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06-Stat Rule 2_VAR_Margin

# 06-Stat Rule 2_VAR_Margin - Value at Risk Standard...

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Value at Risk

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Standard Deviation What does standard deviation tell us that variance doesn’t? Discrete Random Variable Not much Continuous normal PDF Helps us directly answer the following questions: How likely do I get wiped out? Is there some chance I smack a home run? What outcomes are most likely to happen?
Normal Distribution Assume the PDF for your investment return is a normal distribution. If we know E[r] and σ [r] we can integrate under the normal curve over any region using Excel! That is we can find the probability the return will fall within any given range.

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Is the normal PDF right? What PDF generates returns? Is the normal PDF a decent guess?
How Good is the Normal Assumption? Ann Taylor This is a histogram of returns. The x -axis represents possible outcomes for the return. We divide the x -axis into “bins” or “intervals” and count the number of returns that fall into each interval. The y- axis tells us how many days had a return within the corresponding interval.

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Normal Distribution Assume the PDF for your investment return is a normal distribution with E[r]=10% and σ [r]=0.15 P(r<-20%) = normdist(-0.20,0.10,0.15,1)=2.275% P(r>30%)=1-normdist(0.30,0.10,0.15,1)=9.12% P(-20%<r<30)= normdist(0.30,0.10,0.15,1)-normdist(-0.20,0.10,0.15,1 ) =88.60%
Normal Distribution

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5% Value-at-Risk (VAR) Find the losses you expect to incur with 5% probability. Example:
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06-Stat Rule 2_VAR_Margin - Value at Risk Standard...

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