VaR: positive results incorporation

CFA Level III Derivatives
#1

Dear all,

I have been struggling to understand why VaR does not incorporate positive results. I am aware that VaR is a measure of downside potential and hence focused on rather negative results, however since its underlying formula is: exp. return portfolio - z*(stand. dev!), it led me to the conclusion that not only negative results but also positive results among the distrubution are counted, since we take the entire standard deviation and not a downside deviation/semi-variance or something similar.

Here a statement: ‘VaR incompletely measures risk exposure because it does not incorporate positive results into its risk profile’

Thanks for the clarification!

#2

Any clue out there?

#3

VaR only looks at the left side of your distribution (i.e. your loss)

In your formula, positive results would be R+z*stdev - but VaR doesn’t incorporate this as we know in the formula

#4

Back in Level1 Quant Methods, Confidence Intervals, and distributions.

To find probability, we would scale returns based on how many standard deviations from the mean.

i.e. for a 90% CI, with 2.5% tails we would calculate it as:

E® - 1.65(sigma) (left tail, negative) E® + 1.65(sigma) (right tail, positive)

Var, asks us to, given a probability to compute the minimum we could lose over a specified period.

therefore it looks at only the left tail, because everything above that would be above our loss threshold.

So with Var:

E® - 1.65(sigma)

Only measures risk relative to minimum loss, given a probability, over a specified term. It does not incorporate positive results of the profile.

Hope this helps and good luck!

#5

I’ll take a stab at this!

definition of Z-value in wikipedia (yes, ignore the source for these purposes):

“In statistics, the standard score is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores.”

VaR formula subtracts the product of (the positive z-score for the relevant probability %) x (standard deviation)

So by definition we are subtracting the positive portion of the standard deviation and keeping the portion below the mean, that is, the negative return volatility.

#6

thank you! i guess my head was totally fixed to sigma and ignored the signs rest of the formula, my bad. Thank you all and good luck!