LO 48.3: Compute and interpret the RAROC for a project, loan, or loan portfolio,

LO 48.3: Compute and interpret the RAROC for a project, loan, or loan portfolio, and use RAROC to compare business unit performance.
The necessary amount of economic capital is a function of credit risk, market risk, and operational risk. The RAROC for a project or loan can be defined as risk-adjusted return divided by risk-adj usted capital. The basic RAROC equation is as follows:
RAROC=
after-tax expected risk-adj usted net income
economic capital
There is a tradeoff between risk and return per unit of capital with the numerator acting as return and the denominator acting as risk. For example, a business units RAROC needs to be greater than its cost of equity in order to create shareholder value.
Furthermore, measures such as return on equity (ROE) or return on assets (ROA) are based on accounting book values only, and therefore are unable to account for the relevant risks. RAROC has two specific adjustments to these measures. In the numerator, it deducts expected loss (the risk factor) from the return. In the denominator, it replaces accounting capital with economic capital.
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Topic 48 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 17 standard deviation, and (2) the net present value (NPV), which equals the discounted The underlying principles of the RAROC equation are similar to two other common measures of risk/return: (1) the Sharpe ratio, which equals: (expected return risk-free rate) / standard deviation, and (2) the net present value (NPV), which equals the discounted value of future expected after-tax cash flows. The discount rate for the NPV is a risk- adjusted expected return that uses beta (captures systematic risk only) from the capital asset pricing model (CAPM). In contrast to NPV, RAROC takes into account both systematic and unsystematic risk in its earnings figure.
A more detailed RAROC equation to use for capital budgeting decisions is as follows:
RAROC = taxes + return on economic capital d= transfers exp ected revenues cos ts exp ected losses
taxes + return on economic capital d= transfers
economic capital
Where:
Expected revenues assume no losses and costs refer to direct costs. Taxes are computed
using the firms effective tax rate and transfers include head office overhead cost allocations to the business unit as well as transactions between the business unit and the treasury group, such as borrowing and hedging costs.
Expected losses (EL) consist mainly of expected default losses (i.e., loan loss reserve),
which are captured in the numerator (i.e., higher funding cost) so there is no adjustment required in the denominator. Expected losses also arise due to market, operational, and counterparty risks.
Return on economic capital refers to the return on risk-free investments based on the
amount of allocated risk capital.
Economic capital includes both risk capital and strategic risk capital. Risk capital serves as a buffer against unexpected losses. It is the amount of funds that the firm must hold in reserve to cover a worst-case loss (an amount over the expected loss) at a specific confidence level that is usually 95% or more. Therefore, it is very similar to the annual value at risk (VaR).
Strategic risk capital pertains to the uncertainty surrounding the success and profitability of certain investments. An unsuccessful investment could result in financial losses and a negative reputational impact on the firm. Strategic risk capital includes goodwill and burned-out capital. Goodwill is the excess of the purchase price over the fair value (or replacement value) of
the net assets recorded on the balance sheet. A premium price may exist because of the existence of valuable but unrecorded intangible assets.
Burned-out capital represents the risk of amounts spent during the start-up phase of a venture that may be lost if the venture is not pursued because of low projected risk- adjusted returns. The venture may refer to a recent acquisition or an internally generated project. Burned-out capital is amortized over time as the strategic failure risk decreases. Finally, firms may allocate risk capital to any unused risk limits (e.g., undrawn amounts on a line of credit) because risk capacity could be utilized any time. If risk capacity is utilized, the firm would then have to adjust the risk capital amount.
As mentioned, economic capital is designed to provide a cushion against unexpected losses at a specified confidence level. The confidence level at which economic capital is set can be viewed as the probability that the firm will be able to absorb unexpected losses over
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Topic 48 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 17
a specified period. A simple example can help illustrate the concept of unexpected loss and how it is equal to the risk capital allocation. Assume for a given transaction that the expected loss is 20 basis points (bps) and the worst-case loss is 190 bps at a 95% confidence level over one year. Based on this information, the unexpected loss is 170 bps (excess of worst-case loss over expected loss). There is also still a 5% probability that the actual loss will exceed 190 bps.
Example: RAROC calculation
Assume the following information for a commercial loan portfolio: $1.5 billion principal amount
7% pre-tax expected return on loan portfolio Direct annual operating costs of $ 10 million Loan portfolio is funded by $1.5 billion of retail deposits; interest rate = 5% Expected loss on the portfolio is 0.5% of principal per annum Unexpected loss of 8% of the principal amount, or $120 million of economic capital
required) 25% effective tax rate
Assume no transfer pricing issues Compute the RAROC for this loan portfolio.
required
Risk-free rate on government securities is 1% (based on the economic capital
Answer:
First, calculate the following RAROC components:
Expected revenue = 0.07 x $1.5 billion = $105 million Interest expense = 0.05 x $1.5 billion = $75 million Expected loss = 0.005 x $1.5 billion = $7.5 million Return on economic capital = 0.01 x $120 million = $1.2 million
Then, apply the RAROC equation:
RAROC 0 5 – 1 0 – 7 5 – 7 .5 + 1.2 + O)x (1-0.25) =
120
Therefore, maintenance of the commercial loan portfolio requires an after-tax expected rate of return on equity of at least 8.56%.
Note that for capital budgeting projects, expected revenues and losses should be used in the numerator since the analysis is being performed on an ex ante (or before the fact) basis. In contrast, for performance evaluation purposes on an ex post (or after the fact) basis, realized (or actual) revenues and losses should be used.
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Topic 48 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 17
RAROC for Performance Measurement

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