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Decisions in Economics and Finance

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01-06-2017

Reaching nirvana with a defaultable asset?

Authors: Anna Battauz, Marzia De Donno, Alessandro Sbuelz

Published in: Decisions in Economics and Finance | Issue 1-2/2017

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Abstract

We study the optimal dynamic portfolio exposure to predictable default risk, taking inspiration from the search for yield by means of defaultable assets observed before the 2007–2008 crisis and in its aftermath. Under no arbitrage, default risk is compensated by an ‘yield pickup’ that can strongly attract aggressive investors via an investment-horizon effect in their optimal non-myopic portfolios. We show it by stating the optimal dynamic portfolio problem of Kim and Omberg (Rev Financ Stud 9:141–161, 1996) for a defaultable risky asset and by rigorously proving the existence of nirvana-type solutions. We achieve such a contribution to the portfolio optimization literature by means of a careful, closed-form-yielding adaptation to our defaultable asset setting of the general convex duality approach of Kramkov and Schachermayer (Ann Appl Probab 9(3):904–950, 1999; Ann Appl Probab 13(4):1504–1516, 2003).

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Cox and Huang (1989) require the global Lipschitz continuity of the diffusive coefficient for the risky asset-value process [see Conditions A and B at p. 46 in Cox and Huang (1989)]. By contrast, the diffusive coefficient in our setting is the square root of the risky asset value.

See, for instance, Davydov and Linetsky (2001), p. 952, first paragraph, with \(S_{t}=P_{t}\) and \(p=\frac{1}{2}.\)

The objective probability of the asset defaulting within the date \(T>0\) is \({\mathbb {P}}\left[ P_{h}=0,\,0\le h\le T\quad P_{0}=p\,\right] =\Gamma \left( \frac{2\left( r+\xi \right) p}{1-e^{-\left( r+\xi \right) T}},1\right) ,\) where \(\Gamma \left( k,l\right) =\int _{k}^{+\infty }u^{l-1}e^{-u}du,\) \(k\ge 0\) is the incomplete gamma function [see, e.g., the Proposition 1 in Campi and Sbuelz (2005)].

The nonnegativity requirement is innocuous in our setting as the utility function U is \(-\infty \) for negative wealth levels.

Battauz et al. (2015) apply the Kramkov and Schachermayer (1999, 2003) approach to the standard Kim and Omberg (1996) portfolio problem with a non-defaultable risky asset.

There are parameter values that make the investor with \(\phi >1\) take a net short position in the risky defaultable asset.

Similar investment-horizon effects have been found in the literature on dynamic portfolio choice with a risky non-defaultable asset characterized by a mean-reverting drift and a constant volatility [see, for example, Koijen et al. (2009)].

The functions U and V are conjugate if and only if \(U(w)=\inf _{y>0}(V(y)+wy)\) and \(V(y)=\sup _{w>0}(U(w)-wy)\).

The superscript \(\left( \cdot \right) ^{DS}\) refers to the notations of Delbaen and Shirakawa (2002), whereas a, b, c are defined in the statement of Proposition 3.2.

Battauz, A., De Donno, M., Sbuelz, A.: Kim and Omberg revisited: the duality approach. J. Probab. Stat. 2015, Article ID 581854, p. 6 (2015). doi:10.1155/2015/581854

Becker, B., Ivashina, V.: Reaching for yield in the bond market. J. Finance 70, 1863–1902 (2015)CrossRef

Bekaert, G., Ang, A.: International asset allocation with regime shifts. Rev. Financ. Stud. 15(4), 1137–1187 (2002)CrossRef

Branger, N., Larsen, L.S., Munk, C.: Robust portfolio choice with ambiguity and learning about return predictability. J. Bank. Finance 37(5), 1397–1411 (2013)CrossRef

Buch, C., Eickmeier, S., Prieto, E.: Macroeconomic factors and microlevel bank behavior. J. Money Credit Bank. 46(4), 715–751 (2014)CrossRef

Campi, L., Sbuelz, A.: Closed-form pricing of benchmark equity default swaps under the CEV assumption. Risk Lett. 1, ISSN: 1740-9551 (2005)

Chodorow-Reich, G.: Effects of unconventional monetary policy on financial institutions. Brookings Papers on Economic Activity (Spring), pp. 155–204 (2014)

Cox, J.C., Ross, S.: The valuation of options for alternative stochastic processes. J. Financ. Econ. 3, 145–166 (1976)CrossRef

Cox, J.C., Huang, C.F.: Optimal consumption and portfolio policies when asset prices follow a diffusion process. J. Econ. Theory 49, 33–83 (1989)CrossRef

Davydov, D., Linetsky, V.: Pricing and hedging path-dependent options under the CEV process. Manage. Sci. 47(7):949–965 (2001). doi:10.1287/mnsc.47.7.949.9804

Delbaen, F., Shirakawa, H.: A note on option pricing for the constant elasticity of variance model. Financ. Eng. Jpn. Mark. 9(2), 85–99 (2002)

Della Corte, P., Sarno, L., Tsiakas, I.: Volatility and correlation timing in active currency management. In: James, J., Marsh, I.W., Sarno, L. (eds.) Handbook of Exchange Rates. Wiley, Hoboken NJ, USA (2012). doi:10.1002/9781118445785.ch15

