Transcript of Portfolio management lecture
- 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