2. OVERVIE
W
The purpose of this chapter is to study the
concepts of return and portfolio risk in
investment in the capital market. This chapter
will provide a better understanding of:
1. The difference between expected returns
and individual security and portfolio risk.
2. The difference between actual returns,
expected returns, and required returns.
3. The relationship between diversification and
portfolios.
3. Topics covered
Definition of Return and Risk
Estimation of Security Return and
Risk
Portfolio Risk Analysis
Diversification
Estimation of Portfolio Return and
Risk
Impact of Portfolio Weights and
Correlation
Single Index Model
4. Return
Return is one of the factors that motivates investors to invest
and is also the reward for the investor's willingness to bear
the risk of their investments.
Investment return consists of two main components:
1. Yield, the return component that reflects the periodic cash
flow or income obtained from an investment.
2. Capital gain (loss), the return component that represents
the increase (decrease) in the price of a security (whether it's
stocks or long-term debt securities), which can result in gains
or losses for the investor.
Concept of Risk and Return
5. Total Investment Return can be calculated as
follows:
Total Return = Yield + Capital Gain (Loss)
Concept of Risk and Return
6. Realized Return
Realized return refers to the return that has occurred
(actual return) calculated based on historical data (ex-
post data). This historical return is useful as the basis
for determining expected returns and future risk
(conditioning expected returns).
Expected Return
Expected return is the return that an investor
anticipates receiving in the future. Unlike realized
return, which is based on past data (ex-post data),
expected return is an estimation and, as such, has not
occurred yet (ex-ante data).
Concept of Risk and Return
7. Required Return
Required return is the historical return that
represents the minimum level of return
desired by an investor based on the
investor's subjective risk preferences.
Concept of Risk and Return
8. Risk
• Risk is the likelihood of a difference between
the actual return received and the expected
return. The greater the likelihood of such a
difference, the higher the investment risk.
• Several sources of risk that affect investment
risk include:
Concept of Risk and Return
1. Interest Rate Risk,
2. Market Risk,
3. Inflation Risk,
4. Business Risk,
5. Financial Risk,
6. Liquidity Risk,
7. Currency Exchange Risk,
8. Country Risk
9. Systematic risk, or market risk, is the risk associated
with changes that occur in the overall market. Some
authors refer to it as general risk, as it cannot be
diversified.
Unsystematic risk, or specific risk (company-specific
risk), is the risk not related to changes in the overall
market. Company-specific risk is more related to
changes in the micro-level conditions of the issuer of
securities. Company-specific risk can be minimized
by diversifying assets in a portfolio.
SYSTEMATIC RISK AND UNSYSTEMATIC
RISK
10. Calculating Expected Return
To estimate the return of a single asset (stand-alone risk), investors must
consider every possible realization of a specific rate of return, often
referred to as the probability of an event.
Mathematically, expected return can be written as follows:
n
E (R) = ∑ Ri pri
i=1
In this case:
E(R) = Expected return from a security
Ri = The i possible return that may occur
pri = The probability of the i-th return event
n = The number of possible returns that may occur
11. CONTOH: MENGHITUNG RETURN
YANG DIHARAPKAN
Security ABC has economic condition scenarios as
shown in the table below:
Probability Distribution of Security ABC
The calculation of the expected return from security ABC can
be computed using the previous formula, as follows:
E(R) = [(0.30) (0.20)] + [(0.40) (0.15)] + [(0.30) (0.10)]
= 0.15
So, the expected return from security ABC is 0.15 or 15%.
Economics situation Probability Return
Strong Economy 0,30 0,20
Normal Economy 0,40 0,15
Resession 0,30 0,10
12. METHODS FOR ESTIMATING
EXPECTED RETURN Arithmetic
and Geometric Mean.
Expected return estimation can be performed by calculating
the average return using both arithmetic mean and geometric
mean methods. Two methods that can be used are:
1. Arithmetic mean: Arithmetic mean is better suited for
calculating the average value of non-cumulative return
streams.
2. Geometric mean: Geometric mean should be used to
calculate the rate of change in return streams over serial
and cumulative periods (e.g., 5 or 10 consecutive years).
Both of these methods can be used to calculate a series of
return flows over a specific period, for example, the return of
an asset over 5 or 10 years.
14. COMPARISON OF ARITHMETIC MEAN
AND GEOMETRIC MEAN METHODS
The arithmetic mean method can sometimes be misleading,
especially when the distribution pattern of returns over a
period experiences highly fluctuating percentage changes.
On the other hand, the geometric mean method, which can
more accurately depict the "true average value" of a return
distribution over a specific period.
The calculated return using the geometric mean method is
smaller than the result obtained using the arithmetic mean
method.
