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I believe this question is best asked here, as it pertains to risk, rather than English SE.

What is the meaning of conservative in the context of risk management? In general, conservative would mean small or comparatively small, but coming across the term in different industry papers, I get the feeling it is the opposite.

For example, if one applies a conservative haircut to a counterparty's collateral, is this a small haircut?

Another example, this from the Fed's paper on capital planning at bank holing companies:

The federal Reserve expects BHCs to apply generally conservative assumptions throughout the stress testing process.

In this context, I can't figure they are suggesting to make stressed variables small.

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If your looking for a conservative investment it would be a low standard deviation of returns i.e. a bond, fixed income asset, or low beta equity. From the context of equities, the beta is just the standard deviation of an equity divided by the standard deviation of the SP500, so a beta of say 0.8 along with a low standard deviation of returns would be more conservative. a beta of say 1.5 and a high standard deviation of returns would be less conservative. Typically, although not always, lower beta assets mean less returns, where as higher beta assets mean greater returns. A lower standard deviation of returns, means a more predictable asset and thus an asset averaging 3% return a month and 4% standard deviation of returns is less conservative than 0.5% returns a month, and 0.4% standard deviation of returns.

With regards to a haircut, a conservative haircut would be fairly large portion of the notional value of the client's portfolio.

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Conservatism depends on your frame of reference.

To address your question specifically, conservatism refers to the concept of a quantity being marginally higher (or lower) with respect to a relative quantity. I realize this is quite general, but the definition itself is general and depends on what you're describing. Stating a quantity is conservative does not give you a indication of whether it is 'comparatively small', it does not tell you anything about the magnitude of the conservatism. It only indicates direction.

For example, if one applies a conservative haircut to a counterparty's collateral, is this a small haircut?

A conservatism haircut in this case means that you (not the counterparty) will reduce the collateral you post. So if the collateral is assessed at 100, you may use an estimate of 90. You may also use 50. Both are conservative estimates. In terms of best practices, you should apply a haircut that is commensurate to the risks/uncertainties. This is the standard practice. What is riskier: cash or commodity? The common practice is to apply a higher haircut for the commodity. In fact, there are guidelines on how much of a haircut to apply to different product types (see Basel II) if you want to see the relationship yourself.

As for the Fed stress testing, conservative assumptions are exactly as they sound. Don't understate your losses, defaults, exposures, risks...and don't overstate the market factors or economic scenarios relevant to your portfolio.

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