Thông tin bài báo khoa học - CSDL Khoa học

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JED Special Issue 2022

46

Received: 02 December 2021 Revised: 17 February 2022 Accepted: 05 March 2022

The capital asset pricing model in mea- suring risk of stocks on HOSE -

a quantile regression approach

Pham Le My

Mathematics Department, Hue University of Science

Abstract

Purpose - In this paper, we use the quantile regression method to estimate the parameters of the CAPM to test the validity of this model for shares of two groups of stocks in the Viet Nam Stock Exchange: small-size stocks (VNSMALL) and big-size stocks (VN30) when shocking news appears in the financial market.

Findings - The empirical results confirm that the relationship between beta and return is inconstant, both across quantile and across time.

Practical implications - The beta coefficient of VNSMALL stocks fluctuates more than those of the VN30 when the market has the stocks because the volatility of the stocks in the VNSMALL group changes more considerably than that of the stocks in the VN30 group does. Therefore, the investors should identify the purpose of investment, diversify their investment products, avoid focusing only on allocating capital to a group of stocks, even when they are highly profitable. Additionally, it is essential for them to use proper leverage and avoid the herd mentality.

Originality/value - This study provides some valuable evidence on the nexuses between the return and the risk of VNSMALL and VN30 and the quantile regression method is more robust than Ordinary Least Squares (OLS) in capturing the extreme values or the adverse losses evident in return distribution.

Keywords Quantile, quantile regression, Ordinary Least Squares (OLS), CAPM, HOSE.

1. Introduction

A financial market can be considerably influenced by various events such as financial crises, wars, or inappropriate policies. These events cause information shocks in the market that make it difficult for investors to decide. In this context, creating accurate information about the market and avoiding fake news caused by herd behavior are needed for investors and administrators to manage their suitable strategies.

One of the practical models for analyzing and pricing financial assets is the Capital Asset Pricing Model (CAPM). This model is a powerful tool for expressing the relationship between expected return as the sum of the return on the risk-free asset and the expected premium for risk. Ordinary Least Square (OLS) regression is often used for applying this model. However, the OLS method focuses only on the conditional average depending on variables, while lots of information, especially that of values of distribution tails, is omitted. Utilizing quantile regression can overcome this deficit.

Quantile regression was introduced by Koenker and Bassett (1978) and is an extension of classical least-squares estimation of conditional mean models to estimate an ensem-

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47 Special Issue JED 2022

ble of models for conditional quantile functions. An ensemble of estimated conditional quantile functions offers a much more complete view of the effect of covariates on the location, scale, and shape of the distribution of the response variable.

Additionally, the quantile regression parameters estimate the change in a specified quantile of the response variable produced by a one-unit change in the predictor variable. This technique has been used widely in the past decade in many areas of applied econometrics. Applications include investigations of wage structure (Buchinsky and Leslie, 1997), earnings mobility (Eide and Showalter, 1998; Buchinsky and Hunt, 1996), and educational attainment (Eide and Showalter, 1998). Financial applications have been made by Robert and Manganelli (2004) to the problems of Value at Risk and option pricing, respectively. In their work on the cross-section of stock market returns, Barnes and Hughes (2002) applied quantile regression to study the Capital Asset Pric- ing Model (CAPM).

The question raised is when the market is stable or experiences shocks, how does the volatility of beta-coefficients change? Therefore, we would like to test the validity of the CAPM for stocks of the Ho Chi Minh Stocks Exchange (HOSE). This study gives empirical evidence of the reasonability of CAPM in both a stable market and a shocking market. Hopefully, it will support the development of a stable and enduring Vietnam stock market.

The paper is organized as follows: Besides the Introduction in Section 1, in Section 2, the Quantile Regression is introduced. Data and Methodology are described in Section 3, including the data and calculation method. Section 4 presents empirical tests of the CAPM using the Quantile Regression and OLS approach. Section 5 summarizes our findings.

2. Quantile and quantile regression

This section recalls some facts on Quantile regression and the Capital Asset Pricing Model (CAPM) in the next section.

