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Lecture_8_Questions

# Lecture_8_Questions - distribution with a 99 confidence...

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Lecture 8 Questions and Answers 1. Consider a portfolio consisting of both Apple and Yahoo shares. Suppose that the returns on the two shares have a bivariate normal distribution with a correlation of 0.4. The standard deviation of changes in the value of the position in Apple over a one-day period is equal to 100,000 and the standard deviation of changes in the value of the position in Yahoo over a one-day period is equal to 150,000. a) What is the standard deviation of the change in the value of the portfolio consisting of both stocks over a one-day period? Std(A&Y)=sqrt(100,000*100,000+150,000*150,000+2*0.4*100,000*150,000)=211,000 b) Suppose the mean change is zero and the change is normally distributed. What’s the 1-day 99% VaR? What’s the 10-day 99% VaR? (Hint: The inverse of a normal
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Unformatted text preview: distribution with a 99% confidence level=2.325) 1-day 99% VaR=211,000*2.325=490,500 10-day 99% VaR=490,500*sqrt(10)=1,551,100 c) Please calculate the 10-day 99% VaR for only the Apple shares and calculate the 10-day 99% VaR for only the Yahoo shares. (Hint: The inverse of a normal distribution with a 99% confidence level=2.325) Apple 1-day 99% VaR=100,000*2.325=232,500 10-day 99% VaR=232,500*sqrt(10)=735,000 Yahoo 1-day 99% VaR=150,000*2.325=348,700 10-day 99% VaR=348,700*sqrt(10)=1,102,700 d) Using your answers to part b and c, please show if there are any benefits from diversification in terms of VaR. (735,000+1,102,700)- 1,551,100=286,600 is the reduction in VaR therefore benefit from diversification....
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