To find the appropriate zcritical value for the VAR(1%), use the two-tailed value from the table correspondnig to an alpha level of 2%. Under a two-tailed test, half the alpha probability lies in the left tail and half in the right tail. Thus the zcritical 2.32 is appropriate for VAR(1%). For VAR(10%), the table gives the one-tail zcritical value of 1.28. Calculate the percent and dollar VAR measures as follows:
VAR(1%) |
= z1% × σ |
|
= 2.32 × 0.014 |
|
= 0.03248 ≈ 3.25% |
|
|
VAR(10%) |
= z10% × σ × portfolio value |
|
= 1.28 × 0.014 × $243 million |
|
= $4.35 million |
Thus, Statement I is correct and Statement II is incorrect. For Statement III, recall that as the probability in the lower tail decreases (i.e., from 10% to 6%), the VAR measure increases. Thus, Statement III is correct.