2.1. Estimation of OLS (Ordinary Least Square)

Let X and Y be two random variables. Estimating X by Y via OLS method means that finding the value 𝛽𝛽 � 𝛽𝛽�

𝛽𝛽�

min�

1

𝑛𝑛 ��𝑦𝑦�� _�𝛽𝛽�^�

�

��

min_� 1

𝑛𝑛 � �^��𝑦𝑦�� 𝛽𝛽�

�

��

𝛽𝛽��𝑟𝑟�, 𝑟𝑟�� 𝜎𝜎_�^�

𝜎𝜎_�^�

𝑟𝑟�_� � � 𝑤𝑤��𝑟𝑟��

�

𝑤𝑤_�^�� 𝑉𝑉�

∑ 𝑉𝑉� �

𝑟𝑟�� 𝑛𝑛� 𝑝𝑝_� 𝑝𝑝��

that minimizes the following expectation:

min E(Y - Xβ)²

Then the OLS - estimation is the determination of the quantity _{𝛽𝛽 � 𝛽𝛽�}

𝛽𝛽�

min_� 1

𝑛𝑛 ��𝑦𝑦�� 𝛽𝛽�^�

�

��

min_� 1

𝑛𝑛 � �^��𝑦𝑦�� 𝛽𝛽�

�

��

𝜎𝜎��

𝑟𝑟�_�� 𝑤𝑤_��^�𝑟𝑟��

�

𝑤𝑤_�^�� 𝑉𝑉�

∑ 𝑉𝑉� �

so that we obtain the minimum:

𝛽𝛽 � 𝛽𝛽�

𝛽𝛽�

min�

1

𝑛𝑛 ��𝑦𝑦_�� _�𝛽𝛽�^�

�

��

min�

1

𝑛𝑛 � �^��𝑦𝑦_�� _�𝛽𝛽�

�

��

𝛽𝛽_��𝑟𝑟_�, 𝑟𝑟_�� 𝜎𝜎_�^�

𝜎𝜎_�^�

𝑟𝑟_�_�� 𝑤𝑤_��^�𝑟𝑟_��

�

𝑤𝑤_�^�� 𝑉𝑉_�

∑ 𝑉𝑉_� _�

𝑟𝑟_�� 𝑛𝑛� 𝑝𝑝_� 𝑝𝑝_�� for two data sequences (x₁,x₂,..,x_n) and (y₁,y₂,..,y_n).

2.2. Quantile regression

We observe that for the value τ = p = 0.5 then Q_τ is exactly the median of X. If Q_τ (Y/x)

= xβ₀ then β₀ is the solution to the problem:

min E[ρ_τ (Y - Xβ)]

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JED Special Issue 2022

48

where ρ_τ(u) is a control function defined by:

ρ_τ(u) = τ1_(u>0) - (1 - τ)u1_{(u≤ 0)} = u[τ - 1(u≤ 0)]

Then the quantile regression estimation of β₀ is the solution to the following program- ming problem:

𝛽𝛽�

min�

1

𝑛𝑛 ��𝑦𝑦�� _�𝛽𝛽�^�

�

��

min�

1

𝑛𝑛 � �^��𝑦𝑦_�� _�𝛽𝛽�

�

��

𝛽𝛽_��𝑟𝑟_�, 𝑟𝑟_�� 𝜎𝜎_�^�

𝜎𝜎_�^�

𝑟𝑟_�_�� 𝑤𝑤_��^�𝑟𝑟_��

�

𝑤𝑤_�^�� 𝑉𝑉_�

∑ 𝑉𝑉_� _�

𝑟𝑟_�� 𝑛𝑛� 𝑝𝑝_� 𝑝𝑝_��

for two data sequences (x₁,x₂,..,x_n) and (y₁,y₂,..,y_n).

3. Capital asset pricing model (CAPM)

The CAPM was developed by Sharpe (1964) and is one of the most influential con- cepts in modern finance. It is closely related to portfolio theory and applied to portfolio risk management, fund performance measurement, security valuation, among other things. Comprehensive studies by Mossin (1966) and Lintner (1965) have made the CAPM theoretically complete as a classic model in pricing assets.

