This is from one of the solutions at the EOC problems… The solution says: "The increase in expected return would result in a lower calculated VAR (smaller losses). An increase in the correlation would increase the portfolio S.D, which would result in a higher calculated VAR (larger losses). I don’t get this. Assuming 5% VAR: VAR = Expected Return - 1.65(S.D.) If expected return increase, and everything else remains constant, wouldn’t this increase the VAR? And vice versa for increase in the portfolio S.D.? Am I missing something here? The problem is from Book 5, pg.263, no.23 Thanks
i think it’s because it’s a loss, and you should consider it as if it were a negative value… an increase in return would lower the negative value. i got this crap wrong too.
sparty419 Wrote: ------------------------------------------------------- > This is from one of the solutions at the EOC > problems… > > The solution says: "The increase in expected > return would result in a lower calculated VAR > (smaller losses). An increase in the correlation > would increase the portfolio S.D, which would > result in a higher calculated VAR (larger losses). > > > I don’t get this. Assuming 5% VAR: > > VAR = Expected Return - 1.65(S.D.) This formula is just saying how far away from the mean (expected rtn) you are going on the downside. So if everything else stays the same, but you mean is higher your VAR will be lower. > > If expected return increase, and everything else > remains constant, wouldn’t this increase the VAR? > And vice versa for increase in the portfolio S.D.? > Am I missing something here? You are only measuring left tail risk here. As an extreme example: Expected return is 10%, Portfolio $1,000,000 VAR = .10 - 1.65 (.20) * 1,000,000 = -230,000 *this would be a minimum loss of 230k* Now say Expected rtn is 50% VAR = .50 - 1.65 (.20) * $1,000,000 = $170,000 *this would be a min GAIN of 170k* > > The problem is from Book 5, pg.263, no.23 > > Thanks
sparty419 Wrote: ------------------------------------------------------- > This is from one of the solutions at the EOC > problems… > > The solution says: "The increase in expected > return would result in a lower calculated VAR > (smaller losses). An increase in the correlation > would increase the portfolio S.D, which would > result in a higher calculated VAR (larger losses). > > > I don’t get this. Assuming 5% VAR: > > VAR = Expected Return - 1.65(S.D.) > > If expected return increase, and everything else > remains constant, wouldn’t this increase the VAR? > And vice versa for increase in the portfolio S.D.? > Am I missing something here? > > The problem is from Book 5, pg.263, no.23 > > Thanks Consider this example: E® = 10% SD = 20% VAR(5%) = 0.10 - (1.65*0.20) = -0.23 Now, assume that E® increased from 10% to 15%: VAR(5%) = 0.15 - (1.65*0.20) = -0.18 Thus, we can conclude that the increase in expected return would result in a lower calculated VAR (smaller losses). However, when the SD increases, VAR also increases. Try it out numerically with this example. Cheers!!
Whoa…that is weird riskyrider…our made up examples are almost the same. We are being brainwashed by the CFAI.
Thanks a lot guys…makes sense now…I jst have one more question…especially with what mwvt9 has done…might be stupid…but here goes nothing: In your calculations, you’ve multiplied the portfolio value along with the S.D. in the calculation for VAR, but in other solutions and in what risky rider did, they usually haven’t done this. They end up calculating VAR and then multiply the result with the portfolio. I just did a quick calculation, and I guess they lead to the same answer…but what is the reason behind this discrepancy in the formula?
If you mean that I forgot my brackets then follow riskyriders example. I calculated it the same way he did and then took the number multiplied by the portfolio value. By definition Value At Risk has to be a dollar number (to determine the value). Or any other currency. Mine should have read: Expected return is 10%, Portfolio $1,000,000 VAR = .10 - (1.65*.20) * 1,000,000 = -230,000 *this would be a minimum loss of 230k* Now say Expected rtn is 50% VAR = .50 - (1.65*.20) * $1,000,000 = $170,000 *this would be a min GAIN of 170k*
gotcha…