2. RETURN DEFINED
Return represents the total gain or loss on an
investment.
Basic concept: Each investor desires a return for
every single dollar of their investment.
3. EXAMPLE
Damia invests in 10 unit shares valued at RM1000. At
the end of year, she sold all the shares @ RM1100. How
much return received by Damia for her investment?
r = RM1,100 + 0 – RM1,000
RM1,000
= 10% (so holding period rate of return is 10%)
4. EXPECTED RETURN
Expected Return ( r )- the return that an investor expects to
earn on an asset, given its price, growth potential, etc.
Required Return ( r )- the return that an investor requires on
an asset given its risk and market interest rates.
Expected rate of return from investment is determined by the
different possible outcomes such probabilities of the
occurrence of the various states of the economy.
In the unstable situation, it is hard for the investors to be
assured on the expected rate of return.
5. EXPECTED RATE OF RETURN
Expected rate of return - The weighted average of all possible
returns where the returns are weighted by the probability
that each will occur.
OR, WE CAN PUT THIS WAY
r = Pb1*r1 + Pb2*r2 + ...+ Pbn*rn
where;
Pb = probability of occurrence of the outcome
r = return for the outcome
n = number of outcomes considered
6. EXPECTED RATE OF RETURN
EXAMPLE
State of the
economy
Probability
Return
Recession
20%
10%
Normal
30%
12%
Boom
50%
14%
r = (0.2)(10%) + (0.3)(12%) + (0.5)(14%)
= 12.6%
7. EXERCISE
State of the
economy
Probability (Pb)
Return
Company A
Return
Company B
Recession
0.20
4%
-10%
Normal
0.50
10%
14%
Boom
0.30
14%
30%
What is the expected return for each company?
8. RISK DEFINED
Risk is potential variability in future cash flow.
The possibility that an actual return will differ from our
expected return.
The wider the range of possible future events that can occur,
the greater the risk.
Concept: (High risk, high return)
Probability- Chances that an
investment will generate
expected rate of return for
investor.
Return
Risk
9. STANDARD DEVIATION
HOW DO WE MEASURE RISK?
Standard deviation (SD) is one way to measure risk. It
measures the volatility or riskiness of portfolio returns
(dispersion of possible outcomes).
SD ( -sigma) = square root of the weighted average squared
deviation of each possible return from the expected return.
The greater the standard deviation, the greater the
uncertainty, and the greater the risk.
Standard Deviation Formula:
11. STANDARD DEVIATION
Summary
Expected Return
Standard Deviation
Company
A
B
10%
14%
3.46% 13.86%
We can conclude that, company A has lower risk
compared to investment B BUT Company B has higher
return.
Final choice is determined by our attitude toward risk
and there is NO single right answer
12. COEFFICIENT OF VARIATION
It is NOT TRUE to conclude that asset with high standard
deviation has a high risk where comparison of risk was made
between assets with a different expected rate of return.
The coefficient of variation, CV, is a measure of relative
dispersion that is useful in comparing risks of assets with
differing expected returns.
Formula: CV = σr
r
The higher the CV, the higher the risk.
13. COEFFICIENT OF VARIATION
Example
Asset A
Asset B
r
10%
14%
σr
3.46%
13.86%
a. Which assets do you prefer?
b. Is it true that Asset B is more risky compared to Asset A?
CVA = 0.346 while CVB = 0.99
A unit of risk in return for asset B is higher than asset A.
As a conclusion, asset A is less risky than asset B.
In comparing risk, it is more effective if we are using CV
because it’s consider the relative size or the rate of
return of that asset.
14. EXERCISE
2 Assets- Asset C and T are currently being considered by Green
Corp. The distributions are shown in the following table.
Asset C
Asset T
Pb
r
Pb
r
Boom
0.30
15%
0.30
25%
Normal
0.50
10%
0.50
20%
Recession
???
2%
???
1%
a. Calculate the expected rate of return, r, for each of the assets.
b. Calculate the standard deviation, for each of the assets.
c. Calculate the coefficient of variation, CV, for each of the
assets.
15. PORTFOLIO AND RISK DIVERSIFICATION
A portfolio = any collection or combination of several
financial assets (investments) at the same time or period.
Combining several securities in a portfolio can actually
reduce overall risk.
If an investor holds a single asset, he or she will fully suffer the
consequences of poor performance.
This is not the case for an investor who owns a diversified
portfolio of assets.
16. PORTFOLIO WEIGHTED (PW)
You have RM15,000 to invest in a selected
of stocks in Bursa Malaysia as follows:
What is the weighted of portfolio for each
security?
DCLK
=RM2000
KO
=RM3000
INTC = RM4000
KEI
= RM6000
DCLKw = 2000/15000
Kow
= 0.2
INTCw = 0.267
KEIw
= ??
17. PORTFOLIO EXPECTED RETURN
Is the weighted average of expected return
for each security of a portfolio.
FORMULA
m
E ( RP )
w j E(R j )
j 1
19. DIVERSIFICATION
Diversification-spreading out of investments to reduce risks.
Market rewards diversification.
The main motive for holding multiple assets or creating a
portfolio of stocks (called diversification) is to reduce the
overall risk exposure.
The degree of reduction depends on the correlation among
the assets.
Correlation-a statistical measurement of the relationship
between two variables.