In Viet Nam, there are some studies on the application of CAPM. For example, Tran (2015) has used CAPM to test some shares on HOSE, and the empirical results show that the market risk premium and the stock’s risk premium have a linear relationship—

the higher the risk, the higher the return. Tran (2012) has tested the validity of CAPM for stocks listed on HOSE and HNX. The estimation results demonstrated that the risk level of stocks is very different. However, the author has not provided a convincing explanation for the findings. Truong et al. (2012) tested the relationship between return and risk of eighty stocks listed on the Ho Chi Minh Stock Exchange during January 2007-December 2009. The research results show that the higher the risk, the higher the return, and this result also confirms a nonlinear relationship between the risk of stocks and the market risk premium. Truong (2015) also made a similar test for stocks listed on HOSE from January 2007-August 2014.

Therefore, in Viet Nam, research has demonstrated the suitability of the CAPM for stocks on the Vietnamese stock market—the return of stocks or a portfolio of stocks depends on the systematic risk premium. However, these studies only test the validity of CAPM in case the stock market is stable and has no shocks. Therefore, this paper utilized quantile regression and OLS to test the effectiveness of the CAPM for the very young Vietnamese securities market when this market is stable and when it has information shocks.

CAPM has the following form:

r_A – r_f = α + β_A (r_M - r_f) + ϵ Where:

α: the intercept of regression, r_A is the return of the asset ,

r_f is the risk-free interest rate. In many financial markets, r_f is the interest rate of government bonds or the Central Bank.

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49 Special Issue JED 2022

r_M is the market return,

β_A is the systematic risk measure of the asset, given by:

𝛽𝛽�

min_� 1

�

��

min_� 1

𝑛𝑛 � �^��𝑦𝑦�� 𝛽𝛽�

�

��

𝛽𝛽��𝑟𝑟�, 𝑟𝑟�� 𝜎𝜎��

𝜎𝜎��

𝑟𝑟�_�� 𝑤𝑤_��^�𝑟𝑟��

�

𝑤𝑤�� 𝑉𝑉�

∑ 𝑉𝑉� �

𝑟𝑟�� 𝑛𝑛� 𝑝𝑝�

𝑝𝑝�� 𝛽𝛽 � 𝛽𝛽�

𝛽𝛽�

min_� 1

�

��

min_� 1

𝑛𝑛 � �^��𝑦𝑦�� 𝛽𝛽�

�

��

𝛽𝛽_��𝑟𝑟�, 𝑟𝑟�� 𝜎𝜎_�^�

𝜎𝜎_�^�

𝑟𝑟�_� � � 𝑤𝑤��𝑟𝑟��

�

𝑤𝑤_�^� � 𝑉𝑉�

∑ 𝑉𝑉� �

𝑝𝑝��

is the variance of r_M,

ϵ is the random error with E(ϵ) = 0.

A characteristic of the market portfolio can be introduced by:

𝛽𝛽�

min_� 1

�

��

min_� 1

𝑛𝑛 � �^��𝑦𝑦�� 𝛽𝛽�

�

��

𝜎𝜎��

𝑟𝑟_�_�� 𝑤𝑤_��^�𝑟𝑟_��

�

𝑤𝑤_�^�� 𝑉𝑉�

∑ 𝑉𝑉� �

where r_itis the return of period t for the asset i, and the weight w_i^Mis given by 𝛽𝛽 � 𝛽𝛽�

𝛽𝛽�

min_� 1

�

��

min�

1

𝑛𝑛 � �^��𝑦𝑦_�� _�𝛽𝛽�

�

��

𝜎𝜎��

𝑟𝑟_�_� � � 𝑤𝑤_��^�𝑟𝑟_��

�

𝑤𝑤_�^� � 𝑉𝑉�

∑ 𝑉𝑉� �

𝑟𝑟�� 𝑛𝑛� 𝑝𝑝_� 𝑝𝑝�� with V_i is the total market value of asset i.

In reality, the coefficient beta β (or β_A of asset A, β_i of asset i) allows us to measure the systematic risk. It reflects the relation between the risk of an individual asset and that of the whole market.

4. Methodology 4.1. Data

Our analysis is carried out with two groups of stocks in the Viet Nam stocks market:

- Group VN30 consists of stocks of the highest market capitalization and liquidity.

- Group VN30 consists of stocks of small market capitalization.

