PRINCIPLES OF FINANCIAL
ANALYSIS
WEEK 4: LECTURE 4
Lecturer: Chara Charalambous
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Learning Objectives
•
•
•
•
What is expected rate of return ?
What is risk?
How investment risk should be measured?
Explain the relationship between an investor’s
required rate of return and the riskiness of the
investment.
Lecturer: Chara Charalambous
2
Meaning of Risk
 Risk refers to the chance that some unfavourable
event will happen.
 For example, If you engage in skydiving, you are
taking a chance with your life – skydiving is risky.
 If you bet on the horses, you are risking your
money.
 Most people view risk as a chance of loss, but in
reality risk occurs when we cannot be certain
about the outcome of a particular activity so will
not sure what will happen in the future.
Lecturer: Chara Charalambous
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Risk and Investing
The Rules:
– Investing is risky.
– Risk is manageable.
Types of Risk:
– Diversifiable
Risk
– Can be eliminated through
diversification. Is not important to informed investors because
they can eliminate its effect by ‘diversifying ‘ it away. Diversify
means expand, spread, choose more than one alternative. In
finance, diversification means reducing risk by investing in a
variety of assets. Simply put it: it is foolish to invest all your
money in one investment. ‘’Don’t put all your eggs in one
basket’’.
.
– Nondiversifiable Risk – this is the important risk and is bad
in the sense that it cannot be eliminated and if you invest in
anything else than riskless assets, like government assets, you
will be exposed to it.
Lecturer: Chara Charalambous
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Lecturer: Chara Charalambous
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Investment returns
The average rate of return on an investment can be calculated
as follows:
(Amount received – Amount invested)
Return =
________________________
Amount invested
For example, if $1,000 is invested and $1,100 is returned after
one year, the rate of return for this investment is:
($1,100 - $1,000) / $1,000 = 10%.
Lecturer: Chara Charalambous
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What is investment risk?
Investment risk is related to the possibility of
earning a low or negative actual return.
The greater the chance of lower return than
expected or negative returns, the riskier the
investment.
The greater the range of possible events that
can occur, the greater the risk
Lecturer: Chara Charalambous
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Illustration of Riskiness of financial assets
Supposed you have a large amount of money to invest for one year
 You could buy a Government security that has an expected return to
6%. The rate of return in this investment can be determined quite
accurate because the chance of the government defaulting is small:
the outcome is guaranteed which means this is a risk free
investment.
OR
 On the other hand you could buy shares of a newly formed
company which has developed technology that can be used to
extract petroleum. This technology is still in the process of proven
economically affordable so it is not known what returns the
ordinary shareholders will receive in the future. Experts have
appreciate that the expected return of such investment will
probably be 30% but there is also the possibility-the risk that the
company will not survive and so the entire investment will be lost.
The return that the investors will receive can not be determined
accurately because more than one outcome is possible. This is a
risky investment.
Lecturer: Chara Charalambous
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THE RETURN EXPECTED FROM AN
INVESTMENT IS POSITIVELY RELATED TO THE
INVESTMENT RISK – A HIGHER EXPECTED
RETURN REPRESENTS AN INVESTOR’S
COMPENSATION FOR TAKING ON A GREATER
RISK!!!
Lecturer: Chara Charalambous
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Explanation:
• If you buy a bond you expect to receive interest on the bond
(interest payments are the rate of return on your investment).
The possible outcomes on this investment are (1) the issuer
will make the interest payments (2) ) the issuer will fail to
make the interest payments . The higher the probability of
default on the interest payments
the riskier the bond, and
the higher the risk the higher the rate of return you would
require to invest in the bond.
Lecturer: Chara Charalambous
10
Defining and Measuring Risk
We evaluate risk in two different bases:
Stand-Alone Risk is that risk which is associated with an
investment which it is held on its own- in one asset.
Portfolio Risk is that risk which is associated with an investment
which it is held in combination with other assets/investments.
Lecturer: Chara Charalambous
11
Probability Distributions
• An event’s probability is defined as the chance that the event
will occur.
• For example, a weather forecaster might state: “There is a
40% chance of rain today and a 60% chance that it will not
rain.” If all possible events, or outcomes, are listed, and if a
probability is assigned to each event, then the listing is called
a probability distribution. Keep in mind that the probabilities
must sum to 1.0, or 100%.
Lecturer: Chara Charalambous
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Probability Distributions
Probability Distribution:
A listing of all possible outcomes with the
possibility
of
each
option-probability
indicated.
• For example, a weather forecaster might state
“There is a 40 percent chance of rain today
and a 60 percent chance that it will not rain”.
