BF 320: Investment &
Portfolio Management
M.Mukwena
Investment Setting
Objectives:
 Why do individuals invest? What is an
investment?
 How do we measure the rate of return
on an investment?
 How do investors measure risk related
to alternative investments?
 What macroeconomic and
microeconomic factors contribute to
changes in the required rate of return
for investments?
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Why Do Individuals
Invest ?
2 choices with your earnings:
 Save and tradeoff present
consumption for a larger future
consumption
 Riskier option of investments
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Required Rate Of Return
1.
The pure rate of interest is the
exchange rate between future
consumption and present
consumption. Market forces
determine this rate.
Ex: if you can exchange K5 of certain
income today for K50 tomorrow this
rate is 5/50=10%. AKA pure time
value of money
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Pure Rate of Interest
Consumption Today Versus Tomorrow Trade-Off
ZMK 5
ZMK 5
ZMK 4
ZMK 4
ZMK 3
Consumption
ZMK 3
ZMK 2
ZMK 2
ZMK 1
ZMK 1
ZMK 0
ZMK 0
ZMK 10
ZMK 20
ZMK 30
ZMK 40
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ZMK 50
Required Rate Of Return
2. If the future payment will be
diminished in value because of
inflation, then the investor will
demand an interest rate higher than
the pure time value of money to
also cover the expected inflation
expense.
Ex: Investor in Zambia would expect
7% compensation for inflation
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Required Rate Of Return
3. If the future payment from the investment is
not certain, the investor will demand an interest
rate that exceeds the pure time value of money
plus the inflation rate to provide a risk premium
to cover the investment risk.
Ex: A return of 2%
Therefore from above examples an investor would
need compensation of 10%+7%+2% =19%
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Defining an Investment
A current commitment of money (K)
for a period of time in order to
derive future payments that will
compensate for:
◦ the time the funds are committed
◦ the expected rate of inflation
◦ uncertainty of future flow of funds.
These three make up required rate of
return
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Measures of
Historical Rates of Return
Holding Period Return
Ending Value of Investment
HPR 
Beginning Value of Investment
K220

 1.10
K200
K220 after 1 holding period.
beginning worth K200
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Measures of
Historical Rates of Return
Holding Period Yield
HPY = HPR - 1
1.10 - 1 = 0.10 = 10%
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Measures of
Historical Rates of Return
Investment cost K250 and is worth
K350 after 2 years holding period.
350
 HPR=
= 1.40 Note this is for 2
250
years
 Annual HPR= 𝐻𝑃𝑅1/𝑛 1.401/2 =
1.1832
 Annual HPY = Annual HPR-1=
1.1832-1=0.1832
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Measures of
Historical Rates of Return
Arithmetic Mean
where :
AM   HPY/ n
 HPY  the sum of annual
holding period yields
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Measures of
Historical Rates of Return
Geometric Mean
GM   HPR
  the product of
annual HPR
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
1
n
1
Measures of
Historical Rates of Return
Year
End Value of
Investment
HPR
HPY
1
Beginning
Value of
Investment
100
115.0
1.15
0.15
2
115
138.0
1.20
0.2
3
138
110.4
0.8
-0.2

From given table

AM=
0.15+0.2−0.2
3

GM=[ 1.15 1.20 0.8 ]1/3 = 0.03353
=0.05
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Arithmetic Mean versus
Geometric Mean
Inv
beg Y1 Y2 HPR
A
10
20 10 Yr1:20/10=2 Yr1: 2-1=1
Yr2:10/20=0.5 Yr2: 0.5-1=-0.5
B
10
8
12 Yr1: 8/10=0.8
Yr2: 12/8=1.5
HPY
Yr1: 0.8-1=-0.2
Yr2:1.5-1=0.5
AM
1+(−0.5)
2
GM
1/2
-1
=0.25 [(2 0.5 ]
=0
−0.2 +0.5
2
1/2
0.15 [0.8 1.5 ] 1=0.0954
For A the AM is not true (25%) since investment went from 10
to 20 to 10. Therefore GM is better measure.
For B: 10(1.15)(1.15)=13.23 which should be 12. However
10(1.0954)(1.0954)=12. Therefore GM is better measure
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Portfolio of Investments
The mean historical rate of
return for a portfolio of
investments is measured as the
weighted average of the HPYs for
the individual investments in the
portfolio. Example to follow
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Computation of Holding
Period Yield for a Portfolio
Stock
A
B
C
Total
Shares
100,000
200,000
500,000
Begin
Price
K10
K20
K30
Beginning Ending
Mkt.Value Price
1 000 000
K12
4 000 000
K21
15 000 000
K33
K20 000 000
Ending
Mkt.Value
1 200 000
4 200 000
16 500 000
K21 900 000
HPR =
K21 900 000
K20 000 000
=
1.095
HPY =
1.095- 1
=
0.095
=
9.5%
HPR HPY
1.20 20%
1.05 5%
1.10 10%
*Market Weights based on
Beginning Mkt Value
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*Market
Weight
0.05
0.20
0.75
Wtd.
HPY
0.010
0.010
0.075
0.095
Expected Rates of Return
 Risk
is uncertainty that an
investment will earn its expected
rate of return
 Probability is the likelihood of an
outcome
n
 (Probability of Return)  (Possible Return)
i 1
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Risk Aversion
The assumption that most
investors will choose the least
risky alternative, all else being
equal and that they will not
accept additional risk unless they
are compensated in the form of
higher return
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Probability Distributions
Risk-free Investment
Probability
1.00
0.80
0.60
0.40
0.20
0.00
-5% 0% 5% 10%15%
Return
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Probability Distributions
Risky Investment with 3 Possible Returns
Probability
1.00
0.80
0.60
0.40
0.20
0.00
-30%
-10%
10%
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30%
Return
Probability Distributions
Risky investment with ten possible rates of return
Probability
1.00
0.80
0.60
0.40
0.20
0.00
-40% -20%
0%
20% 40%
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Measuring the Risk of
Expected Rates of Return
Variance ( ) 
n
2
(
Probabilit
y)