We take data from the daily close price of stocks on the Ho Chi Minh City Security Exchange (HOSE) in the period from January 4^th, 2016, to August 5^th, 2021. Twelve stocks of VN30 and twenty-two stocks of VNSMALL are randomly chosen, including:

- VN30: BID, BVH, CTG, GAS, KDH, MBB, MSN, PDR, REE, SBT, VCB, VIC.

- VNSMALL: AMD, CCL, CTI, DGW, DHA, RH, HAI, HHS, ITD, JVC, LDG, LHG, NAF, NKG, NTL, QCG, TDH, TNT, TSC, VNE, VPH, VSC.

For each stock, 1396 observed values (close prices) are taken and the risk-free rate is the average of Government bonds in the period of research. Data are taken from 4 websites: www.fpts.com.vn, http://vndirect.com, http://hsx.vn, and http://hnx.vn.

Sequences of returns are determined as:

𝛽𝛽�

min_� 1

𝑛𝑛 ��𝑦𝑦_�� 𝛽𝛽�^�

�

��

min_� 1

𝑛𝑛 � �^��𝑦𝑦�� 𝛽𝛽�

�

��

𝜎𝜎��

𝑟𝑟�� 𝑤𝑤��𝑟𝑟��

�

𝑤𝑤�� 𝑉𝑉�

∑ 𝑉𝑉� �

𝑝𝑝�� where p_t is the closed price of day t.

4.2. Estimation of coefficient Beta by OLS method

After testing the consistency of the regression function, the values of Beta by OLS estimation are obtained and illustrated in Table 1.

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Variable Coefficient Std. Error t-Statistic Prob.

BID 1.500981 0.037966 39.53519 0

BVH 1.284804 0.040573 31.66659 0

CTG 1.459518 0.035794 40.77594 0

GAS 1.363723 0.039527 34.5012 0

KDH 0.621433 0.033578 18.5074 0

MBB 1.209049 0.031831 37.98368 0

MSN 0.925424 0.041417 22.34425 0

PDR 0.526571 0.041984 12.54207 0

REE 0.858334 0.033617 25.53237 0

SBT 0.812059 0.050229 16.16714 0

VCB 1.225695 0.029682 41.29447 0

VIC 0.934733 0.034955 26.74108 0

Table 1.

Values of Beta coefficients for stocks belonging to VN30 with the OLS estimation method

Table 2.

Values of Beta coefficients for stocks belonging to VNSMALL with the OLS estimation method

Variable Coefficient Std. Error t-Statistic Prob.

AMD 0.705239 0.077399 9.11171 0

CCL 0.838882 0.072497 11.57133 0

CTI 0.545612 0.045204 12.07007 0

DGW 0.942777 0.05472 17.22895 0

DHA 0.353352 0.044195 7.995295 0

DRH 0.989938 0.074113 13.3572 0

HAI 0.934069 0.078617 11.8813 0

HHS 1.073716 0.058146 18.46572 0

ITD 0.486153 0.052782 9.210584 0

JVC 0.659823 0.070366 9.376988 0

LDG 1.286111 0.065203 19.72469 0

LHG 0.754809 0.054885 13.75253 0

NAF 0.415266 0.041731 9.951125 0

NKG 1.139217 0.054576 20.87391 0

NTL 0.821535 0.046271 17.75467 0

QCG 0.792397 0.074657 10.61381 0

TDH 0.881002 0.048597 18.12856 0

TNT 0.588804 0.082363 7.148872 0

TSC 0.985249 0.076536 12.87295 0

VNE 0.571264 0.05741 9.95067 0

VPH 0.613027 0.055606 11.0244 0

VSC 0.725744 0.04254 17.06028 0

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By this estimation, we can see that in the case of stable stock market almost the volatility of stocks in the VNSMALL group is smaller than that of the market because these coefficient β is smaller than one. In contrast, the volatility of most of the shares in the VN30 group (such as BID, BVH, CTG, GAS, MBB, VCB, etc.) is bigger than that

Table 3.

