RISK-ADJUSTED RETURN ON CAPITAL
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Derivatives

RISK-ADJUSTED RETURN ON CAPITAL

As its name suggests, risk-adjusted return on capital analysis (RAROC) is a method for factoring risk into the computation and evaluation of financial returns.

As its name suggests, risk-adjusted return on capital analysis (RAROC) is a method for factoring risk into the computation and evaluation of financial returns. It may be applied to individual assets such as loans or trading positions, to complete portfolios, to business units, and even to entire lines of business. Properly performed, it ensures that all units are charged the same cost of capital rates, effectively levelling the playing field for managers and traders whose decisions are being evaluated. This article illustrates how institutions can apply RAROC methodology to derivatives (in this case, a simple interest rate swap) to ensure that products are providing acceptable returns on a risk-adjusted basis.

The basic premise underlying the RAROC method is that riskier products and ventures create greater potential for loss than less risky ventures. Losses that actually occur will ultimately reduce the capital available to the business. Riskier ventures should therefore generate higher profits to compensate for the greater risks they create. RAROC adjusts for higher risk by allocating higher amounts of capital to riskier projects. The riskier venture must therefore earn more absolute profit to achieve the same rate of return on capital as a less risky venture.

 

 

 

 

 

 

 

 

 

 

 

 

 

With RAROC, the amount of capital assigned to a product or unit is generally set equal to the highest loss that the unit is likely to realize over a given period. In the case of an individual instrument, this amount does not represent the full face or notional value, but the change in market value that would result from the most adverse change in interest rates, currency exchange values, or credit default rates that can reasonably be expected to take place.

This largest foreseeable change is usually estimated from historical data. Analysts might see, for example, that in the past five years interest rate fluctuations have averaged ± n basis points per year. About 68% of all outcomes will fall within one standard deviation (*) of this historical mean, and 99% will fall within three standard deviations.

Determining the largest probable exposure is a matter of judgment and experience. A company experienced in managing a certain type of risk might feel comfortable estimating its largest foreseeable exposure as n + 1*, while a conservative firm might want to increase its estimate to n + 3*. An even more conservative firm might adopt a worst case scenario, such as setting the largest foreseeable loss equal to the maximum change seen over a period.

 

A FIXED/FLOATING INTEREST RATE SWAP

Interest rate swaps are commonly used to hedge rate exposures. The following example (see figure) will illustrate the RAROC analysis for a simple swap:

Suppose a manufacturing firm with a sub-investment grade credit rating (Ba1) wants to obtain fixed-rate funds for five years for plant expansion, but does not want to pay the high rate required by the bond market. A multinational bank with a higher credit rating (Aa) wants floating rate funds to match short-term assets, or may simply want to earn the swap fee income.

The fact that differences in short-term borrowing rates between the Ba1 and Aa borrowers are significantly less than differences in their long-term borrowing rates provides the economic rationale for the swap. The manufacturer must pay more for corresponding short-term funds than the bank, but these higher short-term borrowing rates are still less than the cost savings obtained in the long-term market.

Both parties can therefore benefit from a fixed/floating swap in which the bank pays the manufacturer a floating rate while the manufacturer pays the bank a fixed rate over a given period, e.g., five years.

Suppose the notional value of the swap is USD10,000,000 with quarterly payments over a five-year term. While the fixed and floating rates are different, the swap will be structured such that interest rate projections make the swap have a current net present value of zero.

As the counterparty that will receive fixed rate payments and pay out floating rate payments, the bank faces two separate risk scenarios:

* Interest rate risk when interest rates rise. Rising rates reduce the NPV of the fixed payments the bank receives and increase the floating rate it pays. (Note that in this situation the bank does not incur credit risk. If the counterparty defaults on payments, the bank will be better off.)

* Credit risk when interest rates fall. Declining rates increase the NPV of the fixed rate payments the bank receives and decrease the floating rate payments it makes. The swap becomes an income-producing asset; the only risk to the bank is that its counterparty will default on the agreement.

 

CALCULATING THE RAROC VALUE FOR THE SWAP

The market value of the swap is roughly equivalent to the difference in the NPVs of the two interest payment streams. Suppose in our example that a favorable interest rate scenario for the bank (a rate drop of 100 basis points) indicates that the swap will have a maximum positive value of about USD500,000. (Note that this represents only 5% of the swap's notional principal.) This is the actual amount at risk if the counterpart defaults and, if default occurs, the bank cannot expect any recovery from selling the asset. Furthermore, suppose the annual probability of default for companies rated Ba1 is 1.50% with a standard deviation of 1.75%. Bank management wants to protect itself across a range of two standard deviations, which will cover 95% of all probable cases. The bank's target for ROE is 15%.

This total represents 3.75 basis points on the notional principal of the swap. For the swap to be profitable to the bank, it must earn this amount annually from dealer's swap spread or lowered funding costs. Any less means that the swap is unprofitable on a risk-adjusted basis.

 

This week's Learning Curve was written by Dr. R. Philip Giles, Adjunct Professor at the Columbia Business School and President of CBT Worldwide, Inc. of Mamaroneck, NY.

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