




































American International Journal of Business and Management Studies  

Vol. 1, No. 1; 2019 

Published by American Center of Science and Education, USA 

 

1 

 

Systemic Risk and Dynamics of Stock Prices:  A Short and Long Run 

Analysis from Nigeria Capital Market 

 

Mrs. Fortune Bella Charles M Sc 

Department of Banking and Finance  

Rivers State University, Rivers State, Nigeria 

 

Charles Ugochukwu Okoro,  M Sc. 

Department of Accountancy 

Ken Saro-Wiwa Polytechnic, Bori 

Rivers State, Nigeria 

 

 

 

Abstract 

This study examined the effect of systemic risk on the dynamics of stock prices in Nigeria capital market. The 

objective was to investigate the dynamic effect of systemic risk on stock prices traded on the floor of Nigeria stock 

exchange. Time series data was sourced from Central Bank of Nigeria Statistical Bulletin from 1990-2017.  Stock 

prices were modeled as the function of prices risk, liquidity risk, interest rate risk and exchange rate risk. Multiple 

regression with ordinary least square properties of co-integration was used to examine the relationship between the 

dependent and the independent variables. The study found  price and liquidity risk have positive effect on stock 

price while interest rate and exchange rate risk have negative effect on stock prices of equities traded on Nigeria 

stock exchange. It concludes that systemic risk has significant effect on stock prices and recommends, among others, 

that the management of the capital market should ensure that the operating environment is risk minimum to ensure 

appreciable stock prices by developing strategies and policies aim at managing the systematic risk in the operating 

environment and engage a regular environmental impact assessment on systemic risk, to avert it’s negative effect on 

stock prices. 

Keywords: Systemic Risk, Stock Prices, Short and Long Run, Nigeria, Capital Market 

INTRODUCTION  

The history of risk taken can be traced to the existence of man. Relocating a tribe from one place to another in order 

to find food and hunting dangerous animals have been daily decisions in the pre-civilization era. The decisions at 

that time have been most probably based on historic data and gut feeling. This immeasurable justification on 

decisions stayed mostly the same also on the historic era until the concept of probability was invented. While the 

gamblers that lived in Ancient Greece had the concept of numerals and could determine the number of possible 

outcomes they strongly believed that the outcome of games was determined by gods. Zigrand (2014) opined that the 

concept of modern arithmetic, numbers and symbols, came from Hindus during the Dark Ages and that it made the 

analysis of games possible in the 16th century. 

There has been aged long divergence among behavioral finance scholars on the factor that determine stock prices. 

The fundamentalist argue that the value of a corporation’s stock is determined by expectations regarding future 

earnings and by the rate at which those earnings are discounted on time. The technical school of taught on the other 

hand, opposes the fundamentalists’ arguments, and postulate that stock price behaviour can be predicted by the use 

of financial or economic data. The behavioural school of finance holds different view from the above schools of 

thoughts and opined that market might fail to reflect economic fundamentals under three conditions, which are:  The 

first behavioural condition is irrational behaviour. It holds that investors behave irrationally when they do not 

correctly process all the available information while forming their expectations of a company’s future performance. 

The second is systematic patterns of behaviour, which hold that even if individual investors decided to buy or sell 



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without consulting economic fundamentals, the impact on share prices would be limited. As in Inegbedion (2009), 

the third is limits to arbitrage in financial markets ascertain that when investors assume that a company’s recent 

strong performance alone is an indication of future performance; they may start bidding for shares and drive up the 

price. Some investors might expect a company that surprises the market in one quarter to go on exceeding 

expectations. The macroeconomic approach attempts to examine the sensitivity of stock prices to changes in 

macroeconomic variables. The approach posits that stock prices are influenced by changes in money supply, interest 

rate, inflation and other macroeconomic indicators. According to Afego (2012), the random walk theory is a 

component of efficient market hypothesis. It states that current price of any security, fully reflects the information 

content of its historical sequences of price. It is built on the premises that investors react instantaneously to 

information advantage, they have thereby eliminating profit opportunities  

 

The main premise in finance is that there is a connection between risk and return. Higher risk is assumed to lead to 

higher return on stocks with rationale pricing of stocks. Empirical study by Galati and Moessner (2010) concluded 

that despite the wealth of research on systemic risk and stock prices, there is still no consensus on the definition of 

systemic risk.  Empirical validity of theories on factors that determine stock price is based on financial market of the 

developed countries with high degree of perfection while Nigeria financial market is emerging and characterized 

with high level of imperfection. From the above, this paper examined the effect of systemic risk on the stock prices 

of Nigeria firms. 

LITERATURE REVIEW 

Concept of Systemic Risk  

Systematic risk, also known as un-diversifiable risk volatility or market risk, affects the overall market, not just a 

particular stock or industry. According to Pandey (2005) this type of risk is both unpredictable and impossible to 

completely avoid. It cannot be mitigated through diversification, only through hedging or by using the right asset 

allocation strategy. Systemic risk evolves along with the development of financial markets, regulations and 

collective behavior of market participants and it may be prompted by regulatory arbitrage. Systemic risk arises from: 

excessively risky activities of a single or a group of traders, an aggressive type of organizational culture (driven 

towards short-term profits), a collective failure of management in the bank (or across the financial system), which 

leads to inertia and the inability to respond to changed economic circumstances and high (over)exposure of banks to 

the same type of risk (symmetric shock) in the system as a whole. A systemic risk literature review by Galati and 

Moessner (2010) concludes that despite the wealth of research on the subject, there is still no consensus on the 

definition of systemic risk. As in the case of financial stability, there are many systemic risk definitions, but it 

remains difficult to operationalize them. Nevertheless, the operationalization would be most useful from the 

perspective of conducting macro-prudential supervision, aiming at systemic risk prevention. This narrative informs 

that, systemic risk can have a macro- or microeconomic dimension. Nier (2009) indicates that macro-systemic risk 

arises when the financial system becomes exposed to aggregate risk, resulting from, e.g. growth of correlated 

exposures. Micro-systemic risk arises when the failure of an individual institution has an adverse impact on the 

financial system as a whole (default of a SIFI). 

