Impact on VAR of expected return and standard deviation.

I got this wrong in EOC and I’d like to understand

R 26 , EOC 23.

  1. an increase in the expected return on Asia-Pacific equities and 2) an increase in the correlation between Asia-Pacific equities and European equities. Kreuzer comments: “ Considered independently, and assuming that other variables are held constant, each of these changes in capital market expectations will increase the monthly VAR estimate for the Muth portfolio.”

Can someone explain what is the impact?

  1. reduce

  2. increase

Rp - z * standard deviation

Increase in expected return results in in smaller VAR (on absolute value term)

increase in correlation means increase in standard deviation and results in larger VAR (on absolute term)

Analytical $VaR = (expected return - Z x sigma) x portfolio or asset value

If expected return increases --> $VaR decreases

If correlation of assets increase --> sigma increases --> $VaR increases

its counter intituitive from equation.

if expected return increase, shouldn’t the calculated value of VAR increase?

Am I interpreting it wrong?

lets take an example

portfolio value 10

expected return = 15%

std dev = 8%

5% VAR = (0.15 - 1.65 * 0.08) * 10 = 0.18

if expected return increases to 20%

5% VAR = (0.2 - 1.65 * 0.08) * 10 = 0.68

the VAR increased with expected return.

plug in some random numbers for better understanding. We’re looking at absolute values here.

return 8%, z 1.65 and standard dev 14% and portfolio of 1MM. Var is 150k loss

change return to 10% and var becomes 130k

8% - 1.65 * 14% = -15.1%

10% - 1.65 * 14% = -13.1%

Expected return: 10%, alpha: 5%, sigma: 20%, portfolio value: 5 million

–> (10%-1.65x20%)x5,000,000 = -1,150,000


Expected return: 0% , alpha: 5%, sigma: 20%, portfolio value: 5 million

–> ( 0% -1.65x20%)x5,000,000 = -1,650,000

The equation in brackets results in a MINUS number. Think about it :slight_smile:

I don’t think this is valid example since your VAR is positive which rarely happens. in your example, it’s a 18% gain vs 68% gain which is still reduction in VAR. not to mention I can’t remember the last time I’ve seen return > standard deviation besides from risk-free

Got it… your example below makes sense now… somehow I was thinking positive VAR % hence I got confused.

got it… thanks!

^ the problem with this scenario is how narrow the dispersion is. This is an unrealistic example of very high returns (15%), with very low risk (8%). These are better than Madoff’s numbers.

Going back to the OP. I think by “increased returns” they’re indirectly referring to increased risks.Hence , increased VAR.

the correlation part is obvious.

I would get such a question wrong. 20 of these indirectly direct questions and you’ll see me back here next year.