Portfolio Standard deviation
Risk Premium
= Return – Risk free rate
Treasury bills considered risk free.
Coefficient of Variation (CV):
standardized measure of
dispersion about expected value, that shows relative
variability/risk per unit of expected return.
Covariance
How 2 assets move/don’t move tgt. Used to measure how 2
assets’ rate of return vary tgt over same time period. If
portfolio SD much lower than either stock SD and avg of both,
means negative CV due to negative correlation.
Covariance =
XY
XY
X
Y
Correlation Coefficient,
1
≥ ρ
XY
≥
−
1
measures the extent to which 2 securities X and Y move
together
For 2 perfectly /+ correlated stocks,
ρ
= 1.0/ 1.0
2 stocks can combine to form riskless portfolio if
ρ
= 1.0
Risk not reduced at all if 2 stocks have
ρ
= 1.0
W5: Risk & Return 2
Diversification
. ↓variability of returns
w/o equivalent ↓ in expected returns, as worsethanexpected
returns from 1 asset offset by betterthanexpected returns
frm another. Welld portfolios’ total risk (sigma) = systematic
risk (which depends on sensitivity to mkt factors) as firm
specific risk close to 0/variance frm mkt risk. BUT for indiv
asset, total risk measure =/= systematic risk.
Total Risk
= Company specific risk(unsystematic/unique
/diversifiable) + Market risk (systematic, nondiversifibale)
(Note:

B =/= nonsystematic risk)
Standard deviation Total Risk
Diversifiable Risk:
Caused by
random events: lawsuit,
unsuccessful mkting prog, lose
major contract. 1 firm's bad event
can be offset by another's good
events: Effects elim by portfolio
Undiversifiable Risk:
Measured by stock beta Factors that
affect most firms: war, inflation, recession, high i/r. Most firms
affect so mkt risk cant be diversified away by combining
stocks: they'll move in same direction (all benefit/suffer but
diff degrees).
Stock Beta :
Beta Systematic risk (Nondiversifiable risk)
measures responsiveness of a security to movements in mkt
portfolio
Beta is aslope of regression line of asset’s returns on mkt
portfolio returns
Asset Beta
=
covariance
(
investment return,market r
Market portfolioVariance
ρ
ρ
(
¿¿
ℑ)
(
σ
i
σ
M
)
(
¿¿
ℑ)(
σ
i
)(
σ
M
)
σ
M
2
=
¿
β
i
=
cov
(
r
i
,r
M
)
σ
M
2
=
¿
ρ
ρ
(
¿¿
MM
)
(
σ
M
σ
M
)
=
1
(
¿¿
MM
)(
σ
M
)(
σ
M
)
σ
M
2
=
¿
M
=
¿¿
β
¿
Beta
β
P
=
∑
j
=
1
m
(
W
j
)(
β
j
)
Returns
Portfolio return = (stock % of portfolio)(Ra) + (stock
%..)
Tells u an asset's risk relative to avg asset. Mkt Beta = 1,
most stocks: 0.5  1.5

β
i
>
1
: Asset’s systematic risk < mkt’s (security’s
expected return > risk free rate)

β
i
<
1
: Asset’s systematic risk > mkt’s (security’s
expected return < risk free rate)

Beta = 0: risk free asset (Tbill)
Indicates stock's riskiness, if held in a welldiversified portfolio
Systematic risk principle: reward for bearing risk depends on
investmnt’s systematic risk. Expected return of an asset only
depends on that asset's systematic risk.
*** can have diff degrees of market risk for diff portfolio.
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 Winter '14
 Capital Asset Pricing Model, Investing