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In July 1995, First Quadrant, a fund management firm in Pasadena, California, estimated the covariances between the returns of four portfolios: a popular portfolio of

In July 1995, First Quadrant, a fund management firm in Pasadena, California, estimated the covariances between the returns of four portfolios: a popular portfolio of U.S. stocks (asset 1), of Japanese stocks (asset 2), of U.K. stocks (asset 3), and of Canadian stocks (asset 4). The covariances were respectively sigma11 = .0220, sigma12 = .0093, sigma13 = .0191, sigma14=.0181, sigma22 = .0517, sigma23 = .0120, sigma24 = .0096, sigma33 = .0342, sigma34 = .0204, sigma44 = .0290. Calculate the variance of the portfolio of the three national (ignore asset 4) portfolios with weights of x1 = 1/6, x2 = -1/6, and x3 = 1.

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