Is the Structural Approach More Accurate than the Statistical Approach in Bankruptcy Prediction?

Is the Structural Approach More Accurate than the Statistical Approach in Bankruptcy Prediction? Hui Hao Global Risk Management, Bank of Nova Scotia April 12, 2007

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models:

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models: - Altman (1968)

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models: - Altman (1968) - Shumway (2001)

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models: - Altman (1968) - Shumway (2001) Structural models:

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models: - Altman (1968) - Shumway (2001) Structural models: - The standard call option (Merton ( 74) and KMV).

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models: - Altman (1968) - Shumway (2001) Structural models: - The standard call option (Merton ( 74) and KMV). - The barrier call option.

Road Map Theme: Horse racing among two approaches (4 models) on bankruptcy prediction Statistical models: - Altman (1968) - Shumway (2001) Structural models: - The standard call option (Merton ( 74) and KMV). - The barrier call option. The goal is to provide a comprehensive comparison between four models.

Horses: Altman s Z-score Road Map: Cont d

Horses: Altman s Z-score Shumway s score Road Map: Cont d

Road Map: Cont d Horses: Altman s Z-score Shumway s score Default probability in the standard call option.

Road Map: Cont d Horses: Altman s Z-score Shumway s score Default probability in the standard call option. Default probability in the barrier option.

Road Map: Cont d Horses: Altman s Z-score Shumway s score Default probability in the standard call option. Default probability in the barrier option. How relevant is information contained in four models to bankruptcy prediction?

What are structural models We assume a Black-Scholes-Merton setting that the value of a firm follows

What are structural models We assume a Black-Scholes-Merton setting that the value of a firm follows

What are structural models We assume a Black-Scholes-Merton setting that the value of a firm follows d log V = dv = (α.5σ 2 )dt + dtσɛ (1) where V is the asset value of a firm, α and σ the drift and variance term of the Brownian Motion, and ɛ N(0, 1).

What are structural models We assume a Black-Scholes-Merton setting that the value of a firm follows d log V = dv = (α.5σ 2 )dt + dtσɛ (1) where V is the asset value of a firm, α and σ the drift and variance term of the Brownian Motion, and ɛ N(0, 1). The debt X t has a maturity of t + τ.

The standard call option At t + τ, the payoff to the debt holder: min[v, X ].

The standard call option At t + τ, the payoff to the debt holder: min[v, X ]. At t + τ, the payoff to the equity holder: max[0, V X ]. If V < X, the firm files bankruptcy and debt holders take over the firm.

The standard call option At t + τ, the payoff to the debt holder: min[v, X ]. At t + τ, the payoff to the equity holder: max[0, V X ]. If V < X, the firm files bankruptcy and debt holders take over the firm. The equity is a standard call on a firm s value.

Asset Value 150 100 50 Merton (1974): A Standard Call Option asset value starts from 100 dv=µt+t 0.5 σε, ε~φ(0,1) total debt 0 0 100 200 300 Time to Maturity (T=360)

The Barrier (Down-and-Out) Call Option There is a barrier that limits the movement of the firm s value.

The Barrier (Down-and-Out) Call Option There is a barrier that limits the movement of the firm s value. 1 When the asset value has not touched the barrier during the option s life, a down-and-out call option has the same payoff as a standard call.

The Barrier (Down-and-Out) Call Option There is a barrier that limits the movement of the firm s value. 1 When the asset value has not touched the barrier during the option s life, a down-and-out call option has the same payoff as a standard call. 2 When the asset value touches the barrier, the down-and-out call option expires, and an option holder gets nothing. This is also the time the firm files bankruptcy and debt holder take over the firm.

The Barrier (Down-and-Out) Call Option There is a barrier that limits the movement of the firm s value. 1 When the asset value has not touched the barrier during the option s life, a down-and-out call option has the same payoff as a standard call. 2 When the asset value touches the barrier, the down-and-out call option expires, and an option holder gets nothing. This is also the time the firm files bankruptcy and debt holder take over the firm. Some argue that treating equity as a barrier option is more appropriate in areas of risk management and securities pricing.

150 Barrier: A Down and Out Call Option asset value starts from 100 Asset Value 100 50 total debt threshold default 0 0 100 200 300 Time to Maturity (T=360)

Definition of DP call The standard call option assumes that a firm does not need to repay its total liabilities (X t ) until the maturity t + τ.

