Methodological Problems Associated

with the Calculation of Investment

Risk – The ASE Case

Supervisor: Gklezakos Michael

Student: Bektsi Maria

Piraeus, 2015

PORTGRADUATE PROGRAM IN

APPLIED STATISTICS

UNIVERSITYOF PIRAEUS

Introduction

Dissertation

– Aim

testing the problems of investment risk

estimation

– Methodology

implementation of Market & Dimson

models

Problems of Investment Risk

Estimation

Problems of Investment Risk

Estimation

Methodological

Problems of Investment Risk

Estimation

Return Calculation

1

1

tt t t

t

DR P P

P

1

1

t tt

t

P PR

P

,

Methodological

Problems of Investment Risk

Estimation

Methodological

Return Interval

Problems of Investment Risk

Estimation

Methodological

Market Index

Problems of Investment Risk

Estimation

Horizon

Methodological

Problems of Investment Risk

Estimation

Methodological

Thin Trading

Problems of Investment Risk

Estimation

Statistical

Problems of Investment Risk

Estimation

Multicollinearity

Statistical

Problems of Investment Risk

Estimation

Statistical

Multicollinearity

Problems of Investment Risk

Estimation

Heteroscedasticity

Statistical

Problems of Investment Risk

Estimation

Statistical

Heteroscedasticity

Problems of Investment Risk

Estimation

Autocorellation

Statistical

Problems of Investment Risk

Estimation

Bias

Statistical

Problems of Investment Risk

Estimation

Lack of Normality

Statistical

Methodology

• Sample

– Selection Criterion

Marketability

– Stocks Number

20

– Examination Periods

01/00-12/02, 07/03-06/06, 01/09-12/11

• Return Calculation: 1

1

t tt

t

P PR

P

Methodology

Market & Dimson Models

• Market Model

Researchers: Sharpe(1964), Bey & Pinches(1980),

Huang & Jo(1988)

• Dimson Model

Researchers: Fowler et al(1979), Cohen et al(1983)

it i i Mt itR a b R e

,

n

it i k M t k it

k n

R a b R e

Market & Dimson Models

ASE Research

– Superiority of Market Model

Haritou(2000), Vazakides(2006)

[monthly data]

– Superiority of Dimson Model

Karathanassis & Patsos(1997),

Karathanassis et al(1999)

[daily data]

Marketability⟹ Dispersion & Skewness

⟹ Growth: Platykurtic Distribution

Distribution Characteristics

Portfolio Period Mean Max Min RangeStandard

DeviationKurtosis Skewness

Low

Marketability

01/00-12/02 -.255 11.793 -13.107 24.900 3.583 1.738 .237

07/03-06/06 .133 15.562 -12.853 28.415 3.139 4.582 .615

01/09-12/11 -.054 20.215 -18.579 38.794 4.531 3.889 .262

High

Marketability

01/00-12/02 -.107 10.685 -9.764 20.449 2.273 3.448 .380

07/03-06/06 .133 8.417 -8.097 16.514 1.823 2.226 .195

01/09-12/11 -.093 20.032 -13.859 33.891 3.375 3.357 .390

Testing Regression Assumptions

Tests

– Normality

Jarque-Bera

– Homoscedasticity

Levene

– Indepedence

Runs

22 1

36 4

nJB S K

*S: Skewness, Κ: Kurtosis

Stocks: Testing Regression

Assumptions

• Assumptions

– Normality

– Homoscedasticity Economy & Merketability⟹ Homoscedasticity

– Indepedence Economy & Marketability⟹ Depedence

• Economy⟹ Volatility

Low HighMarketability Marketability

Volatility < Volatility

Market & Dimson Models

Results Matching

(High Marketability)

Assumptions: Normality

Homoscedasticity

Independence

Portfolios: Testing Regression

Assumptions - Market Model

Portfolio PeriodNormality

(Jarque Bera test)

Homoscedasticity

(Levene’s test)

Independence

(Run’s test)

Volatility

Coefficient

(beta)

Low

Marketability

01/00-12/02 95.6330 .0958 .2077 1.237

07/03-06/06 726.8508 .0034 .3225 1.131

01/09-12/11 104.7290 .3307 .2312 .493

High

Marketability

01/00-12/02 140.3856 .1646 .3223 .998

07/03-06/06 80.9274 .0862 .3591 1.091

01/09-12/11 102.3306 .4604 .3739 1.068

*Level of Significance: 1%

Range

Standard

Deviation

38.794 4.531

33.891 3.375

Assumptions: Normality

Homoscedasticity

Independence

Multicollinearity

Portfolios: Testing Regression

Assumptions – Dimson Model

Portfolio PeriodNormality

(Jarque Bera test)

Homoscedasticity

(Levene’s test)

Independence

(Run’s test)

Volatility

Coefficient

(beta)

Low

Marketability

01/00-12/02 95.6330 .0279 .2191 1.220

07/03-06/06 726.8508 .0034 .3882 1.128

01/09-12/11 104.7290 .3249 .2186 .494

High

Marketability

01/00-12/02 140.3856 .1665 .2904 .991

07/03-06/06 80.9274 .0946 .3466 1.078

01/09-12/11 102.3306 .5054 .4572 1.068

<1.237

<1.131

<1.493

<1.998

<1.091

=1.068

*Level of Significance: 1%

Conclusions

• Stocks:– Normality & Homoscedasticity

– Recession & Marketability⟹ Homoscedasticity

– Recession & Marketability⟹ Independence

• Portfolio:– Normality

– Homoscedasticity & Independence

Conclusions

• Marketability Level: ATTENTION

• Marketability & Betas Relation:

• Inefficient Implementation of Dimson

Model

• Crisis: Imponderable Factor

Thanks for your

attention