Define risk and return.
Identify risk and return relationship.
Calculate expected return and standard deviation.
Measure coefficient of variation.
Distinguish the different types of investment risks and
methods that is used to measure them.
Explain portfolios and risk diversification.
Calculate required rate of return based on CAPM.
Return represents the total gain or loss on an investment.
You invested in 1 share of Apple (AAPL) for $95 and sold
a year later for $200. The company did not pay any
dividend during that period. What will be the cash return
on this investment?
Cash Return = $200 + 0 - $95 = $105
Rate of Return = ($200 + 0 - $95) ÷ 95 = 110.53%
Expected return is what you expect to earn from an
investment in the future.
It is estimated as the average of the possible returns, where
each possible return is weighted by the probability that it
Pb1 = probability of occurrence of the outcome
r = return for the outcome
n = number of outcomes considered
Expected Return (k^ ) the return that an investor expects to earn on an
asset, given its price, growth potential, etc.
‡Required Return ( k- ) the return that an investor requires on an asset
given its risk and market interest rates.
•This expected rate of return is in the form of cash flow. In referring to
that, we will use cash flows in order to measure rate of return.
• Risk is defined as the chance of suffering a financial
loss. Or the potential variability in future cash flows.
• Risk may be used interchangeably with the term
uncertainty to refer to the variability of returns (possible
•The wider the range of possible future events that can
occur, the greater the risk.
• Potential variability in future cash flow The possibilityʹ
that an actual return will differ from our expected return.
• A greater chance of loss are considered more risky
than those with a lower chance of loss.
• Standard deviation (S.D.) is one way to measure risk. It
measures the volatility or riskiness of returns. (σ -sigma)
• S.D. = square root of the weighted average squared
deviation of each possible return from the expected return.
This variability in returns can be quantified by computing
the Variance or Standard Deviation in investment returns.
the standard deviation, σk, which measures the
dispersion around the expected value.
State of Probability Return
Company A Company B
Recession 0.20 4% -10%
Normal 0.50 10% 14%
Boom 0.30 14% 30%
k (A) = .2 (4%) + .5 (10%) + .3 (14%) = 10%
k (B) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%
Based only on your expected return calculations,
which stock would you prefer?
Have you considered risk??????????
( 4% - 10%)2
(.2) = 7.2
(10% - 10%)2
(.5) = 0
(14% - 10%)2
(.3) = 4.8
Variance = 12
Stand. dev. = 12 = 3.46%
(-10% - 14%)2
(.2) = 115.2
(14% - 14%)2
(.5) = 0
(30% - 14%)2
(.3) = 76.8
Variance = 192
Stand. dev. = 192 = 13.86%
Company A company B
Expected Return 10% 14%
Standard Deviation 3.46% 13.86%
Which company is good. It depends on your tolerance for risk!
We can conclude that, company A has lower risk compared to investment
B BUT Company B has higher return.
Remember, there’s a tradeoff between risk and return.
The coefficient of variation, CV, is a measure of relative
dispersion that is useful in comparing risks of assets with
differing expected returns.
CV = σ / k
The higher the CV, the higher the risk.
CV A = 3.46 % / 10%
CV B = 13.86% / 14%
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.
Return Measurement for a Single Asset:
Expected Return (cont.)
Risk Measurement for a Single
Asset: Standard Deviation (cont.)
Table 1 The
of the Returns
for Assets A
• An investment portfolio is any collection or combination of
• If we assume all investors are rational and therefore risk averse,
that investor will ALWAYS choose to invest in portfolios rather than in
•Investors will hold portfolios because he or she will diversify away a
portion of the risk that is inherent in “putting all your eggs in one
• 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
Portfolio and Diversification
‡ Portfolio: Hold /Invest in different types of assets (or
investments) at the same time or period.
Combining several securities in a portfolio can actually
reduce overall risk.
Invest in different type of securities may lower the risk of
losses. This is because, if we loss in security B, probably, for
security A we will earn profit.
‡Reduction in risk through investing in securities that NOT
perfectly correlated. (assets with a negative correlation)
Portfolio and Diversification
Diversification: spreading out of investments to reduce risks.
Investments across different securities rather than invest
in only one stock.
Reducing a risk of portfolio is depends on the correlation
(r) between all of the stocks.
Correlation is a statistical measurement of the relationship
between two variables.
Possible correlations range from +1 to 1ʹ
‡ If two stocks are perfectly positively correlated, diversification has
NO effect on risk. i.e If correlation (r) = +1, we cannot abolish all the
risk. A correlation of +1 indicates a perfect positive correlation,
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 (r) = -1, we can abolish the risk. A
correlation of -1 indicates a perfect negative correlation, meaning that
as one stock goes up, the other goes down.
