Problem 1: What is the variance of a portfolio with: w1 =0.2, w2 =0.8, ₁² =10, ₂² =20, and ₁₂ =5.

Problem 2: a) If the stocks 1 and 2 have negative correlation ^₁₂ then their covariance ¹² is also negative. Yes, no, uncertain. Explain. b) If stocks 1 and 2 are uncorrelated, i.e. ^₁₂=0 then their covariance is zero, Yes, no, uncertain. Explain c) If stocks 1 and 2 have variance ²=16 each, could their covariance be equal to ¹²= 20?

Problem 3: You have a portfolio of 4 stocks with equal shares invested in each stock. Variances of individual stocks are the same and equal to 2 =16. Correlations between each pair of stocks is a) What would be the covariances between each pair of stocks as function of b) Find the variance of equally-portfolio of these 4 stocks (again as a function of c) What happens to the variance of your portfolio when increases. d) What would be the variance of your portfolio when = 1. Would it be larger or smaller than the variance of individual stocks = 16?

problem 5. Assume you have N stocks 2 =16. Correlations between each pair of stocks is = 0.125 = 1/8. a) What would be pairwise covariances? b) What would be the variance of an equally-weighted portfolio of N stocks c) Using Excel calculate the variance you found in b) for N=1,2,3,, 30 stocks and plot it d) Calculate the % of total portfolio variance coming from pairwise covariances and also plot it as a function of N for N=1,2,3,, 30. Comment on your results.

Transcribed image text