Consider a portfolio which consists of single risky asset. The return of the asset is normally distributed with annual

Question

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.

Help In Homework · Accepted Answer

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

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Consider a portfolio which consists of single risky asset

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