Question

1. A proposed loan of $1m has total annual interest rate and fees of 6%. The loan’s duration is 5.7 years. The lender’s cost of funds is 5.25%. Comparable loans have an interest rate of 5.85%. The expected maximum change in the loan rate due to a change in the credit risk premium for the loan is 1.25% (based on actual change in credit risk premium for the worst 1% of comparable loans over some prior period).

a. What is the RAROC on this loan?

b. If the lender requires RAROC to exceed 12.5%, how could the terms of the loan be changed to make this loan acceptable?

2. If the expected default rate on a 1-year personal loan card is 8.5% and the risk free rate is 3%, what risk premium must a financial institution charge on the credit card in order to have an expected return equal to the risk free rate? (Assume the financial institution assumes a 0% recovery rate in the event of default.)

b. If the expected default rate on a 1-year automobile loan is 3% and the financial institution expects to recover rate 45% of the total loan return in the event of default 45%, what risk premium must a financial institution charge on the automobile loan in order to have an expected return equal to the risk free rate?

3. A 2-year loan has probability of payment for each year as follows: p₁ = 97.5%, p₂ = 92.5% Expected recovery rates in the event of default are: g₁ = 85%, g₂ = 75%. The 1-year risk free rate, i₁, is 3%, and the 1-year forward rate for lending one year from now, f_1,1, is 3.5%. What risk premium must a financial institution charge on this loan in order to have an expected return equal to the risk free return on a 2-year loan?

4a. Obtain Amazon 5 years of monthly returns for a public company that has long term debt (book value) equal to at least 20% of the company’s total market value (enterprise value).

b. Calculate the standard deviation of monthly returns on the company’s stock.

c. Determine the probability that a decline in the company’s value over the next two years will cause it to have insufficient funds to repay its debt.

Answer 1

Soln : RAROC is defined as Risk Adjusted return on Capital Employed

RAROC = (Revenues - Cost - Expected Loss)/ Risk Capital

Expected loss not given so consider it as 0, revenues - cost = (6-5.75)%*1 mn = $7500

Now risk capital will be calculated by using the duration of loan = 5.7 years, capital risk premium = 1.25%, discount factor = 5.85%= 1.0585, as it make it simple, since expected return in market = 5.85%

So, capital risk premium to be discounted = 1.25%/1.0585 = 1.181%

Now, risk adjusted capital = 1.181%*5.7*1mn = $ 67312.00 approx.

RAROC = Net income/risk adjuetd capital = 7500/67312 = 11.14%

b) If RAROC to exceed 12.5%, in that case the numerator has to be increased i.e. Net Income

So, we can say that , 12.5% = Net Income / 67312 or Net Income = 8414

Let x be the new rate of loan including fee to achieve this

So, (x% - 5.25%)*1mn = 8414 or x= 5.25% + 0.8414% = 6.09%

So, loan annual interest rate and fee should be charged more than x% i.e. 6.09% to achieve the required RAROC.

2) Expected default rate = 8.5%, risk free rate = 3%

Now, let y be the rate to be charged as premium on cards.

So, we can say that (1-8.5%)*y% of total amount = 3% of total amount .......................(as recovery rate is 0)

Or , 91.50%*y% = 3% , we will get y = 3.28% i.e.risk premium to be charged for given condition.

2-b) In this case we need to calculate again risk premium Y , with recovery rate = 45% of total amount

So, we can again write the part a eqn:

Y*(1-0.03)* total amount + 0.03 * 45%*total amount = risk free rate * total amount

Y* 0.97 + 0.0135 = 0.03

On calculation, we get Y = 1.7% i.e. the premium to be charged on credit card to have expected return equal to risk free rate.