Financial Distress and the Cross Section of Equity Returns Lorenzo Garlappi University of Texas Austin Hong Yan University of South Carolina National University of Singapore May 20, 2009
Motivation Empirical regularities in the cross section of equity returns Size effect Value premium Momentum Empirical evidence on the role of financial distress in the cross section Griffin and Lemmon (2002) (value premium stronger in distressed firms) Vassalou and Xing (2004) (size and value premium stronger for high default probability firms) Avramov et al (2007) (momentum profits stronger with low credit rating) Lack of a unified framework to understand these anomalies Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 1
Objectives Developing a theoretical framework to simultaneously account for major cross-sectional features of equity returns (value premium and momentum) and their interaction with financial distress Showing how financial leverage can enhance anomalies Demonstrating that potential recovery for shareholders upon financial distress plays an instrumental role in the cross-sectional patterns of stock returns Providing empirical implication using simulated data from a calibrated dynamic model Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 2
Background 1. Real options/neoclassical models of firms assets: [e.g., Berk, Green and Naik (1999), Gomes, Kogan and Zhang (2003), Zhang (2005), Carlson, Fisher and Giammarino (2004), Sagi and Seasholes (2006),... ] Size effect related to growth opportunities w.r.t. assets-in-place B/M effect related to the risk of assets-in-place Momentum driven by growth options 2. Limitations of ignoring financial leverage: Difficult to explain the effect of distress on the cross section Anomalies are significant for equity, not asset, returns [Hecht (2004), Charoenrook (2004), Choi (2008)] Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 3
Features of Our Approach 1. Introducing financial leverage in a real option model of equity value 2. Modeling the outcome of financial distress (e.g., potential shareholder recovery upon financial distress restructuring and debtequity swap, etc.) 3. Generating momentum in stock returns that arises endogenously in high-default-risk firms 4. Demonstrating the robustness of the intuition in a generalized framework with endogenous investment and financing choices Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 4
Basic Model Partial equilibrium, continuous-time model Two types of firms: mature and growth Firms have both operating (c) and financial (l) leverage Default may result in possible recovery to shareholders (e.g. Fan and Sundaresan (2000), Morellec, Nikolov and Schüroff (2008)). Unique source of risk: price of the good produced dp = µp dt + σp dw Constant risk premium λ associated with P. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 5
V m (P t ) = E Equity Value of a Mature Firm τl ξ: scale of operation. 0 }{{} payoff in default ( ξ(p t+s c) l)e rs ds + ηx }{{} m (P m )e rτ L operating profits τ L : default stopping time: τ L = inf {t : P t = P m } P m : endogenous default boundary X m (P m ): residual firm value (e.g., ξc/r: book value of assets) η: fraction of book value of assets captured by shareholders in financial distress (expected shareholder recovery upon financial distress) Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 6
Distribution of η in the cross section From Morellec, Nikolov and Schüroff (2008) structural estimation of η. Frequency 700 600 500 400 300 200 100 0 0 20 40 60 80 100 Shareholder bargaining power (%) Shareholder recovery = η renegotiation surplus 20% of firm value. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 7
Beta and Momentum Measures Let V m (P ) denote equity value: 1. Beta sensitivity of equity return to the state variable P β = V m (P ) P P V m (P ). 2. Autocorrelation sensitivity of expected return to realized return AutoCorr = cov[ λβ, ln(e)] var[ ln(e)] = λ β/β P/P Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 8
Beta of a Mature Firm ( ) ( ) ( ) (ξc l)/r ξc + l (1 + η)ξc + l β = 1 + 1 π V }{{ m ξc l ξc + l }}{{} BE/ME Leverage/Distress π: risk-neutral probability of default: (P/P ) φ, φ < 0. (ξc l)/r : book-to-market equity (BE/ME) V m The BE/ME effect captures all the cross sectional variation in beta (for no-growth firms), i.e. risk of assets in place (as in BGN and CFG) Beta and default probability If η = 0, β increases with default probability If η > 0 β hump-shaped or decreasing in default probability Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 9
