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Consider a portfolio which consists of single risky asset
Consider a portfolio which consists of single risky asset. The return of the asset is normally distributed with annual mean return 6% annual standard deviation 16%. The value of portfolio today is $70 million. Suppose that the time horizon is one month: a) What is the probability that the end of one month portfolio value is less than $50 million? b) Calculate Value at Risk (VaR) at 95% con- fidence level.c) Calculate Value at Risk (VaR) with 98% confidence level.
Expert Solution
In this
a.) mean return(monthly) µ = Annual mean / n = 6% / 12 = 0.5%
std deviation(monthly) σ =
Annual std deviation / n= 16% / 12= 4.62%
Portfolio monthly return = V1 / V0 - 1 = 50/70 - 1 = -28.57%
P(Return ≤ -28.57%) = P[Z < (Return - µ) / σ] = P[Z < (-28.57% - 0.5%) / 4.62%]
= P Z < -6.2941) = 0
b.) VaR at 95% confidence level = σ x Z for 95% = 4.62% x 1.96 = 9.05%
c.) VaR at 98% confidence level = σ x Z for 98% = 4.62% x 2.326 = 10.74%
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