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?
DRP =2.083%
Yes, your calculations are correct. To find the default risk premium (DRP) on the corporate bond, you subtract the yield of the risk-free T-bonds (5.2%) from the yield of the corporate bonds (7.5%). This gives you the "r*" or the additional return required for taking on the additional risk associated with corporate bonds (2.3%).
Next, you need to break down this additional return into its components. Adding the inflation premium, liquidity premium, and maturity risk premium (1.1%, 0.2%, 0.0% respectively), the total additional return required becomes 3.6%.
Since the additional return required (r*) includes the default risk premium, you can rearrange the formula to isolate the DRP. Dividing both sides of the equation r = DRP + 3.6% by 3.6%, you get DRP = (r - 3.6%). Substituting the known values, you find DRP = (7.5% - 3.6%) = 3.9%.
Therefore, the default risk premium on the corporate bond is 3.9%, which is closest to option (c) 5.4%.