RAROC of a Corporate Loan - "Back of the Envelope" Calculations

Your boss, the Head of Corporate Finance of a bank, has been approached by an AA rated corporate borrower for a 3 year $100 million loan. This borrower is your bank’s very old client and has generated big revenues for you. The borrower though rated AA, however, has a chance of being downgraded to a lower rating in six months time by a leading rating agency and your boss suspects that that fact has prompted them to borrow now at a better spread. The current discount rate is 5% (i.e. you have to borrow money at 5%, a very high rate! In reality loan spreads are over Prime Rate or LIBOR) and you have previously charged this client around 20 basis points over the discount rate. Your boss does not want to upset the client by refusing the loan and also your bank stands to make a very good fee on the transaction, of around 0.15%.

Your boss has to get back to the client in two days time and he does not have time for detailed analysis. He calls you in an gives you this problem: to analyze the transaction and give him your opinion – whether to make the loan or not.

You analysis tells you that there are 400 publicly traded bonds in the comparable asset class rated AA (as your borrower) and further over the past one year only 4 bonds out of 400 had their credit risk premium increase by more than the 99% worst case and that premium was equal to 1.1%. (A credit risk premium is defined as the change in yield spread between corporate bonds of a particular credit rating class and the matched duration Treasury bonds). You do some back of envelope calculations and figure out that the probability of default for AA rate loans is around 0.1% and find out from a rating agency’s data that the recovery rate for AA rated loans is around 51.13%.

You now have to make a back of the envelope calculation – so to speak – and get back to your boss with a report. Your bank has to make a quick decision as to whether to approve the loan or not and get back to the client with the next two days. Your bank’s hurdle rate (the IRR) is 10%.

Solution:

Since you need to make a decision fast you need a model of analysis that quickly calculates, first, the risk capital required for the loan and second, the risk adjusted return on the capital for this loan. If the risk adjusted capital return on capital is more than your hurdle rate you would go ahead and make the loan otherwise you won’t. Historically, two approaches have emerged to measure the risk capital in a RAROC calculation: one the Bankers’ Trust approach and the other the Bank of America approach. The original BT approach was to measure the capital at risk as equal to the maximum adverse change in the market value of a loan over the next year. The credit risk component was embedded in the equation as the credit risk premium, that was discounted and the multiplied by the duration and the loan exposure to get the Dollar capital risk exposure. The Bank of America approach, more detailed and more prevalent these days amongst bankers uses experimental and historical approach. However, given the constraints of time you need to use the BT approach and quickly modify the BT equation.

Step 1: Calculate the risk capital

You start off by making a rough estimate of the duration of the loan. That turns out to be 2.7 (please note that this is not an accurate figure). Then you calculate the expected discounted credit risk premium. This number is estimated by taking the credit risk premium of the loan – equal to 1.1% - and discounting it by the prime rate (assumed for simplicity). Then you multiply the expected discounted credit risk premium with the duration and the loan exposure to get the Dollar capital risk exposure or the risk capital. This is calculated as $2,823,194 (please remember that the sign on this is number negative).

Step 2: Calculate the One year adjusted income on the loan.

The one year adjusted income on the loan is calculated by taking the sum of your fees earned from the transaction, the spread on this loan (assuming, that you would borrow at 5% and lend to this client at 5.2%) and then subtracting the Expected Loss on this loan. The expected loss is calculated by multiplying the probability of default, estimated by you as 0.1%, with the Loss given Default (LGD), which in turn is obtained by subtracting recovery rate from one. The expected loss on this loan is $48,870 and the fee earned by you is $150,000 (0.15% of the loan). The spread of 0.2% translates to $200,000. Therefore, the one-year adjusted income for you on this loan is $301,130.

Step 3: Calculate the RAROC

The RAROC is calculated by dividing the one-year adjusted net income by the risk capital. The RAROC of the loan comes out to 10.67% ($310,130 divided by $2,823,194). This number is higher than the hurdle rate of 10% and thus, according to you, the bank should go ahead and make the loan.

You approach with your analysis to your boss and tell him that in your opinion the bank should make this loan. After an hour your boss calls you in and tells you that though your analysis seems correct at first glance he is not comfortable making the loan. And he would definitely not make the loan at 20 basis points spread over the discount rate (i.e. your borrowing cost). He needs to factor in the risk of a downgrade in the spread and also needs to analyze the effect of a downgrade on the RAROC of the loan. He asks you to go back and recalculate. He wants you to be more detailed and thinks “back of the envelope” calculations won’t suffice in this case.

More detailed calculations in two days?? Is he serious?? Would you rather put in your papers and try accounting as a career.

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