[ 2009 FRM Sample Exam ] Quantitative Analysis Q5

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5. Using a daily RiskMetrics EWMA model with a decay factor λ = 0.95 to develop a forecast of the conditional variance, which weight will be applied to the return that is 4 days old?

A. 0.000

B. 0.043

C. 0.048

D. 0.950

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Correct answer is B

Explanation:

A is incorrect. The wrong factor has been squared. The EWMA RiskMetrics model is defined as h t = λ * h t - 1 + (1 - λ)*r 3  t-1. For t=4, and processing r 0 through the equation three times produces a factor of (1-0.95)^3*0.95 = 0.000 for r 0 when t=4.

B is correct. The EWMA RiskMetrics model is defined as h t = λ * h t - 1 + (1 - λ)*r 3  t-1. For t=4, and processing r 0 through the equation three times produces a factor of (1-0.95)*0.95^3 = 0.043 for r0 when t=4.

C is incorrect. The 0.95 has not been squared. The EWMA RiskMetrics model is defined as h t = λ * h t - 1 + (1 - λ)*r 3  t-1. For t=4, and processing r 0 through the equation three times produces a factor of (1-0.95)*0.95 = 0.048 for r 0 when t=4.

D is incorrect. The weight is not simply λ. The EWMA RiskMetrics model is defined as h t = λ * h t - 1 + (1 - λ)*r 3 t-1. For t=4, and processing r 0 through the equation three times produces a factor of 0.95 = 0.950 for r 0 when t=4.

Reference:  Philippe Jorion, Value at Risk, 2nd ed. (New York: McGraw-Hill, 2001), Chapter 8.

Type of Question: Quantitative Analysis