risk and return student.ppt

Principles of Finance
o Lecture 6
o Risk and Return
o 2022
SMS Principles of Finance - 22 Prof. Abdelgadir 1
8/11/2022

Learning objectives
1. States and nature of investment decision making
2. Meaning of risk and return
3. Assessing and measuring the expected return and
risk of a single asset.
4. Discuss the measurement of return and standard
deviation for a portfolio
5. Review the two types of risk and diversification
6. Measurement of systematic risk
7. Explain the capital asset pricing model (CAPM)
2
8/11/2022 SMS Principles of Finance - 22 Prof. Abdelgadir

States/Nature of investment Decision Making
• Certainty: an investment decision leads to a specific outcome
and that outcome is known with certainty: Perfect
information and knowledge
• Risk: an investment decision leads to a number of outcomes
we do not know which one will happen but we can estimate
and know the probability of each one happening: Partial
information/knowledge
• Uncertainty: an investment decision leads to a number of
outcomes we do not know which one will happen and we do
not know the probability of occurrence: complete ignorance.
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Return Defined
8/11/2022

Example 1
• Anas wishes to determine the returns on two of his machines
C & D. C was purchased 1 year ago for $20,000 and currently
has a market value of $21,500. During the year, it generated
$800 worth of after-tax receipts. D was purchased 4 years
ago; its value in the year just completed declined from
$12,000 to $11,800. During the year, it generated $1,700 of
after-tax receipts
8/11/2022

Example 2
• An investor purchased a share last year for
120 pounds and at the end of the year
received 15 pounds as dividend and sold the
share for 117 pounds. What is his return from
this share?
• Return = 15 + (117-120) = 10%
• 120
8/11/2022 SMS Principles of Finance - 22 Prof. Abdelgadir 6

Example3- Calculating Returns
• You bought a stock for $35 and you received
dividends of $1.25. The stock is now selling for
$40.
– What is your dollar return?
• Dollar return = 1.25 + (40 – 35) = $6.25
– What is your percentage return?
• Dividend yield = 1.25 / 35 = 3.57%
• Capital gains yield = (40 – 35) / 35 = 14.29%
• Total percentage return = 3.57 + 14.29 = 17.86%
• Total percentage return = 6.25 / 35 = 17.86%
SMS Principles of Finance - 22 Prof. Abdelgadir
8/11/2022 7

Risk Defined
• In the context of business and finance, risk is defined as the
chance of suffering a financial loss.
• Assets which have a greater chance of loss are considered
more risky than those with a lower chance of loss.
• Risk may be used interchangeably with the term uncertainty
to refer to the variability of returns associated with a given
asset.
• In case of risk we talk expected return and not actual return.
• Total risk is measured by the variance or the standard
deviation

Expected Returns: Single Asset
• Expected returns are based on the
probabilities of possible outcomes
• In this context, “expected” means average if
the process is repeated many times
• The “expected” return does not even have to
be a possible return
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Example: Expected Returns: Single Asset
• Suppose you have predicted the following returns for stocks C and
T in three possible states of nature. What are the expected
returns?
– State Probability C T
– Boom 0.3 15 25
– Normal 0.5 10 20
– Recession ??? 2 1
• RC = .3(15) + .5(10) + .2(2) = 9.99%
• RT = .3(25) + .5(20) + .2(1) = 17.7%
• If the risk-free rate is 6.15%, what is the risk premium?
• Stock C: 9.99 – 6.15 = 3.84%
• Stock T: 17.7 – 6.15 = 11.55%
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Variance and Standard Deviation: Single Asset
• Variance and standard deviation still measure
the volatility of returns
• Using unequal probabilities for the entire
range of possibilities
• Weighted average of squared deviations
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11

Example: Variance and Standard
Deviation
• Consider the previous example. What are the
variance and standard deviation for each stock?
• Stock C
– 2 = .3(15-9.9)2 + .5(10-9.9)2 + .2(2-9.9)2 = 20.29
–  = 4.5
• Stock T
– 2 = .3(25-17.7)2 + .5(20-17.7)2 + .2(1-17.7)2 = 74.41
–  = 8.63
8/11/2022 12

Risk Measurement for a Single Asset:
Coefficient of Variation
• The coefficient of variation, CV, is a measure
of relative dispersion that is useful in
comparing risks of assets with differing
expected returns.
• CV = Standard Deviation/Expected Return
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Risk Measurement for a Single Asset:
Coefficient of Variation
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statistics Asset A Asset B
(1) Expected Return 12% 20%
(2) Standard Deviation 9% a 10%
(3) Coefficient of Variation (2)/(1) 0.75 0.50 a
a : Preferred asset using the given risk measure

Portfolios
• A portfolio is a collection of assets
• The return of a portfolio is measured by the
portfolio expected return
• The total risk of a portfolio is measured by the
standard deviation, just as with individual
assets
8/11/2022 15

