If 10 year T bonds have a yield of 5.2%, 10 year corporate bonds yield 7.5%, the maturity risk premium on all 10 year bonds is 1.1%, and corporate bonds have a 0.2% liquidity premium versus a zero liquidity premium for T bonds, what is the default risk premium on the corporate bond?
a)2.1% b)5.2% c)5.4% D)7.5%
I worked it as follows:
return= r* (risk free rate) + Inflation Premium + Default Risk Premium + Liquidity Premium + Maturity Risk Premium.
7.5% - 5.2% = r*
r= 2.3+ DRP + 0.2% + 1.1%
r= DRP + 3.6%
r/3.6% = DRP
DRP = 2.083%
Is this correct?
no
7.5% - 5.2% = r*
r= 2.3+ DRP + 0.2% + 1.1%
r= DRP + 3.6%
r/3.6% = DRP
DRP = 2.083%
Yes, your calculation is correct.
To find the default risk premium (DRP) on the corporate bond, you subtract the yield of the risk-free rate (T-bonds yield in this case) from the yield of the corporate bond.
In this case, the yield on the corporate bond is 7.5% and the yield on the risk-free rate (T-bonds) is 5.2%.
7.5% - 5.2% = r* (risk-free rate)
So the risk-free rate (r*) is 2.3%.
Next, you need to calculate the total yield as a sum of various risk premiums:
r* (risk-free rate) = 2.3%
Inflation Premium = 0% (not mentioned in the question)
Default Risk Premium (DRP) = ?
Liquidity Premium = 0.2%
Maturity Risk Premium = 1.1%
r* = DRP + 3.6%
DRP = r* - 3.6%
DRP = 2.3% - 3.6%
DRP = -1.3%
However, it's important to note that it is not possible for the default risk premium to be negative. Therefore, the correct answer must be option (c) 5.4% according to the given options.