Stock Price Paper 4

Running head: STOCK PRICE

Stock Pricing Using Arbitrage Model

Author

Institution

STOCK PRICING

Abstract

The price of a single share of the stocks that can be sold by a company can be predicted

by two financial models; the capital asset pricing model and the arbitrage pricing model. With

the arbitrage pricing model, the returns that can be realized from an asset can be predicted by

comparing the relationship that exists between the risk factors and the asset itself. The capital

asset pricing model also advocates for a similar manner of determining the prices of securities by

describing the relationship that exists between the expected returns and the risks that are

associated with an asset. (Brijs, Hobbs & Belmans, 2016) This paper focuses on how the stock

price can be determined using the two models by carrying out an analysis of data from a

reputable company. The aim of analyzing the financial data is to determine how the two models

can be applied to determine stock prices. In analyzing the data, the application of financial

methods and equations will be applied.

Introduction

Face book Inc. is one of the companies that are listed on the Yahoo Finance web

directory. Financial data obtained from the directory will be used to identify on how the two

models; arbitrage pricing model and capital asset pricing model can be used to determine the

stock price of Face book. The problem of the study is to identify how the financial theories,

arbitrage pricing model and the capital asset theory can be applied in determining the stock price

of Face book. The specific method of analyzing data that will be applied includes analyzing the

data by spss top come up with a regression that will lead to the hypotheses. The logic of the

study is based upon the mathematical financial equations with regards to the arbitrage and capital

asset pricing theories.

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Literature Review

The economist Stephen Ross can be given credit for coming up with the arbitrage pricing

theory back in the year 1976. According to Ross, the amount of returns that an asset can give can

be easily predicted by determining the linear relationship that exists between the macroeconomic

factors and the returns of the asset. In his theory, he proposed a framework that acts as the

guideline to both analysts and investors. According to this framework that he developed, the

returns that are realized from the model can be useful in correctly pricing the asset. In the event

that the model price is quite different from the price that the market can offer, then the gap; in

this case the arbitrage can lead to the stabilization of the market price back to its original

favorable price. Most scholars believe that Arbitrage pricing theory is the alternative to the other

model of determining the price of stocks, the Capital Asset Pricing Model. (Noda, Martelanc &

Kayo, 2016) The model makes it possible for both analysts and investors to adopt their research

on the financial markets as environments change so that they can establish the price as they

would have pointed the factors that influence the price of the stocks. The mathematical model of

the arbitrage pricing model is as below;

E(Rit ) = a0 + b1GDPt + b2 INTt + e0 where ;

E(Rit) = Expected return on stock i, period t

a0 = Constant.

bi = Sensitivity of each factor.

GDP = Economic growth rate in period t

INTt = Interest rate in period t

e0 = Random error

STOCK PRICING

The capital asset pricing model on the other hand is specifically tailored to describe the

linear relationship that exists between the risk associated with a security and its expected return.

From the model, the return of a security should be equivalent to the risk-free return plus its risk

premium basing the assumptions on the beta of the same security. The mathematical expression

of this model is as below;

Ra = Rrf + [Ba x (Rm – Rrf)] where

Ra =Expected return on a security

Rrf = Risk-free rate

Ba = Beta of the security

Rm = Expected return on market

In this case, the risk premium can be determined by computing Rm- Rrf.

Method

Basing the information that had been featured in the previous topic, the Literature Review,

This study took the following steps. First, we took Face book as one of the firms listed in Yahoo

Finance to study it how the two models can be applied in prediction of the prices at the stock

exchange. The two models, as expressed by their mathematical equations, were then applied to

the variables to determine how they could be used to predict the stock prices.

Data and Analysis

Basing the research on the financial data released by face book during the financial year

2016, the data served as critical elements for the analysis. The data was predominantly obtained

from the stock report as published in the Yahoo Finance. The reason why this data was preferred

can be attributed to the fact that the firm has been consistent in maintain a fair stock price for

STOCK PRICING

considerably a lengthy period of time. The data was obtained from the most trusted web financial

directory, Yahoo Finance. All the variables from the two models were featured and used for the

data analysis. Those variables include the expected return on security, expected return on stock,

Economic growth rate in the given period t, interest rate and the risk free rate of return.

Hypothesis For the Research

In this research, there are two hypotheses that were formulated since we are

dealing with two models. The first hypothesis was regarding the Arbitrage pricing theory. In this

theory, the hypotheses was that the expected return of security was greatly affected by the

interest rate and GDP. With regards to the capital asset price model, the premium is given by

computing the expression (Rm-Rrf).

Using the equations or the expressions that define the models stated before, the data was

analyzed by the help of Spps version 11 and the following is the regression that was obtained.

Calculation of regression coefficients, T-test and Significance-value

Coefficients

Model

Unstandardized Coefficients

Standardized Coefficients

Std. Error

Beta

Sig.

(Constant)

-0.82

0.06

-14.764

Excess Return

0.78

0.01

0.14

4.797

a. Dependent Variable: Return

Calculation of coefficient of determination

Model Summary

Model

Square

Adjusted R

Square

Std. Error of the

Estimate

.54

.48

.63

.138991

Predictors: (Constant),

Excess Return

STOCK PRICING

Dependent Variable: Return

Calculation of regression coefficients, T-test and Significance-value

Coefficients

Model

Unstandardized Coefficients

Standardized

Coefficients

Std.

