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. 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. 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. 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. 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. 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%
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. 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