Portfolio management lecture

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  • Diversification Portfolio management
  • Portfolio management How a financial manager can exploit interrelationships between projects to adjust the risk-return characteristics of the whole enterprise Diversification theory; dont put all your eggs in one basket. Eliminate/reduce risk by selecting perfect negative correlation between two investments. The extent to which portfolio combination can achieve a reduction in risk depends on the degree of correlation between returns.
  • Attitudes to risk Risk-averse prefer less risk to more risk for a given return Moderately risk-averse Risk indifferent Investors would expect more return for increased risk
  • Two asset portfolio risk Step 1 Expected return The use of probability distribution on projected cash outcomes Given by the formula; n = piXi i=1 or ERp= ERA + (1-)ERB
  • Step 2 Standard deviation Risk of a portfolio expresses the extent to which the actual return may deviate from the expected return. Expressed by standard deviation or variance p= [ 2 2 +(1-)^2 ^2 + 2(1 )] Where; =the proportion of the portfolio invested in A (1-) =proportion invested in B 2 = the variance of the return on asset A 2 = the variance of the return on asset B cov AB=the covariance of the returns on A and B
  • Step 3 Covariance A statistical measure of the extent to which the fluctuations exhibited by two ore more variables are related Correlation coefficient is a measure of the interrelationship between random variables n rAB= cov AB covAB= [pi(RA ERA)(RB-ERB)] A X Bi=1
  • Example Information is available for two shares; B Ltd and G Ltd. The returns of shareholders have been calculated for the last five years. Calculate the mean (expected return), standard deviation and covariance. Year B Ltd G Ltd 1 26% 24% 2 20% 35% 3 22% 22% 4 23% 37% 5 29% 32%
  • Solution Year Rb Rg db dg db2 dg2 db X dg 1 26.00% 24.00% 2.00% -6.00% 0.04% 0.36% -0.12% 2 20.00% 35.00% -4.00% 5.00% 0.16% 0.25% -0.20% 3 22.00% 22.00% -2.00% -8.00% 0.04% 0.64% 0.16% 4 23.00% 37.00% -1.00% 7.00% 0.01% 0.49% -0.07% 5 29.00% 32.00% 5.00% 2.00% 0.25% 0.04% 0.10% 0.50% 1.78% -0.13% Average return 24.00% 30.00% Variance =db2/5 0.1 0.356 Std Dev. =var^0.5 0.316 0.597 Cov(bg) [db x dg]/5 -0.026%
  • Efficient frontier Rp A x y B C
  • Line ABC represents a feasible set of portfolios of asset P and Q As expected investment return increases, the additional subjective satisfaction of an investor declines at an increasing rate Rate of decline is dependent upon the attitude toward risk of the individual investor
  • Benefits of diversification Reduces variability of portfolio returns Reduction in risk which comes with the increase in number of different shares in the portfolio Specific risk- unsystematic risk or diversifiable risk that is unique to a company Market risk-systematic risk or non-diversifiable risk e.g. changes in economic climate determined by inflation, interest rates and foreign exchange rates
  • Multiple-share portfolio risk and return