Question

You own a $10 mil portfolio of IBM bonds. IBM has a daily volatility of 2%. Calculate the VaR over a 10 day-time period at a 99% confidence level.

You also own $5 mil of AT&T, with a daily volatility of 1%. AT&T and IBM have a .7 correlation coefficient.

What is the VaR of AT&T and the combined portfolio?

Answer 1

For 99% confidence Interval,

Z value = 2.326 (from NORMSINV function in EXCEL NORMSINV(0.01)

So, Daily VaR = 2.326*2%* $10 million = $0.4652 million

10 day VaR = $0.4652 million * (10)^0.5 = $1.4713 million

So, 10 day VaR of IBM with 99% confidence Interval is $1.4713 million

Similarly,

Daily VaR of AT&T = 2.326*1%* $5 million = $0.1163 million

10 day VaR = $0.1163 million * (10)^0.5 = $0.3678 million

So, 10 day VaR of AT&T with 99% confidence Interval is $0.3678 million

Now, in the portfolio of $15 million , weight of IBM = $10 million/$15 million = 2/3

Weight of AT&T =1/3

The standard deviation of a portfolio is given by

=((2/3)^2*0.02^2+(1/3)^2*0.01^2+2*2/3*1/3*0.02*0.01*0.7)^0.5

=0.015846486

So  

Daily VaR of Portfolio = 2.326*1%* $15 million = $0.55296658 million

10 day VaR = $0.55296658 million * (10)^0.5 = $1.7486 million

So, 10 day VaR of portfolio with 99% confidence Interval is $1.7486 million