Predicting financial distress of companies

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 Zlt1.81 Bankrupt firms 1.81ltZlt2.67 Grey area Zgt2.67 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)
• Zlt1.21 - 2183
• 1.21ltZlt2.90 - 4245
• Zgt2.90 - 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)
• Zlt1.98 - 2750
• 1.98ltZlt3.25 - 815
• Zgt3.25 - 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
  Assetsasset 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
10
(No Transcript)
11
(No Transcript)
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.