CV
=
Standard Deviation
Expected Rate of Return
/
Mean
=
σ
r
Risk aversion
: assumes investors dislike risk and require higher
rates of return to encourage them to hold riskier securities.
Risk premium
= mean return – risk free rate
PORTFOLIO
Expected Portfolio Return:
!
!
=
!
!
!
!
!
!
!
!
Portfolio Risk / SD
Applying the standard deviation & CV formulas:
SD of 2 Stock Portfolio:
SD of a portfolio can be lower than any of its investments:
negative correlation between stocks → negative covariance
COVARIANCE
: measures how two assets’ rates of return vary
together over the same mean time period.
CORRELATION COEFFICIENT
ρ
XY
: extent to which X & Y move
together → affects variance of portfolio
(-1 to 1)
Standardises the unit of covariance measure
!
!
,
!
=
!"#
!
!
,
!
!
σ
!
σ
!
2 stocks can be combined to form riskless portfolio if p= -1.0
Risk is not reduced at all if the 2 stocks have p = +1.0
As p
à
-1, risk gets eliminated.
As p
à
+1, no risk gets eliminated.
Total Risk = Company-Specific Risk + Market Risk
Company-specific risk (unsystematic risk): can be diversified
away in a portfolio while market risk (systematic risk) cannot.
For a well-diversified portfolio, total risk
σ
is essentially
systematic risk.
MEASURING ASSET’S MARKET RISK – BETA:
(mostly 0.5 – 1.5)
β
i
<1
: asset has less systematic risk than market
β
i
>1
: asset has more systematic risk than market
β
market
= 1 β
risk
free asset
= 0
Portfolio Volatility
: total risk of portfolio (portfolio SD)
Combined stocks positively correlated → risk level drops a bit
Combined stocks negatively correlated → risk level drops a lot
Beta (β):
measures risk of security held in a large portfolio
•
Measures the responsiveness of security to movements in
the market portfolios
•
Slope of the regression line of the asset’s returns on the
market portfolio’s returns.
Depending on the time period, beta will change. Therefore, we
have to compare 2 stocks/markets in the same time period.
SECURITY MARKET LINE (SML):
risk return relationship
between
β
of a security and its required rate of return.
Reward-to-risk ratio
= slope of the line
β
for market ALWAYS 1 hence
Slope = R
M
– R
f
= market risk premium
In equilibrium, all assets and portfolios must have the same
reward-to-risk ratio.
Equilibrium means expected return = required return
CAPITAL ASSET PRICING MODEL (CAPM):
Defines relationship between risk and required return
R
f
: risk-free rate
(R
M
– R
f
): market risk premium
Required risk premium= Beta * market risk premium
Portfolio Beta
: sum of each asset’s beta x portfolio weight
Fairly priced asset: expected return is on the SML
Under-priced asset: above the SML (expected>required)
Over-priced asset: below the SML
Impact of Inflation Change On SML
Impact of a Risk Aversion Change:
More risk averse
à
SML steeper
More risk loving
à
SML less steep
MARKOWITZ PORTFOLIO THEORY:
combining stocks into
portfolios can reduce SD below that from a simple weighted
average calculation
Efficient portfolio
: provides the greatest expected return for
given level of SD/ lowest risk for a given expected return
Efficient frontier:

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