Concept of Stock Prices  

Stock price is the cost of purchasing a security on an exchange. It is affected by a number of things including 

volatility in the market, current economic conditions, and popularity of the company. According to Ronen and Yaari 

(2008), the invention of double entry book keeping in the 14th century led to company’s valuation which is based 

upon ratios such as price per unit of earnings (from income statement), price per unit of net worth (from balance 

sheet) and price per unit of cash flow (cash flow statement). The next advance was to price individual price shares 

rather than the whole company. A price per dividend was the next advancement. Analysts find it appropriate to use 

discounted cash flow that is based on time value of money to estimate the intrinsic value of share rather than price 

per dividend of share prices.  

 

Theoretical framework 

 

The Capital Asset Pricing Model  
The CAPM is a model for pricing an individual security or a portfolio. The CAPM model was developed 

independently by William Sharpe (1964) and Parallel work was performed by Lintner (1965) and Mossin (1966) 

these model marks the birth of asset pricing theory.  

 



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Derivation of the CAPM  
The CAPM is a simple linear model that is expressed in terms of expected return and expected risk. The model 

states that the equilibrium returns on all risky assets are a function of their covariance with the market portfolio.  

Under the assumptions of the CAPM, if a risk-free asset exists, every investor’s optimal portfolio will be formed 

from a combination of the market portfolio and the risk-free asset. The precise combination of the market portfolio 

and the risk-free asset depends on the degree of investors risk aversion. Since investors can choose the combination 

of the market portfolio and the risk-free asset, then the equation of the relationship connecting a risk-free asset and a 

risky portfolio is:  

E (Ri) = R ƒ + im
m

RfRmE


 2

)( 
        1 

Where;  

E (Ri) : Expected return on i
th

 portfolio.  

R ƒ : Return on the risk free asset  

E (Rm) : Expected return on market portfolio  

im : The covariance between asset i and the market portfolio  

2 m: The variance of the market portfolio  

Based on the equation (3) the original CAPM equation can be derived as follows:  

E(Ri) = R ƒ + [ E(Rm) – R ƒ] βi          2 

Equation 4 is known as Capital Asset Pricing Model and it could be shown graphically as the security market line 

(SML) which means the SML fundamentally graphs the results from the capital asset pricing model (CAPM) 

formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk 

premium is determined from the slope of the SML. The SML model states that stocks expected return is equal to the 

risk-free rate plus a risk premium obtained by the price of risk multiplied by the quantity of risk. In a well-

functioning market nobody will hold a security that offers an expected risk premium of less than [E (Rm)-R ƒ] i. 

 

If we think E (Rm) – Rf as the market price of risk for all efficient portfolios, than, it represents the extra return that 

can be gained by increasing the level of risk on an efficient portfolio by one unit. The quantity of risk is often called 

beta, and it is the contribution of asset i to the risk of the market portfolio. In other words, it is the correlation of the 

asset i's return with the return on the market portfolio. If everyone holds the market portfolio, and if beta measures 

each security’s contribution to the market portfolio risk, then it’s no surprise that the risk premium demanded by 

investors is proportional beta. According to the CAPM the total risk of a security could be divided between 

systematic and unsystematic risk. The systematic risk is the portion of the security return variance that is explained 

by market movements such as fiscal changes, swings in exchange rates and interest rate movements. On the other 

hand, the unsystematic risk is the variability in return due to factors unique to the individual firm, such as R&D 

achievements and industrial relations problem. The relevant measure of the risk of an asset is its contribution to the 

systematic risk of an investor’s portfolio defined by its beta rather than the inherent variance in the assets total 

return.  

 

If the beta of an asset is larger (smaller) than 1, then the standard deviation of an asset changes more (less) than 

proportionately in reaction to changes in market conditions. Thus, an asset whose beta is greater (less) than 1 has a 

relatively greater (smaller) contribution to the risk of a portfolio. While beta does not measure risk in absolute terms, 

it is a crucial risk indicator, reflecting the extent to which the return on the single asset moves with the return on the 

market.  

 

Assumptions of the CAPM  
The CAPM rests on several assumptions. The most important are as follows:  

All investors are rationally risk-averse individuals whose aim is to maximize the expected utility of their end of 

period wealth. Therefore, all investors operate on a common single-period planning horizon. All investors are price-

takers; so that, no investor can influence the market price by the scale of his or her own transactions. Asset markets 

are frictionless and information is freely and simultaneously available to all investor. All investors have 

homogeneous expectations about asset returns, this mean that all investors arrive at similar assessments of the 

probability distribution of returns expected from traded securities. This says that investors will not be trying to beat 



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the market by actively managing their portfolios Distributions of expected returns are normal. All securities are 

highly divisible, i.e. can be traded in small packages. All investors can lend or borrow unlimited amounts of funds at 

a rate of interest equal to the rate of risk-free securities. Investors pay no taxes on returns and there are no 

transaction costs entailed in trading securities, so expected return is only related to risk.  

