Square Root of Time Rule Problem

[dennis_cmpe]

I'm having problems applying the square root of time rule for this problem. I converted all the portfolios vars to yearly vars, so that I can compare "apples to apples":

Var2 = Var1 * alpha * squareroot(Time2 / Time1)

So for portfolio #1: 10 * 2.33 * squareroot (252/5) = 165.41

I did this for all the portfolios, but I could not get the order in answer A below. Am I applying the square root of time rule correctly here?

104) Rank the following portfolios from least risky to most risky. Assume 252 trading days a year and there are 5 trading days per week:

Portfolio / Var / Holding Period Days / Confidence Interval
1 / 10 / 5 / 99
2 / 10 / 5 / 95
3 / 10 / 10 / 99
4 / 10 / 10 / 95
5 / 10 / 15 / 99
6 / 10 / 15 / 5

a) 5,3,6,1,4,2
b) 3,4,1,2,5,6
c) 5,6,1,2,3,6
d) 2,1,5,6,4,3

ANSWER: A
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[skcd]

1. 2.33 sqrt(5)
2. 1.645sqrt(5)
3. 2.33 sqrt(10)
4. 1.645sqrt(10)
5. 2.33 sqrt(15)
6. 1.645sqrt(15)

so

1. 5.21
2. 3.6783
3. 7.368
4. 5.2
5. 9.024
6. 6.371

Therefore 5 > 3 > 6 > 1 > 4 > 2

Somehow they mean higher VaR is least risky. I m not sure if that is exactly reverse.

 

[David Harper CFA FRM]

skcd,

I copied them over to EditGrid.
Please see: https://www.editgrid.com/bt/admin/var_misc

You #1 above is correct, so i think you are probably fine with your answer. (note on #6, 5% is probably not a confidence, it is a significance)

David

 

[riskydawn]

Try this:

Port 1: [10*sqrt(252/5)]/2.33 = 30.469
Port 2: [10*sqrt(252/5)]/1.645 = 43.156
Port 3: [10*sqrt(252/10)]/2.33 = 21.544
Port 4: [10*sqrt(252/10)]/1.645 = 30.516
Port 5: [10*sqrt(252/15)]/2.33 = 17.591
Port 6: [10*sqrt(252/15)]/1.645 = 24.916


Least risky to most risky = Answer A. 5 - 3 - 6 - 1 - 4 - 2

 

[David Harper CFA FRM]

riskydawn,

thanks, I misread it. I agree with your calcs; i.e., you covert them all to annual dollar stand. deviation.
I fixed the XLS: https://www.editgrid.com/bt/admin/var_misc

David