Investors should NOT expect to eliminate all risk from their
portfolio. Some risk can be diversified away and some cannot.
Market risk (systematic risk) is nondiversifiable. This type of risk
cannot be diversified away. Such as Unexpected changes in interest
rates. Unexpected changes in cash flows due to tax rate changes,
foreign competition, and the overall business cycle.
Company-unique risk (unsystematic risk) is diversifiable. This
type of risk can be reduced through diversification.
Such as A company’s labor force goes on strike.
A company’s top management dies in a plane crash.
A huge oil tank bursts and floods a company’s production area.
Market portfolio is a portfolio consisting of a weighted sum
of every asset in the market, with weights in the proportions
that they exist in the market.
ƒ Proxy can be used as a market portfolio such as S&P 500
Index in the U.S and Nikkei 225 Index in Japan.
ƒ In Malaysia, Bursa Malaysia (formerly known as KLSE) is one
of the proxies that can be used as market portfolio.
ƒ The movement in these indexes act as a benchmark to the
movement of the market.
Systematic risk called non-diversifiable risk 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.
Market risk measured by beta (β = 1)
Once the asset return and market return obtained, a graph is
prepare to see the relationship between asset return and market
return. Asset return and market return are plot on Y-X-axis.
When all the returns are plotted, draw a line of best-fit through
coordinate point (0,0), which we call Characteristic line.
Measuring market risk
Market returns and assets returns for certain period can be determined by
looking at the percentage of changes in index or price based on the
kt = (Pt / Pt – 1) – 1
Asset Return & Market Return
Period Price Return Index Return
0 19.00 853.42
1 19.29 1.53% 869.10 1.84%
2 20.90 8.34% 900.67 3.63%
3 19.54 -6.51% 901.89 0.14%
4 21.50 10.03% 923.80 2.42%
The slope of the line (beta), represents the average movement of
the firm’s stock returns in response to a movement in the market’s
return i.e the average relationship between a stock’s return and
Interpreting beta ( )ɴ
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.
¾ Most stocks have betas between 0.60 and 1.60
Measuring market risk
Beta is a measure of how an individual stock’s returns
vary with market returns.
Beta measures of the sensitivity of an individual stock’s
return to changes in the market.
It indicates the average response of a stock’s return to the
change in the market as a whole.
β = 1.2 means any increase/decrease by 1% in market return
will cause an increase or decrease by 1.2% in asset return.
Portfolio beta indicates the percentage change on average of
the portfolio for every 1 percent change in the general
The portfolio beta is a weighted average of the individual
asset's beta and assets has its own beta.
β portfolio= Σ wj*βj
Where wj = % invested in stock j
βj = Beta of stock j
Measuring portfolio beta
We know how to measure risk, using standard deviation for
overall risk and beta for market risk.
We know how to reduce overall risk to only market risk through
We need to know how much extra return we should require for
accepting extra risk.
What is the Required Rate of Return?
The return on an investment required by an investor given market
interest rates and the investment’s risk.
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 which is usually estimated from the return on treasury
bills and a risk premium which is a function of both market
conditions and the asset itself.
Required Rate of Return (CAPM)
This linear relationship between risk and required return is
known as the Capital Asset Pricing Model (CAPM).
CAPM equation equates the required rate of return on a
stock to the risk-free rate plus a risk premium for the systematic
The equation indicates that investor’s minimum acceptable rate of
return is equal to the risk-free rate plus a risk premium for assuming
Required Rate of Return (CAPM)
The Security Market Line (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.
Risk-Free Rate: This is the required rate of return or discount
rate for risk-less investments. Risk-free rate is typically measured
by U.S. Treasury bill rate.
Risk Premium: Additional return we must expect to receive for
assuming risk. As the level of risk increases, we will demand
additional expected returns.
The risk premium for a stock is composed of two parts: The
Market Risk Premium which is the return required for investing in
any risky asset rather than the risk-free rate.
Beta, a risk coefficient which measures the sensitivity of the
particular stock’s return to change in market conditions.
Example: ABC Corporation 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%.
K Z = 7% + 1.5 [11% - 7%]
= 13% According to the CAPM, Asset Z should be priced to give a 13% return.
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
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
The risk premium is a function of
both market conditions and the
This linear relationship
between risk and required
return is known as the
Capital Asset Pricing Model
SML – The line that reflect the attitude of investors
regarding the minimal acceptable return for a given level
of systematic risk.
Market Risk Premium
Risk Free Rate