Investment Analysis and Portfolio
Management
Chapter No 5
Portfolio Return Analysis
Introduction to Return
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Introduction to Risk and Return
Risk and return are the two most
important attributes of an
investment.
Research has shown that these
two are linked in the capital
markets and that generally,
higher returns can only be
achieved by taking on greater
risk. Taking on additional risk in
search of higher returns is a
decision that should not be
taking lightly.
CHAPTER 8 – Risk, Return and Portfolio Theory
Return
%
Risk Premium
RF
Real Return
Expected Inflation Rate
Risk
What is return???
 It is a possibility or certainty of earing profit from a project or
business activity for which the analysts and businessmen must
have awareness to achieve.
 It can be defined as;
 The income received on an investment plus any positive change
in the market price shares which is usually expressed in
percentage of the beginning price of the investment is called
return.
 Expected Return:
 It is the weighted average of possible returns with the weights
being the possibilities of occurrence is called expected return.
How to calculate total return??
 Total return= C.F + P.C/P.P
 Where;
 C.F= cash payments received over the
period
 P.C= price change over the period
 P.P= purchase price
Example
 Mr. A invested 500,000 Afs in bonds. The company pays him
12% interest per bond.
 The initial price of bond= 50 Afs
 Current price of bond= 60 Afs
 Find total return ?
 So we know that T.R= C.F+P.C/P.P
To find this we have to follow steps given next
Steps of Finding Total Return
 1. find cash flow or payments received
 Investment per bond×interest rate
50× 12/100 =6
 2. Find price change
 Current price – initial price
60 – 50 = 10
 3. add C.F and P.C and divide by P.P
6+10/ 50 = 0.32
Means 32%
Assignment
 Mr. A invested 100,000 Afs in bonds. The company pays him
25% interest per bond.
 The initial price of bond= 80 Afs
 Current price of bond= 90 Afs
 Find total return ?
 So we know that T.R= C.F+P.C/P.P
To find this we have to follow steps given
How to calculate Actual return
 Actual return=
cash received from investment+
Current price of asset – purchased price of asset divided by
purchase price.
 A.R = C.F + C.P- P.P
P.P
Example
 Mr. Ali bought a Taxi at 400,000 AFS. He earned an amount of
250,000 AFS in 2 years by driving it excluding all other expenses
he made in care repair etc... The current market price of the
Taxi is 350,000 AFS. Find the Actual Return on his investment.
 Use given Formula A.R = C.F + C.P- P.P/ P.P
 250000+350000-400000/400000
 =0.5
 50%
Assignment
 Mr. Ahmad opened school & invested 700,000 AFS. He earned
350000 AFS in 3 years excluding all expenses. Now his friend
offers him 800,oo0 AFS. Calculate actual Return on his
investment.
 Use given Formula A.R = C.F + C.P- P.P/ P.P
Measuring Returns
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Measuring Returns
Ex Ante Returns
 Return calculations may be done ‘before-the-fact,’ in which
case, assumptions must be made about the future
Ex Post Returns
 Return calculations done ‘after-the-fact,’ in order to analyze
what rate of return was earned.
8 - 13
Measuring Returns
As we know that the constant growth can be decomposed
into the two forms of income that equity investors may
receive, dividends and capital gains.
 D1 
kc     g   Income / Dividend Yield   Capital Gain (or loss) Yield 
 P0 
WHEREAS
Fixed-income investors (bond investors for example) can
expect to earn interest income as well as (depending on
the movement of interest rates) either capital gains or
capital losses.
8 - 14
Measuring Returns
Income Yield
 Income yield is the return earned in the form of a periodic cash
flow received by investors.
 The income yield return is calculated by the periodic cash flow
divided by the purchase price.
Income yield 
CF1
P0
Where CF1 = the expected cash flow to be received
P0 = the purchase price
8 - 15
Income Yield
Stocks versus Bonds
 For stocks we find dividend yield while for bond we find interest
yield.
 We can not forecast dividend yield because next year’s
dividends cannot be predicted in aggregate as it is paid from
the net income.
 Reason – risk
 The risk of earning bond income is much less than the risk
incurred in earning dividend income.
(Remember, bond investors are secured creditors. They have first
legally-enforceable contractual claim to interest. But stock
investors are
not secured )
8 - 16
Measuring Returns
Dollar Returns
Investors in market-traded securities (bonds or stock) receive
investment returns in two different form:
 Income yield
 Capital gain (or loss) yield
The investor will receive dollar returns, for example:
 $1.00 of dividends
 Share price rise of $2.00
To be useful, dollar returns must be converted to percentage
returns as a function of the original investment. (Because a
$3.00 return on a $30 investment might be good, but a $3.00
return on a $300 investment would be unsatisfactory!)
Measuring Returns
Converting Dollar Returns to Percentage Returns
An investor receives the following dollar returns a stock
investment of $25:
 $1.00 of dividends
 Share price rise of $2.00
The capital gain (or loss) return component of total return is
calculated: ending price – minus beginning price, divided by
beginning price
P1  P0 $27 - $25
Capital gain (loss) return 

