Upload
gswaiting4u
View
223
Download
0
Embed Size (px)
Citation preview
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 1/13
Chapter 6
Risk and Risk Aversion
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 2/13
p
1-2
6-2
W = 100
W1 = 150 Profit = 50
W2 = 80 Profit = -201-p = .4
E(W) = pW1 + (1-p)W2 = 6 (150) + .4(80) = 122
s2
= p[W1 - E(W)]2
+ (1-p) [W2 - E(W)]2
=.6 (150-122)2 + .4(80=122)2 = 1,176,000
s = 34.293
Risk - Uncertain Outcomes
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 3/13
1-3
6-3
W1 = 150 Profit = 50
W2 = 80 Profit = -201-p = .4
100
Risky Inv.
Risk Free T-bills Profit = 5
Risk Premium = 17
Risky Investments with Risk-Free
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 4/13
1-4
6-4
Investor’s view of risk Risk Averse
Risk Neutral
Risk Seeking
Utility
Utility Function
U = E ( r ) - .005 A 2
A measures the degree of risk aversion
Risk Aversion & Utility
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 5/13
1-5
6-5
Risk Aversion and Value:
U = E ( r ) - .005 A s 2
= .22 - .005 A (34%) 2
Risk Aversion A Value
High 5 -6.90
3 4.66
Low 1 16.22T-bill = 5%
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 6/13
1-6
6-6
Dominance Principle
1
2 3
4
Expected Return
Variance or Standard Deviation
• 2 dominates 1; has a higher return
• 2 dominates 3; has a lower risk
• 4 dominates 3; has a higher return
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 7/131-76-7
Utility and Indifference Curves
Represent an investor’s willingness to trade-
off return and risk.
Example
Exp Ret St Deviation U=E ( r ) - .005As2
10 20.0 2
15 25.5 2
20 30.0 2
25 33.9 2
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 8/131-86-8
Indifference Curves
Expected Return
Standard Deviation
Increasing Utility
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 9/131-96-9
Expected Return
Rule 1 : The return for an asset is theprobability weighted average return in
all scenarios.
= s
sr s P r E )()()(
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 10/131-106-10
Variance of Return
Rule 2: The variance of an asset’s returnis the expected value of the squared
deviations from the expected return.
])()()[( 2
2 = s
r E sr s P s
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 11/131-116-11
Return on a Portfolio
Rule 3: The rate of return on a portfolio is aweighted average of the rates of return of each
asset comprising the portfolio, with the portfolio
proportions as weights.
r p = W1r 1 + W2r 2
W1 = Proportion of funds in Security 1
W2 = Proportion of funds in Security 2
r 1 = Expected return on Security 1
r 2 = Expected return on Security 2
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 12/131-126-12
Portfolio Risk with Risk-Free Asset
Rule 4: When a risky asset is combined with arisk-free asset, the portfolio standard
deviation equals the risky asset’s standard
deviation multiplied by the portfolio proportion
invested in the risky asset.
s s riskyasset riskyasset p w =
8/13/2019 SAPM - Risk Aversion
http://slidepdf.com/reader/full/sapm-risk-aversion 13/131-136-13
Rule 5: When two risky assets with variancess1
2 and s22, respectively, are combined into a
portfolio with portfolio weights w1 and w2,
respectively, the portfolio variance is givenby:
sp2 = w1
2s12 + w2
2s22 + 2W1W2 Cov(r 1r 2)
Cov(r 1r 2) = Covariance of returns for
Security 1 and Security 2
Portfolio Risk