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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.
1.(30 pts) 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.
Given: Standard deviation - 16% (i.e 1.33% per month)
Rate of deviation that $70 million becoming $50Million = 28.57% (i.e 2.38% per month)
Mean(r) - 6% per annum (i.e 0.5% per month)
Value of portfolio - $70Million
Probability (p) = (r-d)/(u-d)
= (1.005 - 0.9867)/(1.0133-0.9867)
= 0.0183/0.0266
=0.69
1-p = 0.31
a.) For portfolio becoming $50Million probaility (p) = (1.005-0.9762)/(1.0238-0.9762)
= 0.0288/0.0476
=0.60
1-p=0.40
b.) calculation of VAR :
Value of Z at 95% confidence level = 1.64
VAR = $70M*16%*1.64
= $18.368 Million
c.) Calculation of VAR:
Value of Z at 98% confidence level - 1.96
VAR = $70M*16%*1.96
=$21.95Million