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Portfolio Analysis - III

The document discusses portfolio risk and investment analysis, focusing on the calculation of risk when combining multiple assets. It introduces concepts such as efficient portfolios, systematic risk, and beta as a measure of non-diversifiable risk. Additionally, it includes examples and calculations related to variance, covariance, and beta estimation for specific securities.

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Lafry Ahamed
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20 views17 pages

Portfolio Analysis - III

The document discusses portfolio risk and investment analysis, focusing on the calculation of risk when combining multiple assets. It introduces concepts such as efficient portfolios, systematic risk, and beta as a measure of non-diversifiable risk. Additionally, it includes examples and calculations related to variance, covariance, and beta estimation for specific securities.

Uploaded by

Lafry Ahamed
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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South Eastern University of Sri Lanka

Programme: Final Year BBA(specialization in accounting) ,


BBA(specialization in Finance) BBA( Special)
Semester –I, Academic year – 2020/2021

Course: FIM 41063 Investement analysis &Portfolio


Management

Topic: Portfolio Analysis-III


Lecturer: Dr. S.Safeena M.G Hassan Ph.D (UJA), M.Sc (SJP),
BBA (Hons.) (Col) and (EUSL)
Senior Lecturer
Department of Management
Faculty of Management and Commerce
Handout No: 04
PORTFOLIO RISK: THE n-ASSET CASE
 The calculation of risk becomes quite involved
when a large number of assets or securities are
combined to form a portfolio.

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Efficient Portfolios of risky securities

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.
3
4
Variance Covariance matrix
You are interested to invest three securities called A,B,C
in the following proportion. A 50%, B 30%, C 20%.
You have already computed the following variance and
covariance matrix.
Security name A B C
A 146 187 145
B 187 854 104
C 145 104 289
i) Calculate the risk of this portfolio.
ii) Prepare the correlation matrix for this portfolio.

5
Systematic Risk

 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.
 Beta can be used to measure the Systematic
risk
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Beta - β
 It is the relevant measure of risk of an
investment is its non- diversifiable risk /
systematic risk.
 All securities do not have the same level of non
diversifiable risk because the level of influence
of economic wide –factors tends to vary
characteristic line.
 Beta =1 shows, if the market portfolio
increased by 1% security i’s return also
increase by 1%
 If the βim>1 – aggressive If βim<1 – Defensive
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Beta Estimation

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Example
Returns on Sensex and Jaya Infotech

9
Example
Beta Calculation for Jaya Infotech Limited

10
Beta Calculation: Example

Estimates for Regression Equation

11
Example-Steps to be followed

12
Cont…

13
Cont…

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Market Model

15
Beta Calculation: Example

The value of  and  in the regression equation are given by the


following equations:
N S X Y - (S X ) (S Y )
b=
N S X 2 - (S X )2
(5) (4,774.49) - (27.42) (19.73)
bj =
(5) (5, 438.58) - (27.42) 2
23,872.45 - 541.00 23,331.45
= = = 0.88
27,192.90 - 751.86 26, 441.04
Alpha = a = Y - bX
Alpha = a j = 3.95 - (0.88) (5.48) = - 0.89

16
Thank you

Acknowledgement:
Keith C. Brown

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