1. Diversification
Portfolio management

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%

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. Efficient frontier
Rp A
x
y
B
C
𝜎𝑝

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

12. Multiple-share portfolio risk and return