# 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?

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My god... Just spend a bit of time to format your questions. It looks so much more understandable after what I just did. –  SRKX Dec 26 '12 at 0:03

## 1 Answer

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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Thank you for the response Freddy. My problem with volatility is simple, volatility can either be good or bad. If a stock,eg, breaks out to the upside and on several large range days, isn't that a large deviation from the mean and therefore would raise volatility?? Yet, when I calculate volatility for stocks it only rises when the stock goes down not up -- this behaivor is really pecular. Not to mention, safe haven assets like the dollar (DXY) and the US Treasuries have higher volatility when their rallying!!! So how does one really compare volatility for different assets? –  gabriel Dec 25 '12 at 19:17
"Yet, when I calculate volatility for stocks it only rises when the stock goes down not up" => May I ask what formula for vol. do you use? –  edouard Dec 25 '12 at 20:11
+1. Good answer Freddy, again! –  SRKX Dec 26 '12 at 0:07
Maybe not so peculiar if you consider the skew. If you take implied volatility of out of the money calls on your asset, and subtract the implied volatility on equivalent out of the money puts, and do for each asset, i would hazard a guess that the signs corresponds to the direction of the vol shifts you're seeing. –  Yugmorf Dec 26 '12 at 2:47
@gabriel, I recommend you clearly differentiate between historical vols/standard deviations and implied volatilities, they are a different animal entirely. Implied vols can drop even when markets strongly bounce to the upside (especially after larger sell-offs) because of certain market perceptions whereas historical vols may not drop just because the sign of the underlying price momentum changes. You need to make clear which volatility measures you are talking about. –  Matt Wolf Dec 26 '12 at 3:21