Question

A portfolio consists of two assets. $1 million is invested in Asset 1 and $2 million is invested in Asset 2. The estimated daily variance for Asset 1 is 0.01, for Asset 2 the daily variance is 0.005. The estimated covariance for the two assets is 0.002. What is the 10-day VaR at the 95% confidence level?

Answer #1

First we calculate the portfolio variance. Assuming the two
assets are s1 , s2 with weights w1, w2 and risks *σ1 and σ2. The
formula for calculating portfolio variance is:*

*Portfolio
variance=**(W1σ1)**2**+**W2σ2**2+2W1W2*covariance(S1S2)*

To calculate weights. Asset 1 has 1 million , Asset 2 has 2 millions, the weights w1 and w2 are 1/3 and 2/3 respectively

Portfolio variance =
0.333^{2}*0.01+0.667^{2}*0.005+2*0.333*0.667*0.002
= 0.00422

Portfolio risk = sqrt(prortfolio variance) = 0.065

one day Var for portfolio risk = 0.065

10 day VaR at 95% confidence interval therefore = -1.65*0.065*sqrt(10) = -0.3391 which is approximately -33.4%

Reason why it is 1.65 is the z value of a one tail confidence interval is 1.65

Formula for calculating VaR for different periods =
*σ _{one day}*sqrt(T)*(Z value for confidence
interval)*

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Deviation) = 10 Asset 2: Mean return = 10, Risk = 20 Asset 3: Mean
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returns of Asset 1 have 20% correlation with returns of all the
other assets. The returns of Asset 2 have 10% correlation with
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Stock
$Amount Invested
Beta
A
4 million
1.7
B
2 million
1.1
C
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1.0
D
1 million
0.7
E
1 million
0.5
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Question-2
An investment advisor has recommended a $100,000 portfolio
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Asset B, with a beta of 1.5; $25,000 will be invested in Asset D,
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YOU MUST SHOW YOUR WORK....

As a portfolio manager for Bank of America Merrill
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