A one year, pure discount, corporate bond has a face value of $100. If the econo

Question

A one year, pure discount, corporate bond has a face value of $100. If the economy is strong or average the issuer will remain solvent and redeem the bond. Unfortunately, if the economy becomes weak the issuer will default and bondholders will be able to recover only $88. All three states of the economy are equally likely. The risk-free rate is 2%. If the bond now sells for $90, what part of the promised 11.1% return is
a) the expected yield?
b) the expected loss rate?
c) compensation for bearing systematic risk?

Explanation / Answer

Probability of getting $100 at the end of one year=(1/3)+(1/3)=2/3

Probability of getting $88 at the end of one year=(1/3)

Expected amount to be received at the end of one year=(2/3)*100+(1/3)*88=$96

Invested amount=$90

EXPECTED YIELD=(96/90)-1=0.0667=6.67%

If Economy becomes weak,

Amount of loss=(90-88)=$2

Loss Rate=2/90=0.0222=2.22%

Probability of Loss=1/3

EXPECTED LOSS RATE =(1/3)*2.22=0.74%

RISK FREE RATE-2%

EXPECTED YIELD=6.67%

COMPENSATION FOR BEARING SYSTEMATIC RISK=(6.67-2)=4.67%

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