Calculating the rate of change in return streams over serial
and cumulative periods is better suited to using the
geometric mean method. Meanwhile, the arithmetic mean
method is more suitable for calculating the average value of
non-cumulative return streams.
15. RISK ESTIMATION
The magnitude of investment risk is
measured by the standard deviation of
expected returns.
Standard deviation is the square root of the
variance, which indicates how much the
random variable deviates from its mean; the
greater the dispersion, the larger the
variance or standard deviation of the
investment.
16. How to Determine the Expected Return
and Standard Deviation
Stock ABC
Ri Pi (Ri)(Pi)
-0.15 0.10 –0.015
-0.03 0.20 –0.006
0.09 0.40 0.036
0.21 0.20 0.042
0.33 0.10 0.033
Sum 1.00 0.090
The
expected
return, R,
for Stock
ABC is
0.09 or
9%
17. Determining Standard
Deviation (Risk Measure)
s = S ( Ri – R )2( Pi )
Standard Deviation, s, is a statistical measure
of the variability of a distribution around its
mean.
It is the square root of variance.
n
i = 1
18. How to Determine the Expected
Return and Standard Deviation
Stock ABC
Ri Pi (Ri)(Pi) (Ri - R )2(Pi)
–0.15 0.10 –0.015 0.00576
–0.03 0.20 –0.006 0.00288
0.09 0.40 0.036 0.00000
0.21 0.20 0.042 0.00288
0.33 0.10 0.033 0.00576
Sum 1.00 0.090 0.01728
20. PORTFOLIO RISK
ANALYSIS
In portfolio management, there is a concept
of risk reduction through the addition of
securities to the portfolio.
The formula for calculating portfolio variance
can be expressed as follows:
21. PORTFOLIO RISK ANALYSIS
Example:
For instance, if the risk of each security is
0.20, and we include 100 stocks in the
portfolio, the portfolio risk will decrease from
0.20 to 0.02.
22. HOW MANY SECURITIES SHOULD BE
INCLUDED IN THE PORTFOLIO?
In the context of a portfolio, the more securities that are
included in the portfolio, the greater the benefit in reducing risk.
However, the benefits of risk reduction in the portfolio will
diminish up to a certain number, beyond which additional
securities will not provide further risk reduction benefits.
23. DIVERSIFICATIO
N
Diversification is the formation of a portfolio
through the selection of a combination of
specific assets in such a way that risk can be
minimized without reducing the expected return.
The challenge of diversification lies in the
determination or selection of specific assets and
the allocation of funds for each of these assets
within the portfolio.
24. DIVERSIFICATIO
N
There are two common principles of
diversification:
1. Random Diversification.
2. Markowitz Diversification.
25. Random Diversification
Random diversification, or "naive diversification,"
occurs when an investor allocates their funds
randomly across various types of stocks or
different types of assets.
Investors select assets to include in the portfolio
without paying much attention to the
characteristics of these assets (such as risk levels,
expected returns, and industries).
In random diversification, the more types of assets
included in the portfolio, the greater the benefit in
risk reduction, but with diminishing marginal risk
reduction.
26. Markowitz Diversification
Unlike random diversification, Markowitz
diversification takes into consideration
various information about the
characteristics of each security to be
included in the portfolio.
Markowitz diversification makes portfolio
formation more selective, especially in the
choice of assets, with the expectation of
providing the most optimal diversification
benefits.
27. The philosophical basis of Markowitz diversification: "Don't put all your
eggs in one basket."
A significant contribution of Markowitz's teachings is that the risk of a
portfolio should not be calculated by summing up all the risks of the assets
within the portfolio, but it should be calculated based on the contribution of
each asset's risk to the portfolio's risk, known as covariance.
The input data required in the Markowitz diversification process is the
variance and covariance structure of securities organized in a variance-
covariance matrix.
Covariance is an absolute measure indicating the extent to which the
returns of two securities in the portfolio tend to move together.
The correlation coefficient measures the degree of association between
two variables, indicating the level of relative co-movements between the
two variables.
Markowitz Diversification
28. Combining securities that are not perfectly,
positively correlated reduces risk.
INVESTMENT
RETURN
TIME TIME
TIME
SECURITY E SECURITY F
Combination
E and F
Diversification and the
Correlation Coefficient
29. Systematic Risk is the variability of return on
stocks or portfolios associated with changes in
return on the market as a whole.
Unsystematic Risk is the variability of return on
stocks or portfolios not explained by general
market movements. It is avoidable through
diversification.
Total Risk = Systematic Risk + Unsystematic
Risk
Total Risk = Systematic Risk +
Unsystematic Risk