Lecturer: Chara Charalambous
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Probability Distributions – example 1
Chance of Rain:
Outcome
Rain
No Rain
Probability
40%
60%
100%
The probabilities must
sum 100% to account
for all the possible
outcomes
Flip a Coin:
Outcome
Heads
Tails
Probability
50%
50%
100%
Lecturer: Chara Charalambous
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Probability Distributions – example 2
• Imagine two firms: Firm A and Firm B and you make
an investment of €10,000 in the shares of one of the
two. A’s sales rise and fall depending on the situation
exist in the economy and also faces high
competition. B on the other hand provides an
essential service necessary to all and doesn't face
competition so its profits are more stable.
Lecturer: Chara Charalambous
15
Probability Distributions – example 2
Firm A and Firm B
Rate of Return on Stock if
State of the
Economy
Probability of This
State Occurring
This State Occurs
Firm A
Boom
Normal
Recession
Firm B
0.2
110%
20%
0.5
22%
16%
0.3
-60%
10%
1.0
Firm’s B rate of return fluctuate much more than this of Firm A. The above table
shows the possible outcomes for investing in Firm A or B. We can see that the most
possible outcome is for the economy to be normal in which A gives a return 22% and
B 16%. But other outcomes are also possible so we need to find a measure that
takes in account – considers all possible outcomes. This measure is the expected
Lecturer: Chara Charalambous
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rate of return.
Expected Rate of Return
The rate of return expected to be realized from an
investment
The weighted average of the outcomes, where the
weights are the probabilities: we multiply each
possible outcome by the probability it will occur and
then sum the results. We designate the expected rate
of return with ^
k
k̂  Pr1k 1  Pr2 k 2  ...  Prn k n

n
 Pr k
i 1
i
i
Lecturer: Chara Charalambous
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Expected Rate of Return
^
k
= 0.2(110%)+0.5(22%)+0.3(-60%)=15.0%
Probability of
This State
State of the
Economy Occurring (Pr i)
(1)
Boom
Normal
Recession
(2)
0.2
0.5
0.3
1.0
Firm A
Return if This State Product:
Occurs (ki)
(2) x (3)
(3)
110%
22%
-60%
^
k =
= (4)
22%
11%
-18%
15%
Lecturer: Chara Charalambous
Firm B
Return if This Product:
State Occurs (ki) (2) x (5)
(5)
20%
16%
10%
^
k =
= (6)
4%
8%
3%
15%
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Continuous versus Discrete
Probability Distributions
We have assumed that only three states of the
economy can exist: this is called discrete because
there is a limited number of outcomes.
Discrete Probability Distribution:
the number of possible outcomes is limited
Actually the situation of the economy could
range from a deep depression to a fantastic boom
and there are an unlimited number of possibilities
between.
Continuous Probability Distribution:
the number of possible outcomes is unlimited
Lecturer: Chara Charalambous
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Discrete Probability Distributions
a. Firm A
Probability of
Occurrence
b. Firm B
Probability of
Occurrence
0.5 -
0.5 -
0.4 -
0.4 -
0.3 -
0.3 -
0.2 -
0.2 -
0.1 -
0.1 -
-60 -45 -30 -15 0 15 22 30 45 60 75 90 110
-10 -5
Rate of
Expected Rate
Return
(%) Chara Charalambous
Lecturer:
of Return (15%)
0 5 10
16 20 25
Expected Rate
of Return (15%)
Rate of
Return (%)
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• The tighter the probability distribution, the more
likely it is that the actual outcome will be close to the
expected value, and, consequently, the less likely it is
that the actual return will be mush different from the
expected return.
Firm B has a relatively tight probability
distribution: its actual return is likely to be
closer to its 15% expected return than that of
Firm A.
A tighter probability distribution is
representative of lower risk.
Lecturer: Chara Charalambous
21
Continuous
Probability Distributions
If we consider more probabilities than we id in
Probability Density
table of slide 17 and the outcomes would be
0.5 continuous curves instead of vertical columns
Firm B :In previous
figure the probability of
obtaining exactly 16%
was 50%. Here is
smaller because there
are
many
possible
outcomes instead of
just three.
Firm B
Firm A
-60
0
15
110
Rate of Return (%)
Expected Rate of
Return
Lecturer: Chara Charalambous
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Measuring Stand-Alone Risk:
The Standard Deviation
• Risk is a difficult concept to grasp, and a great
deal of controversy has surrounded attempts
to define and measure it. However, a common
definition that is satisfactory for many
purposes is stated in terms of probability
distributions.
• The tighter the probability distribution of
expected future returns, the smaller the risk
of a given investment.
Lecturer: Chara Charalambous
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Measuring Stand-Alone Risk:
The Standard Deviation
A measure of the tightness or
variability of a set of outcomes
A tighter probability distribution is representative of
lower risk associated with the investment.