 

Let (M, r M) denote the point corresponding to the market portfolio M. All portfolios chosen by a rational investor 

will have a point (, r ) that lies on the so-called capital market line 

   ,
T - Mr

 + rf=r
M

f 


       3 

 

The efficient Portfolio 

It tells us the expected return of any efficient portfolio, in terms of its standard deviation, and does so by use of the 

so-called price of risk.  

   ,
M

rf - Mr


        4 

The slope of the line, which represents the change in expected return r per one-unit change in standard deviation. 

If an individual asset i (or portfolio) is chosen that is not efficient, then we learn nothing about that asset. It would 

seem useful to know, for example, how frir , the expected excess rate of return is related to the market portfolio. 

The following formula involves just that, where M,i denotes the covariance of the market portfolio with individual 

asset i:  

 

Theorem (CAPM formula) for any asset i 

    ),r(r Mi fif rr        5 

Where 

M

iM
2i

,




           6 

 

Is called the beta of asset i. This beta value serves as an important measure of risk for individual assets (portfolios) 

that is different from ;2

i  it measures the systematic risk part of risk.  

More generally, for any portfolio p = (α1… αn) of risky assets, its beta can be computed as a weighted average of 

individual asset betas:  

   rf)-Mr(rf-r p        7 

Where 

    



n

i

ii
M 1

2

1
p  

pM
= 



      8 

Before providing the above theorem, we point out a couple of its important consequences and explain the meaning 

of the beta. For a given asset i, 
2

i tells us the risk associated with its own fluctuations about its mean rate of return, 

but not with respect to the market portfolio. For example if asset i is uncorrelated with M, then βi= 0 (even 

presumably if 
2
i is huge), and this tells us that there is no risk associated with this asset (and hence no high 



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expected return) in the sense that the variance 
2
i can be diversified away assets and form a portfolio with equal 

proportions thus dwindling the variance to 0 so it becomes like the risk-free asset with deterministic rate of return rf, 

So, in effect, in the world of the market you are not rewarded (via a high expected rate of return) for taking on risk 

that can be diversified away. βi as a measure of non diversifiable risk, the correlated-with-the-market part of risk that 

we can’t reduce by diversifying. This kind of risk is sometimes called market or systematic risk. It is not true in 

general that higher beta value βi implies higher variance 
2

i, but of course a higher beta value does imply a higher 

expected rate of return: you are rewarded (via a high expected rate of return) for taking on risk that cannot be 

diversified away; everyone must face this kind of risk.  

 

Portfolio of asset i and the market portfolio M; (α, 1-α), with α € [0, 1], the rate of return is thus r(α) = αri + (1-α) rM. 

Asset it is assumed not efficient; its point lies in the feasible region but not on the efficient frontier. Thus as α varies 

this portfolio’s point traces out a smooth curve in the feasible (,r) region α  ((α), r (α)) parameterized by α, 

where.  

r(α) = α r i + (1- α) r M          9 

 = α ( r i - r M) + r M,        10 

i., ) -(1  2 + M) - (1 +  )(
22

i
22 M


      11 

MM 222
i

22 M) - iM,(2i.), 2 - M + (       12 

When α = 0 ( (0), r  (0)) = (M, r M) and when α = 1, ((0), r  (0))=  (i, r i). Thus the curve touches the 

capital market line at the market point (M, r M), but otherwise remains off the capital market line but (of course) 

within the feasible region where it also hits the point (M, r M) and therefore when α = 0 the curve’s derivative.  

     

0)(

)(





d

rd
      13 

is identical to the slope of the capital asset line at point M. The slope (the price of risk) of the line is given by (2). 

We thus conclude that when α = 0 

   
M

TMT

d

rd f



 


)(

)(
       14 

The composition rule from calculus yields  

   








dd

drd

d

rd

/)(

/)(

)(

)(
       15 

Differentiating (3) and (4) and evaluating at α = 0 yields  

 
MMiM

MTT

dd

drd i





/,(/)(

/)(
2


        16 

From (5) we deduce that  
M

rMT

MMiM

MTT fi










/,( 2
     17 



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Solving for r i then yields the CAPM formula for asset i, r i – rf = βi ( r M – rf), as was to be shown. For the more 

general portfolio result, observe that  

rp-rf = -rf + i

n

i

ir
 1

         18 

)(
1

rfri

n

i

i 


        19 

)(
1

fii

n

i

i rr 


        20 

)(
1

fMi

n

i

i rr 


 CAPM formula for single asset i       21 





n

i

iirfMr
1

)(           22 

Note that when βp = 1 then pr  = ;Mr  the expected rate of return is the same as for the market portfolio. When βp > 

1, then pr > Mr ; when βp < 1, then pr < Mr .  

Also note that if an asset i is negatively correlated with M, M,i < 0, then βi < 0 and ri< rf; the expected rate of return 

is less than the risk-free rate. Effectively, such a negatively correlated asset serves as insurance against a drop in the 

market returns, and might be viewed by some investors as having enough such advantages so as to make it worth the 

low return. Investing in gold is thought to be such an example.  

Estimating the Market portfolio and betas  

These estimates are computed using sample means, variances and covariance as follows: 

N time points such as the end of each of the last 10 years k = 1, 2… N. rAk and rS&Pk denote the k
th

 such sample 

values for rate of return yielding estimates.  