(Possible
Return
Expected
Return)

i 1
n
(
P
)[R

E(R
)]
 i i
i
i 1
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2
Measuring the Risk of
Expected Rates of Return
Standard Deviation is the square
root of the variance
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Measuring the Risk of
Expected Rates of Return
Coefficient of variation (CV) a measure of
relative variability that indicates risk per
unit of return
Standard Deviation of Returns
Expected Rate of Returns

i
E(R)
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Measuring the Risk of
Expected Rates of Return
Investment A
Investment B
Expected Return
0.07
0.12
Standard Deviation
0.05
0.07
Coefficient of Variation
0.05/0.07 = 0.714
0.07/0.12 = 0.583
B has less risk per unit
and is therefore better
investment
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The Real Risk Free Rate
(RRFR)
◦ Assumes no inflation.
◦ Assumes no uncertainty about
future cash flows.
◦ Influenced by time preference for
consumption of income and
investment opportunities in the
economy
Take note: RRFR was earlier called
pure time value of money as only
sacrifice investor made was
deferring use of money
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Nominal Risk-Free Rate
 Rate
of interest stated in money
terms
 Dependent upon
◦ Conditions in the Capital Markets
◦ Expected Rate of Inflation
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Adjusting For Inflation
Nominal RFR =
(1+Real RFR) x (1+Expected Rate of Inflation) – 1
Ex: If you require a real growth in the purchasing
power of your investment of 8%, and you expect the
rate of inflation over the next year to be 3%, what is
the lowest nominal return that you would be
satisfied with? (1+0.08) x (1+0.03) - 1 = 0.1124
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Systematic Risk
Business
risk
Financial risk
Liquidity risk
Exchange rate risk
Country risk
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Systematic Risk
Business Risk:
• Uncertainty of income flows caused by the nature of a firm’s business
• Sales volatility and operating leverage determine the level of business
risk.
Financial Risk:
• Uncertainty caused by the use of debt financing.
• AKA leveraging risk
• Borrowing requires fixed payments which must be paid ahead of
payments to stockholders.
• The use of debt increases uncertainty of stockholder income and causes
an increase in the stock’s risk premium.
Q: Does a company utilizing only common stock to finance their
investments suffer financial risk?
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Systematic Risk
Liquidity Risk:
 Uncertainty is introduced by the secondary market for an
investment.
 How long will it take to convert an investment into cash?
 How certain is the price that will be received?
Exchange Rate Risk:
 Uncertainty of return is introduced by acquiring securities
denominated in a currency different from that of the investor.
 Changes in exchange rates affect the investors return when
converting an investment back into the “home” currency.
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Systematic Risk
Country Risk:
 Political risk is the uncertainty of returns caused by the possibility of a
major change in the political or economic environment in a country.
 Individuals who invest in countries that have unstable politicaleconomic systems must include a country risk-premium when
determining their required rate of return
f (Business Risk, Financial Risk, Liquidity Risk, Exchange Rate Risk, Country
Risk)
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Systematic Risk
 The
relevant risk measure for an
individual asset is its co-movement
with the market portfolio
 Systematic risk relates the variance
of the investment to the variance of
the market
 Beta measures this systematic risk of
an asset
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Security Market Lines
Rateof Return(Expected)
Low
Risk
RFR
Average
Risk
High
Risk
Security
Market Line
The slope indicates the
required return per unit of risk
Risk
(business risk, etc., or systematic risk-beta)
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Changes in the Required Rate of
Return Due to Movements Along the
SML
Expected
Rate
Security
Market Line
RFR
Movements along the curve
that reflect changes in the
risk of the asset
Risk
(business risk, etc., or systematic risk-beta)
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Change in
Market Risk Premium
Expected
E(R) Return
New SML
Rm'
Rm´
Original SML
Rm
Rm
NRFR
RFR
Risk
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Capital Market Conditions,
Expected Inflation, and the
SML
Expected
Return
Rate
of Return
New SML
Original SML
RFR'
NRFR´
NRFR
RFR
Risk
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