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Risk and Return(Introduction)
Professor: Burcu Esmer
1
Overview
• Rates of Return: A Review
• A Century of Capital Market History
• Measuring Risk
• Risk & Diversification
• Thinking About Risk
• Measuring Market Risk
• Beta
• Risk and Return
• CAPM
• Capital Budgeting and Project Risk
2
Risk and Return
• People make decisions based on expected returns and risksevery day
• Should I attend to the corporate finance class today?
• Return: hour of leisure time
• Risk: you may miss an important topic for the exams
• Which activity would you prefer?
• Shopping
• Gold
• Sky-diving
• Different people have different perceptions of expectedreturns and risk
3
Risk and Return
• Since financial resources are finite, there is a hurdle thatprojects have to cross before being deemed acceptable.
• This hurdle will be higher for riskier projects than for saferprojects.
• A simple representation of the hurdle rate is as follows:
Hurdle rate = Riskless Rate + Risk Premium
• Two basic questions that every risk and return model infinance tries to answer are:
• How do you measure risk?
• How do you translate this risk measure into a riskpremium?
4
Risk Aversion
• How big a win would you require from ‘Heads’ to take thegamble
• You win $10,000 , if it is Heads
• You lose $10,000 , if it is Tails
• It is fair game!
• Would you take the gamble?
• How big a win you require from ‘Heads’ to take the gamble?
• İf you required less than $10,000, you are risk seeking
• İf you required more than $10,000, you are risk averse
5
Risk and Return (cont.)
• What’s Risk? What’s return?
• risk: uncertainty/variability of outcomes
• return: reward for bearing risk
• Even when expected returns and risk are known, people often make different choices about what invest in:
• Risk preferences
• Risk Averse more Risk more Required Return
• Risk Neutral more Risk same Required Return
• Risk Seeking more Risk less Required Return
6
What is Risk?
• Risk, in traditional terms, is viewed as a ‘negative’. Webstersdictionary, for instance, defines risk as ‘exposing to danger orhazard’. The Chinese symbols for risk, reproduced below, givea much better description of risk:
• The first symbol is the symbol for ‘danger’, while the second isthe symbol for ‘opportunity’, making risk a mix of danger andopportunity. You cannot have one, without the other.
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What is Return?
• Income received on an investment (i.e. Stock or bond) plusany change in market price, usually expressed as a percent ofthe beginning market price of the investment
Percentage Return = Capital Gain + Dividend
Initial Share Price
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Return Example
The stock price for Stock A was $75.06 pershare 1 year ago. The stock is currently tradingat $93.29 per share, and shareholders justreceived a $1.37 dividend. What return wasearned over the past year?
$1.37 + ($93.29 - $75.06 )
$75.06R = = 26.1%
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Rates of Return
Dividend Yield = Dividend Initial Share Price
Capital Gain Yield = Capital Gain
Initial Share Price
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Rates of Return
%1.8or 018.
75.06
1.37= Yield Dividend
%24.3or 243.
75.06
18.23= YieldGain Capital
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Rates of Return (ror)Nominal vs. Real
(assume 4.1% inflation rate)
1+ real ror = 1 + nominal ror1 + inflation rate
%1.21ror real
211.1=ror real+1.041 + 1.261 + 1
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Market Indexes
Dow Jones Industrial Average (The Dow)
Value of a portfolio holding one share in each of 30 large industrial
firms.
Standard & Poor’s Composite Index (The
S&P 500)
Value of a portfolio holding shares in 500 firms. Holdings are
proportional to the number of shares in the issues.
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Source: Ibbotson Associates
Index
Investment performance of three portfolios
The Value of an Investment of $1 in 1900
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T-bills here are 3-month bills
T-bonds here have maturity of 10 yrs.
Average rate of returns (1900-2010)
Remember :
Hurdle rate = Riskless Rate + Risk Premium
Rate of return on common stocks =
interest rate on Treasury Bills (risk-free rate) + market risk
premium
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Maturity premium
Rates of Return for Common Stocks
Common Stocks (1900-2010)
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Stock Market vs T-Bills• The stock market is much riskier than investing in T-Bills (Rf).
• If individuals are risk averse we should expect the stock market to have higher average returns.
-50
-30
-10
10
30
50
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99
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02
20
05
20
08
Ret
urn
s (%
)
RF
Mkt
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Stock Market vs T-Bills• The risk premium for investing in the stock market is around 7% per year over
the last 80 years.• - This is the premium necessary to compensate investors for bearing stock market
risk.
0
500
1000
1500
2000
2500
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83
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87
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91
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95
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99
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03
20
07
Val
ue
of
$1
inve
sted
in 1
92
7
$ in RF
$ in Mkt
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Returns and Risk
How are the expected returns and
the risk of a security related?
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Measuring Risk
Variance: Average value of squared deviations frommean. A measure of volatility.
Standard Deviation: Square root of variance. Also a measure of volatility.
What is risk?
How can it be measured?
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Measuring RiskReturn Distributions
Possible Returns
Probability of
return A
B
Do you prefer A or B?
B has higher expected return
but greater risk.
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Histogram of Returns
0
5
10
15
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55
Common Stocks
Return, (percent)
Nu
mber
of
Yea
rs
0
10
20
30
40
50
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55
Treasury Bonds
0
20
40
60
80
-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55
Treasury Bills
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Quantifying Risk and Return
Pr(ri)
E(r)ri
Pr(r)
|rj-E(r)| |ri-E(r)|
Distance ri is
from expected
outcome.
rirj
Likelihood of ri
The most likely outcome, E(r), must be our required return.
Our measure of risk must consider the distance and likelihood
of the unexpected outcomes.