Values of Beta coefficients for stocks belonging VN30 group by the method of quantile regression

0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95 BID (coeff.) 1.586 1.502 1.409 1.421 1.423 1.415 1.417 1.455 1.522 1.567 1.602

Prob. 0 0 0 0 0 0 0 0 0 0 0

BVH(coeff.) 1.454 1.429 1.337 1.232 1.233 1.274 1.227 1.215 1.233 1.345 1.430

Prob. 0 0 0 0 0 0 0 0 0 0 0

CTG(coeff.) 1.515 1.440 1.419 1.400 1.385 1.399 1.421 1.430 1.472 1.522 1.561

Prob. 0 0 0 0 0 0 0 0 0 0 0

GAS(coeff.) 1.483 1.447 1.331 1.309 1.320 1.331 1.317 1.315 1.311 1.365 1.455

Prob. 0 0 0 0 0 0 0 0 0 0 0

KDH(coeff.) 0.682 0.744 0.573 0.476 0.413 0.414 0.409 0.483 0.609 0.735 0.840

Prob. 0 0 0 0 0 0 0 0 0 0 0

MBB(coeff.) 1.305 1.238 1.175 1.151 1.105 1.106 1.105 1.135 1.235 1.274 1.377

Prob. 0 0 0 0 0 0 0 0 0 0 0

MSN(coeff.) 1.103 1.033 1.016 0.921 0.875 0.835 0.863 0.860 0.874 0.919 0.911

Prob. 0 0 0 0 0 0 0 0 0 0 0

PDR(coeff.) 0.656 0.571 0.520 0.456 0.407 0.408 0.443 0.495 0.478 0.515 0.679

Prob. 0 0 0 0 0 0 0 0 0 0 0

REE(coeff.) 0.999 0.952 0.892 0.853 0.812 0.774 0.781 0.778 0.786 0.791 0.958

Prob. 0 0 0 0 0 0 0 0 0 0 0

SBT(coeff.) 1.095 0.994 0.840 0.724 0.590 0.529 0.613 0.683 0.745 0.940 0.983

Prob. 0 0 0 0 0 0 0 0 0 0 0

VCB(coeff.) 1.306 1.186 1.186 1.160 1.174 1.156 1.185 1.204 1.197 1.228 1.246

Prob. 0 0 0 0 0 0 0 0 0 0 0

VIC(coeff.) 1.058 0.929 0.893 0.818 0.741 0.734 0.741 0.829 0.865 1.038 1.041

Prob. 0 0 0 0 0 0 0 0 0 0 0

of the market. A question arising is how the volatility of the stocks in the VNSMALL group and VN30 group fluctuate when the market has shocks?

4.3. Estimation of coefficient Beta by quantile regression method (OLS)

By quantile regression estimation for the parameters in CAPM, it can be seen that, when the market has shocked, the beta coefficient of VN30 shares - including BID, BVH, KDH, MBB, MSN, SBT, and VCB - changes into 1.58, 1.45, 0.68, 1.30, 1.1, 1.09 and 1.30 respectively at the left distribution tail, with quantile level 0.05 or 1.60, 1.43, 0.84, 1.37, 0.91, 0.98, 1.24 at the right distribution tail with quantile level 0.95.

For VNSMALL shares – including CCI, CTI, DGW, DHA, DRC, HHS, NKG and VPH, when the market has shocks, the beta coefficients change into 0.99, 0.62, 1.02, 0.78, 1.14, 0,92, 1.08 and 0.87 respectively at the left distribution tail with quantile level 0.05, or 0.15, 0.37, 0.89, 0.24, 0.64, 0.58, 1.5 and 0.57 respectively at the right

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Table 4.

Values of Beta coefficients for stocks belonging to the VNSMALL group by the method of quantile regression

