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Consider a portfolio which consists of single risky asset

Finance

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.

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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