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Mean and Std. Deviation
N
i
iir rErPVariancei
1
22 )(
Prob. of ri
Squared
distances or
“deviations”
from the mean
Std Dev Variance. . 2
E R Mean P rii
N
i( ) ( )
1
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Example
You start by investing $100. Then two coins are flipped.
for each head starting balance increases by 20%.
for each tail starting balance decreases by 10%.
Possible scenarios : Head + Head = 20 + 20 = 40%
Head + Tail = 20 + - 10 = 10%
Tail + Head = -10 + 20 = 10%
Tail + Tail = -10 + -10 = -20%
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Example (cont.)
Expected Return= 0.25 x 40 + 0.25 x 10 + 0.25 x 10 + 0.25 x -20
= 10%
Variance= 0.25 x (40-10)2 + 0.25 x (10-10)2 + 0.25 x (10-10)2 + 0.25 x (-20-10)2
= 0.25 x 900 + 0.25 x 0 + 0.25 x 0 + 0.25 x 900
= 225 + 0 + 0 + 225 = 450
Standard deviation = (450)0.5 = 21.2%
E R Mean P rii
N
i( ) ( )
1
N
i
iir rErPVariancei
1
22 )(
Std Dev Variance. . 2
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Measuring RiskCoin Toss Game-calculating variance and standard deviation
(1) (2) (3)
Percent Rate of Return Deviation from Mean Squared Deviation
+ 40 + 30 900
+ 10 0 0
+ 10 0 0
- 20 - 30 900
Variance = average of squared deviations = 1800 / 4 = 450
Standard deviation = square of root variance = 450 = 21.2%
27OR:
Variance: sum of squared deviations weighted by probabilities:
= 0.25 * 302 + 0.25 * 0 + 0.25 * 0+ 0.25 * (-30)2 = 450
Variation in Stock Returns Historical Data
Portfolio (1900-2010) Standard Deviation (%)
Treasury Bills 2.8
Long-term government bonds 8.6
Common Stocks 20
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Stock Market Volatility Annualized standard deviation of weekle returns in the Dow 1900-2010
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Risk and Diversification
Diversification
Strategy designed toreduce risk by spreadingthe portfolio acrossmany investments.
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Calculate expected returns and volatilities:
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Scenario Probability Rate of ReturnAuto Stock
Rate of ReturnGold Stock
Recession 1/3 -8% 20%
Normal 1/3 5% 3%
Boom 1/3 18% -20%
e.g. cont.
Auto Stock
Expected Return = 5%
Variance = 112.7
St. Dev. = 10.6%
Gold Stock
Expected Return =1%
Variance = 268.7
St. Dev. = 16.4%
Would anyone be willing to hold gold mining stocks in an investment portfolio?
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Expected return = (-8%+ 5% + 18%) / 3
Variance= ( (-8%-5%)2 +(5%-5%)2 +(18%-5%)2) / 3
YES!!
Asset versus Portfolio Risk
• Suppose autos have a weight of 0.75 and gold has weight of 0.25 in your portfolio (weights are given).
• Portfolio return in recession = 0.75 x -8% + 0.25 x 20% = -1%
• Portfolio return in normal = 0.75 x 5% + 0.25 x 3% = 4.5%
• Portfolio return in boom= 0.75 x 18% + 0.25 x -20% = 8.5%
• Average Portfolio Return = (-1%+4.5%+8.5%)/3 = 4%
Portfolio rate
of return=
fraction of portfolio
in first assetx
rate of return
on first asset
+fraction of portfolio
in second assetx
rate of return
on second asset
((
(())
))
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Example cont.
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Average Portfolio Return = (-1%+4.5%+8.5%)/3 = 4%
Variance = (.0025+.000025+.002025)/3 = .001517Std. Dev = √Variance =.0389
Example cont.
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Portfolio Expected Return= 4%
Portfolio Variance = 15.17
Potfolio Std. Dev = =3.89%
Auto Stock
Expected Return = 5%
St. Dev. = 10.6%
Gold Stock
Expected Return =1%
St. Dev. = 16.4%
Shortcut
36
Auto Stock
Expected Return = 5%
St. Dev. = 10.6%
Weight= 75%
Portfolio Expected Return= 0.75*5% + 0.25*1%= 4%
BEWARE!! YOU CAN NOT DO THIS FOR STANDARD DEVIATION!
Gold Stock
Expected Return =1%
St. Dev. = 16.4%
Weight= 25%
Adding stocks to a portfolio can reduce risk
37
Sum up
• Investors care about the expected return and riskof their portfolio of assets.
• The standard deviation of the returns of anindividual security measures how risky thatsecurity would be if held in isolation. But for aninvestor with a portfolio of assets, how eachsecurity affects the risk of the entire portfolio.
38
The Value of Investments
0
20
40
60
80
100
120
140
160
Network Mining
Ford
Portfolio
Val
ue
(August
2004 =
100)
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Risk and Diversification
0
5 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
devia
tio
n
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Market vs Unique Risk
Unique Risk - Risk factors affecting only that firm. Alsocalled “diversifiable risk or unsystematic risk or specificrisk“
Market Risk - Economy-wide sources of risk that affectthe overall stock market. Also called “systematic risk.”
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0
5 10 15
Number of Securities
Po
rtfo
lio
sta
nd
ard
devia
tio
n
Market risk
Unique
risk
Risk and Diversification
42
Thinking About Risk
• Message 1
• Some Risks Look Big and Dangerous but Really AreDiversifiable (like insurance companies)
• Message 2
• Market Risks Are Macro Risks (airlines, machine toolmanufacturers vs food companies)
• Message 3
• Risk Can Be Measured (by measuring the individualstock’s sensitivity to the fluctuations of the overallstock market– we will learn how to do it in the nextchapter).
43
