Understanding Undiversified Value at Risk (VaR)

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1. Understanding Undiversified VaR

Let’s talk about Undiversified Value-at-Risk (VaR). Consider a simple portfolio containing two positions: A and B. To calculate the Undiversified VaR for this portfolio, all you need to do is:

  • Calculate the individual or standalone VaR for each position — $ \text{VaR}_A $ and $ \text{VaR}_B $.
  • Simply add these two numbers together:
$$ \text{Undiversified VaR} = \text{VaR}_A + \text{VaR}_B $$

This gives you your Undiversified VaR.

2. How to Interpret Undiversified VaR

The key to interpreting this number is in the name itself: undiversified. This measure does not account for any diversification benefits in your portfolio.

When we say “no diversification,” the first thing that may come to mind is the case of perfect correlation:

$$ \rho = 1 $$

This would mean that all risk factors in the portfolio are perfectly correlated and move in the same direction — either up or down. In such a case, there is no offsetting effect between positions.

3. More Accurate Interpretation

However, to put this more accurately: the calculation of Undiversified VaR does allow for risk factors to potentially move in different directions. But — and this is important — it assumes that each risk factor moves in the direction that is against us.

4. Back to our Illustrative Example

Let’s go back to our two-position portfolio:

  • Position A is a long position.
  • Position B is a short position.

When calculating Undiversified VaR, the calculation assumes:

  • The risk factor underlying the long position A moves down — which is adverse for us.
  • The risk factor underlying the short position B moves up — again, adverse for us.

In other words, it assumes a worst-case scenario where positions do not offset each other at all.

5. Quick Recap

Undiversified VaR can be thought of as:

  • The aggregate or sum total of the standalone risk of each portfolio component.
  • A measure that assumes no diversification across positions.
  • A calculation that produces an upper bound for the true risk of the portfolio.

In practice, the actual risk of the portfolio — after accounting for diversification — will generally be lower than this Undiversified VaR figure.

6. Watch the Video

For a full explanation with an example, watch the video below:

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