Example: Portfolio Weights
• Suppose you have $ 20000 to invest and you
have purchased securities in the following
amounts. What are your portfolio weights in
each security?
– $2000 of A
– $5000 of B
– $4000 of C
– $9000of D
•A: 2000/20000 = 10%
•B: 5000/20000 = 25%
•C: 4000/20000 = 20%
•D: 9000/20000 = 45%
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Portfolio Expected Returns
• The expected return of a portfolio is the weighted
average of the expected returns for each asset in the
portfolio
• You can also find the expected return by finding the
portfolio return in each possible state and computing
the expected value as we did with individual
securities
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Example: Expected Portfolio
Returns
• Consider the portfolio weights computed previously.
If the individual stocks have the following expected
returns, what is the expected return for the
portfolio?
– A : 5 %
– B: 10%
– C: 12%
– D: 8 %
• E(RP) = 0.10(0.05) + 0.25(0.10) + 0.20(0.12) +
0.45(0.08) = 9%
8/11/2022 18

Example: Portfolio Variance (risk)
• Consider the following information
– Invest 50% of your money in Asset A
– State Probability A B
– Boom .4 30% -5%
– Bust .6 -10% 25%
• What are the expected return and standard
deviation for each asset?
• What are the expected return and standard
deviation for the portfolio?
Portfolio
12.5%
7.5%
8/11/2022 19

Portfolio Variance
• Compute the portfolio return for each state:
RP = w1R1 + w2R2 + … + wmRm
• Compute the expected portfolio return using
the same formula as for an individual asset
• Compute the portfolio variance and standard
deviation using the same formulas as for an
individual asset
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Portfolio Variance
If A and B are your only choices, what percent are you investing
in Asset B?
Asset A: E(RA) = .4(30) + .6(-10) = 6%
Asset B: E(RB) = .4(-5) + .6(25) = 13%
Variance(A) = .4(30-6)2 + .6(-10-6)2 = 384 Std. Dev.(A) = 19.6%
Variance(B) = .4(-5-13)2 + .6(25-13)2 = 216 Std. Dev.(B) = 14.7%
Portfolio return in boom = .5(30) + .5(-5) = 12.5
Portfolio return in bust = .5(-10) + .5(25) = 7.5
Expected return = .4(12.5) + .6(7.5) = 9.5 or .5(6) + .5(13) = 9.5
Variance of portfolio = .4(12.5-9.5)2 + .6(7.5-9.5)2 = 6 Standard
deviation = 2.45%
8/11/2022 21

Portfolio Variance
• Note that the variance is NOT equal to .5(384)
+ .5(216) = 300 and
• Standard deviation is NOT equal to .5(19.6) +
.5(14.7) = 17.17%
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Total Risk
• Total risk = systematic risk + unsystematic risk
8/11/2022 23

Systematic Risk
• Risk factors that affect a large number of
assets
• Also known as non-diversifiable risk or market
risk
• Includes such things as changes in GDP,
inflation, interest rates, etc.
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Unsystematic Risk
• Risk factors that affect a limited number of
assets
• Also known as unique risk and asset-specific
risk
• Includes such things as labor strikes, part
shortages, etc.
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Risk Measurement
• The standard deviation of returns is a measure
of total risk
• For well-diversified portfolios, unsystematic
risk is very small
• Consequently, the total risk for a diversified portfolio
is essentially equivalent to the systematic risk
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Diversification
• Portfolio diversification is the investment in several
different asset classes or sectors
• Diversification is not just holding a lot of assets
• For example, if you own 50 internet stocks, you are
not diversified
• However, if you own 50 stocks that span 20 different
industries, then you are diversified
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The Principle of Diversification
• Diversification can reduce the variability of
returns without an equivalent reduction in
expected returns
• This reduction in risk arises because worse
than expected returns from one asset are
offset by better than expected returns from
another
• However, there is a minimum level of risk that
cannot be diversified away and that is the
systematic portion
8/11/2022 28

Measuring Systematic Risk
• How do we measure systematic risk?
• We use the beta coefficient to measure systematic risk
• Beta reflects the change in the stock price that results from
the change in the market price
• What does beta tell us?
– A beta of 1 implies the asset has the same systematic risk
as the overall market
– A beta < 1 implies the asset has less systematic risk than
the overall market
– A beta > 1 implies the asset has more systematic risk than
the overall market
8/11/2022 29

Total versus Systematic Risk
• Consider the following information:
Standard Deviation Beta
– Security C 20% 1.25
– Security K 30% 0.95
• Which security has more total risk?
• Which security has more systematic risk?
• Which security should have the higher
expected return?
8/11/2022 30