   



N

k

rAk
N

Ar
1

1
        23 





N

k

PkSPS r
N

r
1

&&

1
      24 

The variance 
2
s&p is then estimated by  

).ˆ()ˆ(
1

&

1

&& ATrrr
N

Y PkS

N

k

PSPkS  


      25 

The beta value is then estimated by taking the ratio X/Y. 



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More on Systematic risk  

With the CAPM formula in mind, for a given asset i let us express ri as 

    ri = rf +βi( r M – rf ) + i,        26 

Where  i= ri – rf- βi ( r M - rf),        27 

a random variable, is the error term. Note how we replaced deterministic rM with random rM in the CAPM to do this. 

Our objective is to determine some properties of the error term.  

It is immediate form the CAPM formula that E(i) = 0. Moreover Cov (i, rM) = 0 as is seen by direct computation 

and the definition of βi: 

Cov (€i, rM) = cov (ri – rf – βi ( r M- r f),rM)       28 

  = cov (ri – βi ( r M –rf),rM)        29 

  = cov ( r i, rM) – βicov(r M  – rf, rM)       30 

  = cov ( r i, rM) – βicov (rM, rM)       31 

  = M2

2M

iM,
 - iM, 



        32 

  = iM,- iM,          33 

= 0          34 

 

So the error term has mean 0 and is uncorrelated with the market portfolio. It then follows by taking the variance of 

both sides of (6) that  


2
i = β

2
i 

2
M + var (i)           35 

We conclude that the variance of asset i can be broken into two orthogonal components. The first, β
2
i 

2
M, is called 

the systematic risk and represents that part of the risk (of investing in asset i) associated with the market as a whole. 

The other part, var (i), is called the nonsystematic risk. Nonsystematic risk can be reduced (essentially eliminated) 

by diversification, but the systematic risk, when β
2
i>0, cannot be diversified away. Solving for  in terms of r  in 

the capital market line yields the inverse line for efficient portfolios. 

   M
rfMr

rfr






       

36 

Using the CAPM formula r p- r f = βp( r M-rf) and plugging into this inverse line formula, we conclude that for any 

efficient portfolio p, p = βpαM; there is only systematic risk for efficient portfolios, no nonsystematic risk. This 

makes perfect sense: clearly M has only systematic risk since βM = 1.it is known that all efficient portfolios are a 

mixture of M and the risk-free asset (e.g., they all have points on the capital market line). Since the risk-free asset is 

deterministic it does not contribute to either the variance or the beta of the portfolio, only M does; so all of the risk is 

contained in M which is just pointed out is pure systematic risk.  

Arbitrage Pricing Theory  
The Arbitrage Pricing Theory (APT) is another model of asset pricing based on the idea that equilibrium market 

prices should be perfect, in such a way that prices will move to eliminate buying and selling without risks (arbitrage 



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opportunities). The basis of this theory is the analysis of how investors construct efficient portfolios and offers a new 

approach to explaining the asset prices and also states that the return on any risky asset is a linear combination of 

various macroeconomic factors that are not explained by this theory.  It is probably safe to assume that both the 

CAPM and APJ will continue to exist and will be used to price capital assets. 

 

Assumptions of the APT  
Asset markets are perfectly competitive and frictionless; all investors have homogeneous expectations that returns 

are generated randomly according to a k-factor model. Investors have monotonically increasing concave utility 

functions; the number of assets existing in the capital market from which portfolios are formed is much larger than 

the number of factors. There are no arbitrage opportunities.  

 

Pricing assets  

Consider an asset with price P = X0 at time t=0, payoff (random) Q – X1 and expected payoff Q = E (X1) at time 

t=1. Then by definition r  = (E(X1) – X0)/X0 =  ./) PPQ   Solving for P yields  

    P = ),1/( rQ 
       

37 

Which expresses the price as the discounted payoff (present value) if using r  as the discount rate. But since r =rf + 

β( r M-rf) from the CAPM formula, we conclude that  

 )(Pr
)(1

formulaCAPMofversionicing
rMrr

Q
P

ff 



   

38 

We can re-express this formular by using r = (Q – P)/P = (Q/P) – 1, then computing  

Con(r,rM) = Cov((Q/P) – 1, rM                               39 

  = Cov((Q/P), rM        40 

  = MrMQCov
P

2/),(
1


       

41 

Obtaining  MrMQCov
P

2/),(
1

 
      

41 

Plugging into the pricing version of CAPM formula yields 

.

)()/),((
1

1 2 rfrMrMQCov
P

r

Q
P

Mf 




      

42 

Solving for P yields 

.
1

)()/),((
2

2

f

M

M

r

rfrMrMQCov
Q

P




 



       

 43 



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This equation is interesting, since it expresses the price as the present value of an “adjusted” expected payoff. If the 

asset is uncorrelated with the market, then the price is exactly  ),1/( rfQ       

        

M

M rfrrMQCov
2

)(),((





         

44 

Yields a lower price if the asset is positively correlated with the market and a higher price if the asset is negatively 

correlated with the market 

Empirical Review 

Izova, Bollerslev, Osterrieder, Tauchen (2011)  investigated the  relationship  between risk and return using,  

Fractional Cointegration based on daily data for the S&P 500  and the VIX volatility index. Their series were 

divided into different components. The findings indicated that the relationship between volatility and the volatility-

risk reward is strongly direct and positive. They also found that fractionally cointegrated VAR. in addition they find 

that corresponding the qualitative conceptions from that same theoretical and their study represent variance risk 

premium estimated as the long-run equilibrium relationship within the fractionally co integrated system results in 

non-trivial return predictability over longer inter-daily and monthly return horizons. 

