Corporate Finance

Chapter 18 (Section 18.1):

18.1): Expected Returns vs. Stated Yields

Yields Measuring the Impact of Default Risk

Risk

“Expected Returns” versus “Stated Yields” . . . In a bond or mortgage (capital asset with contractual cash flows): Stated Yield (aka “Contractual Yield”) = YTM based on contractual obligation. Expected Return (aka “Expected Yield” or “Ex Ante Yield”) = E[r] = Mean of probability distribution of future total return on the bond or mortgage investment. •Quoted yields are always stated yields. •Contract yields are used in mortgage design and evaluation. •Expected return is more fundamental measure for mortgage investors. • For making investment decisions.

Difference:

Stated Yield – Expected Return

Impact of Default Risk in ex ante return investor cares about.

about.

18.1.1 Yield Degradation & Conditional Cash Flows… “Credit Losses” = Shortfalls to the lender (mortgage investor) as a result of default and foreclosure. “Realized Yield” = What the lender (investor) actually receives (as an IRR). “Yield Degradation” = Impact of credit losses on the lender’s realized yield as compared to the contractual yield (expressed in IRR units). Contractual Yield - Yield Degradation -------------------------= Realized Yield Yield Degradation (“YDEGR”) = Lender’s losses measured as a multiperiod lifetime return on the original investment (IRR impact). Due to Credit Losses

Numerical example of Yield Degradation:

Degradation: • $100 loan. • 3 years, annual payments in arrears. • 10% interest rate. • Interest-only loan. Here are the contractual terms of the loan as an NPV equation:

0 = −$100 + $10 $10 $110 + + 1 + (0.10) (1 + (0.10) )2 (1 + (0.10) )3

Contractual YTM = 10.00%.

Suppose: • Loan defaults in 3rd year. • Bank takes property & sells in foreclosure, but • $33 ==“Credit Losses”. • 70% “Recovery Rate”. • Bank only gets 70% of OLB: $77. • 30% = “Loss Severity”. Here are the realized cash flows of the loan as an NPV equation:

0 =...