 .08  8%
P0
$25
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Measuring Returns
Total Percentage Return
 The investor’s total return (holding period return) is:
[8-3]
Total return  Income yield  Capital gain (or loss) yield
CF  P  P
 1 1 0
P0
 CF   P  P 
  1 1 0
 P0   P0 
 $1.00   $27  $25 


 0.04  0.08  0.12  12%


$
25
$
25

 

8 - 19
Measuring Returns
Total Percentage Return – General Formula
 The general formula for holding period return is:
Total return  Income yield  Capital gain (or loss) yield
CF  P  P
 1 1 0
P0
 CF1   P1  P0 



P
P
 0   0 
8 - 20
Measuring Average Returns
Ex Post Returns
 Measurement of historical rates of return that have been
earned on a security.
 It allows us to identify trends or tendencies that may be useful
in predicting the future.
 There are two different types of ex post mean or average
returns used:
 Arithmetic mean
 Geometric mean
Measuring Average Returns
Arithmetic Average
n
Arithmetic Average (AM) 
r
i 1
i
n
Where:
ri = the individual returns
n = the total number of observations
 Most commonly used value in statistics
 Sum of all returns divided by the total number of observations
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Measuring Average Returns
Geometric Mean
[8-5]
1
n
Geometric Mean (GM)  [(1  r1 )( 1  r2 )( 1  r3 )...( 1  rn )] -1
 Measures the average or compound
growth rate over multiple periods.
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Measuring Average Returns
Geometric Mean versus Arithmetic Average
If all returns (values) are identical,
the geometric mean = arithmetic average.
If the return values are volatile.
the geometric mean < arithmetic average
The greater the volatility of returns, the greater the difference
between geometric mean and arithmetic average.
8 - 24
Measuring Average Returns
Average Investment Returns and Standard Deviations
Table 8 - 2 Average Investment Returns and Standard Deviations, 1938-2005
Annual
Arithmetic
Average (%)
Government of Canada treasury bills
Government of Canada bonds
Canadian stocks
U.S. stocks
5.20
6.62
11.79
13.15
Annual
Geometric
Mean (%)
Standard Deviation
of Annual Returns
(%)
5.11
6.24
10.60
11.76
So urce: Data are fro m the Canadian Institute o f A ctuaries
The greater the difference,
the greater the volatility of
annual returns.
4.32
9.32
16.22
17.54
Measuring Expected (Ex Ante) Returns
 While past returns might be interesting, investor’s are most
concerned with future returns.
 Sometimes, historical average returns will not be realized in the
future.
 That’s way investors are supposed to calculate expected ex
ante returns.
 Ex ante return calculation is also called forecasting expected
returns.
8 - 26
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns
Example:
This is type of forecast data that are required to make an ex ante
estimate of expected return.
State of the Economy
Economic Expansion
Normal Economy
Recession
Probability of
Occurrence
25.0%
50.0%
25.0%
8 - 27
Possible
Returns on
Stock A in that
State
30%
12%
-25%
Measuring Expected (Ex Ante)
Returns
 We can calculate it by using two different
methods.
 1. spread sheet method
 2. general formula method.
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns Using a Spreadsheet Approach
Example Solution:
Sum the products of the probabilities and possible returns in each
state of the economy.
(1)
State of the Economy
Economic Expansion
Normal Economy
Recession
(2)
(3)
(4)=(2)×(3)
Possible
Weighted
Returns on
Possible
Probability of Stock A in that Returns on
Occurrence
State
the Stock
25.0%
30%
7.50%
50.0%
12%
6.00%
25.0%
-25%
-6.25%
Expected Return on the Stock =
7.25%
8 - 29
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns
 The general formula
n
[8-6]
Expected Return (ER)   (ri  Prob i )
i 1
Where:
ER = the expected return on an investment
Ri = the estimated return in scenario i
Probi = the probability of state i occurring
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns Using a Formula Approach
Example Solution:
Sum the products of the probabilities and possible
returns in each state of the economy.
n
Expected Return (ER)   (ri  Prob i )
i 1
 (r1  Prob1 )  (r2  Prob 2 )  (r3  Prob 3 )
 (30%  0.25)  (12%  0.5)  (-25%  0.25)
 7.25%
8 - 31