Pollet, Kräussl, Jegadeesh (2010) investigated the risk and returns of PE investments and LPEs using the market 

Prices of FOFs that invests in unlisted private equity funds. Their findings indicate that the market expects for PE to 

earn abnormal return is approximately 0.5 percent and for LPEs is approximately close to zero after fees. Private 

equity fund returns are negatively related to the credit expand and positively related to Gross Domestic Product 

growth.  In addition they find that both listed and unlisted PE has betas near to one.  

Chudhary, Chudhary (2010) examined the relationship between stock returns and systematic risk based on capital 

asset pricing model (CAPM) in the Bombay Stock Exchange.  The sample search is 287 top companies of Bombay 

(BSE) Stock Exchange that the data were collected over thirteen years period from January1996 to December 2009. 

Their findings (about intercept and slop of CAPM equation states that intercept should be equal from zero and slop 

should be excess returns) rely on negate hypotheses of capital asset pricing model and offer evidence against the 

CAPM. In addition, this paper investigated whether the CAPM adequately captures all -important determinants of 

returns including the residual variance of stocks. The results represent that residual risk has no effect on the expected 

returns of portfolios. 

McCurdy and Morgan (2011) investigated equilibrium model for the inter-temporal evolution of the basis in foreign 

currency markets. The weights are specified in a hedged by the prices of futures and spot contracts position and by 

Internal and external interest rates.  Evaluating this hedged position using inter temporal asset pricing model, leads 

to a testable equilibrium model of the futures basis. Systematic risk will be commensurate to the conditional 

covariance of the basis with a generalized discount factor. Empirical implementation uses a conditional (CAPM) in 

which both the quantity and the price of covariance risk are free to vary over time. However, for this application, the 

estimated inter-temporal risk is insignificantly different from zero the risk in the futures market offsets that in the 

spot, providing an effective hedge. 

Aduda et al. (2012) found out that, macro-economic factors such as stock market liquidity, institutional quality, 

income per capita, domestic savings and bank development are important determinants of stock market development 

in the Nairobi Stock Exchange. There is no relationship between stock market development and macroeconomic 

stability - inflation and private capital flows. The results also show that Institutional quality represented by law and 

order and bureaucratic quality, democratic accountability and corruption index are important determinants of stock 

market development because they enhance the viability of external finance. They concluded that there is a 

relationship between stock market developments and stock market liquidity, institutional quality, income per capita, 

domestic savings and bank development.  

 



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Methodology 

This study used the ex post Facto Research Design. This is because the study attempts to explore the cause nature 

that affects relationships, where causes already exist and cannot be manipulated. The choice of model for this 

research is the Ordinary Least Squares because it provides satisfactory results for estimates of structural parameters. 

This method involves decision on whether the parameters are statistically significant and theoretically meaningful. It 

also verifies the validity of estimates and whether they actually represent economic theory. However, due to 

conventional reasons, we used E-view statistical package in the analysis for a reliable result. The researcher used 

only the secondary source of data due to the nature of information. The data were generated from the publications by 

from CBN statistical bulletin of various years, and stock exchange fact-book.  In an attempt to examine the impact 

of exchange rate on profitability of manufacturing firms in Nigeria (1990-2017); the research adopted multiple 

regression analysis in order to test the three objectives. Thus  

SP = f (PR, LIQR, INTR, EXR)                                                                                45 

SP  = α0 + α1PR + α2LIQR + α3INTR + α4EXR + µ                                                               46 

Where: 

SP = Stock Prices  

PR = price risk proxy by volatility of real inflation 

LIQR = liquidity risk proxy by volatility of money supply  

INTR =  interest rate risk proxy by volatility of real interest rate 

EXR = exchange rate risk proxy by volatility of naira exchange rate per US dollar  

µ  = Error Term  

Therefore, a priori expectation (α1>α2>α3,> α4,>0)                                                                                         47 

Stationarity (Unit Root) Tests 

The study investigates the stationarity properties of the time series data using the Augmented Dickey Fuller (ADF) 

test. According to Nelson and Plosser (1982), Chowdhury (1994) there exist a unit root in most macroeconomic time 

series. Non stationary time series will have a time varying mean or a time- varying variance or both. If a time series 

is non stationary, we can study its behaviour only for the time period under consideration, and cannot generalize it to 

other time periods, and hence remain of little practical value if we intend to forecast (Gujarati, 2003). It should be 

noted that a time series is a set of observations on the values that a variable takes at different times (daily, weekly, 

monthly, quarterly, annually, etc). Stationary test therefore checks for the stationarity of the variables used in the 

models. If stationary at level, then it is integrated of order zero which is 1(0). Thus, test for stationarity is also called 

test for integration. It is also called unit root test. Stationarity denotes the non existence of unit root. 

Etyiyy t

m

i
tt  


 1

1
121 

         48 

Where:  

ty
   = change time t 

1 ty
 = the lagged value of the dependent variables  

t   = White noise error term  



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If in the above 


=0, then we conclude that there is a unit root. Otherwise there is no unit root, meaning that it is 

stationary. The choice of lag will be determined by Akaike information criteria. 