Definition of DP call The standard call option assumes that a firm does not need to repay its total liabilities (X t ) until the maturity t + τ. Therefore DP is the probability of the event that the firm s value is less than X t at t + τ.

Definition of DP call The standard call option assumes that a firm does not need to repay its total liabilities (X t ) until the maturity t + τ. Therefore DP is the probability of the event that the firm s value is less than X t at t + τ. A graphical presentation of DP call follows...

Default Probability from the Call Option 50 Logarithm of Asset Value 40 30 20 10 0 Initial firm value v 0 N(v 0 +µt,tσ 2 ) Total liability 10 359.5 359.55 359.6 359.65 359.7 359.75 359.8 359.85 359.9 359.95 360 Time to Matureity (T=360)

Definition of DP barrier We measure the probabilities of two events in DP barrier :

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case:

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case:

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case: - when the firm s value touches the barrier.

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case: - when the firm s value touches the barrier. Not-so-intuitive Case:

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case: - when the firm s value touches the barrier. Not-so-intuitive Case:

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case: - when the firm s value touches the barrier. Not-so-intuitive Case: - though the value does not touch the barrier, the firm cannot pay off its maturing debt (D).

Definition of DP barrier We measure the probabilities of two events in DP barrier : Intuitive Case: - when the firm s value touches the barrier. Not-so-intuitive Case: - though the value does not touch the barrier, the firm cannot pay off its maturing debt (D). Illustrations of two cases to follow...

Default Probability from the Barrier 160 The First Event 140 Initial Firm Value v 0 Logarithm Asset Value 120 100 80 60 40 Barrier 20 Default Maturing Debt 0 0 50 100 150 200 250 300 350 Time to Maturity (T=360)

Default Probability from the Barrier 160 The Second Event 140 Initial Firm Value v 0 Logarithm Asset Value 120 100 80 60 40 20 Barrier Maturing Debt Default 0 0 50 100 150 200 250 300 350 Time to Matureity (T=360)

Data Sample:

Data Sample:

Data Sample: - 294 bankruptcies filed during 1996-2000.

Data Sample: - 294 bankruptcies filed during 1996-2000. - 2773 non-bankrupt firms as a control group.

Data Sample: - 294 bankruptcies filed during 1996-2000. - 2773 non-bankrupt firms as a control group. We compare four models out-of-sample forecast accuracy for three horizons: one year, two years, and three years prior to the event.

Racing Rules In horse racing:

Racing Rules In horse racing:

Racing Rules In horse racing: - We check which horse finishes first.

Racing Rules In horse racing: - We check which horse finishes first. In our comparison of forecast accuracy:

Racing Rules In horse racing: - We check which horse finishes first. In our comparison of forecast accuracy:

Racing Rules In horse racing: - We check which horse finishes first. In our comparison of forecast accuracy: - We use a table and an index (Area Under Curve).

Executive Summary We find 36% of non-bankrupt firms and 44% of bankrupt firms have a barrier that is significantly different from zero.

Executive Summary We find 36% of non-bankrupt firms and 44% of bankrupt firms have a barrier that is significantly different from zero. Structural models dominate statistical models in out-of-sample forecast.

Executive Summary We find 36% of non-bankrupt firms and 44% of bankrupt firms have a barrier that is significantly different from zero. Structural models dominate statistical models in out-of-sample forecast. Hypothesis test results show that the standard call option significantly out-performs all three models.

Table 3.5 Comparison of Forecast Accuracy Percentile Altman Shumway Call Barrier Default within one year bucket 1 90-100% 0.3756 0.4195 0.6000 0.5366 bucket 1-2 80-100% 0.5220 0.6683 0.7805 0.6634 bucket 1-3 70-100% 0.6585 0.7561 0.8781 0.7902 bucket 1-4 60-100% 0.7639 0.8390 0.9219 0.8488 bucket 1-5 50-100% 0.8489 0.8878 0.9608 0.8829 bucket 1-6 40-100% 0.8878 0.9268 0.9805 0.9171 bucket 7-10 0-40% 0.1122 0.0732 0.0195 0.0829 No.BKT/NBKT Firms 205/2159 Area Under Curve (AUC) 0.764 0.814 0.898 0.847

Figure 3.5 Barrier vs Call Sensitivity 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 - Specificity index Barrier Merton/KMV

Figure 3.4 Shumway (2001) vs Call Sensitivity 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 - Specificity Index call sh

Figure 3.3 Altman (1968) vs Call Sensitivity 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 - Specificity Index alt call