As I mentioned in Understanding Value at Risk (VaR), prerequisite for computing VaR is to have data points. It could be theoretical value or theoretical profit or loss of the portfolio over a certain period. Problem with this historical data is that, it may not have experienced certain scenarios like 2008 crisis. Computing VaR on such data may give a false illusion that we are relatively safe and in turn might lead to maintaining inadequate market risk capital. It is not only in the interest of the financial entity to test such scenarios, it is also a regulatory requirement. This type of scenario testing is also called Stress testing and the resultant VaR is called Scenario VaR or Stressed VaR.

In Scenario VaR, we shift the values to resemble stressed market conditions. You see, the data points we use are not real, they are hypothetical! Like any other blog of mine, this too is going to be quite simplified so that anyone, even without a financial and statistical background, can appreciate what’s being done and why. Let’s begin.

Data setup

We have this famous and highly liquid stock Lax_Stock in our portfolio:

My trading so far in this stock has been going great and here is the theoretical value of my portfolio.

Risk Factor Setup

As mentioned earlier, in scenario VaR we shift the values to resemble stressed market environment. But what should that value be? For that, we must identify the risk factor. When I am holding a stock, what is the risk? It is adverse movement in the stock price, simple! In our case the risk factor is equity price. Let’s have the risk factor setup.

You can see we have added “External Id” as one of the attributes of risk factor. Don’t mistaken to the external id field in the instrument definition properties window. It is the identifier that must match to the identifier in the scenario file. It is either entered manually or can be automated using a hook.

Scenario File

This is where we shift the prices in line with the scenario being modelled. To keep things simple, I have defined only five shifts.

Structure of the scenario file is quite cryptic and overwhelming. Lets understand it better with the help of below graphic.

Star (*) character indicates a comment. These rows are ignored when file is imported, and scenario is created in Prime.
FObject identifier must match with the one in Risk Factor Setup. Based on Risk Factor Type selected, it could either be an instrument, an yield curve, or something else.
Relative and Absolute shifts indicate quantum of change expected in the instrument price. If price of stock is 100, then Shock_1 will result into (TheoPrice * Relative shift) + Absolute shift = (100 * 1.1) + 1 = 111.

Creating a scenario

Lets go back to Trading Manager. Right click on Theoretical Value column and follow below graphic.

Understanding Scenario Editor

Name => A descriptive name that indicates the scenario being tested.
Display Type => It can either be absolute or relative. I will explain this more when we see scenario output in the Trading Manger.
Risk Factor Setup => Name of the risk factor we have setup above.
Attribute and Value => Since we only have one Risk Factor Collection in our setup, we are not required to set this. But lets set it anyway. You will understand this better when we discuss Portfolio scenario VaR.
Scenario File => Path to scenario file.
Keep rest of the parameters as is.

Applying scenario

Once you hit OK, our new scenario should be available in Prime. Select it and click Open.

You should see new columns inserted in the sheet.

Great, we achieved our first milestone. If you have been following till this point, you can break for a coffee.

Observations

Column group name is set to scenario name.
Column names are set to labels in the scenario file.
Shock_1 = ((TheoPrice * Relative shift) + Absolute shift) * Position = ((100 * 1.1) + 1) * 1000 = 111,000
Shock_2 = ((100 * 1.2) + 2) * 100 = 122,000
Likewise for other columns.

Scenario display type “Relative”

For portfolio value, it is easier to think in relative terms than absolute terms. Given Shock_1, it is easier and intuitive to say that this shock will move my portfolio by 11,000 instead of saying it will make it 111,000. So lets set the display type to Relative.

You can see that now each column shows relative change in the portfolio value.

Calculating VaR

First step is to sort change in portfolio value in ascending order.
-27000, -5000, 11000, 22000, 44000

Since we have 5 values, probability of each value = 5/100 = 20%.
Now recall the cricket bowling example we discussed here Understanding Value at Risk (VaR).
What if I ask you, what would be outcome on the left for a 20% probability? By now you should be able to answer this easily. For 20% probability, the outcome is -27000. While calculating VaR our focus is always on the left tail since that is where losses are.

This method of calculating VaR by sorting values in ascending order and taking percentile from left tail is also called historical simulation. It is different from Parametric VaR which is calculated purely based on volatility (standard deviation), correlation and z-table values. We will discuss this in a separate blog.

Let’s verify if our understanding is correct. Go to Trading Manager and add “Scenario Value at Risk” column.

We need to set some more parameters:

You might get confused with confidence level. There is no simple way to define this but in short, when we say 80% confidence level, it means 80% of the time we will either be in profit or make losses less than the value indicated by VaR.

Once you hit OK, you can see VaR column in the sheet.

Hurray! Our calculation of -27000, does match with VaR column value. Second milestone achieved! Time for a beer may be?

Lets see what would be VaR at 90% confidence level.

Strangely, it is still -27000. That is because we just have one value in the 80% to 100% region. In the scenario file, if we had 10 shifts, 90% VaR would have given us 1st value while 80% VaR would have given us 2nd value from left.

Portfolio Scenario VaR

It is very rare, that you would have just one asset class in the portfolio. Usually your portfolio will be comprised of equity, fixed income, fx, commodity etc. You would be more interested to know VaR for each asset class and portfolio total VaR. Risk Factor Setup and scenarios can be easily configured for such needs. I have modified our Risk Factor Setup to include bonds.

When creating scenario in Prime, Attribute and Value can be used to define scope of scenario.

Each of these scenarios would result into a column in Prime giving us appropriate VaR.

Conclusion

We discussed Scenario VaR in a simplified way and with a simple setup. Production grade setup will have portfolios with mix of instruments. Scenarios too can get pretty complex. But I believe this blog will surely help you get started and venture into more complex scenarios.