Alternative Method for Determining Industrial Bond Ratings

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Alternative Method for Determining Industrial
Bond Ratings

• Lie-Jane Kao
• Department of Finance and Banking, KaiNan Univ.,
• Cheng-Few Lee
• Department of Finance, National Chiao-Tung Univ.

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Financial-ratio based Credit-Scoring Models

• The combination of several weighted financial
  ratios to provide index/indices that classifies
  businesss failure or bond ratings.

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Classes of Credit Scoring Model (Altman and
Saunder, 1998)

• (i) The linear probability model,
• (ii) The logit model,
• (iii) The probit model,
• (iv) The discriminant analysis model.

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Altmans Z-score model (1968)
Z 0.012X1 0.014X2 0.033X3 0.006X4 0.999X5

• X1working capital/total assets,
• X2retained earnings/total assets,
• X3earnings before interest and taxes/total
  assets,
• X4market value equity/book value of total
  liabilities,
• X5sales/total assets.

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Financial Ratios Selection

• A list of 22 potentially helpful ratios are
  chosen on the basis of their popularity in the
  literature and their potential relevancy to the
  study (Altman, 2000).
• Later, 27 financial ratios that include measures
  found in other studies thought to be potentially
  helpful as well in providing statistical evidence
  of impending failures are listed (Altman, 2000).

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Altmans Zeta model (1977)

• Earnings before taxes and interest/Total assets
• Earnings before taxes and interest/Total Interest
  Payments
• Retained earnings since inception/Total assets
• Market value of equity/Total capital
• Current ratio
• The standard error of estimate around a five to
  ten-year trend in X1
• Firms' total assets.

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Useful Financial Ratios (Chen ,1981)

• A summary of 25 predictive studies shows there
  is a total of 65 financial ratios, 41 of these
  are considered useful yet, every study cited a
  different set of ratios as being the most
  effective indication of firms failure or bonds
  rating.

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• The design of a credit-scoring model involves
• Principle I Meaningful financial variables
  selection,
• Principle II Classification Accuracy,
• (Basel Committee on Banking
  Supervision, 2005)

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Stepwise Discriminant Analysis (Pinches and
Mingo, 1973, 1975)

• Financial variable selection Factor analysis
  (Principle component analysis)
• Bond classification Multiple discriminant
  analysis.

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Stepwise Discriminant Analysis Financial
variable selection

• 35 financial variables are classified into 7
  factors
• (1) Size
• (2) Leverge
• (3) Long-term capital intensiveness
• (4) Short-term capital intensiveness
• (5) Return on investment
• (6) Earning stability
• (7) Debt coverage.

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Stepwise Discriminant Analysis Bond
classification

• Three discriminant functions Y1, Y2, Y3 are
  obtained using multiple discriminant analysis
  (MDA)
• Y1 subordination (90)
• Y2 net incomeinterest/interest (5)
• Y3 issue size (4)
• The percentage correctly predicted is 69.70

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Financial Variable Selection

• Principle component analysis a statistical tool
  to group correlated financial variables into a
  few linear functions that account for the
  majority of the variance by the original set of
  financial variables, i.e., to extract a few
  components that retain a maximium of information
  contained in the original data, or, have the
  maximal explanatory power.

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Bond Classification

• Multiple discriminant analysis a statistical
  tool to find linear functions of financial
  variables that maximize the between group
  variance while minimizing the within group
  variance among these variables, so that
  different bond rating groups can be
• distinguished, i.e., to extract a few
  components that have the maximal discriminant
  power.

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Maximization of Explanatory Power

• Financial variables X(X1,, Xp)?,
• The principal components Y1?1?X, , Yu?u?X
• If the first i-1 principle components are
  determined, Yi is determined by choosing ?i that
  maximizes the variance of Yi ,
• i.e.,
• var(Yi)
  (1)
• ? is the variance-covariance matrix of the
  whole population. The maximization is subject to
  the constraints ?j??i0 for all jlti and ?i??i1.

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Maximization of Discriminant Power

• Financial variables X(X1,, Xp)?,
• k populations with common variance-covariance ?,
• The discriminant functions D1?1??-1/2X, ,
  Du?u??-1/2X,
• If the first i-1 discriminant functions are
  determined, Di is determined by choosing ?i that
  maximizes the ratio comparing the variability
  between the groups to that within the groups,
• i.e.,
• 
  (2)
• The maximization is subject to the
  constraints ?j??i0 for all jlti and ?i??i1.

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Two Conflicting Objectives

• Theorem If a set of r linear components
  M1?1??-1/2X, , Mr?r??-1/2X, r?min(k-1, p),
  that maximizes (1) and (2) simultaneously,
  subject to the constraints
  
• for all jlti and ?i??i1,
  exists, then the two matrices
• and
  ?
• share the same set of eigenvectors.
  
  

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A Compromise Solution

• Pareto efficient solution Achieved level of any
  of the objectives cannot be improved without
  worsening the achieved level of any other
  objective (Tamiz, 1996, 1998).

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Goal Programming

• Form of multi-objective optimization,
• Ignizio in the 1970s,
• Each of the objectives is given an aspiration
  level and unwanted deviation, the unwanted
  deviations from these aspiration levels are
  minimized in an achievement function.

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Goal Programming

• Aspiration Level - Specific value associated with
  the desired or acceptable level of the objective,
• Goal Deviation - Difference between the
  aspiration level and what we accomplish w.r.t.
  the objective,
• Achievement Function - To measure the achievement
  of the objective.

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Three Goal Programming Variants

• Weighted Goal Programming Minimize weighted sum
  of goal deviations,
• Lexicographic Goal Programming Minimize an
  ordered set of goal deviations,
• Minmax Goal Programming Minimize the worst
  deviation.

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Formulation of MINIMAX GP

• Let
  and ?1??2?...??pgt0
• be the eigenvalues of
• A1
• A2 ?
• , respectively.

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Formulation of MINIMAX GP

• Achievement function
• Min D
  
• Constraints
• u1?D
• u2?D
• g1(?s)u1
• g2(?s)u2?s
• h1(?s)?s??s -10
  
• hj(?s)0 for jlts
• u1, u2 represent the under achievement of the
  target values and ?s , respectively.

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Emperical Analysis

• A total of 132 industrial corporate bonds rated
  B, Ba, Baa, A, Aa based on Moodys ratings from
  January 1, 1967 to December 31, 1968 (Pinches and
  Mingo, 1973).

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Comparing Four Multivariate Techniques

• Principle Component Analysis,
• Multiple Discriminant Analysis,
• Stepwise Discriminant Analysis,
• MOP Discriminant Analysis.

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Principle Component Analysis
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Principle Component Analysis
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Multiple Discriminant Analysis
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Multiple Discriminant Analysis
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Stepwise Discriminant Analysis
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Stepwise Discriminant Analysis
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MOP Discriminant Analysis
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MOP Discriminant Analysis
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Summary