Standard deviation   
 
2

n
i 1

2
k i - kˆ Pri
A measure of stand alone risk
 ‘sigma’ provides a specific value that represents the “tightness”
of the probability distribution.
A lower standard deviation indicates a tighter probability distribution, and
therefore the less risk connected
with the particular stock.
Lecturer: Chara Charalambous
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• First we need to Calculate the expected rate of return.
• Second deduct the expected rate of return
from
each possible outcome to obtain a set of deviations.
• Then multiply the deviations by the probability of
occurrence for its related outcome. Sum these
products to obtain the variance of the probability
distribution:
n
 k
i 1

2
i
- k̂ Pri
•Finally, find the square root of the variance to obtain
the standard deviation:
Standard deviation     
2
Lecturer: Chara Charalambous
 k
n
i 1

2
i
- k̂ Pri
25
Thus, the standard deviation is essentially a weighted average of
the deviations from the expected value, and it provides an idea of
how far above or below the expected value the actual value is
likely to be.
Larger standard deviation indicates a greater variation of
returns and thus a greater chance that the actual return will
turn out to be substantially lower than the expected return.
Therefore, is a riskier investment than other investments with
lower SD when held alone.
Lecturer: Chara Charalambous
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Calculating Firm’s A Standard Deviation
Expected
Payoff Return
ki
k^
(1)
(2)
110%
15%
22%
15%
-60%
15%
ki - k^
(1) - (2) = (3)
95
7
-75
^2
(k i - k)
(4)
9,025
49
5,625
Probability
(5)
^2
(k i - k) Pr i
(4) x (5) = (6)
0.2
1,805.0
0.5
24.5
0.3
1,687.5
Variance   2  3,517.0
Standard Deviation   m   m2  3,517  59.3%
Lecturer: Chara Charalambous
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• Firm’s B standard deviation is 3.6%. The larger
standard deviation of Firm’s A indicates a
greater variation of returns, thus a greater
chance that the expected return will not be
realized. Therefore Firm A would be consider a
riskier investment.
Lecturer: Chara Charalambous
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Risk Aversion & Risk Premium
• If you choose the less risky investment, you are
risk averse. Most investors are indeed risk averse
– this is a well document fact, and certainly the
average investor is risk averse.
• Risk-averse investors require higher rates of return
to invest in higher risk securities.
• Risk premium – is the difference between the
return on a risky asset and less risky asset and
serves as compensation for investors to hold
riskier securities.
Lecturer: Chara Charalambous
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Portfolio Returns
A portfolio is a combination of two or more securities.
Combining securities into a two portfolio reduces risk
^
Expected return on a portfolio, kp The weighted average
expected return on the stocks held in the portfolio
k̂ p  w 1k̂1  w 2 k̂ 2  ...  w N k̂ N
N
  w j k̂ j
W1 is that stocks portion of the
portfolio’s dollar value; therefore the
sum of the W’s must equal 1.
j1
Lecturer: Chara Charalambous
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Example of Portfolio
Expected returns on four large companies:
Stocks/ Investments
Expected Return
1.AT&T
10%
2.General Electric
13%
3.Microsoft
30%
4.Citigroup
16%
If we formed a €100,000 portfolio investing €25,000 in
each stock the WEIGHTS OF THE PORTFOLIO ARE:
AT&T
€25000
WAT&T=25000/100000= 0.25
General Electric
Microsoft
Citigroup
€25000
… and the same is valid for the other
€25000
investments.
€25000
Lecturer: Chara Charalambous
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€100000
• If we formed a €100,000 portfolio investing €25,000
in each stock the expected portfolio return would
be 17.25%:
kp=0.25(10%)+0.25(13%)+0.25(30%)+0.25(16%)=17.25%
^ or ^Kj is the same: the expected rate of return on
Kp
the j or p stock.
Lecturer: Chara Charalambous
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CAPM: THE RELATIONSHIP BETWEEN RISK
AND RATES OF RETURN
• We know that investors demand a premium for bearing risk; that
is, the higher the risk of a security, the higher its expected return
must be to induce investors to buy (or to hold) it. However, if
investors are primarily concerned with the risk of their portfolios
rather than the risk of the individual securities in the portfolio,
then how should the risk of an individual stock be measured?
• One answer is provided by the Capital Asset Pricing Model
(CAPM), an important tool used to analyze the relationship
between risk and rates of return.
• The primary conclusion of the CAPM is this: The relevant risk of an
individual stock is its contribution to the risk of a well diversified
portfolio. A stock might be quite risky if held by itself, but—since
about half of its risk can be eliminated by diversification—the
stock’s relevant risk is its contribution to the portfolio’s risk, which
is much smaller than its stand-alone risk.
