Risk Management is, at last, getting our industry’s full attention. I hope that we can move forward and engage in constructive dialogue with our regulators and remain compliant. Risk Management encompasses several areas of the derivatives value chain. We’ll cover each area in turn: Price Risk, Operational Risk, etc.
Market Risk is calculated using Value-At-Risk or VAR. VAR calculates a probability statement such as: “I’m x% confident we won’t lose more than V dollars over the next N days”. It allows institutions to have a single number to define their market risk given the parameters used. Regulators require banks to report a 99% confidence level over the next 10 days. BIS requires the banks to have three times their 10 day VaR in capital.
Bank Trading desks use the 99% & 95% VAR number for 1 day (tomorrow).
Hedge Funds use a one day 95% confidence figure.
So bank traders want to know how the other side of their trade might respond if the market moves big the next day. Although most money center banks now use Monte Carlo simulation, not a normal distribution. But using volatility (the square root of variance which presumes the % returns are normally distributed) is easier to conceptualize.
There are three accepted methods of calculating VaR: For the sake of brevity, we will only discuss variance-co-variance in detail.
The historical simulation uses the ACTUAL returns of the assets in which the bank has open positions. They typically use the previous 200–500 days of actual price changes. EXAMPLE: using the last 200 days and calculating the daily returns they give you the actual 180th worst loss (given the Bank’s current position). Whatever loss is the 180th worst loss, while be reports as their VaR. The 180^{th} worst loss out of 200 changes gives you the 90% confidence, one day VaR (180/200 = 90%)
The easiest way to view Monte Carlo Simulation begins with thinking of it as similar to Historical Simulation. Except, Historical Simulation implies the actual 180^{th} worst loss in the past 200 days can re-occur on the exact same date over the next time frame (10 days or 1 day). Monte Carlo uses a random number generator and uses 10,000 “trials” (you can view this as daily changes) to estimate the price return of the asset at the end of the analysis horizon (10 or 1 day).
The variance-co-variance method uses the historical volatility of the asset over the past X number of days (typically 200 – 500 days).
Perhaps you recall the bell-shaped curve. If not, let’s run through it quickly now: Normal distribution presumes the mean of the data series is zero. The resulting volatility number you hear in the market (i.e. , VIX) is the annual volatility. We can use the annual volatility to make probability statements which are described as standard deviations from the mean:
If you look at the N= file attached here, you’ll see a 99% confidence interval on a normally distributed as is ~ 2.33 standard deviations.
We can adjust the annual volatility to a shorter time frame by adjusting the annual figure by the square root of time. Let’s calculate the daily VaR, using the following example:
EXAMPLE: | long a single asset valued at 100 million. |
<200 day historical volatility is 25%. | |
For 10-day volatility we need to adjust our annual number by the SQRT of 365/10 as there are 365 CALENDAR days in a year. PLEASE NOTE: WE ARE NOW USING CALENDAR DAYS. | |
10-day Volatility = SQRT () = 6.0415 | |
10 day Vol = .25 / 6.0415=4.303% PER 10 calendar day period. | |
We now need to adjust our daily volatility figure to reflect 2.33 stdev’s | |
4.303% * 2.33 = 9.97% | |
$100 million * .0997 = 10- day 99% var of $9,997,000 | |
“I’m 99% confident we won’t lose more than $9.997 million on this position over the next 10 calendar days. ” |
It may be obvious that VaR focuses on the likely losses, but says little about the black swans. For a while, we performed backtesting and stress testing to ensure our VaR variables were correct. But notice, even if the volatility estimate was correct, the furthest I could go is “I’m 1% confident I’ll lose more than VaR tomorrow”. It could not tell me the size of that tail risk. For this reason, VaR has been challenged and looking to be replaced by Potential Exposure. This and other Trading Desk related risk measurements will come under the umbrella of Fundamental Review of the Trading Book (FRTB).