P1-T4 Measures of Financial Risk (Dowd) pratice problems

[pd_sn]

27.1. Dowd defines an arithmetic, absolute value at risk (VaR) given by VaR(%) = -drift + volatility*deviate. For a portfolio with current value of $1.0 million, expected return of 15.0% and volatility of 40% per annum, which of the following is nearest to the 99.0% confident 20-day absolute VaR (assume T = 250 days per year)?
a) $88,750
b) $103,500
c) $188,400
d) $251,200




Hi David,
In the solution, to this problem as given below, can you plz explain second term in the equation?
when you calculate volatility for 20 days, shudnt it be 20*40/sqrt(250)?

99% 20-day absolute VaR(%) = -15%*20/250 + 40.0%*SQRT(20/250)*2.33 = 25.1412%
PLz explain it.
--pd_sn

 

[David Harper CFA FRM]

Hi pd_sn,

source is here @ http://forum.bionicturtle.com/threads/p1-t4-27-normal-value-at-risk-var-fundamentals-k-dowd.5652/

given answer is:

99% 20-day absolute VaR(%) = -15%*20/250 + 40.0%*SQRT(20/250)*2.33 = 25.1412%; or, with exact deviate, 25.1196%
99% 20-day absolute VaR($) = 25.1412% * $1,000,000 = $251,412; or, with exact deviate, $251,196

40% per annum volatilty is scaled by * SQRT (20 day horizon we want / 250 day in the per annum)

another way to think of this: variance scales by time, so

• 40%^2 is the per annum variance
• we want to go from the 205 per annum variance to a 20-day variance,
• 20-day variance = 40%^2 * 20/250; i.e., linear multiplier
• the 20-day volatility = SQRT[40%^2 * 20/250] .

I hope that helps,

 

[pd_sn]

Hi David,

Thanks for the crisp explanation. I got it !

-- pd_sn