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Consider an investment universe with n securities, S1,S2,...,Sn. Given a xed investment horizon, we denote...

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Finance

Consider an investment universe with n securities, S1,S2,...,Sn. Given a xed investment horizon, we denote by r = (r1,r2,...,rn)T, the vector of random returns of the securities, and by = E(r) and = cov(r) the Expected Return and Variance-covariance matrix respectively. We assume that an investor has a fully invested equally weighted Portfolio dened by a vector of weights or holdings = (1,2,...,n)T with random return rp().

1.Give the expression of p()2, the variance of the portfolio as a function of and n.

2.Prove that, In the limit, an equally weighted portfolios risk converges to the average covariance between all securities returns.

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