Corporate Financing under Ambiguity: A Utility-Free Multiple-Priors Approach

1. Corporate Financing under Ambiguity: A Utility-Free Multiple-Priors Approach Date: 15th/November/2012 Author: C.C. Chen

2. Outline • Stage 1 • Central issue of this study • Motivation and Background • Stage 2 • Trick to address the central issue • A novel ambiguity model and its application on financing decision • Stage 3 • Findings on the central issue • Quantitative/Empirical results and conclusion

3. Stage 1 • Background about corporate financing • Central question How do firms make optimal financing decision? • A wide range of issues accompanied by corporate financing • Default forecast, Capital structure, Debt valuation, Agency problem, ,Risk management • A vast literature on these topics • Modigliani and Miller (1958); Jensen and Meckling (1976); Mello and Parsons (1992); Leland (1994); Leland and Toft (1996); Leland (1998); Goldstein et al. (2001); Morellec (2001); Ju et al. (2005), Miao (2005); Hackbarth et al. (2006); Carlson and Lazrak (2010); and Chen (2010)

4. Stage 1 • Motivation • An unrealistic assumption underlying existing literature • Rational expectation equilibrium under a complete information structure “No role for uncertainty (or ambiguity) to play in the model” • The relevance of ambiguity aversion in the context of decision-theory • Knight (1921) and Keynes (1936) emphasize that ambiguity is crucial for economic decision-making • Ellsberg (1961): the distinction between risk and ambiguity is behaviorally meaningful • Epstein and Wang (1994), Chen and Epstein (2002), and Ju and Miao (2011): the hypothesis of rational expectation faces serious difficulties when confronting with asset market data • What I do in this study • Understanding and assessing the implications of ambiguity aversion for features of a firm’s financing decision • leverage choice; debt capacity, the decision on default; term structure of credit spread; asset substitution-based agency conflict; hedging intention

5. Stage 2 • Preliminary introduction • The difference between Risk and Ambiguity • Risk a situation where there is a probability measure to guide choice • Ambiguity a situation where the agent is uncertain about the probability measure used for decision-making due to informational constraints • Two classical widely applied theories: “Max-Min” expected utility theory (Gilboa and Schmeidler, 1989) and “Smooth” theory (Klibanoff et al. 2005) • A utility-free multiple-priors model • Two key assumptions • There exists a perfectly-liquid asset well-diversified market portfolio • The representative firm’s assets are partially-tradable the return on assets cannot be perfectly replicated from the well-diversified market portfolio

6. Stage 2 • A utility-free multiple-priors model----Basic structure • Model misspecification within good-deal price bounds • Reference model • Approximating model • Stochastic discount factor within good-deal price bounds of Cochrane and Saa- Requejo (2000) , , • Uncertainty over the risk compensation for assets’ invisible idiosyncratic shock. • Measuring the model misspecification: discounted relative entropy • The entropy between the approximating models and reference model (as in Hansen and Sargent, 2001; Hansen et al., 2006) • The upper constraint on model misspecification • Max-min infinite value program under ambiguity aversion • The dynamic of conjectural asset value based on public market information , • Max-min decision program of managers , ,

7. Stage 2 • A utility-free multiple-priors model • Some basic implications • Both managers and outside investors cannot exactly learn asset return through public market-based observations, because of uncertainty about the risk compensation for firm’s non-observed idiosyncratic shock. • They face a set of approximating asset-return models under distorted risk- adjusted measures in determining the value of the associated claims on firm’s assets. • In making the financing decision, the objective of ambiguity-averse managers is to choose an optimal coupon level that maximizes firm’s net levered value under the worst-case belief about the asset performance. • Ellsberg Paradox • Constrained robust control problem of Hansen and Sargent (2001, 2008) and Hansen et al. (2006) • Max-min expected utility theory of Gilboa and Schmeidler (1989)

8. Stage 2 • A utility-free multiple-priors model • Two attractive features • The exogenous determination of ambiguity magnitude • Quasi arbitrage (good deals-”high Sharpe ratios”)-free condition • Without specifying the preference of decision makers utility-free type • The explicit separation between information constraint, measured as the proportion of systematic risk to aggregate risk, and ambiguity • Several potential advantages • It is more tractable for empirical assessments, due to the freedom from estimating those abstract parameters in a utility function and from concerning about heterogeneity among various types of preferences. • It provides empirical research a useful guide to construct the proxy variable of economic uncertainty using the upper limit of market’s Sharpe ratios. • It can be applied to explaining the relation between systematic risk exposures and the cross section of corporate decisions or between systematic risk exposures and the price structure in derivative markets, because of the availability of analyzing the comparative statics with respect to information constraint. • It is relatively more suitable for studying the firm-based decision behavior • Standard assumption of utility homogeneity within traditional models v. s.Utility heterogeneity in the reality of corporate decision making with multiple planners

9. Stage 2 • Application on financing theory: Revisiting Leland (1994) • Step 1: Time-independent security model under ambiguous beliefs • ODE followed by any perpetual claims on the firm’s assets • Debt • Tax benefit • Bankruptcy cost • Total levered value • Equity • Step 2: Endogenous bankruptcy case • Smooth-pasting condition • Bankruptcy-triggered threshold • Step 3: Solving the optimal control of managers • Optimal coupon choice • Leverage ratio • Coupon rate • Debt capacity

