Financial integration of the European transition ...

ASERS

J

ournal of Advanced Studies in Finance

Biannually Volume VII Issue 1(13) Summer 2016 ISSN 2068 – 8393 Journal DOI http://dx.doi.org/10.14505/jasf

Journal of Advanced Studies in Finance

is an advanced e-publisher struggling to bring further worldwide learning, knowledge and research. This transformative mission is realized through our commitment to innovation and enterprise, placing us at the cutting-edge of electronic delivery in a world that increasingly considers the dominance of digital content and networked access not only to books and journals but to a whole range of other pedagogic services. In both books and journals, ASERS Publishing is a hallmark of the finest scholarly publishing and cutting-edge research, maintained by our commitment to rigorous peer-review process. Using pioneer developing technologies, ASERS Publishing keeps pace with the rapid changes in the e-publishing market. ASERS Publishing is committed to providing customers with the information they want, when they want and how they want it. To serve this purpose, ASERS publishing offers digital Higher Education materials from its journals, courses and scientific books, in a proven way in order to engage the academic society from the entire world.

1

Summer 2016 Volume VII Issue 1(13) Editor in Chief Laura GAVRILĂ (formerly) ŞTEFĂNESCU Spiru Haret University, Romania

Contents:

Co-Editor Rajmund MIRDALA Technical University of Kosice, Slovak Republic

1 The Role of Asymmetries and Banking Sector

Indicators in the Interest Rate Pass-Through in Malta Brian MICALLEF, Noel RAPA,Tiziana Marie GAUCI

Editorial Advisory Board Mădălina Constantinescu Spiru Haret University, Romania Rosaria Rita Canale University of Naples Parthenope, Italy

External Financing Patterns for Small and Medium

2 Firms in Eastern Europe and Central Asia: Does Financial and Institutional Development Matter? Octavian PORUMBOIU

Francesco P. Esposito Allied Irish Bank, Group Market Risk Management Lean Hooi Hooi Universiti Sains Malaysia, Malaysia

3

Terence Hung United International College, Hong Kong Renata Karkowska Faculty of Management, University of Warsaw, Poland

Piotr Misztal The Jan Kochanowski University in Kielce, Faculty of Management and Administration, Poland

…38

Sergey BLINOV

Assessment of Economic Indicators for Evaluation of Mihaela COCOŞILĂ

Daniel Stavarek Silesian University, Czech Republic Laura Ungureanu Spiru Haret University, Romania

…70

A Note on Credit Spread Forwards

5 6

Markus HERTRICH

Applications of Simulation - based Methods in Finance: The Use of ModelRisk Software Hamed HABIBI, Reza HABIBI

Andreea Pascucci University of Bologna, Italy Rachel Price-Kreitz Ecole de Management de Strasbourg, France

…14

How to Stabilize the Currency Exchange Rate

4 Financial Performance

Kosta Josifidis University of Novi Sad, Serbia Ivan Kitov Russian Academy of Sciences, Russia

…5

ASERS Publishing http://www.asers.eu/asers-publishing ISSN 2068-8393 Journal's Issue DOI: http://dx.doi.org/10.14505/jasf.v7.1(13).0

Wing-Keung Wong Department of Economics, Institute for Computational Mathematics, Hong Kong Baptist University 2

...77

...82

Call for Papers Volume VII, Issue 2(14), Winter 2016


The Journal aims to publish empirical or theoretical articles which make significant contributions in all areas of finance, such as: asset pricing, corporate finance, banking and market microstructure, but also newly developing fields such as law and finance, behavioral finance and experimental finance. The Journal will serve as a focal point of communication and debates for its contributors for the better dissemination of information and knowledge on a global scale. The primary aim of the Journal has been and remains the provision of a forum for the dissemination of a variety of international issues, empirical research and other matters of interest to researchers and practitioners in a diversity of subjects linked to the broad theme of finance. The Editor in Chief would like to invite submissions for the 7th Volume, Issue 2(14), Winter 2016 of the Journal of Advanced Studies in Finance (JASF). Journal of Advanced Studies in Finance is indexed in EconLit, RePEC, CABELL's Directories, EBSCO, ProQuest, CEEOL databases. All papers will first be considered by the Editors for general relevance, originality and significance. If accepted for review, papers will then be subject to double blind peer review. Deadline for Submission: Expected Publication Date: Web: E-mails:

