3. (Principal components ) Suppose there are a random variables.x.x2. ., and let V be the corresponding covariance matrix. An eigenvector of V is a vector v=(. . . ) such that Vvv for some 2 (called an eigenvalue of V) The random variable x + ++ is a principal component. The first principal component is the one corresponding to the largest eigenvalue of V, the second to the second largest, and so forth A good candidate for the factor in a one-factor model of asset returns is the first principal component extracted from the returns themselves; that is, by using the principal eigenvector of the covariance matrix of the returns Find the first principal component for the data of Example 82 Does this factor (when normalized) resemble the return on the market portfolio? [Note For this part, you need an eigenvector calculator as available in most matrix operations packages]