Decision Rule 

t-ADF (absolute value) > t-ADF (critical value) : Reject Ho (otherwise accept H1) 

Note that each variable will have its own ADF test value. If the variables are stationary at level, then they are 

integrated of order zero i.e 1(0). Note that the appropriate degree of freedom is used. If the variables are stationary at 

level, it means that even in the short run they move together. The unit root problem earlier mentioned can be 

explained using the model: 

Y= Yt-1 + I                                                                                                              49 

Where; Yt is the variable in question; i is stochastic error term. Equation (a) is termed first order regression 

because we regress the value Y at time “t” on its value at time (t- 1). If the coefficient of Yt-i is equal to 1, then we 

have a unit root problem (non stationary situation). This means that if the regression. 

Y= Yt-1 + I                                                                                                             50   

Where Y and I are found to be equal to 1 then the variable Yt has a unit root (random work in time series 

econometrics). 

If a time series has a unit root, the first difference of such time series are usually stationary. Therefore to salve the 

problem, take the first difference of the time series. The first difference operation is shown in the following model: 

Y=(L-1)Yt-1I                                                                                                       51 

Yt-1 + I                                                                                      52 

 (Note:  =1-1= 0; where L =1; Yt = Yt - Yt-i)         53 

Integrated Of Order 1 or I (I) 

Given that the original (random walk) series is differenced once and the differenced series becomes stationary, then 

the original series is said to be integrated of order I or I (1). 

Integrated of Order 2 or I (2) 

Given that the original series is differenced twice before it becomes stationary (the first difference of the first 

difference), then the original series is integrated of order 2 or 1(2). 

Therefore, given a time series has to be differenced Q times before becoming stationary it said to be integrated of 

order Q or I (q). Hence, non stationary time series are those that are integrated of order 1 or greater. 

The null hypothesis for the unit root is: Ho: a = 1; 

The alternative hypothesis is Hi: a < 1. 

We shall test the stationarity of our data using the ADF test. 

 

 



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Co-integration Test (The Johansen Test) 

It has already been warned that the regression of a non stationary time series on another non stationary time series 

may lead to a spurious regression. The important contribution of the concept of unit root and co-integration is to find 

out if the regression residual are stationary. Thus, a test for co-integration enables us to avoid spurious regression 

situation. If the residuals from the regression are 1(1) or 2(2), i.e. stationary, then variables are said to be co-

integrated and hence interrelated with each other in the long run. This approach is based on conducting unit root test 

on residual obtained from the estimated regression equation. If the residual is found to be stationary at level, we 

conclude that the variables are co-integrated and as such as long-run relationship exists among them. 

tijt

j

i

iit

i

i

tOt TATAwTA 1

11

  








                                                                   54 

Granger Causality Test 

One of the objectives of this study is to investigate the causality between the independent and the dependent 

variables. Granger causality test according Granger (1969) is used to examine direction of causality between two 

variables. Causality means the impact of one variable on another, in other-words; causality is when an independent 

variable causes changes in a dependent variable. The rationale for conducting this test is that it enables the 

researcher to know whether the independent variables can actually cause the variations in the dependent variable. 

Thus, Granger causality test helps in adequate specification of model. In Granger causality test, the null hypothesis 

is: no causality between two variables. The null hypotheses is rejected if the probability of F* statistic given in the 

Granger causality result is less than 0.05.  

The pair-wise granger causality test is mathematically expressed as:  

111

1

11

1

uxYxY t

x
n

i

t

y
n

i

ot  







 
                                                            55 

and  

1
V

1y
xxdp1

n

1i

1Yt
y
1

dp
n

1i
o

dp
t

x 










                                                             56 

Where xt and yt are the variables to be tested white ut and vt are the white noise disturbance terms. The null 

hypothesis
011  yy dp

, for all I’s is tested against the alternative hypothesis 
01 x

 and 
.01 ydp
if the co-

efficient of 

x

1 are statistically significant but that of 
ydp1

 are not, then x causes y. If the reverse is true then y 

causes x. however, where both co-efficient of 

x

1 and 

ydp1 are significant then causality is bi – directional. 

 

Vector Error Correction (VEC) Technique 

The presence of co-integrating relationship forms the basis of the use of Vector Error Correction Model. E-views 

econometric software used for data analysis, implement vector Auto-regression (VAR) - based co-integration tests 

using the methodology developed by Johansen (1991, 1995). The non-standard critical values are taken from 

Osterward Lenun (1992). 

 



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RESULTS AND DISCUSSION OF FINDINGS 

Table i: Presentation of Level Series Result 

Variable Coefficien

t 

Std. Error t-Statistic Prob.   

PR 3.143241 0.360824 2.396983 0.0054 

LIQR 0.673035 0.590774 1.139242 0.0074 

INTR -1.829224 1.626006 -1.124980 0.2733 

EXR -1.649833 1.549582 -1.064696 0.2991 

C 51.64218 34.57035 1.493829 0.1501 

R-squared 0.786098    Durbin-Watson stat 2.365587 

Adjusted R-squared 0.545763   Prob(F-statistic) 0.024421 

F-statistic 3.993920   

Table ii: Diagnostic Test  

 Coefficient Uncentered Centered 

Variable Variance VIF VIF 

PR  0.130194  1.017090  1.012920 

LIQR  0.349014  1.527845  1.115794 

INTR  2.643896  1.069012  1.044450 

EXR  2.401204  1.876702  1.145503 

C  1195.109  2.453434  NA 

Table iii: Test of Unit Root 

SP   t-Statistic   Prob.* 

Augmented Dickey-Fuller test statistic -5.352753  0.0002 

Test critical values: 1% level  -3.711457  

 5% level  -2.981038  

 10% level  -2.629906  

 

