悉尼大学资本市场与公司财务课件Lecture5.ppt

Example 6.4 Calculate the correlation coefficient for BHP and CCL for 2007, given that the standard deviation of returns on the two stocks were 6.7% and 5.8% and the covariance is –0.00002. _______________________________________________ Label BHP security i, and CCL security j. Correlation coefficient (cont) Correlation coefficient (cont) If ρ = 1 the securities are said to be perfectly positively correlated – returns vary in a directly uniform manner (deterministic) If ρ = -1 they are said to be perfectly negatively correlated – changes in returns are inversely proportional (deterministic) If ρ = 0, there is no association between returns on the two securities (independent) A correlation coefficient of –0.30 indicates a mild negative relationship between the return on BHP and CCL (statistical) The risk of a portfolio is related to the riskiness of the stocks and the degree of correlation The variance of returns (σp2) on a portfolio is calculated as follows: where: xi,xj = proportion of the portfolio invested in security i or j σij = variance of security i if i = j, or  the covariance of returns on security i and j if i ≠ j Calculating the risk of portfolios (6.12) Equation 6.12 can be expanded (in the case of a 2-asset portfolio) as follows: where: σ1,σ2 = the standard deviation of returns on asset 1 and 2 x1,x2 = proportion of the portfolio invested in asset 1 or 2 σ12 = the covariance between assets 1 and 2 Calculating the risk of portfolios (cont) (A6.2.4) Example 6.5 Calculate the risk of a $1 million portfolio, comprising $0.5 million in BHP and $0.5 million in CCL. Their standard deviations of returns are 6.2% and 3.4% and the covariance of return on the stocks is -0.00002. _______________________________________________ Label BHP security i, and CCL security j. Calculating the risk of portfolios (cont) Components of risk The risk of investing in a single security can be reduced by combining the