15th October , 2016 Dcember, 2016 www.asers.eu/journals/jasf/ [email protected] [email protected]

3


Volume VII Issue1(13) Summer 2016

DOI: http://dx.doi.org/10.14505/jasf.v7.1(13).06

Applications of Simulation-Based Methods in Finance: The Use of ModelRisk Software Hamed HABIBI Faculty of Science and Engineering, Curtin University, Perth, Australia [email protected] Reza HABIBI Iran Banking Institute, Central Bank of Iran, Tehran, Iran [email protected] Suggested Citation: Habibi, H., Habibi, R. (2016). Applications of Simulation-Based Methods in Finance: The Use of ModelRisk Software, Journal of Advanced Studies in Finance, (Volume VII, Summer), 1(13): 82-89. DOI:10.14505/jasf.v7.1(13).06. Available from: http://www.asers.eu/journals/jasf/curent-issue. Article’s History: Received May, 2016; Revised June, 2016; Accepted July, 2016. 2016. ASERS Publishing. All rights reserved. Abstract: This paper has two parts. The first part considers the statistical arbitrage detection using the simulation-based approaches. The statistical arbitrage is the opportunity of attaining gain at future with a high probability with zero investment at the current time. Simulated methods relies on the direct use of three famous theorems in the field of stochastic process, namely (i) the arc-sine laws, (ii) the first passage of time, and (iii) optional sampling theorem. It is very important for investors to use the simulated approaches by user-friendly software like the ModelRisk of Excel which is done in this note. In the second part, the conditional NPVaR (CNPVaR) of a cash flow stream in the presence of exchange rate risk. The distribution of risk factors are assumed to be a specified location-scale distribution. The application of dynamic programming and quadratic programming are studied. Keywords: arc-sine laws; CNPVaR; dynamic and quadratic programming; exchange rate risk; first passage of time; optional sampling theorem; statistical arbitrage. JEL Classification: C15, C53, C61.

1. Introduction This paper contains two parts. The first part studies the statistical arbitrage based on simulated algorithms. The arbitrage opportunity is, by constructing a portfolio, attaining the risk free profit at future with zero investing at the current time. The statistical arbitrage is achieving the profit at future with a high probability (Bondarenko 2003). The current note considers the statistical arbitrage detection using the simulation-based approaches. Simulated methods relies on the direct use of three famous theorems in the field of stochastic process, namely (i) the arc-sine laws, (ii) the first passage of time, and (iii) optional sampling theorem. These theorems may have many financial applications. For example, if there are strong criteria such that the logarithm of a price of stock follows a Brownian motion, then 𝜏𝑎 (the first passage) is the first time that the logarithm of price hits the level 𝑎. Therefore, it is very important (for investors, for example) to simulate them by user-friendly software like Excel. The ModelRisk (Vose company) is an adds-in software of Excel designed to perform simulation, sensitivity analysis, optimization and risk analysis with applications in finance models, see Vose (2010). This note considers the simulation-based approach to detect statistical arbitrage opportunities. The second part studies the conditional NPVaR (CNPVaR) of a cash flow stream in the presence of exchange rate risk. 82



Part 1 The statistical arbitrage The rest of this part is organized as follows. In the next section, the simulation-based approaches and some simulation results are presented. A real data analysis is considered in section 3. To these ends, consider a portfolio containing a long position in a stock 𝑆𝑡 and 𝛾 portion of a riskless bond 𝐵𝑡 , with risk free rate growth 𝑟 in short position. The value of portfolio is 𝑣𝑡 = 𝑆𝑡 − 𝛾𝐵𝑡 . 2. Simulated methods This section is organized for presenting simulation-based approaches. 2.1. Arc-Sin law The first approach uses the arc-sin law which is given by (Calin 2012). The probability that a Brownian 2

𝑡

motion 𝐵𝑡 does not have any zeros in the interval (t1 , t 2 ) is equal to 𝑃(𝐵𝑡 ≠ 0, 𝑡 ∈ (𝑡1 , 𝑡2 )) = 𝜋 arcsin √𝑡1 . 2

To use the arc-sin law, it is assumed that 𝛾 is a time varying parameter, that is, 𝛾 = 𝛾𝑡 . Let 𝑣0 = 0, then, 𝛾0 = 𝑆0 , let the probability of having possible arbitrage is pt = P(vt > 0). It is assumed that 𝑆𝑡 follows a Black𝐵0

