Question

Investment A

Common stock: General Motors

Position value: $500,000

Average daily log return %: 0%

σ (SD) of daily log return %: 0.88%

Confidence Interval: 95%

Time period: 10 days

10 days VaR%: 4.47%

Investment B

Common stock: Exxon Mobil

Position value: $10,000,000

Average daily return %: -0.06%

σ (SD) of daily return %: 1.61%

Confidence Interval: 99%

Time period: 5 days

5 days VaR%: 8.28%

Which of the two VaR numbers is the higher % of the position value? Explain why.

Note: The returns used in the example are log-returns.

Answer 1

For comparing the VaR limit, we have to bring both the VaR limits in same parameters. We have equalize the confidence interval and time period for both
Lets equalize VaR by converting both of the numbers to 99% confidence interval and 5 days period

bringing 95% confidence level to 99% for GM
VaR is a function of std dev
VaR= z level for confidence level * stddev

Confidence	# of Standard Deviations (σ)
95% (high)	- 1.65 x σ
99% (really high)	- 2.33 x σ

Hence, converting 95% to 99% confidence-
99VaR= 95VaR/-1.65*-2.33
6.312%

bringing 10 days VaR to 5 days VaR for Gm
VaR is a function of squareroot of no of days
converting 10 days VaR to 5 days VaR
10VaR=5VaR *(5/10)^(0.5)
4.463%

Now we have both VaR values for equal parameters i.e. 5 days and 99% confidence level

VaR(GM)=	4.463%
VaR(Exxon)=	8.280%

Both these numbers are as a % of total position value. As it can be seen- VaR for Exxon Mobil is higher than that for General Motors