Value-at-Risk is both simple and complicated: In principal, it's quite simple, but in detail it's complicated. You want the 95% confidence VaR? Simple: Take the portfolio's expected return distribution and count, from right to left, until you've covered 95% of the area under the curve. That point is the 95% VaR.

The interpretation is simple: 95% of the time, the portfolio shouldn't lose more than that amount. Said differently, 5% of the time, the portfolio should lose more than that amount. And that's what lets us test how accurate the methodology really is. If the portfolio isn't losing more than that amount about 5 days out of every 100, then something's wrong. This is called back-testing, and it's very important if you want to know whether your VaR number is accurate.

But the details matter, and because there are so many ways to determine the expected return distribution, IA uses several models to calculate VaR. It's also important to keep in mind that no single model is best and that no single model will ever capture everything that's going on in the market. It is always a good idea to question the results and test the assumptions.

IA's approach to parametric VaR is to take advantage of the flexibility of the model so that each client can specify how to treat their investments. While others choose to proxy "similar" securities with indices (such as modeling any US stock as "the S&P 500"), IA models each security separately, but can substitute any other security or index in its place.

Specifically, three things are needed for each investment/security: an exposure, a volatility and the set of correlations to all other investments/securities. Exposure is simply the total amount of money controlled by the investment subject to the volatility. IA usually uses the security's own price history to determine the relevant volatility but we can use any security's price history. For example, illiquid instruments may be proxied with a relevant index. An option will use the price history of the underlying security (and we'll adjust the exposure to be the delta-equivalent exposure). That same price history is also used to determine the correlations with all the other securities. Volatilities and correlations are usually exponentially weighted but do not have to be.

Because of IA's proprietary implementation of these concepts, we also calculate all the correlations and betas between any groupings of securities in your portfolio and a list of indices. This lets you see how one set of investments relates to other investments and to the market.



A simplification of the parametric VaR approach is to take the actual returns of the securities in the portfolio and "build up" a hypothetical portfolio return distribution that would have resulted had those investments been in place for some amount of time. The VaR from the resulting distribution can be read off by simply determining the point that is to the left of 95% of the distribution. This approach does not involve volatility or correlation calculations (they are folded into the return histories), so these analytics are not available. However it does provide a good comparison to the parametric VaR, and it also allows for the calculation of a portfolio's skewness and kurtosis.


There are many ways to calculate a security's or sub-portfolio's contribution to a portfolio's overall risk. IA uses two complimentary methods: "simple-removal" and "sigma-loss."

Simple-Removal: This model bases a security's contribution to risk on how the risk of the portfolio's VaR changes by removing that security. The difference in the two VaRs is attributed to that security. The same thing can be applied to any group of securities: remove the group and re-calculate VaR to measure its contribution. This model, since it completely removes a security from the portfolio, does not include the effects of that security's correlation with the portfolio.

Sigma-Loss: This model fully takes into account the correlation of the security when determining its marginal risk. The correlation matrix tells us how each security moves with respect to every other security, so that we can calculate the expected return of every security in the portfolio for a given market shock. The shock we apply is to take a security in the portfolio and assume it suffers a 1 standard deviation loss. Using the correlations, we estimate the returns of all the other securities in the portfolio to calculate the expected portfolio value. The difference in value before and after the shock is attributed to the shocked instrument.


Each client views the market differently, and each client has a set of benchmarks or indices that are relevant to them. IA compiles these indices into lists that we call Market Models. We then provide comparisons, sensitivities, and we calculate the betas of the securities in your portfolio to the indices in your Market Models. By treating the indices in your Market Model as risk factors and using the betas as investment weights into those factors, we are able to calculate your portfolio's VaR. Factor VaR provides yet another comparison to parametric VaR.

Factor VaR also allows us to determine the risk of a Fund-of-Funds that does not have complete transparency from all underlying managers. By determining the betas of the non-transparent funds to the components of the Market Model (by regressing monthly returns for instance), we are able to model the non-transparent manager as a synthetic basket made of different amounts of each of the indices in the Market Model. This way, even non-transparent managers can be included in the same VaR calculation as fully transparent managers.