Scholes formulae, thus St = S0 e P (e

σ2 (μ− )t+σwt 2

σ2 2

(μ− )t+σwt

, where 𝑤𝑡 is the Wiener process. Thus, pt = P(St > γt Bt ) =

γ

> γ t ert ). 0

Let μ = r +

σ2 2

wt √t

. Then, pt = P (

γ

1

−1

γ

> σ t log (γ t )). Define rt = σ t log (γ t ) or equivalently, γt = √

√

0

−σrt √t

0

γ0 e . Then, 𝑝𝑡 = 𝑁(𝑟𝑡 ), where 𝑁 is the CDF of standard normal distribution. Suppose that as t → ∞, then rt → ∞ and therefore, 𝑝𝑡 → 1. Next, suppose that t → ∞, then rt → 0 and √trt → 0 therefore, pt → 1 0.5. However, the Arc-Sin law presents a better result. Notice that for t ∈ (t1 , t 2 ), then pt = (2) P(|wt | > 1

1

t

|rt |) ≥ ( ) P(|wt | > |rt |, t ∈ (t1 , t 2 )) ≈ arcsin √ 1 . These results are correct if 𝑤𝑡 follows a Wiener 2 π t 2

process. As follows, the behavior of pt is studied for rt = t, et , e−t in Table 1. Table 1 - The behaviour of pt r

rt = t

rt = et

rt = e−t

p1

p2

p3

0.001

0.001

1.001001

0.999

0.500399

0.841587

0.841103

0.002

0.002

1.002002

0.998002

0.500798

0.841829

0.840861

0.003

0.003

1.003005

0.997004

0.501197

0.842071

0.840619

0.028

0.028

1.028396

0.972388

0.511169

0.848118

0.834571

0.029

0.029

1.029425

0.971416

0.511568

0.84836

0.83433

0.03

0.03

1.030455

0.970446

0.511966

0.848602

0.834088

0.031

0.031

1.031486

0.969476

0.512365

0.848843

0.833846

0.032

0.032

1.032518

0.968507

0.512764

0.849085

0.833604

0.06

0.06

1.061837

0.941765

0.523922

0.855845

0.826843

0.061

0.061

1.062899

0.940823

0.52432

0.856086

0.826602

0.062

0.062

1.063962

0.939883

0.524719

0.856327

0.826361

0.063

0.063

1.065027

0.938943

0.525117

0.856568

0.82612

0.09

0.09

1.094174

0.913931

0.535856

0.863061

0.819623

83



It is seen that as t → ∞, then pt → 1, for rt = t, et and pt → 0.5 for rt = e−t . 2.2 The first passage of time Here, another approach is proposed using the first passage time theorem. Let 𝜏𝑎 be the first time the 2

Brownian motion Bt hit a. Then, τa has a Pearson (5) distribution given by density fτa (x) =

|a| −a e 2x √2π

−3

x2 ,x>

0. Next, we suppose that γt = γ0 is fixed. The aim is to find the stopping time τ such that P(vτ > 0) = 1. σ2

w

Hence, the stopping time τ is the first time that t t hits the level a = r + 2 − μ. Again, this first passage is simulated using ModelRisk software. While μ = r = 0.05, σ = 0.25, the level is 0.03125. Here, using a Monte w Carlo simulation (with 1000 repetition), 1000 paths of t t t = 0.001(0.001)1, are generated and the empirical estimate of τa is obtained 0.05 with standard deviation 0.196. The histogram estimation of its density is given by Figure 1. A Pearon (5) distribution is fitted with a = 0.03125. The SIC, AIC, HQIC and LR goodness of fit are 8182.5, 8192.38, 8188.66 and 1, respectively. The following Table 2, gives the mean and standard deviation of τa for various values of parameters.

