In evaluating credit risk discuss the statement An increase

In evaluating credit risk, discuss the statement: \"An increase in collateral is a direct substitute for an increase in default risk.\" In your discussion, evaluate the credit risk premium on a one-year loan with and without collateral using the following formula and values:

Risk Premium: k-i = [(1+i) / (y+p - py)] - (1+i)

where, k = required yield on a risky loan, i = 0.1 (default risk free interest rate), (1-p) = 0.1 (probability of default over the year), and = 0.9 (the portion of the loan collateralized).

Solution

(1-p) = 0.1 =>p=1-.1=.9

credit risk premium on a one-year loan with collateral( = 0.9)

= [(1+i) / (y+p - py)] - (1+i)= [(1+i) / (y*(1-p)+p)] - (1+i)

= [(1+.1) / (.9*.1+.9)] - (1+.1)

= [(1.1) / (.99)] - (1.1)

=0.0111=1.11%

credit risk premium on a one-year loan without collateral ( =0)

= [(1+i) / (y+p - py)] - (1+i)= [(1+i) / (y*(1-p)+p)] - (1+i)

= [(1+.1) / (0*.1+.9)] - (1+.1)

= [(1.1) / (.9)] - (1.1)

=0.1222=12.22%

Thus  the credit risk premium on a one-year loan without collateral (12.22%) is greater than the the credit risk premium on a one-year loan with collateral(1.11%).