Basel Market Risk notes

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A brief summary of the Basel Final Market Risk rule that was published in August 2012 and effective January 2013

Capital requirement for market risk determination of the multiplication factor

At each quarter, compare 250 most recent business days of trading losses with corresponding daily VaR-based measure calibrated ot a one-day holding period and at a one-tail 99.0 % confidence level.

Risk-adjusted capital ratio = Total adjusted capital / Risk-based capital ratio denominator

Total adjusted capital = Equity + Near Equity Instruments

Risk-based capital ratio denominator = Adjusted Risk-Weighted Assets + Market Risk Equivalent Assets

VaR-based capital requirement

One-tail 99.0 percent confidence level with a 10 business day holding period and a historical observation of one year. This can be modelled using the following:

  1. Historical VaR. Take this historical empirical distribution of daily data over a period of one year and select the 1%/5% percentile.

  2. Monte-Carlo simulation. Generate a probabilistic distribution using copulas, GARCH, etc. and take the 1%/5% percentile.

  3. Variance-covariance VaR. To calculate the VaR from volatility see the following:

\begin{equation*} \text{VaR}_{0.95,d} \cong -1.65 \times \sigma_{d} \end{equation*}
\begin{equation*} \text{VaR}_{0.99,d} \cong -2.33 \times \sigma_{d} \end{equation*}

To convert a daily volatility to a monthly/annual volatility use the following:

\begin{equation*} \sigma_{x} \cong \sigma_{d} \times \sqrt{T} \end{equation*}
\begin{equation*} \sigma_{m} \cong \sigma_{d} \times \sqrt{20} \end{equation*}
\begin{equation*} \sigma_{y} \cong \sigma_{d} \times \sqrt{250} \end{equation*}

Once you have the monthly/annual volatility use the following to obtain the VaR:

\begin{equation*} \text{VaR}_{0.99,T} \cong -2.33 \times \sigma_{d} \times \sqrt{T} \end{equation*}
\begin{equation*} \text{VaR}_{0.99,10} \cong -2.33 \times \sigma_{d} \times \sqrt{10} \end{equation*}
\begin{equation*} \text{VaR}_{0.95,m} \cong -1.65 \times \sigma_{d} \times \sqrt{20} \end{equation*}
\begin{equation*} \text{VaR}_{0.99,y} \cong -2.33 \times \sigma_{d} \times \sqrt{250} \end{equation*}

Stressed VaR-based capital requirement

In this case, the data used to calculate the VaR measure is selected from a period of significant financial distress appropriate to the bank's current portfolio. This measure is calculaed weekly and is expected to be no less than the VaR-based measure.

Modeling standards for specific risk

One or more internal models are expected to measure the specific risk of portfolios of debt/equity. The internal models need to explain

  • Changes in historical price variation in the portfolio.

  • Be responsive to changes in market conditions.

  • Robust to an adverse environment.

  • Capture all material aspects of specific risk for debt/equity positions.

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