1. Predicting financial distress of companies

2. Models discussed Z score model Vasicek –Kealhofer model Black Scholes Merton Model Compensator model

3. Z-Score Model Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5 X1 = Working Capital/total assets (liquidity) X2 = Retained Earnings/total assets (earned surplus, leverage) X3 = Earnings before interest and taxes/total assets (earning power) X4 = Market value equity/book value of total liabilities (solvency) X5 = Sales/total assets (sales generating capability) Z = Overall index Z<1.81 – Bankrupt firms 1.81<Z<2.67 – Grey area Z>2.67 – Healthy firms

4. 8098 firms Bankrupt – 2023 Grey – 2258 Healthy - 3817

5. Revised Z-score model Substituting the book values of equity for Market value in X4. Z’ = 0.717(X1) + 0.874(X2) + 3.107(X3) + 0.420(X4) + 0.998(X5) Z’<1.21 - 2183 1.21<Z’<2.90 - 4245 Z’>2.90 - 1670

6. Further revision Model without sales/total assets. Done to minimize potential industry effect(which is more likely to take place when an industry-sensitive variable as asset turnover is included ) Z’’ = 6.56(X1) + 3.26(X2) + 6.72(X3) + 1.05(X4) Z’’<1.98 - 2750 1.98<Z’’<3.25 - 815 Z’’>3.25 - 4533

7. VK model Net worth of a firm = Market Value of Assets – Default Point Default point lies between total liabilities and current short term liabilities. Default Point = Total Liabilities – Long Term Debt [Dist to default] = [Market value of Assets]-[default point] [Market value of Assets][asset volatility] Naïve implementation : [Dist to default] = [Asset Value]-[default point] [Standard deviation of Asset values]

8. Calculating Asset Volatility It is the standard deviation of the annual percentage change in the asset value.It can be calculated from the value of the increase or decrease in percentage of asset value upon 1 standard deviation change in the asset value Various ways of calculating asset volatility – Implied asset volatility. Unlike equity volatility asset volatility is impossible to measure directly from market prices.

9. Black Scholes Model

12. Calculating cumulative normal prob

13. Calculating volatility Using the lognormal property of stock/equity values. Step 1: Compute S(t)/S(t-1), where S(t) is quarter t equity value. Step 2: Compute u(t)= Step 3: Find the Standard deviation of u(t). This estimates the quarterly volatility. Step 4: If the volatility is v for one unit of time, then the volatility for t units of time is. Thus we go from quarterly volatility to annual volatility by multiplying by 2.

14. Solving the BS equation Method 1 – Simplifying assumption – balance sheet data is an unbiased estimate of market data. Calculate asset volatility through historical values. Use the book value implied asset volatility equation: Method 2 – Solve the BS equation and the above equation – use Newton Iterative search for non – linear systems of equations. Method 3 – Use BS and equity-implied asset volatility equation and solve. (Numerical Analysis)

15. Alternative volatility calculation methods Current volatility calculation gives equal weight to all u(t)’s. Makes sense to give more weight to recent data. 1) Can use the exponentially weighting moving average model. 2)Garch(1,1) model.