Figure 1. Histogram plot of τa

The surface of mean and standard deviation of τa are given in Figures 1 and 2, respectively. It is seen as μ gets large and σ is small, the results are more accurate. Table 2 - The mean and standard deviation of τa E(τa ) μ/σ

0.100

0.200

0.250

0.300

0.350

0.400

0.500

0.01

0.033

0.036

0.03

0.043

0.034

0.023

0.060

0.03

0.049

0.055

0.03

0.01

0.06

0.061

0.057

0.05

0.014

0.041

0.05

0.05

0.023

0.017

0.024

0.07

0.0247

0.03

0.031

0.06

0.035

0.0158

0.0253

0.09

0.021

0.0286

0.0246

0.027

0.043

0.015

0.039

0.1

0.0433

0.048

0.0286

0.041

0.049

0.022

0.043

0.12

0.039

0.021

0.027

0.087

0.053

0.04

0.026

84


Volume VII Issue1(13) Summer 2016 stdev(τa )

μ/σ

0.1

0.2

0.25

0.3

0.35

0.4

0.5

0.01

0.116

0.152

0.142

0.161

0.151

0.161

0.203

0.03

0.176

0.192

0.213

0.225

0.206

0.22

0.193

0.05

0.099

0.178

0.196

0.183

0.104

0.123

0.091

0.07

0.093

0.146

0.124

0.203

0.154

0.047

0.118

0.09

0.077

0.145

0.109

0.143

0.16

0.039

0.172

0.1

0.16

0.178

0.124

0.174

0.187

0.111

0.176

0.12

0.16

0.1

0.11

0.25

0.19

0.168

0.128

Figure 2 - Mean Surface of τa

Figure 3 - Stdev surface of Tau

2.3. The optional sampling theorem The theorem is as follows. Let Mt , t ≥ 0, be a right continuous Ғt -martingale (Ғt is a filtration) and τ be a stopping time with respect to Ғt . If either one of conditions of the following conditions holds: 1. τ is bounded, i.e. ∃ N < ∞ such that τ ≤ N; 2. ∃ c > 0, such that E[|Mt |] ≤ c, ∀t > 0, then E(Mτ ) = E(M0 ). In this case, it w is assumed that Mt∗ = t t is not a martingale with respect to Ғt . Therefore, an important question is if E(Mτ∗ ) = 85



E(M1∗ ) = 0. Again, this question is answered through simulations. Assuming μ = r = 0.05, σ = 0.25, the histogram of Mτ∗ is plotted as follows in Figure 4. The following Table 3 gives the Monte Carlo estimate of E(Mτ∗ ) for various selections of μ and σ. The surface of mean and standard deviation of Mτ∗ are given in Figures 4 and 5, respectively. For almost all cells, the standard deviation is high and the mean of Mτ∗ has sharp changes in sign and values, indicating there is no robust inference about the Mτ∗ , because it is not a martingale. In the next section, a real data set is analyzed and statistical arbitrage is detected. 3. Real data set In this section, existence the statistical arbitrage in stock of Intel corporation, a multinational technology company, is surveyed. The daily stock price are collected for period of study 20th February 2015 to 18th February 2016, including 250 log-returns. They are taken from

Figure 4 - Histogram plot of Mτa Table 3 - The mean and standard deviation of Mτ∗ E(Mτ∗ ) 𝜇/𝜎

