Risk & Return Stand-alone and Portfolio Considerations.
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Transcript of Risk & Return Stand-alone and Portfolio Considerations.
Risk & Return
Stand-alone and Portfolio Considerations
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.
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
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?
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)
Probability Distribution
Rate ofreturn (%) 50150-20
Stock X
Stock Y
Distribution of Annual Returns
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
)(
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 =
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
Example: Variance and Std. Dev.
E(RC) = 9.9%; E(RT) = 17.7%
Stock C
Stock T
n
iii RERp
1
22 ))((σ
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 =
Portfolio Return & Variance
m
jjjP REwRE
1
)()(
n
iii RERw
1
22 ))((σ
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
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?
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
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
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
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
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?
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 +… =
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
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)
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)?
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
)()(
SML
r (%)
bi
8
1.0
Risk Compensation
Riskfree Rate
Market Risk Premium
Premium for Riskier Stock
1.9
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
r (%)
0 0.5 1.0 1.5 b
1412
7 5
New SML
Δ Inflation = 2%
Impact of Inflation on SML
Original SML
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
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%
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