Expected Return vs Default Probability No recovery (η = 0) Recovery (η = 5%) 0.6 60 0.03 4 0.4 40 Expected Return 0.2 20 0.02 2 Beta 0 0 0.01 0 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 10
B/M effect, value premium and default probability ( ) ( ) ( ) (ξc l)/r ξc + l (1 + η)ξc + l β = 1 + 1 π V }{{ m ξc l ξc + l }}{{}}{{} BE/ME L > 1 D(η, π) 0 Leverage effect: L > 1 and in l = amplifying effect of leverage Book-to market effect If η = 0, D > 0 = β increases in BE/ME If η > 0 and π high, D < 0 = β may decrease in BE/ME Value premium: β high B/M β low B/M If η = 0 = Increasing with default probability If η > 0 = Declining or Hump-shaped in default probability: Positive/Increasing for low π, negative/decreasing for high π Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 11
Intuition for Value Premium 0.024 0.022 Expected return 0.02 0.018 0.016 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 12
Intuition for Value Premium 0.024 0.022 Expected return 0.02 0.018 0.016 high B/M ratio 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 13
Intuition for Value Premium 0.024 0.022 higher expected return Expected return 0.02 0.018 0.016 high B/M ratio 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 14
Intuition for Value Premium 0.024 0.022 low B/M ratio higher expected return Expected return 0.02 0.018 0.016 high B/M ratio 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 15
Intuition for Value Premium 0.024 0.022 low B/M ratio higher expected return Expected return 0.02 0.018 0.016 0.014 lower expected return high B/M ratio 0.012 Value Premium > 0 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 16
Intuition for Value Premium 0.024 0.022 Expected return 0.02 0.018 0.016 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 17
Intuition for Value Premium 0.024 0.022 high B/M ratio Expected return 0.02 0.018 0.016 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 18
Intuition for Value Premium 0.024 0.022 high B/M ratio Expected return 0.02 0.018 0.016 0.014 lower expected return 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 19
Intuition for Value Premium 0.024 0.022 high B/M ratio Expected return 0.02 0.018 0.016 0.014 low B/M ratio lower expected return 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 20
Intuition for Value Premium 0.024 0.022 higher expected return high B/M ratio Expected return 0.02 0.018 0.016 0.014 low B/M ratio lower expected return 0.012 Value Premium < 0 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 21
Momentum and default probability The momentum measure for mature firms is AutoCorr = λ [ 1 β π ( γ1 ) ( l + ξc(1 + η) βe m r )], γ 1 < 0. 1. If η = 0 or low default prob. AutoCorr < 0, no momentum. 2. If η > 0 and high default prob. AutoCorr > 0, momentum. Potential recovery to shareholders crucial for momentum in highly levered firms. Mean reversion and growth options not necessary for generating this type of momentum. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 22
Intuition for Momentum 0.024 0.022 Expected return 0.02 0.018 0.016 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 23
Intuition for Momentum 0.024 0.022 Expected return 0.02 0.018 0.016 negative realized return 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 24
Intuition for Momentum 0.024 0.022 higher expected return Expected return 0.02 0.018 0.016 negative realized return 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 25
Intuition for Momentum 0.024 0.022 positive realized return higher expected return Expected return 0.02 0.018 0.016 negative realized return 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 26
Intuition for Momentum 0.024 0.022 positive realized return higher expected return Expected return 0.02 0.018 0.016 0.014 lower expected return negative realized return 0.012 AutoCorr < 0 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 27
Intuition for Momentum 0.024 0.022 Expected return 0.02 0.018 0.016 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 28
Intuition for Momentum 0.024 0.022 negative realized return Expected return 0.02 0.018 0.016 0.014 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 29
Intuition for Momentum 0.024 0.022 negative realized return Expected return 0.02 0.018 0.016 0.014 lower expected return 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 30