0.1

0.2

0.25

0.3

0.35

0.4

0.5

0.01

0.254

-0.945

-0.0255

-0.696

-0.252

-6.18

-2.18

0.03

-0.42

6.65

0.388

4.27

-0.164

-1.17

-1.43

0.05

-2.86

1.52

0.89

3.125

-0.84

7.54

-2.76

0.07

1.17

-1.59

-1.47

0.75

4.27

-0.82

4

0.09

0.046

-1.75

1.75

-1.66

-0.5

0.185

-3.49

0.10

0.695

1.024

0.438

-1.47

1.52

0.95

1.89

0.12

-0.37

2.56

1.4

4

4.88

2.09

3.89

stdev(Mτ∗ ) 𝜇/𝜎

0.1

0.2

0.25

0.3

0.35

0.4

0.5

0.01

29.42

27.26

24.94

26.27

22.9

24.06

23.85

0.03

26.41

24.85

25.9

23.61

25.64

24.52

27.17

0.05

26.66

23.21

24.72

22.73

26.24

25.3

25.35

0.07

23.3

24.51

25.11

24.64

25.04

27.13

23.91

0.09

22.06

23.49

24.02

24.65

23.46

23

25.16

0.1

22.68

24.14

25.56

26.76

25.9

22.3

22.42

0.12

21.22

25.46

24.47

23.85

22.66

23.66

25.71

86



Figure 5 - Mean surface of Mτ∗

Figure 6 - Stdev surface of 𝑀𝜏∗

Google-finance website. Time series plot of return series is given by Figure 7. The p-value chi-squared normality test is 0 which shows the log-returns (ri ) are not normally distributed. It is seen that a t 3 (student-t with 3 degrees of freedom) is suitable for returns. The S0 = 34.41 and B0 = 100, then γ0 = 0.3441. The risk free rate is 0.19 taken from https://www.treasury.gov. Here, it is assumed that γt = γ0 . The probability of having statistical arbitrage is pt = P(St > γt Bt ) = P(S0 ∏ti=1(1 + ri ) > γ0 Bt ) = P(∏ti=1(1 + ri ) > ert ) = ∑ti=1 log(1+ri )

P(

t

> 𝑟) ≈ P(r̅t > 𝑟).

-0.10

-0.05

0.0

0.05

Time series plot of log-return

0

50

100

150

200

250

Figure 7 - Time series plot of log-returns

The last equality uses this fact that log(1 + ri ) ≈ ri . A central limit theorem implies that r̅t has approximately normal distribution with mean 3 and variance 6⁄t. The plot of pt is given as follows in Figure 8.

87



0.70

0.75

0.80

0.85

0.90

0.95

1.00

The probability of statistical arbitrage

0

50

100

150

200

250

Figure 8 - The probability of statistical arbitrage

Part 2 CNPVaR for foreign exchange risk Rockafellar and Uryasev (2000) proposed an approach to optimizing a financial portfolio by minimizing conditional value-at-risk (CVaR) rather than minimizing value-at-risk (VaR). Ye and Tiong (2000) studied the NPVaR method in infrastructure project investment evaluation. Thus, Wang and Gao (2012) applied the NPVaR criteria in foreign exchange risks of international construction projects. In this note, the minimizing CNPVaR for projects, in the presence of foreign exchange risk. Following Wang and Gao (2012), the NPV of project involving ai f i the foreign exchange risk is: NPV = ∑∞ i=1 (1+r)i , where a i is the exchange rate of i-th currency to reference currency and fi is the cash flow at time i base on i-th currency. The ai is random variable while r is non-random interest rate. Variables fi can be interpreted as the difference of volume of cash-in-flow and cash-out-flow of i-th currency. The aim of this note, is to maximize the CNPVaR with respect to {fi }. However, in a exchange shop, for example, in each time, a portfolio of currencies are sold or bought. In this note, a simple case is considered where at time i in project, the volume of cash flow of fi of i-th currency is achieved. The rest of the current part is organized as follows. In section 4, the CNPVaR is formulated for a location-scale distribution is obtained. In section 5, the application of quadratic and dynamic programming is studied. 4. CNPVaR in location-scale distribution Suppose that all variables ai are independent and normally distributed with mean μi and variance σ2i . Then, NPV is normally distributed with the mean (μ) and variance σ2 (assuming σ2 < ∞), where: ∞

∞

i=1

i=1

μi fi σ2i fi2 2 μ=∑ and σ = ∑ . (1 + r)i (1 + r)2i Following Sarykalin et al. (2008) for normally distributed variables the CVaR (here, the CNPVaR) is given 1 by: CNPVaR = μ + k1 (α)σ, where k1 (α) = 2π exp(−(1 − α)(erf −1 (2α − 1))2 ) where erf(z) = 2 z 1 ∫ e−0.5z . √2π 0

It is easy to see that erf

−1 (x)

√

= N −1 (x + 0.5), where N−1 is the quantile function of normal

distribution. For example, assuming α = 0.01, then k1 (α) = 3.047 or k1 (0.05) = 1.264. ∂CNPVaR ∂fi

Notice that:

μ

k (α)σ2 f

1 i i i = (1+r) i + σ(1+r)2i = 0, then, fi =

88

μi (1+r)i σ

f

−k1

j

μ

. Therefore, fi = μi × (α)σ2 i

j

σ2j σ2i

× (1 + r)i−j .



Remark 1. When there is one currency in NPV, then

fi fi−1

= (1 + r).

