risk & return stand-alone and portfolio considerations
TRANSCRIPT
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Risk & Return
Stand-alone and Portfolio Considerations
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Efficient Market Hypothesis
Securities are in equilibrium: “Fairly priced” 100,000+ analysts (MBAs, CFAs, PhDs)
work for investment firms Analysts have access to data and $$
to invest Thus, price reflects news almost
instantaneously
One cannot “beat the market” except through good luck or inside information.
Doesn’t mean you can’t make money.
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Weak Form EMH Any information in historical prices is
reflected in stock prices Semi-Strong Form EMH
All public information is reflected in stock prices
Strong Form EMH All information, even inside info, is
embedded in stock prices
EMH
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Return Total dollar return
income from investment + capital gain (loss)
Percentage return dividend yield + capital gains yield
You bought a stock for $35 and you received dividends of $1.25. The stock now sells for $40. What is your dollar return?
What is your percentage return?
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Risk Returns generally are uncertain. The greater the chance of a return
below the expected return, the greater the risk.
Risk Premium “Extra” return earned for taking on risk Return above the risk free rate (Treasury
bills are considered risk-free)
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Probability Distribution
Rate ofreturn (%) 50150-20
Stock X
Stock Y
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Distribution of Annual Returns
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Expected Returns Expected returns are based on the
probabilities of possible outcomes “Expected” means average if the
process is repeated many times
n
iiiRpRE
1
)(
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Example: Expected Returns
What are the expected returns for Stocks C & T? State Probability C
T Boom 0.3 15%
25% Normal 0.5 10
20 Recession??? 2 1
RC = RT =
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Variance and Standard Deviation
Both measure the volatility of returns Variance is the weighted average of
squared deviations
Std. Dev. is the square root of the variance (σ)
n
iii RERp
1
22 ))((σ
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Example: Variance and Std. Dev.
E(RC) = 9.9%; E(RT) = 17.7%
Stock C
Stock T
n
iii RERp
1
22 ))((σ
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Example State Prob. ABC, Inc. (%)
Boom .25 16 Normal .50 8 Slowdown .15 5 Recession.10 -3
What is the expected return, variance, and std dev? E(R) = Variance = Standard Deviation =
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Portfolio Return & Variance
m
jjjP REwRE
1
)()(
n
iii RERw
1
22 ))((σ
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Example Evenly split investment between A &
B State Prob. A B Boom .4 30% -5% Bust .6 -10% 25%
Expected return and standard deviation Each state
The portfolio
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Another Example
State Prob. X Z Boom .25 15% 10% Normal .60 10% 9% Recession.15 5% 10%
What are the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Z?
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Types of Risk Systematic
Risk factors that affect a large number of assets
Non-diversifiable risk, Market risk
Unsystematic Risk factors affecting a limited number
of assets Unique risk, Asset-specific risk,
Idiosyncratic risk
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Portfolio Diversification Investment in several different
asset classes 50 internet stocks - not diversified 50 stocks across 20 industries -
diversified Can substantially reduce returns
variability without reducing expected returns
A minimum level of risk cannot be diversified away
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Unsystematic Risk Diversifiable or unsystematic risk
can be eliminated by combining assets into a portfolio
Total risk = systematic risk + unsystematic risk Std. dev. of returns measures total risk If diversified, unsystematic risk is very
small
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Systematic Risk Reward for bearing risk
No reward for unnecessary risk Beta (β) measures systematic risk
Relative to overall market What does beta tell us?
β =1: asset has ____systematic risk as the market
β < 1: asset has ____systematic risk than the market
β > 1: asset has ____systematic risk than the market
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Total versus Systematic Risk
Std Dev Beta Security C 20% 1.25 Security K 30% 0.95
Which has more total risk? Which has more systematic risk? Which should have the higher
expected return?
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Example: Portfolio BetasSecurity Weight Beta A .2 2.7 B .3 0.2 C .1 2.0 D .4 1.5
What is the portfolio beta? βP = w1β1 + w2β2 + w3β3 +… =
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Beta and the Risk Premium
Risk premium = expected return – risk-free rate
Higher beta ~ higher risk premium Can estimate the expected return
when we know this relationship
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Beta & Returns
Rf
E(RA)
A0%
5%
10%
15%
20%
25%
30%
0 0.5 1 1.5 2 2.5 3
Beta
Exp
ecte
d R
etur
n
Slope = Rise / Run = (E(RA) – Rf) / (A – 0)
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Reward to Risk Ratio
Slope of beta & return relationship Reward to risk ratio or the risk
premium
What if an asset has a reward-to-risk ratio of 8 (asset plots above the line)?
What if an asset has a reward-to-risk ratio of 7 (asset plots below the line)?
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Security Market Line
SML represents market equilibrium In equilibrium, all assets and portfolios must
have the same reward-to-risk ratio SML slope is the reward-to-risk ratio:
(E(RM) – Rf) / M = E(RM) – Rf = mkt risk premium
M
fM
A
fA RRERRE
)()(
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SML
r (%)
bi
8
1.0
Risk Compensation
Riskfree Rate
Market Risk Premium
Premium for Riskier Stock
1.9
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Capital Asset Pricing Model
CAPM - relationship between risk and return
E(RA) = Rf + A(E(RM) – Rf) Risk free rate Return for bearing systematic risk Amount of systematic risk
If we know an asset’s systematic risk, we can use the CAPM to determine its expected return
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r (%)
0 0.5 1.0 1.5 b
1412
7 5
New SML
Δ Inflation = 2%
Impact of Inflation on SML
Original SML
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rM = 18%
rM = 15%SML1
r (%) SML2 : Increased Risk Aversion
Risk, β
18
15
8
1.0
Δ RPM = 3%
Impact of Risk Aversion on SML
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Example - CAPM
If the risk-free rate is 3% and the market risk premium is 8%, what is the expected return for each?
Security
Beta
A 2.7 B 0.4 C 2.1 D 1.6
Expected Return
3% + 2.7*8%3% + 0.4*8%3% + 2.1*8%3% + 1.6*8%
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New Example
If the risk-free rate is 4% and the market risk premium is 6%, what is the expected return for each?
Security
Beta Expected Return
A 2.0
B 0.8