Dell’Ariccia, G., Laeven, L., Marquez, R.: Monetary policy, leverage, and bank risk-taking. J. Econ. Theory 149, 65–99 (2014)CrossRef

Detemple, J.B., Garcia, R., Rindisbacher, M.: A Monte-Carlo method for optimal portfolios. J. Finance 58, 401–446 (2003)CrossRef

Detemple, J.B., Garcia, R., Rindisbacher, M.: Intertemporal asset allocation: a comparison of methods. J. Bank. Finance 29(11), 2821–2848 (2005)CrossRef

Diamond, D.W., Rajan, R.G.: The credit crisis: conjectures about causes and remedies. Am. Econ. Rev. 99(2), 606–610 (2009)CrossRef

Di Maggio, M.: Market Turmoil and Destabilizing Speculation. Columbia Working Paper (2013)

Di Maggio, M., Kacperczyk, M.T.: The unintended consequences of the zero lower bound policy. J. Financ. Econ. (JFE) (2016). doi:10.2139/ssrn.2458587 (forthcoming)

Gennaioli, N., Martin, A., Rossi, S.: Sovereign default. Domestic banks, and financial institutions. J. Finance 69(2), 819–866 (2014)CrossRef

Gollier, C.: Discounting an uncertain future. J. Public Econ. 85, 149–166 (2002)CrossRef

Gozzi, F., Russo, F.: Verification theorems for stochastic optimal control problems via a time dependent Fukushima–Dirichlet decomposition. Stoch. Process. Appl. 116(11), 1530–1562 (2006)CrossRef

Guidolin, M., Timmermann, A.: Asset allocation under multivariate regime switching. J. Econ. Dyn. Control 31, 3503–3544 (2007)CrossRef

Guidolin, M., Hyde, S.: Can VAR models capture regime shifts in asset returns? A long-horizon strategic asset allocation perspective. J. Bank. Finance 36(3), 695–716 (2012)CrossRef

Ioannidou, V., Ongena, S., Peydro, J.-L.: Monetary policy, risk-taking, and pricing: evidence from a quasi-natural experiment. Rev Finance 19, 95–144 (2015)

Jiménez, G., Ongena, S., Peydró, J.L., Saurina, J.: Hazardous times for monetary policy: what do twenty-three million bank loans say about the effects of monetary policy on credit risk? Econometrica 82(2), 463–505 (2014)CrossRef

Kacperczyk, M., Schnabl, P.: How safe are money market funds? Q. J. Econ. 128, 1073–1122 (2013)CrossRef

Kim, T.S., Omberg, E.: Dynamic nonmyopic portfolio behavior. Rev. Financ. Stud. 9, 141–161 (1996)CrossRef

Klebaner, F., Lipster, R.: When a stochastic exponential is a true martingale. Extension of a method of benes. Theory Probab. Appl. 58(1), 38–62 (2014)CrossRef

Koijen, R.S.J., Rodríguez, J.C., Sbuelz, A.: Momentum and mean reversion in strategic asset allocation. Manag. Sci. 55, 1199–1213 (2009)CrossRef

Kramkov, D., Schachermayer, W.: The asymptotic elasticity of utility functions and optimal investment in incomplete market. Ann. Appl. Probab. 9(3), 904–950 (1999)CrossRef

Kramkov, D., Schachermayer, W.: Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 13(4), 1504–1516 (2003)CrossRef

Larsen, L.S., Munk, C.: The costs of suboptimal dynamic asset allocation: general results and applications to interest rate risk, stock volatility risk, and growth/value tilts. J. Econ. Dyn. Control 36(2012), 266–293 (2012)CrossRef

Lioui, A., Poncet, P.: International asset allocation: a new perspective. J. Bank. Finance 27(11), 2203–2230 (2003)CrossRef

Liu, J.: Portfolio selection in stochastic environments. Rev. Financ. Stud. 20, 1–39 (2007)CrossRef

Martin, I.: On the valuation of long-dated assets. J. Polit. Econ. 120(2), 346–358 (2012)CrossRef

Merton, R.C.: Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory 3, 373–413 (1971)CrossRef

Nielsen, L.T., Vassalou, M.: The instantaneous capital market line. Econ. Theor. 28, 651–664 (2006)CrossRef

Rajan, R.: Has Financial Development Made the World Riskier? Proceedings, Federal Reserve Bank of Kansas City, August, pp. 313–69 (2005)

Wachter, J.: Portfolio and consumption decisions under mean-reverting returns: an exact solution for complete markets. J. Financ. Quant. Anal. 37, 63–91 (2002)CrossRef

Weitzman, M.L.: Why the far-distant future should be discounted at its lowest possible rate. J. Environ. Econ. Manag. 36, 201–208 (1998)CrossRef

Weitzman, M.L.: On modeling and interpreting the economics of catastrophic climate change. Rev. Econ. Stat. 91, 1–19 (2009)CrossRef

Title: Reaching nirvana with a defaultable asset?
Authors: Anna Battauz
Marzia De Donno
Alessandro Sbuelz
Publication date: 01-06-2017
Publisher: Springer Milan
Published in: Decisions in Economics and Finance / Issue 1-2/2017
Print ISSN: 1593-8883
Electronic ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-017-0192-x

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