Question

Consider a position consisting of a $200,000 investment in Microsoft shares and a $300,000 investment in BP shares. Suppose that the daily volatilities of these two assets are 0.95% and 1.02%, respectively, and that the coefficient of correlation between their returns is 0.56. What is the 10-day 97.5% value at risk for the portfolio? By how much does diversification reduce the VaR?

Answer 1

Value at Risk (VAR): VAR is a stastical tool designed to measure the maximum possible loss at a certain confidence level over a certain period of time horizen.

VAR of a Individual Stock

Here: x = value of the position or portfolio

z = value in the left tail

= volatilities

VAR of the potfolio

Here: r is the coefficient of corelation

We have been given: $200,000 , daily 0.95%

   $300,000 , daily 1.02%

  

Also at 2.5% in the left tail z = 1.96

Part a.) 10 Day VAR of the Portfolio:-

Step: 1. Daily VAR of Microsoft Shares:

  

  

  

Step: 2. Daily VAR of BP Shares

  

  

Step: 3. Dail VAR of the Portfolio:

Step: 4. 10 Day VAR of the Portfolio

Interpretation: We are 97.5% confidence that the maximum 10 Day loss would be $27,359.78

Therefore 10 Day VAR of the Portfolio at 97.5% confidence level is $27,359.78

Part b.) Benefit of Diversification:

Step: 1. VAR of the Diversified portfolio: $27,359.78

Step: 2. VAR of the un-diversified portfolio:

If the two stocks are perfectly positive corelated i.e. r is +1

daily VAR

10 Day

Step: 3 Benefit of Diversification: = 30,742.62 - 27,359.78

= 3,382.84

Therefore diversification redices VAR with $3,382.84

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