Equity Portfolios

Microsoft
Google
Apple

VAR - Single Stock Portfolio
Stock 1, market cap 25m, annual volatility 35%
252 trading days in a year
In this case, the 1 day VAR with a 95% confidence level (1.645 standard deviation) is:

VAR = "market value of portfolio" x "no of standard deviations" x ( "volatility" / ("days" ^ 0.5) )
VAR = 25m x 1.645 x ( 0.35 / (252^0.5) )
VAR = 906,721

VAR - Two Stock Portfolio
Stock 1, market cap 12.5m, annual volatility 35%
Stock 2, market cap 12.5m, annual volatility 28%
Assume perfect correlation.
In this case, the 1 day VAR with a 95% confidence level is:

Combined volatility = [ [ (0.5^2) x ( (35/100)^2 ) ] +
[ (0.5^2) x ( (28/100)^2 ) ] +
[ 2 x "correlation = 1" x 0.5 x (35/100) x 0.5 x (28/100) ]
] ^0.5

Combined volatility = (0.03063 + 0.0196 + 0.049) ^ 0.5
Combined volatility = 0.315

VAR = "market value of portfolio" x "no of standard deviations" x ( "volatility" / ("days" ^ 0.5) )
VAR = 25m x 1.645 x ( 0.315 / (252^0.5) )
VAR = 816,048.9
(this is less than before)

Now let's assume that the two stocks are not perfectly correlated but in fact have a correlation of 0.2.
Combined volatility = [ [ (0.5^2) x ( (35/100)^2 ) ] +
[ (0.5^2) x ( (28/100)^2 ) ] +
[ 2 x "correlation = 0.2" x 0.5 x (35/100) x 0.5 x (28/100) ]
] ^0.5

Combined volatility = (0.03063 + 0.0196 + 0.0098) ^ 0.5
Combined volatility = 0.245

VAR = "market value of portfolio" x "no of standard deviations" x ( "volatility" / ("days" ^ 0.5) )
VAR = 25m x 1.645 x ( 0.245 / (252^0.5) )
VAR = 634,704.72
(this is even lower, because Stock 2 has a lower volatility and the 2 stocks do not move together)

VAR - 3 Stock Portfolio