portfolio by rachit.pptx

8/14/2019 portfolio by rachit.pptx

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EFFICIENTPORTFOLIOS&

EFFICIENTFRONTIERS


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EFFICIENTVS. INEFFICIENT

PORTFOLIOS

It is impossible to predict in advance which

portfolios will be the most efficient as this would

require knowing in advance asset classperformance and correlations.

A portfolio that has been diversified into a variety

of asset classes should be close to efficient over

the longer term, provided it is rebalancedregularly.


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3PORTFOLIOPROGRAMMING

INA NUTSHELL

Various portfolio combinations may result in a

given return

The investor wants to choose the portfolio

combination that provides the least amount of

variance


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4PORTFOLIOPROGRAMMING

INA NUTSHELL(CONTD)

Example

Assume the following statistics for Stocks A, B,

and C:

Stock A Stock B Stock C

Expected return .20 .14 .10

Standard deviation .232 .136 .195


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5

PORTFOLIOPROGRAMMING

INA NUTSHELL(CONTD)

Example (contd)

The correlation coefficients between the three

stocks are:

Stock A Stock B Stock C

Stock A 1.000

Stock B 0.286 1.000

Stock C 0.132 -0.605 1.000


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6


INA NUTSHELL(CONTD)

Example (contd)

An investor seeks a portfolio return of 12%.

Which combinations of the three stocksaccomplish this objective? Which of thosecombinations achieves the least amount ofrisk?


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7


INA NUTSHELL(CONTD)

Example (contd)

Solution: Two combinations achieve a 12% return:

1) 50% in B, 50% in C: (.5)(14%) + (.5)(10%) = 12%

2) 20% in A, 80% in C: (.2)(20%) + (.8)(10%) = 12%


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8


INA NUTSHELL(CONTD)

Example (contd)

Solution (contd):Calculate the variance of the

B/C combination:

2 2 2 2 2

2 2

2

(.50) (.0185) (.50) (.0380)

2(.50)(.50)( .605)(.136)(.195)

.0046 .0095 .0080

.0061

p A A B B A B AB A Bx x x x


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9


INA NUTSHELL(CONTD)

Example (contd)

Solution (contd):Calculate the variance of the

A/C combination:2 2 2 2 2

2 2

2

(.20) (.0538) (.80) (.0380)

2(.20)(.80)(.132)(.232)(.195)

.0022 .0243 .0019

.0284

p A A B B A B AB A Bx x x x


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10


INA NUTSHELL(CONTD)

Example (contd)

Solution (contd):Investing 50% in Stock B and

50% in Stock C achieves an expected return of

12% with the lower portfolio variance. Thus,

the investor will likely prefer this combinationto the alternative of investing 20% in Stock A

and 80% in Stock C.


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11 CONCEPTOFDOMINANCE

Dominanceis a situation in which investors

universally prefer one alternative over another

All rational investors will clearly prefer one

alternative


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12

CONCEPTOFDOMINANCE

(CONTD)

A portfolio dominates all others if:

For its level of expected return, there is no other

portfolio with less risk

For its level of risk, there is no other portfolio

with a higher expected return


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13

CONCEPTOFDOMINANCE

(CONTD)

Example (contd)

In the previous example, the B/C combination dominates the

A/C combination:

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.005 0.01 0.015 0.02 0.025 0.03

Risk

Expe

cted

Return

B/C combination

dominates A/C

H M


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14

HARRYMARKOWITZ:

FOUNDEROFPORTFOLIO

THEORY


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15 INTRODUCTION

Harry Markowitzs Portfolio SelectionJournal of Financearticle (1952) set thestage for modern portfolio theory

The first major publication indicating theimportant of security return correlation inthe construction of stock portfolios

Markowitz showed that for a given level ofexpected return and for a given securityuniverse, knowledge of the covariance andcorrelation matrices are required


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16 EFFICIENTFRONTIER

Construct a risk/return plot of all possible

portfolios

Those portfolios that are not dominated

constitute the efficient frontier


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IMPROVINGTHEEFFICIENT

FRONTIER

Investors desire higher returns with lower risk. There is however a

limit to what can be achieved with a particular set of assets, that limit

is drawn on charts as the efficient frontier.

By adding more assets we can change the shape of the efficient

frontier. Assets carry two items of interest to us, their returns and

their correlation with the rest of the portfolio.