Error

Beta

ig.

Constant

.086

.0039

0.0111

000

GDP

.018

.0012

.3806

000

Interest

-.138

.016

-.7124

8.611

000

Results

CAPM Results

As said earlier, the effect of excess return on stock can be determined by the use of the

premium expression. In this case, Rm- Rrf gives us the excess return. When computed, the

results of the above regression indicated a regression model as in our data. The T –test has

indicated that o,ooo is the value of excess return as far as the stock was concerned. The result is

obviously smaller than the value that the beta gives so the conclusion here is that excess return

influences the stock returns in a positive manner. From the coefficient of determination, the

square of R was around 14 . This then sends the implications that only 14 % of the stock can be

accounted by the independent variable while the rest 82% is controlled by unanimous factors

that are not identified.

Results of APT

As usual, the GDP played a crucial role in determining the price and as a result, the

equation was applied. The two factors that were influential in determining the regression of this

model are interest rate and the Gross Domestic Product (GDP). As usual comparison with beta

was necessary and the result was that the two variables in question i.e. GDP and interest rate

STOCK PRICING

play a big role in determining the rate of returns and hence the rate of return. The coefficient of

determination was defined by the square of R and it was found to have a 18.6 rate of stock return.

Discussion

From the information that was used to come up with the last regression on this paper, there is an

outright indication that the excess return variable influences the stock in a positive manner. What

this means is that if there are high returns that are realized on the stock market, then there would

be higher stock prices in the future. (Subrahmanyam, 2012) The results also indicate that the

stock prices of the company could go high in the future as the rate of return is expected to rise in

the future. Financial analysts recognize the importance that the rate of return holds in forecasting

the future stock prices.

From this research, it was identified that the research variation could only account for

14% of the total predictions. This then means that the rest, 86 5 could not be accounted for any

of the variables that were stated down before. This then sends the impression that Face book Inc,

a tech giant needs to come up with an effective strategy that can be used in predicting the future

stock prices. There are various reasons why stock prices of companies that deal with tech

products cannot be effectively predicted. Chief among of the reasons why tech companies stock

prices cannot be accurately described by the variables stipulated in the two equations, is the fact

that the product that they deal with, i.e. tech products are highly dynamic. For instance, during

the 80s Yahoo was among the leading tech companies but the two models must have

inaccurately predicted the stock prices because they were not aware of future changes. They

were not aware of the fact that there would be future innovations that would see social media

STOCK PRICING

companies such as Face Book the company that is in study for this case study becomes the

world’s biggest companies. The variables that are prescribed by the two models do not account

for factors that act as the base of tech giants such as innovation instead focus on the traditional

factors such as inflation, rate of interest and the projected GDP.

Recommendations

This research paper has come up with several recommendations on how the hypothesis

can be established using a more comprehensive approach. That approach involves coming up

with a model that incorporates all the other factors that were not featured by the two models.

This will however mean that those models could be redefined as they would not be found in the

category of Arbitrage Price model neither will the model be considered to be part of the capital

asset model. What will be exceptional about the new models however is that they will be

comprehensive as they will include all other factors that are not featured in the models that are

used to predict the prices of a tech giant company as the one in progress. Business empires come

and go and innovation technology and globalization can greatly affect this and this is what the

new models should incorporate. The models might sound a bit expensive to deploy as the

analysts and researchers will have to dedicate funds for carrying how research studies, coming

u0p with prototypes and surveying the market value to determine what it really entails. In this

way the company can be able to determine the rate or return and consequently predict the prices

of stocks.

In conclusion, all factors notwithstanding, the two models are somewhat very

instrumental in predicting the stock prices. With the arbitrage pricing model, the returns that can

be realized from an asset can be predicted by comparing the relationship that exists between the

risk factors and the asset itself. The capital asset pricing model also advocates for a similar

STOCK PRICING

manner of determining the prices of securities by describing the relationship that exists between

the expected returns and the risks that are associated with an asset.

STOCK PRICING

References

Brijs, T., Hobbs, B., & Belmans, R. (2016). Price-Based Unit Commitment Electricity Storage

Arbitrage with Piecewise Linear Price-Effects. SSRN Electronic Journal.

http://dx.doi.org/10.2139/ssrn.2759774.

Goldenberg, D. (2016). Arbitrage, Markov Processes, and Asset Price Paths. SSRN Electronic

Journal. http://dx.doi.org/10.2139/ssrn.2731101.

Kurihara, Y., & Fukushima, A. (2014). Exchange Rates, Stock Prices, and Commodity Prices:

Are There Any Relationships?. Advances in Social Sciences Research Journal, 1(5), 107-

115. http://dx.doi.org/10.14738/assrj.15.456.

Noda, R., Martelanc, R., & Kayo, E. (2016). The Earnings/Price Risk Factor in Capital Asset

Pricing Models. Revista Contabilidade & Finanças, 27(70), 67-79.

http://dx.doi.org/10.1590/1808-057x201412060.

Roll, R., & Ross, S. (1980). An Empirical Investigation of the Arbitrage Pricing Theory. The

Journal of Finance, 35(5), 1073. http://dx.doi.org/10.2307/2327087.

Subrahmanyam, A. (2012). Comments and Perspectives on ‘The Capital Asset Pricing Model’.

Abacus, 49, 79-81. http://dx.doi.org/10.1111/j.1467-6281.2012.00388.x.

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