1 Inefficient portfolios have lower return and higher risk Investment Opportunity Set The nAsset Case 2 An efficient portfolio is one that has the highest expected returns for a given level of risk ID: 435143
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Slide1
Mean-variance Criterion
1
Inefficient portfolios
- have lower return and higher riskSlide2
Investment Opportunity Set:
The n-Asset Case
2
An
efficient portfolio
is one that has the highest expected returns for a given level of risk.
The efficient frontier is the frontier formed by the set of efficient portfolios.
All other portfolios, which lie outside the efficient frontier, are
inefficient portfolios
.Slide3
Efficient Portfolios of risky securities
3
An
efficient portfolio
is one that has the highest expected returns for a given level of risk. The
efficient frontier
is the frontier formed by the set of efficient portfolios. All other portfolios, which lie outside the efficient frontier, are
inefficient portfolios
. Slide4
PORTFOLIO RISK: THE n-ASSET CASE
4
The calculation of risk becomes quite involved when a large number of assets or securities are combined to form a portfolio.Slide5
N-Asset Portfolio Risk Matrix
5Slide6
6Slide7
RISK DIVERSIFICATION:
SYSTEMATIC AND UNSYSTEMATIC RISK
7
When more and more securities are included in a portfolio, the risk of individual securities in the portfolio is reduced.
This risk totally vanishes when the number of securities is very large.
But the risk represented by covariance remains.
Risk has two parts:
Diversifiable (unsystematic)
Non-diversifiable (systematic)Slide8
Systematic Risk
8
Systematic risk arises on account of the economy-wide uncertainties and the tendency of individual securities to move together with changes in the market.
This part of risk cannot be reduced through diversification.
It is also known as
market risk
.
Investors are exposed to market risk even when they hold well-diversified portfolios of securities.Slide9
Examples of Systematic Risk
9Slide10
Unsystematic Risk
10
Unsystematic risk arises from the unique uncertainties of individual securities.
It is also called
unique risk
.
These uncertainties are diversifiable if a large numbers of securities are combined to form well-diversified portfolios.
Uncertainties of individual securities in a portfolio cancel out each other.
Unsystematic risk can be totally reduced through diversification.Slide11
Examples of Unsystematic Risk
11Slide12
Total Risk
12Slide13
Systematic and unsystematic risk and
number of securities
13Slide14
COMBINING A RISK-FREE ASSET AND
A RISKY ASSET
14Slide15
A Risk-Free Asset and A Risky Asset: Example
R
f
, risk-free rateSlide16
Borrowing and Lending
16
Risk-return relationship for portfolio of risky and risk-free securitiesSlide17
MULTIPLE RISKY ASSETS AND
A RISK-FREE ASSET
17
In a market situation, a large number of investors holding portfolios consisting of a risk-free security and multiple risky securities participate.Slide18
18
We draw three lines from the risk-free rate (5%) to the three portfolios. Each line shows the manner in which capital is allocated. This line is called the
capital allocation line.
Portfolio
M
is the optimum risky portfolio, which can be combined with the risk-free asset.
Risk-return relationship for portfolio of risky
and risk-free securitiesSlide19
19
The capital market line (CML)
is an efficient set of risk-free and risky securities, and it shows the risk-return trade-off in the market equilibrium.
The capital market lineSlide20
Separation Theory
20
According to the separation theory, the choice of portfolio involves two separate steps.
The first step involves the determination of the optimum risky portfolio.
The second step concerns with the investor’s decision to form portfolio of the risk-free asset and the optimum risky portfolio depending on her risk preferences.Slide21
Slope of CML
21Slide22
CAPITAL ASSET PRICING MODEL (CAPM)
22
The capital asset pricing model (CAPM) is a model that provides a framework to determine the required rate of return on an asset and indicates the relationship between return and risk of the asset.
The required rate of return specified by CAPM helps in valuing an asset.
One can also compare the expected (estimated) rate of return on an asset with its required rate of return and determine whether the asset is fairly valued.
Under CAPM, the security market line (SML) exemplifies the relationship between an asset’s risk and its required rate of return.Slide23
Assumptions of CAPM
23Slide24
Characteristics Line
24Slide25
Security Market Line (SML)
25
Security market lineSlide26
26
Security market line with normalize systematic riskSlide27
IMPLICATIONS AND RELEVANCE OF CAPM
27Slide28
Implications
28
Investors will always combine a risk-free asset with a market portfolio of risky assets. They will invest in risky assets in proportion to their market value.
Investors will be compensated only for that risk which they cannot diversify.
Investors can expect returns from their investment according to the risk.Slide29
Limitations
29
It is based on unrealistic assumptions.
It is difficult to test the validity of CAPM.
Betas do not remain stable over time.Slide30
THE ARBITRAGE PRICING THEORY (APT)
30
The act of taking advantage of a price differential between two or more markets is referred to as
arbitrage
.
The
Arbitrage Pricing Theory (APT)
describes the method of bring a mispriced asset in line with its expected price.
An asset is considered
mispriced
if its current price is different from the predicted price as per the model.
The fundamental logic of APT is that investors always indulge in arbitrage whenever they find differences in the returns of assets with similar risk characteristics.Slide31
Concept of Return under APT
31Slide32
Concept of Risk under APT
32Slide33
Steps in Calculating
Expected Return under APT
33Slide34
Factors
34Slide35
Risk premium
35
Conceptually, it is the compensation, over and above, the risk-free rate of return that investors require for the risk contributed by the factor.
One could use past data on the forecasted and actual values to determine the premium.Slide36
Factor beta
36
The beta of the factor is the sensitivity of the asset’s return to the changes in the factor.
One can use regression approach to calculate the factor beta.