Quantile 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95

AMD(coef) 0.290 0.931 1.017 0.890 0.744 0.701 0.593 0.673 0.797 0.266 0.001

Prob. 0 0 0 0 0 0 0 0 0 0 0.05

CCL(coef) 0.992 1.053 0.900 0.853 0.707 0.682 0.804 1.001 0.993 0.778 0.152

Prob. 0 0 0 0 0 0 0 0 0 0 0.04

CTI(coef) 0.623 0.632 0.660 0.555 0.506 0.417 0.463 0.495 0.513 0.594 0.375

Prob. 0 0 0 0 0 0 0 0 0 0 0.03

DGW(coef) 1.021 0.993 0.902 0.891 0.896 0.880 0.891 0.982 1.083 1.028 0.899

Prob. 0 0 0 0 0 0 0 0 0 0 0

DHA(coef) 0.459 0.454 0.427 0.391 0.358 0.335 0.315 0.317 0.364 0.329 0.247

Prob. 0 0 0 0 0 0 0 0 0 0.004 0.002

DRC(coef) 0.782 1.231 1.102 1.008 0.937 0.825 0.851 1.031 1.132 1.166 0.243

Prob. 0 0 0 0 0 0 0 0 0 0 0.021

HAI(coef) 0.294 1.065 1.135 1.066 0.976 0.954 0.912 0.999 1.204 0.748 0.045

Prob. 0 0 0 0 0 0 0 0 0 0 0.041

HHS(coef) 1.148 1.236 1.124 1.083 1.019 0.987 1.048 1.078 1.222 1.173 0.642

Prob. 0 0 0 0 0 0 0 0 0 0.002 0.007

ITD(coef) 0.590 0.633 0.534 0.435 0.347 0.290 0.330 0.398 0.503 0.636 0.541

Prob. 0 0 0 0 0 0 0 0 0 0 0.029

JVC(coef) 0.546 0.826 0.905 0.844 0.731 0.549 0.604 0.718 0.689 0.658 0.46

Prob. 0 0 0 0 0 0 0 0 0 0.022 0.0483

LDG(coef) 1.499 1.351 1.408 1.389 1.344 1.307 1.264 1.234 1.300 1.424 1.056

Prob. 0 0 0 0 0 0 0 0 0 0 0.004

LHG(coef) 0.924 0.978 0.891 0.872 0.784 0.725 0.680 0.731 0.696 0.574 0.589

Prob. 0 0 0 0 0 0 0 0 0 0.001 0.003

NAF(coef) 0.506 0.335 0.372 0.385 0.389 0.378 0.374 0.378 0.413 0.377 0.580

Prob. 0 0.001 0 0 0 0 0 0 0 0 0

NKG(coef) 1.088 1.242 1.118 1.099 1.070 1.085 1.127 1.171 1.251 1.448 1.507

Prob. 0 0 0 0 0 0 0 0 0 0 0

NTL(coef) 0.889 0.942 0.901 0.789 0.747 0.739 0.747 0.761 0.745 0.890 0.831

Prob. 0 0 0 0 0 0 0 0 0 0 0

QCG(coef) 0.514 1.016 0.995 1.002 0.948 0.788 0.743 0.850 0.812 0.749 0.23

Prob. 0.004 0 0 0 0 0 0 0 0 0.007 0.051

TDH(coef) 1.056 0.969 0.892 0.868 0.860 0.765 0.767 0.857 0.849 0.867 1.015

Prob. 0 0 0 0 0 0 0 0 0 0 0.004

TNT(coef) 0.300 0.801 0.834 0.709 0.558 0.369 0.363 0.462 0.562 0.439 0.158

Prob. 0.019 0.002 0 0 0 0 0 0 0.004 0.032 0.047

TSC(coef) 0.746 1.037 1.063 1.066 0.959 0.880 0.977 1.061 1.150 1.259 0.109

Prob. 0.003 0 0 0 0 0 0 0 0 0 0.398

VPH(coef) 0.870 0.747 0.734 0.539 0.515 0.479 0.542 0.529 0.573 0.649 0.575

Prob. 0 0 0 0 0 0 0 0 0 0 0.003

VSC(Coeff.) 0.762 0.739 0.664 0.670 0.670 0.688 0.666 0.758 0.782 0.711 0.759

Prob. 0 0 0 0 0 0 0 0 0 0 0

distribution tail with quantile level 0.95. That means, when the market decreases or in- creases, the volatility of the stocks in the VNSMALL group changes stronger than that of the stocks in the VN30 group. Values of the coefficient beta of the VN30 group and the VNSMALL group are given in Table 3 and Table 4.

Software R was used to write a program which is to illustrate the dynamics of stock returns depending on market returns. The results are shown in Figure 1 and Figure 2.

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53 Special Issue JED 2022

Figure 2.

Stock returns depend on market returns for stocks belonging to group VNSMALL Figure 1.

Stock returns depending on market returns for stocks belonging to group VN30

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Figure 3.

The confidence interval for the Beta-coefficient of stocks in VN30 at the 95%

significance level

Figure 4.

