RISK AND RETURN
MODERN PORTFOLIO CONCEPT
Return Defined
• The return is the total gain or loss experienced on an investment over
a given period of time.
Pt  Pt 1  Ct
kt 
P
t 1
Where:
•
•
•
•
kt
=
actual, expected, or required rate of return during period t
Pt =
price (value) of asset at time t
Pt-1 =
price (value) of asset at time t - 1
Ct =
cash (flow) received from the asset investment in the time
period t - 1 to t
Return Measurement
n
k   k i  Pri
i 1
• Where:
Approach 1
▫ ki = return for the ith outcome
▫ Pri = probability of occurrence of the ith outcome
▫ n = number of outcomes considered
Example:
Weighted value
Possible
Probability
Return
[(I) x (2)]
outcomes
(1)
(2)
(3)
-----------------------------------------------------------------------------------------Asset A
-----------------------------------------------------------------------------------------Pessimistic
.25
13%
3.25%
Most likely
.50
15
7.50
Optimistic
.25
17
4.25
Total
1.00
Expected return
15.00%
-----------------------------------------------------------------------------------------Asset B
-----------------------------------------------------------------------------------------Pessimistic
.25
7%
1.75%
Most likely
.50
15
7.50
Optimistic
.25
23
5.75
Total
1.00
Expected return
15.00%
n
k 
k
i 1
i
n
Approach 2
Periode pengamatan
Tingkat return
Probabilitas
2001
16%
20%
2002
18%
20%
2003
20%
22%
2004
17%
20%
2005
21%
23%
Hitunglah expected return berdasarkan 2 metode di atas!
Risk Defined
• Risk is the chance of financial loss.
• A government bond that guarantees its holder $100 interest after
30 days has no risk, because there is no variability
associated with the return.
• A $100 investment in a firm's common stock, which over the
same period may earn anywhere from $0 to $200, is very risky
due to the high variability of return.
Risk Preferences
• Feelings about risk differ among managers
(and firms).
▫ Risk-indifferent
▫ Risk-averse
▫ Risk-seeking
Risk of a Single Asset
• Risk Assessment
▫ Risk can be assessed using sensitivity analysis and probability
distributions, which provide a feel for the level of risk embodied in a
given asset.
▫ Sensitivity Analysis:
 Uses a number of possible return estimates to obtain a of the
variability among outcomes.
 One common method involves estimating the pessimistic (worst),
the most likely (expected), and the optimistic (best) returns
associated with a given asset.
 The asset's risk can be measured by the range, which is found by
subtracting the pessimistic outcome from the optimistic
outcome.
 The greater the range for a given asset, the more variability, or
risk, it is said to have.
Asset A
Asset B
----------------------------------------------------------Initial investment
$10,000 $10,000
Annual rate of return
Pessimistic
13%
7%
Most likely
15%
15%
Optimistic
17%
23%
Range
4%
16%
Probability Distributions
• A probability distribution is a model
probabilities to the associated outcomes.
that
relates
• The simplest type of probability distribution is the bar chart,
which shows only a limited number of outcome-probability
coordinates.
Continous Probability Distribution for
asset A and B
Risiko
Unsystematic Risk
Systematic risk
Jumlah jenis saham
• Unsystematic risk disebut juga Diversifiable risk,
resiko yang masih dapat dihindari
Mis : mogok karyawan, lawsuits
• Systematic Risk disebut juga nonDiversifiable
risk, resiko yang tidak dapat dihindari
Mis : interest rate risk, liquidity risk, market risk
Types of Risk
•
•
•
•
•
•
•
•
•
Business risk
Financial risk
Interest rate risk
Liquidity risk
Market risk
Event risk
Exchange rate risk
Purchasing power risk
Tax risk
Firm-Specific Risks
Shareholder-Specific
Risks
Firm and Shareholder
Risks
Firm Specific Risk
• Business Risk : berkaitan erat dengan
keuntungan
• Financial Risk : berkaitan dengan utang
Shareholders Specific Risk
• Interest Rate Risk : berkaitan dengan perubahan
tingkat bunga di pasar
• Liquidity Risk : berkaitan dengan penjualan
asset yang secara mudah dengan harga yang
wajar di pasar
• Market Risk : berkaitan dengan index harga
saham
Firm and Shareholders Risk
• Event Risk : berkaitan dengan even2 atau
peristiwa yang dapat mempengaruhi nilai
perusahaan
• Exchange Rate Risk : berkaitan dengan nilai
tukar mata uang di kemudian hari beserta
fluktuasinya
• Purchasing – Power Risk : berkaitan dengan
inflasi dan deflasi
• Tax Risk : berkaitan dengan perubahan hukum
pajak
Risk Measurement
• Risk is measure with standard deviation,  k
k 
n
2
(
k

k
)
 Pri
 1
Approach 1
i 1
n
k 
2
(
k

k
)
 1
i 1
n 1
Approach 2
Coefficient of Variation
• Coefficient of variation, CV, is a measure of relative dispersion
that is useful in comparing the risk of assets with differing expected
returns.
