PM 4-2 Risk and Return Models.pdf

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PORTFOLIO
MANAGEMENT
COURSE
4 RISK AND RETURN MODELS
4.2. RISK AVERSION AND CAPITAL ALOCATION
PORTFOLIO MANAGEMENT
PORTFOLIO MANAGEMENT
1.
Introduction
2.
Fixed Income Portfolio Management
3.
Equities Portfolio Management
4.
Risk & Return Models
5.
Portfolio Performance and Risk Evaluation
6.
Investment Process and Policy
7.
Group Presentations
4. Risk & Return Models
Risk & Return
Risk Aversion and Capital Allocation
Optimal Risky Portfolios
The Capital Asset Pricing Model (and Index Models)
MARIA JOAO TEIXEIRA
PORTFOLIO MANAGEMENT
3
4.2 Risk Aversion and Capital Allocation
RISK, SPECULATION AND GAMBLING
SPECULATION – to assume considerable investment risk to obtain
considerable gain (above risk free alternative). It is NOT:
GAMBLING – to bet on an uncertain outcome. Ex. Risky investment
with a risk premium of zero (fair game)
Difference between the two is the: risk premium to compensate risk
aversion.
Risk Aversion and speculation are consistent !
Risk averse
investors only consider
risk free or speculative
investments with
positive risk premiums
(and reject fair games).
They penalise the expected return of a risky portfolio by the risk
involved.
MARIA JOAO TEIXEIRA
PORTFOLIO MANAGEMENT
4
4.2 Risk Aversion and Capital Allocation
RISK AVERSION AND UTILITY VALUES
How to chose a portfolio between a group where risk increases with
return?
% Risk
Expected
Premium Return %
2
7
4
9
8
13
Risk (SD)
%
5
10
20
Low risk bonds
High risk bonds
Equity
RF rate 5%
UTILITY - Quantify how the investor trades off return against risk
U = E (r) - �½ A ²
, where A is the investors risk aversion
ᵟ
A=0 risk neutral
A<0 risk lover
U increases with expected return and decreases with risk
For the risk free portfolio: U=E(r)
MARIA JOAO TEIXEIRA
PORTFOLIO MANAGEMENT
5

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