Distress risk puzzle and analyst forecast optimism

Abstract

A general consensus in the literature is that financial analysts make optimistic forecasts. That is, they tend to underreact to negative but overreact to positive information. In this study, we invoke this idea to provide an explanation for the distress risk puzzle, the phenomenon that high distress risk firms deliver anomalously low subsequent returns. We find that analysts underestimate the implication of the poor performance of higher distress risk firms, and thus make EPS and sales forecasts that are generally more optimistic than those for the lower distress risk firms. Because market respond to the analyst forecasts, investors initially overvalue the high distress risk firms; later on, when those firms report less than expected performance, analysts revise their forecasts downwards that in turn cause the high distress risk firms to earn low future returns composing of both immediate-forecast-revision responses and post-forecast-revision price drifts. We further document that (quarter) earnings announcements convey a substantial amount of information that roughly drives more than 60% of the analyst forecast revisions and 30% of the revision-related market responses.

Appendices

Appendix 1

See Table 7.

Table 7 Definitions of the major variables

Appendix 2: Distress risk measures

In this Appendix, we highlight the methods to calculate the three distress risk measures used in this paper. For further technical details, please refer to the reference papers being cited.

2.1 Appendix 2.1: O-SCORE

Similar to Dichev (1998), O-SCORE for firm j at the end of fiscal year t is calculated by Eq. (A1) below with the coefficients from the Model 1 in Ohlson (1980). For simplicity, firm and time subscripts are skipped.

$$\begin{aligned} {\text{O}} - {\text{SCORE}}_{{({\text{t}})}} & = - 1. 3 2- 0. 40 7*{ \log }\left( {{\text{total assets}}/{\text{GNP price}} - {\text{level index}}} \right) \, + { 6}.0 3*\left( {{\text{total liabilities}}/{\text{total assets}}} \right) \\ & \quad - 1. 4 3*\left( {{\text{working capital}}/{\text{total assets}}} \right) \, + \, 0.0 7 6*\left( {{\text{current liabilities}}/{\text{current assets}}} \right) - 1. 7 2*\left( { 1 {\text{ if total liabilities }} > {\text{ total assets}};{\text{ else }}0} \right) \\ & \quad - 2. 3 7*\left( {{\text{net income}}/{\text{total assets}}} \right) - 1. 8 3*\left( {{\text{funds from operations}}/{\text{total liabilities}}} \right) + \, 0. 2 8 5*\left( { 1 {\text{ if net loss for the last 2}} {\text{years}};{\text{ else }}0} \right) \\ & \quad - 0. 5 2 1*\left( {{\text{net income}}_{{({\text{t}})}} - {\text{net income}}_{{({\text{t}} - 1)}} \left] / \right[\left| {{\text{net income}}_{{({\text{t}})}} } \right| \, + \, \left| {{\text{net income}}_{{({\text{t}} - 1)}} } \right|} \right] \\ \end{aligned}$$

(A1)

2.2 Appendix 2.2: Probability of default

The probability of default (PD) for every firm each year is calculated in the spirit of the Merton (1974) model. When the market value of a firms’ total assets (hereafter, firm value) is greater than the face value of the firm’s debt outstanding, equity holders find it profitable to continue owning the firm. Otherwise, the equity holders declare bankruptcy. PD thus refers to the probability that the firm goes into bankruptcy within a certain period of time.

Firm value, V (> 0), is assumed following geometric Brownian motion:

$$dV = {{\upmu }}Vdt + \sigma_{v} VdW,$$

where µ is the expected return (continuously compounded) on V, $\sigma_{v}$ is the volatility of V and dW is the standard Wiener process. The firm has an outstanding pure discount bond with face value F maturing in T years. Thus, the equity of the firm is a European call option on the underlying value of the firm with strike price and time-to-maturity equal F and T. By the Black–Scholes-Merton formula (Black and Scholes 1973), the value of the equity today, E, is given by

(B1)

where E is the market value of the firm’s equity, r is the instantaneous risk-free rate, Ɲ(·) is the cumulative standard normal distribution function, ${\text{d}}_{1} = \frac{{\ln \left( {\frac{V}{F}} \right) + \left( {r + 0.5\sigma_{v}^{2} } \right)T}}{{\sigma_{v} \sqrt T }}$ and ${\text{d}}_{2} = {\text{d}}_{1} - \sigma_{v} \sqrt T$. Furthermore, by the Ito’s lemma:

(B2)

where $\sigma_{E}$ is the volatilities of the equity. Equation (B2) is to translate the volatility of equity to the volatility of total assets because the market value of total assets and its volatility are unobservable.

Following Bharath and Shumway (2008), Eqs. (B1) and (B2) are solved by an iterative procedure for V’s and $\sigma_{v}$’s every day in the previous year. (Specially, the initial value of $\sigma_{v}$ is set to $\sigma_{E}$[E/(E + F)], where $\sigma_{E}$, E and F are observable parameters. We then calculate the implied log return on assets each day and use the returns series to generate new estimates of $\sigma_{v}$ and µ. The procedure is repeated until the calculated $\sigma_{V}$ converges, i.e., the absolute difference in adjacent $\sigma_{v}$‘s is less than 10⁻³). Then the distance to default (DD) is calculated as ${\text{DD}} = \frac{{\ln \left( {\frac{V}{F}} \right) - \left( {{{\upmu }} - 0.5\sigma_{v}^{2} } \right)T}}{{\sigma_{v} \sqrt T }}$, and the corresponding (implied) probability of default within 1 year (assuming T = 1) is:

2.3 Appendix 2.3: Credit rating

The third proxy for distress risk is credit rating (RATING) that evaluate the credit risk of a firm as a debtor. The higher its credit rating, the higher the chance the firm will be able to pay back its outstanding debts (i.e., lower distress risk). Credit ratings of sample firms are obtained from Compustat, and following Avramov et al. (2013), we assign a numeric value to each symbolic ratings as AAA = 1, AA + = 2, etc. If the rating is below B–, the value is set to 17. The higher number of RATING, the higher the financial risk.

Appendix 3

See Table 8.

Table 8 Monthly EPS and sales forecast errors and forecast revisions