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• A simple example will help make this point clear. Suppose you
are offered the chance to flip a coin. If it comes up heads, you
win $20,000, but if it’s tails, you lose $16,000. This is a good
bet—the expected return is 0.5($20,000) + 0.5(−$16,000) =
$2,000. However, it’s a highly risky proposition because you
have a 50% chance of losing $16,000. Thus, you might well
refuse to make the bet. Alternatively, suppose that you were
to flip 100 coins and that you would win $200 for each head
but lose $160 for each tail. It is theoretically possible that you
would flip all heads and win $20,000, and it is also
theoretically possible that you would flip all tails and lose
$16,000, but the chances are very high that you would
actually flip about 50 heads and about 50 tails, winning a net
of about $2,000. Although each individual flip is a risky bet,
collectively you have a low-risk proposition because most of
the risk has been diversified away.
• This is the idea behind holding portfolios of stocks rather than
just one stock. The difference is that, with stocks, not all of
the risk can be eliminated by diversification—those risks
related to broad, systematic changes in the stock market will
remain.
Lecturer: Chara Charalambous
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• Are all stocks equally risky in the sense that
adding them to a well-diversified portfolio will
have the same effect on the portfolio’s risk? The
answer is “no.”
• Different stocks will affect the portfolio
differently, so different securities have different
degrees of relevant risk. How can the relevant
risk of an individual stock be measured? As we
have seen, all risk except that related to broad
market movements can, and presumably will, be
diversified away. After all, why accept risk that
can be eliminated easily? The risk that remains
after diversifying is called market risk, the risk
that is inherent (natural) in the market.
Lecturer: Chara Charalambous
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• CAPM is a model that is used to determine the
rate of return that investors will require on a
stock in order to compensate them for taking
the risk.
Lecturer: Chara Charalambous
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Beta β
Lecturer: Chara Charalambous
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• The primary conclusion reached in the preceding section is
that the relevant risk of an individual stock is the amount of
risk the stock contributes to a well-diversified portfolio. The
benchmark for a well-diversified stock portfolio is the market
portfolio, which is a portfolio containing all stocks. Therefore,
the relevant risk of an individual stock, which is measured by
its beta coefficient, is defined under the CAPM as the amount
of risk that the stock contributes to the market portfolio. In
CAPM terminology, ρiM is the correlation between Stock i’s
return and the market return, σi is the standard deviation of
Stock i’s return, and σM is the standard deviation of the
market’s return. The beta coefficient of Stock i, denoted by bi,
is found as follows:
• bi = σi
σM
* ρiM
Lecturer: Chara Charalambous
38
• This tells us that a stock with a high standard deviation,
σi, will tend to have a high beta, which means that,
other things held constant, the stock contributes a lot
of risk to a well-diversified portfolio. This makes sense,
because a stock with high stand-alone risk will tend to
destabilize the portfolio. Note too that a stock with a
high correlation with the market, ρiM, will also tend to
have a large beta and hence be risky. This also makes
sense, because a high correlation means that
diversification is not helping much, with most of the
stock’s risk affecting the portfolio’s risk.
Lecturer: Chara Charalambous
39
Beta β
• A measure of the extent to which the returns on
a given stock move with the stock market
β = Covariance of Market Return with Stock Return
Variance of Market Return
• β<1:
Movement of the asset is generally in the same direction as,
but less than the movement of the market
• β=1 :
Movement of the asset is generally in the same direction
as, and about the same amount as the movement of the market
• β>1:
Movement of the asset is generally in the same direction
as, but more than the movement of the market
Lecturer: Chara Charalambous
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• Suppose correlation coefficient between
market and share price of Company P is 0.75;
standard deviation (σ) of market is 15% and
that of share price is 8%, beta can equals
0.40 (=0.75 × 8%/15%).
Lecturer: Chara Charalambous
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The Relationship between Risk and Rates of
Return
^
• kj = expected rate of return on the j stock.
•
•
•
•
kj = required rate of return on the stock.
k RF = risk – free rate of return.
βj= beta of the stock.
k M = Required rate of return on a portfolio consisting
of all stocks, which is the market portfolio
• RP M= k M - k RF Market risk premium. This is an
additional return above the risk free rate required to
compensate an average investor for an average
amount of risk.
Lecturer: Chara Charalambous
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The Relationship between Risk and
Rates of Return
• Equation of Rate of Return
kj = k RF + (kM-kRF )βj
Example: A government bond has a rate of return 6% and the portfolio X has a
required return 14%. Also beta is 0.5 and the market risk premium is
8%. Find the required return that investors claim.
kx = 6% + ( 14% -6%)*0.5= 10%
Lecturer: Chara Charalambous
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Conclusion of CAPM
^ = expected rate of return on the j stock is
• If kj
higher than the kj = required rate of return on
the stock then the proposed portfolio is
efficient.
Lecturer: Chara Charalambous
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