LO 48.4: Explain challenges that arise when using RAROC for performance measurement, including choosing a time horizon, measuring default probability, and choosing a confidence level.
Time Horizon
In computing RAROC, the focus so far has been on one period (i.e., one-year time horizon) since it is convenient from a business planning cycle perspective and it represents the probable amount of time needed for a firm to recover from a significant unexpected loss. At the same time, it is possible to look at multi-period RAROC to obtain a more accurate RAROC measure for longer-term transactions and loans. One issue that arises is how much economic capital to allocate if the risk of a transaction changes dramatically in subsequent periods. For example, using an averaging method would give rise to periods of overcapitalization and periods of undercapitalization.
Risk capital could be thought of as the firms one-year VaR at a specific confidence level (e.g., 95% or 99%). For both credit risk and operational risk, no adjustments are required from one-year VaR to compute risk capital. For market risk, short time horizons such as one day (risk monitoring) or 10 days (regulatory capital) require adjustments to determine the correct one-year risk capital allocation.
One basic approach is the square root of time rule whereby one-year VaR is estimated by multiplying the one-day VaR by the square root of 252 business days in the year. This approach needs to be fine-tuned by considering that even in a worst-case scenario, the firm might only be able to reduce its risk to a core risk level to retain its status as a financially viable business for the rest of the year. Furthermore, the computation must also factor in the time needed to lower the current risk level to the core risk level (i.e., time to reduce). That amount of time corresponds to the relative liquidity (during difficult market conditions) of the firms investment positions taken. As a result, a large amount of time may be required for a reasonable liquidation of the positions.
Example: Risk capital for market risk
Assume the following information where the core risk level is below the current risk level: Daily value at risk (VaR) = 80 Core risk level = 60 Days needed to reduce current risk level to core risk level =10 (i.e., risk reduction of
2 VaR per day)
Number of business days per year = 252 Compute the required risk capital as a percentage of annualized VaR.
2018 Kaplan, Inc.
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Topic 48 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 17
Answer:
Risk capital = square root
sum of squares + core risk level squared x (number of business days per year days needed to reduce current to core) square root = square root
(802 + 782 + 762 + 742 + 722 + 702 + 682 + 662 + 642 + 622) + 602 x(252 10) ^921,940 = 960.18 square root [50,740 + (3,600 x 242)] = = ^921,940 = 960.18
Note that annualized VaR = 80 x square root of 252 = 1,269.96
Therefore, the risk capital required is approximately 75.6% of annualized VaR (960.18/ 1,269.96).
There is a lot of subjectivity in selecting the time horizon for RAROC calculation purposes. A longer time horizon could be selected to account for the full business cycle; it may not always increase the risk capital required since the confidence level required to maintain a firms solvency will fall as the time horizon is increased. A key consideration with the selection of a time horizon is the fact that risk and return data for periods over one year is likely to be of questionable reliability.
Default Probability
A point-in-time (PIT) probability of default could be used to compute short-term expected losses and to price financial instruments with credit risk exposure. A through-the-cycle (TTC) probability of default is more commonly used for computations involving economic capital, profitability, and strategic decisions.
A firms rating is more likely to change when analyzed under the PIT approach versus the TTC approach. As a result, the TTC approach results in a lower volatility of economic capital versus the PIT approach. From time to time, it is advisable to compare the result of PIT versus TTC for RAROC computations at a stable portion of the economic cycle and at the lowest portion of the cycle.
Confidence Level
In computing economic capital, the confidence level chosen must correspond with the firms desired credit rating. A high rating such as AA or AAA would require a confidence level in excess of 99.95%, for example. Choosing a lower confidence level will reduce the amount of risk capital required/allocated and it will impact the risk-adj usted performance measures. The reduction may be dramatic if the firm is primarily exposed to operational, credit, and settlement risks where large losses are rare.
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2018 Kaplan, Inc.
Topic 48 Cross Reference to GARP Assigned Reading – Crouhy, Galai, and Mark, Chapter 17
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