Perfect Positive Correlation
(p = + 1.0) In this case, Portfolio standard deviation is the weighted average of the standard deviation or returns on individual assets. Portfolio variance is given by the Equation 3.7.
Perfect positive correlation between asset returns yields a direct and linear relationship between risk and return of portfolio. This implies a risk-return trade-off. As the proportion of high return and high risk asset is increased, higher return on portfolio comes with higher risk. For instance, for every 1 per cent increase in return, portfolio risk also goes up by 1 per cent (Table 3.4).
Portfolio Opportunities Set for Different Degrees of Correlation
Thus, diversification does not lead to reduction of risk for given level of return. Besides, diversification does not lower the portfolio risk below the risk of individual assets comprising the portfolio. For example, if the assets comprising the portfolio have equal risk, say, standard deviation of 10 percent, the portfolio standard deviation is also 10 per cent (= W1 * 10 + W2 * 10; where W1 + W2 = 1).