Performance and Volatility Modelling for Shariah Compliant Stocks in Malaysia Using Exponentially Weighted Moving Average

(1)

65

Performance and Volatility Modelling for Shariah Compliant Stocks in Malaysia Using Exponentially Weighted Moving Average

J Assan

¹

, A M Jaapar

²

and S R Hamzah

³

1,2,3

Universiti Sains Islam Malaysia, Bandar Baru Nilai 71800, Malaysia

E-mail: ([email protected]); ([email protected]); ([email protected])

Abstract. The diversity of an investment in Malaysia provides an excellent platform to gauge volatility.

Malaysia as an emerging market with a rich Islamic culture serves as an inspiration to randomly model a portfolio of 50 Shariah compliant stock returns from 2015 to 2020. The systematic risk of the company’s stock returns is measured through computing the volatility and downside volatility for the said period. The Exponentially Weighted Moving Average (EWMA) method is used to outline the risk levels of Shariah compliant for the recent stipulated period. The results indicate a statistical difference between beta and downside beta for Shariah compliant portfolio. This signals investors to be cognisant of the semi-variant characteristics of returns in estimating volatility. Meanwhile, there is no significant difference in performance using the Sharpe and Sortino ratio on the beta and downside beta scores respectively. Consequently, this suggests that investors

can always measure performance to a sufficient degree of accuracy regardless of their choice in volatility.

Keyword: Beta; Downside beta; Shariah-compliant stocks; EWMA; Sortino ratio; Sharpe ratio.

Introduction

First introduced by [1], the introduction of the beta function in the Capital Asset Pricing Model (CAPM) is a common method used in outlying systematic risks. An alternate measure of risk is the downside beta in asset pricing, which was first introduced by [2]. The downside beta model focuses on downside loss rather than the common Capital Asset Pricing Model (CAPM) practice of merging both downside and upside risk as one. This alternative approach to the [1] mean variance theory is regarded as the mean semi variance theory. The downside beta is given by [3]:

𝛽𝛽𝑖𝑖−=𝐶𝐶𝐶𝐶𝐶𝐶(𝑟𝑟_𝑖𝑖,𝑟𝑟_𝑚𝑚 |𝑟𝑟_𝑚𝑚< 𝑢𝑢_𝑚𝑚)

𝑉𝑉𝑉𝑉𝑟𝑟(𝑟𝑟_𝑚𝑚 |𝑟𝑟𝑚𝑚< 𝑢𝑢𝑚𝑚) (2)

where,

𝑟𝑟_𝑖𝑖

: The return on the 𝑖𝑖

^𝑡𝑡ℎ

asset,

𝑟𝑟_𝑚𝑚

: Return on the market,

𝑈𝑈𝑚𝑚

: The average market excess return.

Material and methods

The daily stock returns are retrieved from Yahoo Finance and was cross referenced with FTSE Bursa Malaysia EMAS

SHARIAH listings to ensure the selected stocks fulfil the Sharia compliant requirement. The data covers the period

January 1st, 2015 to January 1st, 2020. The method for calculating volatility is the EWMA. It is an instrument that

allows for detection of smaller fluctuations in the mean of data points constrained by time. It also assigns more weight

to recent returns over past returns.

(2)

66 Figure 1. Flowchart indicating the structure of the research Results and discussions

Figure 2. Beta plot for shariah compliant

portfolio Figure 3. Downside beta plot for shariah

compliant portfolio .

y = -0.0007x + 0.3354 R² = 0.0056

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

0 10 20 30 40 50

Beta (Volatility)

Company

Beta

y = -0.0005x + 0.2253 R² = 0.0061

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

0 10 20 30 40 50

Downside Beta (Volatility)

Company

Downside Beta

SORTINO RATIO Method:

EWMA

Volatility Modelling for Sharia Compliant Stocks in Malaysia using

EWMA

Objective 1: Model the beta and downside beta of Shariah compliant portfolio using EWMA

Objective 2: Assess the level of performance for Shariah compliant portfolio.

Downside Beta Beta

SHARPE RATIO

Method:

EWMA

(3)

67 Figure 4. Sharpe ratio plot for shariah

compliant portfolio Figure 5. Sortino ratio plot for shariah compliant portfolio

Conclusions

The study successfully modelled beta and downside beta using the EWMA. There is statistically significant difference that beta valuations are higher than downside beta for Sharia compliant portfolio using t-test. However, the performance reactions of the Shariah compliant portfolio is insignificant between beta and downside beta. Generally, the boundaries for 𝛽𝛽 lies between 10.75%

and on upper level of 57.77%. The average downside boundaries for SCS lies between 6.74% and 40.53%. Considering the research objective in comparing beta and downside beta in Shariah compliant portfolio, the inference is that distinguishing between upsides and downsides has substantial effects on the estimation of volatility.

Furthermore, after assessing the level of performance for Shariah compliant portfolio and keeping in mind the earlier conclusion, it can be established that beta and downside beta are indifferent when it comes to performance of Shariah compliant stock using the Sharpe and Sortino ratio respectively. This opens the possibility that the Sharpe ratio is suited for beta while the Sortino ratio pairs well with downside beta. This seamless relationship opens up a more dynamic computation of volatility with sufficient accuracy.

Recommendations

Although there is preference for downside beta over beta, the level of attention given to modelling series using downside beta is very limited. Therefore, future researchers can focus on using different approaches to model downside beta. Multivariate GARCH is one such model to consider. Furthermore, the research can be extended to capture other portfolios such as conventional portfolio, cryptocurrency etc.

References

[1] Markowitz H 1952 Portfolio Selection J. Finance vol. 7, no 1 p 77

[2] Roy A D 1952 Safety First and the Holding of Assets Econometrica vol 20 no 3 p 431

[3] Estrada J 2007 Mean-semivariance behavior: Downside risk and capital asset pricing Int. Rev. Econ. Finance vol 16 no 2 p 169

y = 8E-06x + 4E-05 R² = 0.0039

-0.60%

-0.40%

-0.20%

0.00%

0.20%

0.40%

0.60%

0.80%

0 10 20 30 40 50

Sharpe (Performance)

Company

Sharpe

y = 1E-05x + 9E-05 R² = 0.0048

-1.00%

-0.50%

0.00%

0.50%

1.00%

1.50%

0 10 20 30 40 50

Sortino (Performance)

Company