Positive Correlation
Negative Correlation
Possible correlations range from +1 to –1
20. PORTFOLIO
If two stocks are perfectly positively correlated,
diversification has NO effect on risk. i.e If correlation (c) = +1,
we cannot abolish all the risk meaning that both stocks move
in the same direction together.
If two stocks are perfectly negatively correlated, the portfolio
is perfectly diversified. i.e If correlation (c) = -1, we can
abolish the risk meaning that as one stock goes up, the other
goes down.
21. TYPES OF INVESTMENT RISKS
Investors should NOT expect to eliminate all risk from their
portfolio. Some risk can be diversified away and some cannot.
2 TYPES OF RISKS
i.
Market risk
(systematic risk) is non diversifiable. This type of risk cannot
be diversified away.
ii.
Company-unique risk
(unsystematic risk) is diversifiable. This type of risk can be
reduced through diversification
22. TYPES OF INVESTMENT RISKS
Company-Unique Risk (Unsystematic)
Risk affects only a specific firm.
This risk can be reduced simply by investment
diversification.
Example of the events: a company’s labor force goes
on strike, the outcome of unfavorable litigation & CEO
changes.
23. TYPES OF INVESTMENT RISKS
Market Risk (Systematic)
Risk affects all firms because it is beyond the control of
the investor and the firm.
Systematic risk reflects mainly macroeconomic shocks
that affect aggregate behavior of the economy.
measured by beta
Example unexpected changes in interest rates, tax rate
changes, war, turbulent political events & foreign
competition.
25. MEASURING MARKET RISK
Once the individual asset return and market return obtained,
a graph is prepare to see the relationship between that asset
return and market return.
Asset return is plot on Y-axis and market return on X-axis.
When all the returns are plotted, draw a line of best-fit for all
the stock returns relative to market returns which we call
Characteristic line.
The slope of the characteristic line is called BETA. It measures
of the firm’s market risk.
Example 6- XYZ returns are 1.2 times as volatile on average as
those of the overall market.
β = 1.2 means any increase/decrease by 1% in market return
will cause an increase or decrease by 1.2% in asset return
27. MEASURING MARKET RISK - BETA
Interpreting beta (β)
Specifically, beta is a measure of how an individual stock’s
returns response (sensitivity) to a change is market returns.
The market’s beta is 1
• A firm that has a beta = 1 has average market risk. The
stock is no more or less volatile than the market.
• A firm with a beta >1 is more volatile than the market.
• A firm with a beta < 1 is less volatile than the market.
• A firm with a beta=0 has no systematic risk.
Most stocks have betas between 0.60 and 1.60
28. MEASURING MARKET RISK - BETA
The portfolio beta indicates the percentage change on
average of the portfolio for every 1 percent change in the
general market
It is a weighted average of the individual assets’ beta and
asset has its own beta.
j% invested in portfolio
β of stock j
βportfolio= ∑ wj βj
Exercise: What is the Beta of the portfolio?
Asset Beta
Proportions
1
1.35
.10
2
1.12
.20
3
1.67
.30
4
1.04
.20
5
1.55
.20
29. REQUIRED RATE OF RETURN - CAPM
Investor’s required rate of returns is the minimum rate of
return necessary to attract an investor to purchase or hold a
security.
The required return for all assets is composed of two parts:
the risk-free rate and a risk premium.
The risk-free rate (Rf) is usually
estimated from the return on
treasury bills
The risk premium is a function of
both market conditions and the
asset itself.
30. REQUIRED RATE OF RETURN - CAPM
Risk-free rate is the rate of return or discount rate for
risk-less investments that is typically measured by
Treasury bill rate.
The risk premium for a stock is composed of 2 parts:
a. The Market Risk Premium which is the return
required for investing in any risky asset rather than the
risk-free rate.
b. Beta, a risk coefficient which measures the
sensitivity of
the particular stock’s return to changes
in market conditions.
31. REQUIRED RATE OF RETURN - CAPM
Example
HD Corporation, a growing computer software
developer, wishes to determine the required
return on asset Z, which has a beta of 1.5. The
risk-free rate of return is 7%; the return on the
market portfolio of assets is 11%. Substituting βZ
= 1.5, rf = 7%, and rp = 11% into the CAPM yields a
return of:
rZ = 7% + 1.5 [11% - 7%]
= 13%
So, if the expected rate of return is
a) 15% and b) 10%, is the stock underpriced or
overpriced?
32. REQUIRED RATE OF RETURN - CAPM
CAPM (Capital Asset Pricing Model) is a model to measure
the investor’s required rate of return (provides a risk-return
trade off in which risk is measured in terms of beta).
CAPM provides for an intuitive approach for thinking about
the return that an investor should require on an investment,
given the asset’s systematic or market risk.
CAPM equation equates the expected rate of return on a
stock to the risk-free rate plus a risk premium for the
systematic risk.
SML is a graphic representation of the CAPM, where the line
shows the appropriate required rate of return for a given
stock’s systematic risk.
33. SML – The line that reflect the attitude of investors
Required
rate of
return
regarding the minimal acceptable return for a given level
of systematic risk.
(SML)
.
13%
11%
Risk Premium
Market Risk Premium
Risk-free
rate of
return
(7%)
Risk Free Rate
1.0
1.5
This linear relationship
between risk and required
return is known as the
Capital Asset Pricing Model
(CAPM).
Beta
33