Remark 2. It is not reasonable to assume the normal distribution for ai ′s. Usually they have distributions fi with fat tails, like student-t or generalized error distribution (GED). However, when (1+r) i are bounded, using the central limit theorem, the above results are satisfied. 1

α

Remark 3. Following Acerbi (2002), the CNPVaR is given by CNPVaR α = α ∫0 NPVaR β dβ. Using the Monte Carlo estimate the above integral is estimated. 𝑎𝑖 −𝜇 ), the 𝜎

Remark 4. Assuming a scale-location family for 𝑎𝑖 , like the 𝑔0 ( 𝑘𝛼 is the 𝛼-th quantile of distribution of 𝑔0 .

𝑁𝑃𝑉𝑎𝑅𝛽 is 𝜇 − 𝑘𝛽 𝜎, where

1 𝛼 Remark 5. Considering the above remarks, then 𝐶𝑁𝑃𝑉𝑎𝑅𝛼 = 𝜇 + 𝑘̅ 𝜎, where 𝑘̅ = ∫0 𝑘𝛽 𝑑𝛽. Again, 𝛼 𝑓𝑖 𝑓𝑗

𝜎2

𝜇

= 𝜇 𝑖 × 𝜎𝑗2 × (1 + 𝑟)𝑖−𝑗 . 𝑗

𝑖

5. Quadratic and dynamic programming Hereafter, the application of quadratic programming is studied. According to the Remark 5, CNPVaR α = μi σ2i ∗2 2 0.5 ∗2 ∗ + k̅ (∑∞ σ f ) , where μ = and σ = . Considering some constrains like i=1 i i i

∗ ∑∞ i=1 μi fi ∗ ∑∞ i=1 μi bi

i

≤

∗2 b and ∑∞ i=1 σi di

(1+r)i

(1+r)2i

≤ d, this problem reduces to a quadratic programming.

Example 1: −1 α Consider two cash flows where g 0 (x) = e−x , x > 0. Notice that k̅ = ∫0 ln(1 − β)dβ which is 1 + (1−α)ln(1−α) . α

α

For α = 0.05, it is 0.02543. Suppose that μ1 = μ2 = σ1 = σ2 = 1, and r=0.05. Then, the linear f

f2

f

f2

1 2 1 2 programming is: maxZ = 1.05 + 1.1025 + 0.02543√1.1025 + 1.2155 such that f1 + f2 ≤ 1 and f′s are

positive. Then, f1 = 1 and f2 = 0 and Z=0.9766. Next, to brows the dynamic programming setting here, let: 2 0.5 ∗2 2 0.5 2 0.5 CNPVaR n,α = ∑ni=1 μ∗i fi + k̅ (∑ni=1 σ∗2 and 𝜌𝑛 = CNPVaR α = (∑∞ − (∑ni=1 σ∗2 i fi ) i=1 σi fi ) i fi ) . Then, max(CNPVaR α ) = max(CNPVaR n,α + 𝜌𝑛 ), which defines the dynamic programming approach for maximizing the CNPVaR α . References [1] Acerbi, C. 2002. Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking and Finance, 26:1505–1518. [2] Bondarenko, O. 2003. Statistical Arbitrage and Securities Prices. Review of Financial Studies, 16: 875–919. [3] Calin, O. 2012. An introduction to stochastic calculus with applications. On-line lecture notes. [4] Rockafellar, R. T., and Uryasev, S. 2000. Optimization of conditional value-at-risk. Journal of Risk, 3: 21-41. [5] Sarykalin, S., Serraino, G., and Uryasev, S. 2008. Value-at-risk vs. conditional value-at-risk in risk management and optimization. Tutorials in Operations Research. C @ Informs: 270-298. [6] Vose, D. 2010. Risk analysis: a quantitative guide. Wiley. [7] Wang, X. Q., and Gao, B. 2012. Dynamic measurement and evaluation on foreign exchange risks of international construction projects. Proceedings of the 2012 IEEE IEEM. USA. [8] Ye, S., and Tiong, R. L. K. 2000. Npv-at-risk method in infrastructure project investment evaluation. Journal of Construction Engineering and Management, 3: 227-233.

89


ASERS


6 Web: www.asers.eu URL: http://www.asers.eu/asers-publishing

E-mail: [email protected] [email protected] ISSN 2068 – 8393 Journal DOI: http://dx.doi.org/10.14505/jasf Journal’s Issue DOI: http://dx.doi.org/10.14505/jasf.v7.1(13).00

90