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1. 01 Calculating IM

# Calculating IM

In most cases IM is re-calculated daily to reflect the changing composition of the portfolio, changing market conditions and daily updates to scenarios.

Common methods of calculating IM include:

• Value at Risk (VaR) using historical simulation
• Value at Risk using Monte Carlo simulation
• Sensitivity mapping, such as used in the ISDA SIMM

### Make a list

Underlying VaR is statistical approach which involves making a list of profits and losses. Your list will be generated from Scenarios. Those scenarios can be History or Random or a mixture of both.

• In the case of History, your list shows the profit or loss your portfolio would have made, if the market conditions at that point in history occurred now.
• In the case of Random scenarios (or Monte Carlo) you truly generate random market conditions of rates, fx and equity prices and re-value your portfolio. Random scenarios are useful to exercise portfolios which contain options.

### Hold That Period

One additional step after generating the scenario profits and losses, is to apply a holding period. The holding period represents the number of days over which you would work to neutralise the risk in a portfolio, or sell it in the market. The possible losses over 10 day holding period could be much larger than those over a one day period.

### Your list is your Distribution

The diagram below shows how the P&L of your portfolio, mapped over all your scenarios, behaves. The chart is the result of revaluing your portfolio using scenarios, and applying a holding period.

• On the left your portfolio could make a very large loss, but this occurs rarely
• In the middle, your portfolio value remains about the same, and this happens frequently
• On the right, your portfolio makes a massive profit, but that also happens rarely

### How to derive IM from a distribution

There are at least three ways to find an IM result from the above distribution

• Take the worst. Use the biggest loss on the left hand side, that becomes your IM. This was the method used by SwapClear for many years. This was seen to be volatile, as the worst loss could vary from day to day.
• Take the loss which occurs around 95% of the time. Not the worst, but nearly. This suffers from the same volatility.
• Take an average of the 10 worst losses - called "Expected Shortfall". This smoothes the IM amount as the 10 worst scenarios can change but the resulting IM may be similar each day.

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