CV 
k
k
• The higher the coefficient of variation, the greater the risk.
Return of a Portfolio
n
k p  (w1  k1 )  (w2  k 2 )  ...(wn  k n )   w j  k j
• Where:
j 1
▫ wj = proportion of the portfolio's total dollar value
represented by asset
▫ kj = return on asset j
Risk of Portfolio
• Portfolio return :
∑ (Proportion x Return X)+ (Proportion x Return Y)
n
k 
 (k
i 1
1
 k)
n 1
2
Correlation
• Correlation is a statistical measure of the relationship, if any,
between series of numbers representing data of any kind, from
returns to test scores.
▫ +1 for perfectly positively correlated series
▫ - 1 for perfectly negatively correlated series
▫ Uncorrelated
Diversification
• The concept of correlation is essential to developing an
efficient portfolio.
• Combining negatively correlated assets can reduce the
overall variability of returns.
• For example, assume that you manufacture machine
tools. The business is very cyclical, with high sales when
the economy is expanding and low sales during a
recession. If you acquired another machine-tool
company, with sales positively correlated with those of
your firm, the combined sales would still be cyclical, and
risk would remain the same.
• Alternatively, however, you could acquire a
sewing-machine manufacturer, which is countercyclical.
It typically has low sales during economic expansion and
high sales during recession (when consumers are more
likely to make their own clothes). Combination with the
sewing-machine manufacturer, which has negatively
correlated sales, should reduce risk.
Correlation, Diversification, Risk,
and Return
• The lower the correlation between asset returns,
the greater the potential diversification of risk.
T A B L E 6. 6,
Correlation, Return, and Risk for Various Two-Asset Portfolio Combinations
Correlation
coefficient
+ 1 (perfect positive)
0 (uncorrelated)
-1 (perfect negative)
Range of return
Range of risk
Between returns of two assetsBetween risk of two
held in isolation
assets held in isolation
Between returns of two assetsBetween risk of most
held in isolation
risky asset and an
amount less than risk
of least risky asset but
greater than 0
Between returns of two assetsBetween risk of most
held in isolation
risky asset and 0
Example
• A firm has calculated the expected return and the risk for each of two
assets-R and S.
Asset
R
S
Expected return
6%
8
Risk (standard
3%
8
deviation), 
Risk and Return: The Capital
Asset Pricing Model (CAPM)
• Total security risk = nondeversifiable risk + diversifiable
risk
• Diversifiable risk, sometimes called unsystematic risk,
represents the portion of an asset's risk that is associated with
random causes that can be eliminated through diversification
(strikes. lawsuits, regulatory actions)
• Nondiversifiable risk, also called systematic risk, is
attributable to market factors that affect all firms; it cannot be
eliminated through diversification.
• Factors such as war, inflation international incidents, and political
events account for nondiversifiable risk.
Beta Coefficient
• Beta coefficient, b, measures nondiversifiable risk. It is an index of the
degree of movement of an asset's return in response to a change in the
market return.
• An asset's historical returns are used in finding the asset's beta coefficient.
• The market return is the return on -the market portfolio of all traded
securities.
• Beta Individual:
n (∑XY) – (∑X) (∑Y)
n (∑X2) – (∑X)2
Dimana X adalah Return pasar (IHSG)
• Beta portfolio:
∑ (Proporsi x beta A) + (Proporsi x beta B)
 Jika beta >1 berarti saham tersebut memiliki
risiko yang lebih tinggi dari risiko pasar
(IHSG) dan saham tersebut termasuk saham
agresif.
 Sebaliknya jika Beta < 1 maka risiko lebih
rendah dari risiko IHSG  saham defensif
Hitunglah Beta (β) individu dari return A!
Tentukan Beta (β) portfolio V dan W !
The Model: CAPM
• The capital asset pricing model (CAPM) links
together nondiversifiable risk and return for all
assets.
 CAPM:
Risk Free (SBI)  beta = 0
Return Market (IHSG)/ beta pasar  beta =1
 CAPM= Rf + (β x (Rm-Rf))
The Graph: The Security Market
Line (SML)
• When the capital asset pricing model is depicted graphically, it is called
the security market line (SML).
• The SML will, in fact, be a straight line.
• It reflects the required return in the marketplace for each level of
nondiversifiable risk (beta).
• In the graph, risk as measured by beta, b, is plotted on the x axis, and
required returns, k, are plotted on the y axis.
• Jika Expected return, E(R)
< SML =
overvalue
• Dan Jika Expected return, E(R) > SML =
undervalue
• Risk free rate= 15%
• Market return= 20%
Tentukan return yang diisyaratkan (CAPM/ SML) untuk
setiap asset di atas dan gambarlah grafik SML serta
tentukan Asset yang undervalue atau overvalue!
Grafik SML
SML
C
Required return
25
A = E(R)A E(R)
C
20
15
E(R)
B
B
R
f
Undervalue
Equilibrium
Overvalue
10
5
0.5
1.0
1.5
2.0
2.5
Risk (Beta)