3.a.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 (i)with and (ii) without collateral using the following formula and values:

Risk Premium with collateral:

where,k = required yield on a risky loan,

i = 0.02 (default risk free interest rate),

(1-p) = 0.05 (probability of default over the year), and

g = 0.8 (the portion of the loan collateralized for certain).

3.b.Suppose the expected probability of survival in year 2 decreases from p1= 0.95 in year 1 to 0.80 in year 2 (p2).During the same period, the default risk free interest rate stays the same at 2 percent.What will be the risk premium for the second year, assuming the same collateral structure if the firm survives through year 1?What is the cumulative probability of default over the 2-year period? (HINT: Cp = 1 - (p₁)(p₂) ).

3.c.If the portion of the loan collateralized was not known for certain in year 1 and could vary between g=0.9 and g=0.0 with a probability of 0.8 it would be 0.9 and a probability of 0.1 it would be 0.3, what is the risk premium in this case? Would the risk premium be higher than in 3.a. without collateral? The risk premium in this case is:

3.d.Given the information in 3.a. and 3.b. above, what should the interest rate be in the initial period for a two year default risky loan with the above default characteristics?(HINT: Use the unbiased expectations hypothesis as shown in Question 1 to compute the 2-year default risky interest rate.)