Following on from the "Beat the Experts" thread, John Philpott posed some excellent questions on the differences between the Value at Risk (VaR) and Standard Portfolio Analysis of Risk (SPAN) market-risk measurement methods.

His questions are highly on-topic, especially given the central-clearing mandate set to go into effect for Tier 2 firms on 10 June, 2013. The impact on such firms will include a significant drag on returns for their portfolios, if they are engaged in hedging strategies using cleared derivatives.

One of the significant causes of the drag, other than fees, is the initial margin (IM) required to be deposited upon trade execution to the Futures Commission Merchant (FCM), Clearing Broker and through to a clearing house. The IM needs to be maintained throughout the life cycle of the derivative trade. It is therefore essential to be aware of the difference between the IM calculation methods, which are usually either VaR based or SPAN based.

The brief Q&A below contains some of John's questions, but it also covers VaR and SPAN questions posed at a higher level. Obviously there's enough to explain about VaR and SPAN to cover an entire textbook, but for brevity I've chosen the select few questions below. If anyone wishes for me to delve deeper into the topics discussed (such as the different types of VaR, the various ways of measuring "shifts", more detail about how exchanges determine SPAN scanning ranges, etc.)  i'd be happy to follow this up with a sequel to this post.

Q: On a high level, how are SPAN and VaR calculated?

A: SPAN uses 16 scenarios in which a risk factor (e.g. today's price, today's volatility), or combination of risk factors, are shifted by an amount determined by the clearing house. The portfolio market value (MV) is recalculated under the 16 different market shifts, and the differences between these and the original portfolio MV are calculated. The largest of these 16 differences, representing the most severe loss in market value, is used to set the SPAN requirement for the portfolio margin.

VaR (or, to be more specific, historical VaR) can use any number of scenarios, typically 1,250 or 2,500 scenarios. Today's risk factors (e.g. interest rate yields) are shifted by an amount determined by how they've moved historically. The MV of the portfolio is recalculated under all 1,250/2,500 shifted scenarios, and the differences these and the original Portfolio MV are calculated. These differences are then ranked in order (from largest +ve MV difference to the largest -ve MV difference), and the VaR requirement for the portfolio margin is determined by where the clearing house wants to cut off this distribution of losses. For example, if the clearing house uses a 99% VaR model, then the VaR requirement is the portfolio MV difference value that 99% of the scenarios fall above (and 1% of the scenarios fall below). This percentage cutoff is called the "confidence level".

Q: How are the sizes of those "risk-factor shifts" determined?

A. For SPAN, the clearing houses tend to choose 14 shifts that represent reasonable moves in the risk factors (such as price and volatility), and 2 shifts that represent "extreme" moves in the risk factors. For VaR, as mentioned in the previous answer, the shifts tend to be historically determined.

However, the clearing house needs to decide how many days' movement in the markets a risk-factor shift represents. For SPAN, the risk-factor shifts are typically presumed to occur under a 1-day or 2-day "time horizon" (i.e. the size of the shift represents two days' worth of movement in that particular risk factor). For VaR, the time horizons depend on the relationship between the client and the clearing house, as well as the financial product under consideration. For example, IR swaps cleared directly through LCH.Clearnet SwapClear use a 5-day time horizon for IM calculation [for Members], but IR swaps cleared through LCH via an FCM use a 7-day time horizon [for Clients].

Q: You've just called LCH.Clearnet SwapClear's methodology "VaR", but on their website they call it "PAIRS"… why did you do that?

A: Because VaR may be (and often is) used colloquially to describe any "VaR-like" methodology, even if there are slight variations and enhancements to it. The LCH Portfolio Approach to Interest Rate Scenarios (PAIRS) is very similar to VaR; the main differences are:

• (i) Instead of taking the MV difference that represents the percentile-cutoff value of the distribution as the margin requirement (i.e. the VaR), they instead take a mean-average of all the MV-difference values that fall below the percentile-cutoff value. This is called an Expected Shortfall (ES) measure.
• (ii) They filter the historical returns to give more weight to recent historical movements, instead of using raw historical-returns.

Q: Why is SPAN a suitable risk-measure for exchange traded derivatives (e.g. equity/commodity options), but not a suitable risk measure for customisable OTC derivatives (e..g IR swaps)?

A: This is due to the properties of the exchange-traded instruments vs. the OTC derivatives. Exchange-traded options tend to have fixed properties (e.g. expiry, strike) so that the risk-factor shifts for SPAN (e.g. price, volatility) can be applied easily to the exchange-traded contracts, and contracts in the portfolio can be easily netted together. In addition, the risk-factors tend to be constant in time (as each exchange-traded option has a fixed maturity) so one doesn't have to be concerned with the term structure of risk factors.

For OTC derivatives (such as IR swaps) the maturity dates are flexible, so the risk factors possess a term structure dependence. SPAN therefore isn't suitable  because its shifts tend to be simple and constant in time (e.g. "shift the implied volatility by +10%"). If a similar logic were applied to an entire yield curve (e.g. "shift the yield curve up by 10 basis points"), then this would contain an embedded assumption as to how instruments in the yield curve tend to move together (i.e. a correlation assumption- in this case the correlation between all the yield curve instruments is 100%). Such parallel shifts aren't realistic, as the correlation assumption of 100% doesn't reflect how yield curves move in reality. Therefore, in order to reflect realistic yield curve movements in the scenario shifts, historical VaR is used, as the historical data set already has the correlation information embedded within it.

Q: How do the differences between the SPAN and VaR measures impact the margin calculations? Is the VaR requirement larger than the SPAN requirement?

A: Apart from the different time-horizons, the major difference lies in the relatively static nature of SPAN parameters vs. the relatively dynamic nature of historical VaR parameters.

SPAN parameters don't tend to change frequently, so the 16 shifts are constant until the parameters of the model are updated. Historical VaR, however, tends to have a look back period of 5y (in the case of 1,250 scenarios) from today's date. This means that every business day, the oldest historical simulation will "roll off" and the newest historical simulation (using yesterday's market values) will "roll on".

The upshot here is that, unless the historical simulations are filtered or smoothed, the daily difference between historical VaR calculations will be volatile if the oldest scenarios took place during times of significant market distress. So therefore, depending on the historical market conditions in the market-cycle, the IM requirements calculated by VaR can be greater than those calculated by SPAN. If, however, no significant periods of financial distress are included in the look back window for historical VaR, then the IM requirements calculated by VaR can be smaller than those calculated by SPAN.

So there is no definitive answer as to which historical VaR or SPAN will result in the greatest margin requirements- this depends on the prevailing historical market conditions at the time when the risk-measures are calculated.

Ben Larah, Sapient Global Markets.