Following the introduction of the new market risk capital requirements recommended by the Basle Committee, this article will address some concerns raised about the methods of calculating the capital charges.
The general market risk capital requirement is based on value at risk estimates calibrated to a 10-day, 99th percentile standard--if the 10-day, 99th percentile VaR estimate is equal to USD100, the bank would expect to lose more than USD100 on only one out of 100 10-day periods. The common supervisory standard is imposed to ensure the capital charge entails a consistent prudential level across banks. VaR estimates must be calculated on a daily basis using a minimum historical observation period of one year, or the equivalent if weighted over time. The capital charge for general market risk is equal to the average VaR estimate over the previous 60 trading days (approximately one quarter of the trading year) multiplied by a "scaling factor," which is generally equal to three.
Several aspects of this calculation have generated considerable discussion;
* The 10-day holding period. The period has been criticized as overly conservative, since under normal market conditions many positions in a bank's trading portfolio could be liquidated in less time than this.
This requirement reflects the need to address the risks posed by options and other positions with nonlinear price characteristics. Because options' sensitivities to changes in market risk factors can grow at a rate disproportionate to the size of changes in the risk factors, a longer holding period can reveal risk exposures that might not be evident with the smaller risk factor movements associated with shorter holding periods. The 10-day holding period stems from the view VaR estimates used in the capital calculation should incorporate the impact of instantaneous 10-day-sized price moves in the market risk factors. In the language of options, the 10-day holding period serves to calibrate the coverage of gamma risk.
* The minimum historical observation period. Critics characterize the year-long minimum as intrusive and argue that longer observation periods have not been shown to result in more accurate VaR estimates.
The minimum historical observation period requirement primarily reflects concerns about the variability of the capital requirement across institutions, rather than a judgment by supervisors about the historical observation period likely to produce the most accurate VaR estimates for capital or risk management purposes.
The basic idea is that banks with similar risk exposures should face similar capital charges. Evidence suggests shorter observation periods tend to generate VaR estimates that are more volatile over time. For a set of banks with similar risk exposures, this implies that dispersion of VaR estimates across banks will tend to be greater when some banks are using short observation periods. The minimum one-year historical observation period is an attempt to limit this disparity.
* The scaling factor. Critics argue the scaling factor is an ad hoc supervisory adjustment that undercuts the benefits of basing a capital charge on internal models. In this view, the key advantage of using internal risk measurement models is they provide more accurate measures of an individual bank's risk exposure than do broad supervisory measures. Accordingly, some have argued a bank that can demonstrate convincingly its model is accurate should be subject to a scaling factor of one.
It is important to recognize the overall purpose of the scaling factor is to produce the desired degree of coverage for the market risk capital charge. The market risk capital requirements are intended to ensure that banks hold sufficient capital to withstand the consequences of prolonged and/or severe adverse movements in the market rates and prices affecting the value of their trading portfolios. The key assumption behind the internal models approach is that a VaR estimate calibrated to a 10-day, 99th percentile standard is well-correlated with the degree of such risk inherent in the portfolio, and thus a reasonable base for a minimum capital standard.
Nonetheless, by itself, even a perfectly measured 10-day, 99th percentile VaR figure may not provide a sufficient degree of risk coverage to serve as a prudent capital standard. For one, such a standard implies that a bank is expected to have trading portfolio losses that exceed its required capital in one 10-day period out of a hundred, or about once every four years. An environment in which banks depleted their market risk capital so frequently could be highly unstable, particularly if such events happened to many banks at the same time (which could occur if banks adopted similar trading strategies). Further, VaR estimates based only on recent historical market data may not incorporate the possibility of severe market events. Thus a capital standard based on unadjusted VaR estimates might not provide sufficient capital for a bank to withstand the effects of market breaks or unanticipated regime shifts.
The role of the scaling factor is to translate VaR estimates into an appropriate minimum capital requirement, reflecting considerations about the accuracy of a bank's VaR model and prudent capital coverage. The capital cushion should cover possible losses because of market risk over a reasonable capital planning horizon--which is generally seen to reflect a period between one quarter and one year--while at the same time reflecting that banks' trading positions change rapidly over time. As an alternative to the scaling factor, supervisors could have based the capital charge on VaR estimates calibrated to a very stringent prudential standard (for example, a one-year holding period or a 99.999th percentile standard). In practice, however, it is difficult to derive reliable and verifiable VaR estimates for such extreme parameter values. Actual observations of such "tail events" are few, greatly complicating the task of verifying that any model is accurately measuring the probability of these occurrences. Instead of representing a more "scientific" alternative to the scaling factor, a requirement of this kind would simply introduce a false sense of precision into the capital standards.
By contrast, the scaling factor is simple and easy to implement. It does not require banks to make (or supervisors to evaluate) complex calculations intended to model rare or as-yet unobserved events, such as regime shifts or market breaks. At the same time it does seek to provide a capital cushion against such incidents. In addition, it is similar to the techniques used by some banks for internal capital allocation, in which one-day VaR estimates are extrapolated to a much longer holding period (for example, six months or one year) by multiplying by the square root of time (in the case of 10-day value-at-risk estimates, this calculation for a one-year holding period implies a multiplication factor of five). Moreover, comparisons of 10-day, 99th percentile VaR estimates with banks' actual daily trading results suggest the scaling factor of three provides an adequate level of capital coverage. The results of bank stress-testing programs were also a key input in the decision to use a scaling factor of three.
This week's Learning Curve was written by Darryll Hendricks and Beverley Hirtle of the Federal Reserve Bank of New York. It was adapted from "Bank Capital Requirements for Market Risk: The Internal Models Approach," published in the December issue of the New York Fed's Economic Policy Review.