Intuition for Momentum 0.024 0.022 negative realized return Expected return 0.02 0.018 0.016 0.014 positive realized return lower expected return 0.012 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 31
Intuition for Momentum 0.024 0.022 higher expected return negative realized return Expected return 0.02 0.018 0.016 0.014 positive realized return lower expected return 0.012 AutoCorr > 0 0.01 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 32
V g (P t ) = E Equity Value of a Growth Firm τl τ G 0 op. profits {}}{ ( P t+s c l)e rs ds + (V m (P ) I)E [ ] e rτ GI {τg <τ L } + ηx g (P g )E[e rτ LI {τl <τ }{{} G }] }{{} growth option value expected payoff in default τ L : stopping time for default. τ L = inf {t : P t = P g } τ G : stopping time for growth. τ G = inf { t : P t = P } P g : endogenous default boundary. P : endogenous growth threshold X g (P g ) residual firm value (e.g., c/r: book value of assets) V m (P ): equity value of mature firm at P I: investment cost (borne by shareholders) η: recovery to shareholders Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 33
Growth vs. Mature firms: Autocorrelation Plot of return autocorrelation for growth vs. mature firms No recovery (η = 0) Recovery (η = 10%) 5 4 3 5 4 3 Mature Growth 2 2 AutoCorr 1 0 1 Mature Growth AutoCorr 1 0 1 2 2 3 3 4 4 5 5 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 34
Implications from the Basic Model Financial leverage and distress probability affects equity risk β dependent upon firm characteristics, thus time-varying Value premium vs. Default probability: Increasing if η = 0, i.e., no expected recovery for shareholders Humped if η > 0, i.e., positive expected shareholder recovery Momentum profits higher if: Default probability high, and High likelihood of shareholder recovery upon financial distress Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 35
The need for a general model Robustness of the implications Exogenous vs endogenous investment and financing decisions Static vs dynamic frameworks Consistency with existing empirical findings: A more general model that can be calibrated to produce moments to match the data Simulations of the model produce the appearance of α due to model misspecification for risk adjustment. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 36
Features of the general model Firm i s output at time t is described by Y i,t = K α i,t e X t+z i,t, X t : systematic, Z i,t : firm-specific Pricing kernel specified to allow for a counter-cyclical risk premium Frictions: capital adjustment costs and costs for equity financing Each period, the firm maximizes equity value when making decision on investment (level of capital) and choosing financing means Financial distress (or default) occurs when the equity value is below a threshold (ηr with R being the residual asset value at the time) Dynamic programming problem with 5 state variables. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 37
Sample moments Variable Model Data Annual risk-free rate 0.021 0.018 Annual Sharpe ratio 0.404 0.430 Annual volatility of real interest rate 0.028 0.030 Annual equity premium 0.092 0.060 Annual investment rate 0.108 0.150 Market-to-book ratio 1.224 1.492 Market leverage 0.285 0.290 1-year EDF 0.049 0.040 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 38
Expected Returns and default probability 0.09 No recovery (η = 0) Recovery (η = 10%) 0.02 0.08 0.018 0.07 Expected return 0.06 0.05 0.04 0.03 0.016 0.014 0.012 0.01 0.02 0.01 0.008 0 0.006 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 39
Value premium and default probability 0.08 No recovery (η = 0) Recovery (η = 10%) 10 x 10 3 0.07 0.06 8 Value premium 0.05 0.04 0.03 6 4 2 0.02 0.01 0 0 2 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 40
Momentum and default probability 0 No recovery (η = 0) Recovery (η = 10%) 12 x 10 3 0.02 0.04 10 Momentum profits 0.06 0.08 0.1 0.12 8 6 4 0.14 2 0.16 0.18 0 0.2 2 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 41
Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 42
Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j 5 4 3 = 0 2 FF-α 1 0 1 2 3 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 43
Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j 5 4 3 = 0 2 FF-α 1 0 1 = 0.1 2 = 0.25 3 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 44
Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j 5 4 3 = 0 2 all FF-α 1 0 1 = 0.1 2 = 0.25 3 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 45
