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 11
.0220, 12
.0093,

13
.0191, 14
.0181, 22
.0517,

23
.0120, 24
.0096, 33
.0342,

34
.0204, and 44
.0290. Calculate the variance of the portfolio (of the four national portfolios) with weights, x1
1/6, x2
1/3, x3
1/4, and x4
1/4.

AppendixLO1