     PR   t-Statistic   Prob.* 

Augmented Dickey-Fuller test statistic -5.890783  0.0001 

Test critical values: 1% level  -3.737853  



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 5% level  -2.991878  

 10% level  -2.635542  

 

LIQR   t-Statistic   Prob.* 

Augmented Dickey-Fuller test statistic -4.618607  0.0011 

Test critical values: 1% level  -3.711457  

 5% level  -2.981038  

 10% level  -2.629906  

 

INTR   t-Statistic   Prob.* 

Augmented Dickey-Fuller test statistic -6.354402  0.0000 

Test critical values: 1% level  -3.752946  

 5% level  -2.998064  

 10% level  -2.638752  

 

EXR   t-Statistic   Prob* 

Augmented Dickey-Fuller test statistic -5.698327  0.0001 

Test critical values: 1% level  -3.724070  

 5% level  -2.986225  

 10% level  -2.632604  

 

Table iv: Cointegration Test 

Hypothesized  Trace 0.05   

No. of CE(s) Eigenvalue Statistic Critical Value Prob.**  

None *  0.801051  91.90307  69.81889  0.0003  

At most 1 *  0.636167  56.37951  47.85613  0.0065  

At most 2 *  0.562561  34.13619  29.79707  0.0149  

At most 3 *  0.449156  15.94619  15.49471  0.0427  

At most 4  0.120607  2.827520  3.841466  0.0927  

Table v: Normalized Cointgration Test 



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SR PR LIQR INTR EXR  

 1.000000 -23.33280  83.09287 -112.8707  69.60283  

  (7.29967)  (13.4946)  (26.0309)  (21.3629)  

Table vi: Error Correction Model  

Error Correction: D(SR) D(PR) D(LIQR) D(INTR) 

CointEq1 -0.173825 -0.295014  0.062647  0.017755 

  (0.29462)  (0.07001)  (0.06632)  (0.03444) 

 [-0.59000] [-4.21361] [ 0.94463] [ 0.51547] 

C -1.097063  5.909431  0.655582  0.372893 

  (31.7356)  (7.54180)  (7.14369)  (3.71020) 

 [-0.03457] [ 0.78356] [ 0.09177] [ 0.10050] 

 R-squared  0.707868  0.943769  0.754404  0.690037 

 Adj. R-squared  0.415736  0.887539  0.508807  0.380075 

 Sum sq. resids  192439.3  10867.99  9750.913  2630.227 

 S.E. equation  138.7225  32.96663  31.22645  16.21798 

 F-statistic  2.423110  16.78393  3.071722  2.226195 

 Log likelihood -125.5894 -95.41278 -94.27394 -80.51589 

 Akaike AIC  13.00851  10.13455  10.02609  8.715799 

 Schwarz SC  13.55564  10.68168  10.57322  9.262930 

 Mean dependent -0.854762  3.900476 -3.780952  0.021429 

 S.D. dependent  181.4857  98.30452  44.55503  20.59809 

 Determinant resid covariance (dof adj.)  1.24E+12   

 Determinant resid covariance  6.39E+10   

 Log likelihood -380.4368   

 Akaike information criterion  41.18445   

 Schwarz criterion  43.77089   

Table vii: Estimated Error Correction Model 

Variable Coefficient Std. Error t-Statistic Prob.   

C -21.91316 28.11665 -0.779366 0.4558 



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D(SP(-1)) -0.707197 0.372778 -1.897099 0.0903 

D(PP(-1)) -0.487469 0.428622 -1.137295 0.2848 

D(PP(-2)) -0.771063 0.450238 -1.712567 0.1209 

D(PP(-3)) -0.762335 0.425431 -1.791909 0.1067 

D(LIQR(-1)) -1.732736 1.024718 -1.690939 0.1251 

D(LIQR(-2)) -2.767740 1.051625 -2.631871 0.0273 

D(LIQR(-3)) -0.633063 0.635972 -0.995426 0.3455 

D(INTR) -2.412426 1.761922 -1.369202 0.2041 

D(EXR) 1.044424 4.496768 0.232261 0.8215 

ECM(-1) -0.410690 0.393671 -1.043230 0.3241 

R-squared 0.816098     Mean dependent var 0.848000 

Adjusted R-squared 0.611763     S.D. dependent var 186.0282 

S.E. of regression 115.9117     Akaike info criterion 12.64503 

Sum squared resid 120919.6     Schwarz criterion 13.19268 

Log likelihood -115.4503     Hannan-Quinn criter. 12.75193 

F-statistic 3.993920     Durbin-Watson stat 2.365587 

Prob(F-statistic) 0.024421    

 

Table viii: Granger Causality Test 

 Null Hypothesis: Obs F-Statistic Prob.  