Factor loadings - β mkt R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j 1.2 1.15 1.1 = 0 1.05 = 0.1 β mkt 1 0.95 all 0.9 0.85 = 0.25 0.8 0.75 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 46
Factor loadings - β smb R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j 1 0.8 0.6 = 0.1 β smb 0.4 = 0 0.2 0 = 0.25 0.2 all 0.4 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 47
Factor loadings - β hml R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j 1.2 1 0.8 = 0.1 0.6 β hml 0.4 0.2 = 0 0 0.2 all 0.4 = 0.25 0.6 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 48
Conclusions Propose a new perspective for cross-sectional anomalies in equity returns. Expected outcome of financial distress affects the link between default probability and: 1. Beta/Expected returns 2. Value premium 3. Momentum A simple risk-based explanation for major cross-sectional features in returns Financial distress risk is reflected in beta and manifested in value premium and momentum A structural understanding, without having to introduce new risk factors Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 49
Additional Slides Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 50
Empirical Analysis Data Moody s KMV EDF: Expected Default Frequency TM Inspired by the Black-Scholes-Merton Model (Kealhofer (2003)) Time period: January 1969 December 2003 Number of observations: 1,430,713 firm-month No financial firms CRSP Monthly equity returns COMPUSTAT Accounting variables Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 51
Value Premium and Default Probability Full Sample Low EDF High EDF High-Low t-value B/M VW Returns Low 0.96 1.02 0.71 0.72 0.63 0.63 0.05-0.01-0.20 0.19-0.77-1.50 Medium 1.05 1.11 1.19 1.16 1.23 1.10 1.11 1.32 0.81 0.48-0.57-1.10 High 0.97 1.13 1.30 1.41 1.33 1.27 1.74 1.36 1.55 1.42 0.45 1.02 High - Low 0.00 0.11 0.59 0.69 0.71 0.64 1.69 1.37 1.74 1.23 t-value 0.01 0.48 2.27 2.49 2.59 2.38 5.68 3.95 4.55 3.16 B/M EW Returns Low 1.13 1.01 0.86 0.79 0.62 0.72 0.33 0.55 0.66 1.76 0.63 1.21 Medium 1.15 1.27 1.34 1.34 1.46 1.35 1.38 1.34 1.35 1.79 0.63 1.43 High 1.32 1.34 1.42 1.66 1.58 1.65 1.78 1.79 1.87 2.13 0.81 2.11 High - Low 0.19 0.33 0.56 0.87 0.96 0.93 1.45 1.24 1.21 0.37 t-value 1.01 1.55 2.55 3.75 4.15 4.13 6.15 4.42 4.26 1.22 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 52
Value Premium and Default Probability Stocks with price $5 Low EDF High EDF High-Low t-value B/M VW Returns Low 0.95 1.06 1.07 0.50 0.73 0.76 0.59 0.74 0.27-0.44-1.40-3.61 Medium 0.99 1.04 1.10 1.14 1.11 1.10 1.22 1.25 0.96 0.92-0.07-0.18 High 1.03 1.04 1.23 1.19 1.26 1.38 1.23 1.38 1.25 1.52 0.48 1.45 High - Low 0.08-0.02 0.16 0.69 0.53 0.62 0.64 0.63 0.98 1.96 t-value 0.34-0.09 0.64 2.69 1.82 2.05 2.15 2.19 3.51 6.15 B/M EW Returns Low 1.15 1.14 0.98 0.86 0.77 0.76 0.67 0.73 0.23-0.02-1.18-3.73 Medium 1.08 1.14 1.30 1.28 1.33 1.30 1.25 1.45 1.19 1.10 0.02 0.06 High 1.19 1.26 1.35 1.43 1.42 1.56 1.48 1.59 1.44 1.43 0.24 0.90 High - Low 0.03 0.11 0.36 0.57 0.65 0.80 0.81 0.86 1.22 1.45 t-value 0.16 0.52 1.57 2.38 2.72 3.26 3.34 3.55 5.29 6.14 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 53
Empirical Proxies for shareholder recovery (η) From Garlappi, Shu and Yan (2006): 1. Asset size. High asset size recovery more likely [Franks and Torous (1994) and Betker (1995)] 2. R&D expenditures/assets. High R&D recovery less likely [Opler and Titman (1994) and Fan and Sundaresan (2000)] 3. Herfindahl Index of sales. High Hfdl index recovery more likely [Shleifer and Vishny (1992)] Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 54
Momentum and Default Probability Methodology: Independently sort stocks into: 1. terciles of EDF 2. terciles of η proxy 3. and quintiles of losers/winners (past 6 month) Record equal-weight return over future 6-month period Report results in top EDF tercile. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 55
Momentum and Default Probability Asset Value Loser 2 3 4 Winner W-L t-stat Low 2.09 1.90 1.93 2.03 2.03-0.06-0.27 Med 0.65 1.18 1.34 1.45 1.70 1.05 3.82 High 0.36 1.01 1.29 1.25 1.53 1.14 3.07 High-Low 1.20 3.92 R&D Loser 2 3 4 Winner W-L t-stat Low 1.05 1.36 1.54 1.57 1.68 0.63 2.43 Med 1.98 1.85 2.07 1.94 1.96 0.04 0.14 High 2.73 2.53 2.30 2.39 2.52-0.34-1.23 Low-High 0.97 3.73 SalesHfdl Loser 2 3 4 Winner W-L t-stat Low 1.71 1.65 1.76 1.81 1.81 0.10 0.43 Med 1.68 1.69 1.75 1.97 2.07 0.39 1.49 High 1.34 1.52 1.60 1.61 1.81 0.47 1.74 High-Low 0.37 1.65 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 56