Answer:
Number of securities in a portfolio = N
Expected returns on all the securities E_i = 0.01
Variances of their returns =0.01
i. Covariances of the returns between two securities = 0.005
Expected return of the portfolio is E(R) = w1R1 + w2Rq + ...+ wn Rn
E(R) =[tex]( \frac{1}{N}*0.01 + \frac{1}{N}*0.01 + .... + \frac{1}{N}*0.01 ) * N[/tex]
E(R) = 0.01
Expected return of N asset portfolio E(R) = 0.01
Variance of N asset portfolio [tex]\sigma ^2 = \frac{ \sum_{k=1}^{n}(r_k- E(r))^2}{n-1}[/tex]
where,
k is the specific return of the asset,
E(r) is the expected return.
ii. As N gets large, the portfolio's diversified risk rapidly decreases.
iii. The portfolio is well-diversified if the assets in a well-diversified portfolio exhibit a negative correlation or less correlation to each other.
