Unformatted text preview: FIXED INCOME SECURITIES
DECEMBER 2, 2010 CREDIT RISK and CORPORATE DEBT SECURITIES PART I Fall 2010 FNCE 235/725 Prof. Stephan Dieckmann 1 NAME OF INITIATIVE OR GROUP Business Cycles, Defaults, Credit Spreads Source: Hui Chen, 2009 2 Business Cycles, Recovery Rates Source: Hui Chen, 2009 3 Rating Agencies Source: Standard & Poors, 2008 4 Rating Agencies Source: Standard & Poors, 1997 5 Modeling Credit Risk
What should a model contain? 6 Modeling Credit Risk
What should a model contain? Likelihood of default Amount recovered in case of default The firms capital structure / leverage Value of the firm and its uncertainty Junior versus senior debt Longterm versus shortterm debt Measurement of the credit spread 7 Structural Model
Economic Intuition Consider a leveraged firm, with firm value V(t), equity value S(t), and defaultable debt value D(t) Accounting consistency leads to V(t) = S(t) + D(t) Debt contract is a zero coupon bond with face value F Firm value at maturity is V(t+1) What is the payoff of the debt contract at maturity? 8 Structural Model
Economic Intuition If V(t+1) >= F, then no default, payoff F If V(t+1) < F, then default occurs, payoff V(t+1) In the event of default, bondholders take over the firm and seize the asset value Payoff to D(t) is min [F, V(t+1)] = F max [0,FV(t+1)] What is max [0,FV(t+1)] ? 9 Structural Model
Simple Example Suppose V(t)=200, can increase to 300 or decrease to 100 over one year Firm has a debt contract outstanding F = 200 , maturing in one year Also tradable is a zero coupon bond without default risk, price is 90.90 for 100 face value If V was tradable, what is the replicating portfolio for D(t)? The price of the debt contract is 145.45. 10 Structural Model
Simple Example What is the credit spread? The contractual payoff is 200, the value is 145.45, what is the implicit yield? 145.45 = 200 / (1+R), R = 37.5% R is the yield to maturity of the bond assuming it will be repaid in full The credit spread is defined as the difference between R and the risk free rate, R r = 37.5%  10% = 27.5% 11 Merton Model (1974) where N(.) is the cumulative density of a normal distribution What we need to utilize the model is: today's firm value, V(t), annualize volatility of changes in firm value, V, the risk free interest rate r, the face value of debt, F, and it's maturity, T
12 Merton Model (1974)
Some Assumptions A firms has only one type of debt (simple capital structure) The debt that the firm has issued is a simple zero coupon bond maturing in T years Payment to bondholders in the case of default is made in accordance with principles of absolute priority You can buy and rebalance the replicating portfolio 13 Merton Model (1974)
An Implementation S&P reports an average leverage ratio for a BBBrated firm of 44.5% A realistic value for asset volatility is 28% The risk free rate is 5%, and we consider longterm debt, T=10 What is the face value of debt that produces a leverage ratio D/V of 44.5%? V F sigma T r d1 d2 N(d1) N(d2) N(d1) N(d2) Equity Debt D/V 100 87.29 0.280 10 0.050 1.1610 0.2756 0.8772 0.6086 0.1228229 0.3914459 55.5000 44.5000 0.445000 14 Merton Model (1974)
An Implementation What is the predicted credit spread? 44.50 = 87.29 exp(R*10) The predicted credit spread is 173 basis points The average longterm credit spreads for a BBB rated firm is approximately 180 basis points Not bad ! D R Rr Spread 44.5 0.0673696 0.017370 173.69647 15 Merton Model (1974)
Some Limitations It is possible to interpret N(d2) as the probability of default, but in a risk neutral world It is generally difficult to estimate a value for firm volatility. Assuming the Merton model is correct, we can infer firm volatility from stock market volatility It can not capture large surprises to firm value. The path of firm value is assumed to be smooth, and default becomes predictable the closer maturity T is 16 Implications
How does leverage affect the credit spread? 17 Implications
How does firm volatility affect the credit spread? 18 ...
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 Spring '09
 ROUSSANOV
 Debt, Merton Model, · Firm

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