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Risk and Return
Risk Preference, Risk Premium, and
Capital Allocation
Last Time
±
Course overview
±
Financial assets and markets
±
Cost of trading
±
Margin trading
2/24/2010
FINS5513
2
±
Short selling
±
Characterizing financial assets:
²
Expected return and risk
²
Others?
±
Characterizing investors:
²
Risk aversion and utility
Today
²
Behavioral patterns
±
Capital allocation between riskfree and risky assets
2/24/2010
3
Asset Return
±
Holding period return as a random variable:
P
E di
i
$24
−
−
+−
==
tt
t1
t
PDP
rH
P
R
P
2/24/2010
4
t
= Ending price = $24
P
t1
= Beginning price = $20
D
t
= Dividend = $1
r
t
= ( 24  20 + 1 )/ ( 20) = 25%
Microsoft Price (RHS)
& Adjusted Returns (LHS)
0
50
100
150
200
0
10
20
2/24/2010
5
200
150
100
50
20
10
1/1/1988
12/31/1989
1/1/1992
12/31/1993
1/1/1996
1/1/1998
1/1/2000
1/1/2002
1/1/2004
1/1/2006
1/2/2008
1/1/2010
Microsoft Daily Return
Distribution
025
0.3
0.35
0.4
2/24/2010
6
0
0.05
0.1
0.15
0.2
0.25
0.10
0.08
0.06
0.04
0.02
0.00
0.02
0.04
0.06
0.08
0.10
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View Full DocumentReturn as a Random
Variable
±
Probability distribution
²
discrete or continuous
±
Describing probability distributions
²
Location: expected value
2/24/2010
7
²
Dispersion: variance or standard deviation
²
Symmetry: skewness
²
“Tail” properties: kurtosis
Expected Value
and Variance
±
Expected value =E(r) =
±
Variance = var(r) =
²
Standard deviation =
σ
∑
m
1
=
k
k
r
×
)
k
Pr(
=
σ=
−
∑
m
22
kk
k1
Pr(k)[r
E(r )]
2/24/2010
8
±
Given a sample r
1
, r
2
, …, r
T
, the sample mean and the
sample variance are
=
=
∑
T
t
t1
1
rr
T
=
=−
−
∑
T
t
1
s[
r
r
]
T1
Covariance and
Correlation
±
Covariance
Cov(r
A
,r
B
)=E[(r
A
E(r
A
))(r
B
E(r
B
))]
±
Sample covariance
∑
T
1
2/24/2010
9
±
Correlation coefficient
±
Note that Cov(r
A
,r
B
)= Cov(r
B
,r
A
) and Cov(r
A
,r
A
)=Var(r
A
).
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 Three '10
 WangJianxin

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