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18

EFFICIENTFRONTIER

(CONTD)

Standard Deviation

Expected Return100% investment in security

with highest E(R)

100% investment in minimumvariance portfolio

Points below the efficient

frontier are dominated

No points plot above

the line

All portfolios

on the line

are efficient


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19

EFFICIENTFRONTIER

(CONTD)

The farther you move to the left on the efficient

frontier, the greater the number of securities in

the portfolio


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20

EFFICIENTFRONTIER

(CONTD)

The efficient frontier with a risk-free rate:

Extends from the risk-free rate to point B

The line is tangent to the risky securities efficient

frontier

Follows the curve from point B to point C


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21

LESSONSFROM

EVANSANDARCHER

Introduction

Methodology

Results

Implications

Words of caution


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22 INTRODUCTION

Evans and Archers 1968Journal of Financearticle

Very consequential research regarding portfolioconstruction

Shows how nave diversificationreduces the

dispersion of returns in a stock portfolio

Nave diversification refers to the selection ofportfolio components randomly


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23 METHODOLOGY

Used computer simulations:

Measured the average variance of portfolios of

different sizes, up to portfolios with dozens of

components

Purpose was to investigate the effects of portfolio

size on portfolio risk when securities are

randomly selected


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24 DEFINITIONS

Systematic riskis the risk that remains after no

further diversification benefits can be achieved

Unsystematic riskis the part of total risk that is

unrelated to overall market movements and can

be diversified

Research indicates up to 75 percent of total risk is

diversifiable


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25 DEFINITIONS(CONTD)

Investors are rewarded only for systematic risk

Rational investors should always diversify

Explains why beta (a measure of systematic risk)

is important

Securities are priced on the basis of their betacoefficients


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26 GENERALRESULTS

Number of Securities

Portfolio Variance


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27

BIGGESTBENEFITSCOME

FIRST

Increasing the number of portfolio components

provides diminishing benefits as the number of

components increases

Adding a security to a one-security portfolio

provides substantial risk reduction

Adding a security to a twenty-security portfolio

provides only modest additional benefits


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28 DIVERSIFICATIONANDBETA

Beta measures systematic risk

Diversification does not mean to reduce beta

Investors differ in the extent to which they will

take risk, so they choose securities with different

betas

E.g., an aggressive investor could choose a

portfolio with a beta of 2.0

E.g., a conservative investor could choose a



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MODERNPORTFOLIOTHEORY

Modern portfolio theory(MPT) is a theoryof investment which attempts to maximizeportfolio expected return for a given amount ofportfolio risk, or equivalently minimize risk for agiven level of expected return, by carefullychoosing the proportions of various assets.Although MPT is widely used in practice in thefinancial industry and several of its creators won

a Nobel memorial prize for the theory, in recentyears the basic assumptions of MPT have beenwidely challenged by fields such as behavioraleconomics.


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MATHEMATICALMODEL

MPT was developed in the 1950s through the early

1970s and was considered an important advance in

the mathematical modeling of finance. Since then,

many theoretical and practical criticisms have been

leveled against it. These include the fact that financial

returns do not follow a Gaussian distribution or

indeed any symmetric distribution, and that

correlations between asset classes are not fixed but

can vary depending on external events (especially incrises). Further, there is growing evidence that

investors are not rational and markets are

not efficient.


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In 1952, Harry Markowitz published a formal

portfolio selection model in The Journal of

Finance. He continued to develop and publishresearch on the subject over the next twenty

years, eventually winning the 1990 Nobel Prize

in Economics for his work on the efficient frontier

and other contributions to modern portfolio

theory.


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EXAMPLE


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33 DIVERSIFICATIONANDBETA

Beta measures systematic risk

Diversification does not mean to reduce beta

Investors differ in the extent to which they will

take risk, so they choose securities with different

betas

E.g., an aggressive investor could choose a


E.g., a conservative investor could choose a



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34 INTRODUCTION

The Capital Asset Pricing Model (CAPM)is a

theoretical description of the way in which the

market prices investment assets

The CAPM is apositivetheory


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35

SYSTEMATICAND

UNSYSTEMATICRISK

Unsystematic risk can be diversified and is

irrelevant

Systematic risk cannot be diversified and is

relevant

Measured by beta

Beta determines the level of expected return on a

security or portfolio (SML)


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36 CAPM

The more risk you carry, the greater the expected

return:

( ) ( )

where ( ) expected return on security

risk-free rate of interest

beta of Security

( ) expected return on the market

i f i m f

i

f

i

m

E R R E R R

E R i

R

i

E R


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portfolio by rachit.pptx

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