After studying this chapter you will be able to understand: Portfolio theory – continued, two assets portfolio, portfolio selection, risky and risk-free assets, implications for investment. | Portfolio Management Lecture: 27 Course Code: MBF702 Outline Portfolio Theory - continued Two assets Portfolio Portfolio Selection Risky and risk-free assets Implications for investment Portfolio Theory Two asset portfolios - mathematics Investment Return Risk Proportion in portfolio (by MV) A ra σa x B rb σb (1 – x) What will be the return and risk of the portfolio? The return will be a weighted average of the two average returns, but the risk will depend on how much the fluctuations in A and B counteract each other. The extent to which this happens will depend on the correlation between the two investments returns. Formulae for risk and return of a two asset portfolio: The final element of this two asset portfolio risk equation is the vital part: It is this correlation coefficient which determines how much diversification is possible. Covariance and Correlation coefficient - calculation One way of calculating the correlation coefficient of returns between two investments in a . | Portfolio Management Lecture: 27 Course Code: MBF702 Outline Portfolio Theory - continued Two assets Portfolio Portfolio Selection Risky and risk-free assets Implications for investment Portfolio Theory Two asset portfolios - mathematics Investment Return Risk Proportion in portfolio (by MV) A ra σa x B rb σb (1 – x) What will be the return and risk of the portfolio? The return will be a weighted average of the two average returns, but the risk will depend on how much the fluctuations in A and B counteract each other. The extent to which this happens will depend on the correlation between the two investments returns. Formulae for risk and return of a two asset portfolio: The final element of this two asset portfolio risk equation is the vital part: It is this correlation coefficient which determines how much diversification is possible. Covariance and Correlation coefficient - calculation One way of calculating the correlation coefficient of returns between two investments in a two-asset portfolio is to begin by calculating the covariance of the returns from the two investments. The correlation coefficient for the returns of two investments (A and B) in a two asset portfolio is calculated as: This is the covariance of returns from investments A and B, divided by [the standard deviation of returns from investment A multiplied by the standard deviation of returns from investment B]. Standard deviation of return for a two-asset portfolio The overall standard deviation of the return from a two-asset portfolio can be calculated using the following formula Expected return from a two-asset portfolio Illustration Example Solution Implications for investment The implications of this diversification process for investment are: an investor should not consider an investment's risk and return characteristics in isolation but compare it to existing investments in order to identify any diversification opportunities; it is therefore possible to reduce the risk of the investor’s .
