# Basel Market Risk notes

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.