chapter no 5 investment analysis and portfolio management portfolio return analysis
TRANSCRIPT
Chapter No 5
Investment Analysis and Portfolio Management
Portfolio Return Analysis
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.
Introduction to Risk and Return
CHAPTER 8 – Risk, Return and Portfolio Theory
Return %
RF
Risk
Risk Premium
Real Return
Expected Inflation Rate
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.
What is 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
How to calculate total return??
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
Example
Steps of Finding Total Return
1. find cash flow or payments received Investment per bondinterest rate 506 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%
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
Assignment
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
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.
Measuring Returns
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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.
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.
Yield loss)(or Gain Capital Yield Dividend / Income
0
1
g
P
Dkc
8 - 14
Measuring Returns
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.
Where CF1 = the expected cash flow to be received
P0 = the purchase price
Measuring ReturnsIncome Yield
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yield Income 0
1
P
CF
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 )
Income Yield Stocks versus Bonds
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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 ReturnsDollar 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
Measuring ReturnsConverting Dollar Returns to Percentage Returns
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%808.$25
$25-$27 return (loss)gain Capital
0
01
P
PP
The investor’s total return (holding period return) is:
Measuring ReturnsTotal Percentage Return
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%1212.008.004.025$
25$27$
25$
00.1$
yield loss)(or gain Capital yield Income return Total
0
01
0
1
0
011
P
PP
P
CF
P
PPCF
[8-3]
The general formula for holding period return is:
Measuring ReturnsTotal Percentage Return – General Formula
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yield loss)(or gain Capital yield Income return Total
0
01
0
1
0
011
P
PP
P
CF
P
PPCF
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 ReturnsEx Post Returns
Where:ri = the individual returnsn = the total number of observations
Most commonly used value in statistics Sum of all returns divided by the total number of
observations
Measuring Average ReturnsArithmetic Average
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(AM) Average Arithmetic 1
n
rn
ii
Measures the average or compound growth rate over multiple periods.
Measuring Average ReturnsGeometric Mean
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11111(GM)Mean Geometric 1
321 -)]r)...(r)(r)(r [( nn[8-5]
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.
Measuring Average ReturnsGeometric Mean versus Arithmetic Average
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Annual Arithmetic
Average (%)
Annual Geometric Mean (%)
Standard Deviation of Annual Returns
(%)
Government of Canada treasury bills 5.20 5.11 4.32Government of Canada bonds 6.62 6.24 9.32Canadian stocks 11.79 10.60 16.22U.S. stocks 13.15 11.76 17.54
Source: Data are from the Canadian Institute of Actuaries
Table 8 - 2 Average Investment Returns and Standard Deviations, 1938-2005
Measuring Average ReturnsAverage Investment Returns and Standard Deviations
The greater the difference, the greater the volatility of
annual 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.
Measuring Expected (Ex Ante) Returns
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Estimating Expected ReturnsEstimating 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 EconomyProbability of Occurrence
Possible Returns on
Stock A in that State
Economic Expansion 25.0% 30%Normal Economy 50.0% 12%Recession 25.0% -25%
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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) (2) (3) (4)=(2)×(3)
State of the EconomyProbability of Occurrence
Possible Returns on
Stock A in that State
Weighted Possible
Returns on the Stock
Economic Expansion 25.0% 30% 7.50%Normal Economy 50.0% 12% 6.00%Recession 25.0% -25% -6.25%
Expected Return on the Stock = 7.25%8 - 29
The general formula
Where:ER = the expected return on an investmentRi = the estimated return in scenario i
Probi = the probability of state i occurring
Estimating Expected ReturnsEstimating Ex Ante (Forecast) Returns
)Prob((ER)Return Expected 1
i
n
iir[8-6]
Estimating Expected ReturnsEstimating 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.
7.25%
)25.0(-25%0.5)(12% .25)0(30%
)Prob(r)Prob(r )Prob(r
)Prob((ER)Return Expected
332211
1i
n
iir
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