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# Portfolio management lecture

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### Portfolio management lecture

1. 1. Diversification Portfolio management
2. 2. Portfolio management  How a financial manager can exploit interrelationships between projects to adjust the risk-return characteristics of the whole enterprise  Diversification theory; “don’t 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.
3. 3. 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
4. 4. Two asset portfolio risk  Step 1 Expected return  The use of probability distribution on projected cash outcomes  Given by the formula; n  𝑋 = ∑ piXi i=1 or  ERp= 𝛼ERA + (1-𝛼)ERB
5. 5.  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  𝜎p= [𝛼 2 𝜎𝐴2 +(1-𝛼)^2 𝜎𝐵^2 + 2𝛼(1 − 𝛼)𝑐𝑜𝑣𝐴𝐵]  Where; 𝛼 =the proportion of the portfolio invested in A (1-𝛼) =proportion invested in B 𝜎𝐴2 = the variance of the return on asset A 𝜎𝐵2 = the variance of the return on asset B cov AB=the covariance of the returns on A and B
6. 6.  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)] 𝜎A X 𝜎Bi=1
7. 7. 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%
8. 8. 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%
9. 9. Efficient frontier Rp A x y B C 𝜎𝑝
10. 10.  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
11. 11. 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
12. 12. Multiple-share portfolio risk and return