VaR Daily vs Annual

CFA Level III
#1

There’s an example in Kaplan secret sauce and just wondering what am I doing wrong.

Daily Std Dev = 0.0011 1Day Rtn = 0.00085 Value of Portfolio=100m

So var at 5% significance: VaR(daily) = [0.00085 - 1.65(0.0011)] * 100m = -96,500

I am trying to convert this to Annual VaR now considering 250 days

VaR(annual) = [0.00085*250 - 1.65(0.0011*(sqrt(250)))]* 100m = 18,380,233

Why my VaR is positive?

Thanks in advance for any help.

#2

What is the right answer according Kaplan ?

#3

Paste this in google

0.00085*250-1.65*(0.0011*15.8)*100000000

-2,867,699.78

#4

This is due to MV multiplication at the end. Take that out and var is positive. :confused:

#5

schweser only has daily var calculated.

#6

What?

#7

Google this

0.00085*250-1.65*(0.0011*15.8)

or

[0.00085*250-1.65*(0.0011*15.8)]*100000000

#8

Oh, now I see it.

The Sharpe ratio for annual VAR is 12.07.

Makes sense since the daily VAR is 0.09% of the portfolio, and that scales down when you increase the time period.

#9

So nothing I am doing wrong :slight_smile:

#10

nah, it’s just the figures are a little bit unfortunate here - the daily var was slightly negative but because you multiply returns by 250 and volatilty by only 250^0.5, the outcome happens to be positive

#11

Well . . . .

I ran a Monte Carlo simulation using the data you gave (assuming that the returns are normally distributed), compounding the daily return for 250 days. The results are:

  • Mean annual return = 2.37% (which is consistent with 0.85% compounded for 250 days)
  • Annual standard deviation of returns = 2.15%, which is a lot more than 0.11% × √ 250 (=1.7393%)

That’s probably why they didn’t compute the statistics for the annual return: it isn’t remotely as simple as you’d imagine.

#12

I don’t think compounding mean returns is a good idea.

#13

Maybe not.

But the data aren’t clear on whether that mean return is to be compounded or not.

#14

I mean from a statistical prespective, since this is a single period model, and we’re using standard deviation.