in one-month-ahead forecasts. Our paper extends their perspective. It shows that both models have no out-of-sample predictive ability over multi months horizons. This is not just due to factor premia uncertainty, but due to high variability and mean reversion of (shrunk industry) factor loadings. Our findings are robust to a broad range of estimation procedures. In sum, the evidence suggests that corporate executives are better off not using the CAPM or FFM models to infer differential opportunity costs of equity capital for longer-term projects. Under the reasonable hypothesis that fixed-income securities have lower expected rates of return than equity securities, the logical conclusion is that managers should calculate project costs of capital based only on how levered their projects are. We call this asset class based capital budgeting (ABC).
Andreas Tsanakas, Cass Business School, UK
"Parameter uncertainty and insolvency risk”
Risk measurement is sometimes viewed as a 2-stage process: first a model is estimated, then a decision is taken, for example regarding the level of economic capital needed for a portfolio of liabilities. However, this does not allow quantifying and controling of the reduction in the effectiveness of decisions, which is induced by estimation errors. In fact, the decision rule itself (eg the risk measure) needs to be modified to reflect the potential for parameter and model error. Focusing on economic capital calculation, one can consider the capital as a random quantity, due to its dependence on random samples. Thus, risk assessment changes to a situation where the both the future loss and the capital held are viewed as random. When the risk measure used is VaR, it can be shown that for several commonly used loss distributions, the probability of insolvency (viewed as the expected frequency of exceedances over capital) can be effectively controlled. This is either by adjusting the confidence level of the risk measure or by calculating VaR under a Bayesian predictive distribution with probability matching priors. For more general classes of positive homogenous risk measures, such as TVaR, one can define a notion of residual parameter risk that generalises the previous arguments. For location-scale families, the effectiveness of Bayesian prediction, as well as other methods, is again demonstrated. In solvency-related applications, the residual risk is minimised by introducing a positive bias in the estimation of the capital requirement. It is not clear though that this is still desirable in other applications, such as reinsurance pricing, where, in a diversified portfolio, such biases may needlessly inflate prices.