VAR for Muth Portfolio Reading #26 pg 203 #23

Whats up with this problem? The answer in the curriculum goes through an iteration of Var as:

-Var = portfolio return - 1.65(standard deviation)

this isnt how it is explained in the book and corresponding BBs and EOCs except for this problem. can someone explain this?

shouldnt an increase in E® increase the VAR dollar amount?

shouldnt an increase in correlation increase the standard deviation leading to a lower VAR dollar amount?

thoroughly confused here…

VAR = Return - 1.65 * Std Dev

And VAR is a negative number - remember

So originally - consider a number R=10%, Std Dev = 10% -> VAR = -6.5%

Now if E® increases to 12% -> 12 - 16.5 = -4.5% - so VAR decreased.


If Variance increases - VAR will move the other way - in that it will INCREASE.

Does this help?

yeah that makes much more sense now…appreciate the help! thanks!

in schweser they say that VAR can sometimes actually be a positive number. so in that case would it be the opposite is true?

never heard of VAR being a positive number. It is usually used in reference to losses – so it would be negative.

Maybe credit var - from the buyer of credit’s perspective could be positive … but am not sure about this.

VAR can be positive if the E® is positively large and SD is small —> ending up with a potive VAR…though I don’t know if there is such an asset in real life.

^Risk free asset?

VAR assumes E®=0 or capped at Rf. This means the E® part is smaller than k*SD, as many said above VAR looks at the negative side.

My way of cracking this: as VAR=value at risk,

* higher potential return --> less loss potential => less VAR

* higher SD (ie higher risk) => higher VAR

* higher probability (more confident to estimate lower loss than bigger loss) --> lower VAR