10. Stage 3 • Model calibration • Initial asset’s total value: normalized value ($100) • Aggregate asset risk: estimate of Cecchetti et al. (2000) and Chen (2010) (20%) • Risk-free interest rate: historical calibrated result of Chen (2010) (1.47%) • Tax rate: partial loss offset effect (Chen, 2010) (32%, same as that chosen by Carlson and Lazrak, 2010) • Bankruptcy cost rate: estimate of Ju et a;. (2005) (50%) • Upper bound on observed Sharpe ratios: Ross (1976), Shanken (1992), Cochrane and Saa-Requejo (2000), and Hung and Liu (2005) (double of market-index Sharpe ratio) • Market index-Sharpe ratio: Ju and Miao (2009), Carlson and Lazrak (2010), and Chen (2010) (0.33) • Assets’ correlation with market: Cochrane and Saa-Requejo (2000) (90%) • Assets’ Sharpe ratio under market-based expectation: CAPM theory • Benchmark Model • Endogenous bankruptcy case of Leland (1994) with

11. Stage 3 • Quantitative result (i) the decision to default • Bankruptcy-triggering threshold and expected debt recovery rate • Remarks • Under ambiguity aversion, assets are always under-valued in terms of expectation. • Managers learn the real value of assets in place only through a bankrupt liquidation. • In view of downsidedistortion in the expected asset value, managers choose a lower bankruptcy triggering threshold to prevent debt holders from reclaiming too much asset value at liquidation point. • A lower default boundary implies a smaller expected recovery rate.

12. Stage 3 • Quantitative result (i) the decision to default • Subjective cumulative default probability and density distribution • Remarks • Left-ward clustering effect on default density-distribution • Ambiguity-based increment on the term structure of subjective cumulative default probabilities • Expected time to default calculated by our model is earlier. • Compared to ambiguity-neutral managers, ambiguity-averse managers subjectively have a higher possibility to abandon the firm soon.

13. Stage 3 • Quantitative result (ii) optimal leverage ratio • Firm total levered value as a function of leverage ratio • Remarks • Optimal leverage ratio reduces from 57.55% to 48.36% : Under-leverage puzzle? • Net tax advantage falls to 8.49% from 13.41%, (empirical estimate 6-9%) • Credit spread (76bps and 279bps);10-year default rate (5.56% and 4.91%) • My model outputs at optimal leverage are much closer to the estimate of Graham (2000), Korteweg (2010), Van Binsbergen et al. (2010), and Morellec et al. (2011) and market data reported by Huang and Huang (2003), compared to the outputs of benchmark model.

14. Stage 3 • Quantitative result (iii) credit spread • Credit spread as a function of leverage • Remarks • Large ambiguity premiums on credit spread : Credit spread puzzle? • Matching the 10-year data in Huang and Huang (2003): for Ba- /Baa-rated bonds with 53.53% /43.28% leverage ratio, credit spread by our model (312 bps /251bps), by standard model (66 bps/48 bps), by data (320 bps/ 194 bps) • Asymmetric time horizon effects on credit spread: 10-year v.s. Infinite maturity

15. Stage 3 • Quantitative result (iv) managerial risk-shifting incentives : asset substitution effects and hedging intention • Effects of a change in asset risk on debt, equity, and firm value at optimal leverage • Remarks • Both the prevalence of asset substitution problem within leveraged firms and managerial hedging intention will be overstated, if lenders’ aversion to ambiguity is ignored. • Hedging activities v.s. Agency conflict (e.g., Campbell and Kracaw, 1990)

16. Stage 3 • Empirical results • Base sample : A cross section of S&P 500 firms covering 1992 to 2011 • Data sources: Compustat/Datastream/3000 Xtra • Parameter estimation/Target financial variables (see Table 4) • How big are the impacts of ambiguity aversion on the features of corporate financing? • 22.8% of under uses of financial leverage • 185 bps yield spread without raising leverage • 8.9% (4.5%) of over-prediction on the equity (debt) value-risk elasticity • One third net tax benefits • 21% default boundary • Does ambiguity aversion matter? A perspective on model goodness-of-fit • Moment comparisons and prediction-error tests • Financial leverage (Table 6) • Corporate yield spread (Table 7) • Value-risk elasticity (Table 8)

17. Stage 3 • Summary of basic findings and contribution • This paper develops a novel utility-free ambiguity model that has substantial empirical and theoretical advantages over traditional models. • This paper applies the proposed new ambiguity model to a contingent claim -based capital structure framework. The modified capital structure model • helps understand how managers make the response to lenders’ aversion to ambiguity over the asset return when considering the decision to default • goes a long way to explain low-leverage puzzle and credit spread puzzle about corporate debts • highlights the relevance of ambiguity preferences in measuring the agency conflict and hedging demand beyond debt service • offers an ambiguity-based explanation for the link between corporate financing/default policies and exposures to systematic risk • The magnitude of ambiguity aversion effect within the present model is large enough to improve the goodness-of-fit of the model with respect to leverage, yield spread, and value-risk elasticity significantly.

18. Thanks for your listening!! • Any comments and questions are welcome!!