Example: Portfolio Betas
• Consider the previous example with the following
four securities
– Security Weight Beta
– A 0.10 2.685
– B 0.25 0.195
– C 0.20 2.161
– D 0.45 2.434
• What is the portfolio beta?
• 0.10(2.685) + 0.25(.195) + 0.20(2.161) + 0.45(2.434)
= 1.845
8/11/2022 31

Beta and the Risk Premium
• Remember that the risk premium = expected
return – risk-free rate
• The higher the beta, the greater the risk
premium should be
• Can we define the relationship between the
risk premium and beta so that we can
estimate the expected return?
– YES!
8/11/2022 32

The Capital Asset Pricing Model
(CAPM)
• The capital asset pricing model defines the
relationship between risk and return
• E(RA) = Rf + A(E(RM) – Rf)
• If we know an asset’s systematic risk, we can
use the CAPM to determine its expected
return
• This is true whether we are talking about
financial assets or physical assets
8/11/2022 33

Relationship Between Risk & Expected Return
Expected
return
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Example - CAPM
• Consider the betas for each of the assets given
earlier. If the risk-free rate is 2.13% and the market
risk premium is 8.6%, what is the expected return for
each?
Security Beta Expected Return
A 2.685 2.13 + 2.685(8.6) = 25.22%
B 0.195 2.13 + 0.195(8.6) = 3.81%
C 2.161 2.13 + 2.161(8.6) = 20.71%
D 2.434 2.13 + 2.434(8.6) = 23.06%
13-35

Tutorial
1.The excess return required from a risky asset over that required from a risk-free asset is called
a. risk premium.
b. variance..
c. excess return.
d. average return.
2.The average squared difference between the actual return and the average return is called the:
a. volatility return.
b. variance.
c. standard deviation.
d. risk premium.
3.The standard deviation for a set of stock returns can be calculated as the:
a. positive square root of the average return.
b. average squared difference between the actual return and the average return.
c. positive square root of the variance.
d. average return divided by N minus one, where N is the number of returns.
8/11/2022 36

Tutorial
4- A year ago, you purchased 300 shares of IXC Technologies, Inc. stock at a price of $9.03 per share. The stock
pays an annual dividend of $.10 per share. Today, you sold all of your shares for $28.14 per share. What is your
total dollar return on this investment?
a. $5,703
b. $5,733
c. $5,753
d. $5,763
5- You purchased 200 shares of stock at a price of $36.72 per share. Over the last year, you have received total
dividend income of $322. What is the dividend yield?
a. 3.2 percent
b. 4.4 percent
c. 6.8 percent
d. 9.2 percent
6- You just sold 200 shares of Langley, Inc. stock at a price of $38.75 a share. Last year you paid $41.50 a share
to buy this stock. Over the course of the year, you received dividends totaling $1.64 per share. What is your
capital gain on this investment?
a. -$550
b. -$222
c. -$3
d. $550

Tutorial
7- Risk that affects a large number of assets, each to a greater or lesser degree, is called _____ risk.
a. idiosyncratic
b. diversifiable
c. systematic
d. asset-specific
8- Risk that affects at most a small number of assets is called _____ risk.
a. portfolio
b. undiversifiable
c. market
d. unsystematic
9- You are comparing stock A to stock B. Given the following information, which one of these two stocks should
you prefer and why?
Rate of Return if
State of Probability of State Occurs
Economy State of Economy Stock A Stock B
Boom 60% 9% 15%
Recession 40% 4% -6%
a. Stock A; because it has an expected return of 7 percent and appears to be more risky.
b. Stock A; because it has a higher expected return and appears to be less risky than stock B.
c. Stock A; because it has a slightly lower expected return but appears to be significantly less risky than stock B.
d. Stock B; because it has a higher expected return and appears to be just slightly more risky than stock A.
e. Stock B; because it has a higher expected return and appears to be less risky than stock A.

Tutorial
10- You own a portfolio with the following expected returns given the various states of the economy. What is the
overall portfolio expected return?
State of Probability of Rate of Return
Economy State of Economy if State Occurs
Boom 15% 18%
Normal 60% 11%
Recession 25% -10%
a. 6.3 percent
b. 6.8 percent
c. 7.6 percent
d. 10.0 percent
11- What is the portfolio variance if 30 percent is invested in stock S and 70 percent is invested in stock T?
State of Probability of Returns if State Occurs
Economy State of Economy Stock S Stock T
Boom 40% 12% 20%
Normal 60% 6% 4%
a. .002220
b. .004056
c. .006224
d. .008080
12- Your portfolio is comprised of 30 percent of stock X, 50 percent of stock Y, and 20 percent of stock Z. Stock X has a beta of .64,
stock Y has a beta of 1.48, and stock Z has a beta of 1.04. What is the beta of your portfolio?
a. 1.01
b. 1.05
c. 1.09
d. 1.14

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