The confidence interval for the Beta-coefficient of stocks in VNSMALL at the 95%

significance level

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Redline express estimation by OLS and blue lines represent estimation by quantile regression corresponding to quantile orders 0.05, 0.1, 0.25, 0.50, 0.75, 0.90, 0.95. From these results we can see, estimations by OLS are rather far from real data and we cannot estimate values at the distribution tail as we can do it by quantile regression. It means the method of OLS only gives us the main trend of returns distribution but does not reflect returns values at the tail of distribution as by quantile regression. Therefore, when there is a stock market shock, the OLS method is not suitable for estimating Beta values.

Figure 3 and Figure 4 show that there are dramatic changes in stocks returns for various quantile levels corresponding to some shocks in the market. Stocks returns in the VNSMALL group get change heavier than these of VN30, particularly in their tails of distribution relatively quantile levels 0.05, 0.1, 0.9, and 0.95.

The Beta - coefficients of VNSMALL-stocks increase or decrease much more than these of VN30 when the market is not a rather stable, especially with the quantile 0.05, 0.1, 0.9, and 0.95. So, the risk levels for investing in these stocks are higher than stocks in VN30. It means also that stocks in the VNSMALL group are riskier than these of VN30. This situation is suitable only for a short-range investment and it suggests an appropriate decision for investors. And the fluctuation of the Beta coefficient for assets of the VNSMALL group is large and has sudden changes when some shocks occur. It follows that, in the case of the fluctuated market, for large capital companies (VN30), speculative investors do have not enough capacity resources to manipulate the stock market. They buy many small-cap stocks (VNSMALL) to minimize the risk. Therefore, the volatility of stocks of VNSMALL is stronger than that of stocks of VN30.

5. Conclusion

In this study, quantile regression models are used to estimate parameters in CAPM.

The combination of CAPM and quantile regression models is then applied to eval- uate the risks of two classes of stocks on HOSE —VNSMALL and VN30. The results of this study show that a quantile regression approach is appropriate to study the dynamics of stock return in comparison with returns of the market. Specifically, our analysis has demonstrated the movement rules of stocks. The VNSMALL class stocks constantly change abnormally and suddenly when the financial market has positive or negative shocks. These changes are because those stocks have low capitalization, so large and non-transparent investors are often easily manipulated and speculated. The herd mentality of investors is also impactful. Therefore, the volatility of stocks of this type changes more strongly in an unstable financial market. Conversely, stocks of the VN30 group have large capitalization, which then speculation and manipulation are more challenging. It can be concluded that VN30 stocks are also more stable than those from the VNSMALL group.

Since 2020, the Vietnamese economy and the stock market have faced challenges due to the Covid-19 pandemic. However, with the government’s appropriate management of the epidemic, Vietnam’s stock market has recovered rapidly. Indeed, Vietnam’s stock market is regarded as one of the ten best-resistant and resilient stock markets globally.

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Acknowledgments

The author acknowledges financial support from the Research Project of Hue University, code DDH2019-01-141.

The strong recovery of the stock market, record low-interest rates, and strong partic- ipation of new investors have pushed market liquidity to unprecedented levels. This shows that the cash flow is better spread in the blue-chip group than in midcap and penny stocks.

There are several recommendations on solutions for investors in 2022. First, in the context of new trends and challenges, investors should mention that profit-related is- sues are always risky; so, defining the purpose of investment clearly and diversifying investment products is necessary. Secondly, it is also essential to use proper leverage, avoid the herd mentality, and be a wise investor. It is further advisable to learn about the business to understand the primary factors and avoid focusing only on allocating capital to a group of stocks, even when they are highly profitable.

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Corresponding author

Pham Le My can be contacted at: phamlemy@hueuni.edu.vn

Tran, V.T. (2012), “Application of capital asset pricing model (CAPM) to select investment stocks”, Journal of Banking Technology, Vol. 76, pp. 50-54.

Truong, D.L and Tran T.H.P (2012), “Testing the relationship between profit and risk of stocks listed on Ho Chi Minh Stock Exchange”, Economic Development Journal, 251, pp. 2-8.

Truong, V.K (2015), “Testing the CAPM model with stocks on HOSE”, Journal of Economics and Forecasting, Vol. 14, pp. 41-43.