Question

6. You’re given with the following information for the bank’s stock portfolio. Suppose that there are three mutually independent funds in your portfolio. The standard deviations of these fund are provided in the following table 1.  

                                                            Table 1:

                                    

Asset	(in %)
Fund 1	3.4086
Fund 2	2.975
Fund 3	4.7056

Answer the following questions:

a) Suppose your allocations for the portfolio are given as 1/6 for asset one, 1/3 for asset two, 1/2 for asset three, what is the standard deviation for this portfolio?

b) Suppose that your portfolio has initial value as $300 million, given that your confidence level as 95% and assuming the normal distribution for asset returns, what is the VaR (Value at Risk) for your portfolio? What is the meaning of VaR? Is the normality assumption appropriate for the assessment of VaR?

Answer 1

a) Suppose your allocations for the portfolio are given as 1/6 for asset one, 1/3 for asset two, 1/2 for asset three, what is the standard deviation for this portfolio?

Standard deviation of portfolio SDp = sqrt[(w1^2 * SD1^2 + w2^2 * SD2^2 + w3^2 * SD3^2 )]

(The Correlation between the annual returns on the two portfolios is zero as they are mutually independent funds)

Where,

w1 is the weight of fund 1 = 1/6

SD1 is the standard deviation of fund 1 = 3.4086%       

w2 is the weight of fund 2 = 1/3

SD2 is the standard deviation of fund 2 = 2.975%              

w3 is the weight of fund 3 = 1/2

SD3 is the standard deviation of fund 3 = 4.7056%            

Therefore,

Standard deviation of portfolio SDp =sqrt [(1/6)^2 * 3.4086%^2 + (1/3)^2 * 2.975^2 + (1/2)^2 * 4.7056%^2]

=sqrt(6.842)

= 2.6157%

b) Suppose that your portfolio has initial value as $300 million, given that your confidence level as 95% and assuming the normal distribution for asset returns, what is the VaR (Value at Risk) for your portfolio? What is the meaning of VaR? Is the normality assumption appropriate for the assessment of VaR?

Formula to calculate daily value at risk at the 95% confidence level

VaR of portfolio = V0 * (z *?)

Where,

V0 is the value of investment = $300 milion

Z-score at 95% confidence interval = 1.645

And standard deviation of portfolio ? = 2.6157%

Therefore

VaR = $3,000,000* (1.645 *2.6157%)

= $20,000,000* 0.04303

= $129,084.06

Value at risk is a measure of the risk of loss for our investments. It estimates that with a given probability, what portion of investments you may loss in a certain time period in a normal market conditions.

Therefore here the meaning of VaR is that at 95% of the time, you will not lose more than $129,084.06 of your investments in a day if market conditions are normal. The normality assumption is appropriate for the assessment of VaR.