Interpreting Volatility, VaR, and Portfolio Risk
Summary
The document discusses how to interpret parametric value at risk and standard deviation when assessing an asset or portfolio. Its answer cautions that VaR relies on assumptions and leaves out important dimensions of risk, so it should not serve as a complete measure of risk taking. Standard deviation calculated from returns is expressed in percentage terms; volatility calculated from prices or other quantities needs conversion before it can be read that way.
For evaluating risk and return, the answer recommends considering historical and expected performance, drawdowns and recovery time, correlation with other holdings, and the asset’s contribution to total portfolio risk and risk-adjusted returns. It notes that the Sharpe ratio expresses excess return per unit of return volatility, while acknowledging that the ratio penalizes upside variation. These are qualitative recommendations rather than a worked comparison or empirical demonstration, and the suitability of any measure depends on whether past risk and return reasonably inform future expectations.
Key ideas
- Parametric VaR has assumptions and does not capture every important aspect of risk.
- Standard deviation of returns is measured in percentage terms, while price volatility needs normalization for that interpretation.
- Risk assessment can include drawdowns, recovery time, correlations, and contribution to portfolio risk.
- The Sharpe ratio relates excess return to return volatility but also penalizes upside variation.
- Historical risk and return should be used cautiously when they may not represent future conditions.
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Full text
# How to interpret/use VaR and Standard Deviation? # How to interpret/use VaR and Standard Deviation? The parametric VaR is defined as follows: $$VaR=Z_a*Vol$$ - Is this the best way to interpret how much risk is being taken on for a particular asset? - How does one interpret volatility on its own if its not converted into a percent figure? - Therefore, wouldn't be better if sharp ratios were expressed in VaR's? - I mean, what does it really mean if a Portfolio Manager is gaining 2% return for 1 unit of risk. What does 1 unit of risk mean? - Shouldn't risk only be defined only in percentage terms -- having a hard time wrapping my head around this concept of volatility as a risk measure. - What do you guys think? ## Answer by Matt Wolf (score 3, accepted) https://quant.stackexchange.com/a/4844 VaR is not a good measure of risk taking, in my opinion. It suffers from inherent faulty assumptions (check out VaR Wiki to start) and it omits many other important aspects of risk measurement. When I evaluate an asset's risk and return I like to start looking at the following: - Historical risk and returns of an asset. This leads to the Sharpe Ratio, though I prefer a slightly different ratio which does not penalize for excess performance to the upside (Sharpe Ratio does penalize) - Expected returns and risk. Can I have confidence that historical risk and return figures are a reasonable predictor of future risk and return. If not then, is there a way to make adjustements? If not then I should not take into consideration historical risk and return values when evaluating future expected risk and returns. - Drawdowns of an asset's return. Alongside the drawdown I want to know how long it took for the asset's subsequent returns to make it back to the pre-drawdown return. - Correlation of the asset with other assets. Is the asset uncorrelated or potentially even negatively correlated with other assets? - Contribution of the asset to the portfolio overall. Does the asset contribute to a lower portfolio risk and portfolio risk adjusted returns. Regarding your points: - "How does one interpret volatility on its own": It is a measure of variation around a certain mean, either historically around a historical mean or around expected value. Standard deviation is expressed in percentage terms if it is calculated using returns as input. If you calculate volatility on prices or other metrics then you need to convert to percentage figures. - "What does the 1 unit of risk mean": The one unit of risk you refer to is in percentage terms so Sharpe Ratio expresses the excess return in percent per percent of risk. Its a very clear cut and simple way to comprehend risk, in my opinion.
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