 PR does not Granger Cause SP  22  1.61549 0.2279 

 SP does not Granger Cause PR  0.48833 0.6220 

 LIQR does not Granger Cause SP  25  2.99209 0.0430 

 SP does not Granger Cause LIQR  0.37445 0.6924 

 INTR does not Granger Cause SP  25  1.02109 0.3782 

 SP does not Granger Cause INTR  0.91251 0.4176 

 EXR does not Granger Cause SP  25  0.35297 0.7069 

 SP does not Granger Cause EXR  1.52981 0.2409 

Source: extract from E-view 9.0 

 



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Analysis and Discussion of Findings  

From table i, the value of the intercept which is 51.64218 shows that stock prices of quoted firms in Nigeria will 

experience 51.64218 unit increases when all other variables are held constant. The coefficient of price risk is 

0.143241. This shows that price risk is positively related to stock prices of quoted firms in Nigeria that a unit 

increases in price risk is followed by an increase in stock prices in Nigeria. The coefficient of liquidity risk is -

0.673035. This shows that liquidity risk is positively related to stock prices of quoted firms in Nigeria, that a unit 

increase in liquidity risk is followed by an increase in stock prices traded on the floor of Nigeria stock exchange. 

Furthermore, the value of interest rate risk  shows a negative  relationship with stock prices of quoted firms in 

Nigeria with a value of -1.829224 this implies a unit increase in stock prices  in Nigeria is been followed by an 

increase in interest rate risk  in Nigeria. The OLS result indicates that price fluctuation has a positive relationship 

with stock prices again the p-value shows that the coefficient is statistical significant. Therefore, we reject the null 

hypothesis and conclude that price fluctuation has significant impact on stock prices in Nigeria within the year 

under-review. The coefficient of exchange rate risk shows that exchange has negative and insignificant effect on 

stock prices within the period covered in the study. The probability value is greater than the critical level of 0.05 at 

5% level of significant, we accept null hypothesis that exchange rate risk have no significant effect on stock prices.  

f- test: If the f-calculated is greater than the f-tabulated (f-cal > f-tab) reject the null hypothesis (H0) that the overall 

estimate is not significant and conclude that he overall estimate is statistically significant. From the result, f-

calculated (3.993920) is greater than the f-tabulated (1.94), that is, f-cal > f-tab. Hence we reject the null hypothesis 

(H0) that the overall estimate has a good fit which implies that our independent variables are simultaneously 

significant. 

Goodness of Fit Test (R
2
): The (R

2
) shows the amount of the variation in the dependent variables (stock price) that 

are explainable by the explanatory variable. The (R
2
) which measures the overall goodness of fit of the entire 

regression shows the value of 0.786098= 78.6% approximately 80%. This indicates that the independent variables 

accounts for about 80% of the variation in the dependent variable. 

Durbin Watson Statistics: The computed DW is 2.365587, at 5% level of significance with three explanatory 

variables and observations, the tabulated DW for dI and du are 1.16 and 1.64 respectively. The value of DW is 

greater than the lower limit. Therefore, we conclude the there is evidence of positive first order serial correlation. 

The Augmented Dickey-Fuller (ADF) was employed to test for the existence of unit roots in the data using trend and 

intercept. The test results were presented in table ii. The result shows that none of the variables; was stationary at 

levels using Augmented Dicey Fuller test. This is because their critical values were greater than ADF test statistics 

in absolute value at 5 percent level of significance. However, all the variables considered became stationary after 

first difference since their ADF test statistics were greater than their critical values in absolute value. The results 

show that the series are integrated of the same order; I (1) with the application of both ADF test. Therefore, the 

variables are fit to be used for the analytical purpose for which they were gathered 

Johansen co-integration test determines whether there exist long-term relationship occurs in variables or not. The 

test envisages that there can be just one relationship between variables in long term. In most cases, it two variables 

that are I (1) are linearly combined, the combination will also be I(1). More generally, if variables with differing 

orders of integration are combined, then the combination will have an order of integration equal to the largest. The 

model with lag 1 was chosen with the linear deterministic test assumption and the result is presented in table iii. 

Under the Johansen Co-integration test, Co-integration is said to exist if the values of computed Eigen values are 

significantly different from zero or if the trace statistics is greater than the critical value at 5 percent level of 

significance, the results of the co-integration in table iii above indicated 3 cointegrating equation, the critical value at 

5 percent level of significance in only of the hypothesized equations. Similarly, the computed Eigen value is 

significantly different from zero in one of the hypothesized equations. Hence, 3 of the hypothesized equations 

satisfy this condition and therefore the null hypothesis of 3 co-integration equations among the variables is accepted 

in at least all equation. Therefore there is long run relationship between the variables used for the analysis in Nigeria 

within the period under study 1990-2017. 

  



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Normalized cointegration test presented in table IV found that price risk and interest rate risk have negative long run 

effect on stock price while liquidity risk and exchange rate risk have positive run effect on stock prices traded on 

Nigeria stock exchange. Table v and table vi presented the error correction model of the variables. Evidence from 

the result shows the large explained variation (table iv) while the coefficient of error correction model prove that 

adjustment speed of 41 percent. The causality results prove that the variables have no causal relationship except bi-

directional relationship from liquidity to stock prices. The positive findings of the study confirm the findings of 

Izova, Bollerslev, Osterrieder, Tauchen (2011) that the relationship between volatility and the volatility-risk reward 

is strongly direct and positive. The findings of Pollet, Kräussl, Jegadeesh (2010) that the market expects for PE to 

earn abnormal return is approximately 0.5 percent and for LPEs is approximately close zero after fees and the 

findings of Aduda et al. (2012) that macro-economic factors such as stock market liquidity, institutional quality, 

income per capita, domestic savings and bank development are important determinants of stock market development 

in the Nairobi Stock Exchange.  

CONCLUSION AND RECOMMENDATIONS 

This paper applied multiple regression analysis to study the effects of systematic risk on stock prices in Nigeria. The 

analysis covered firms listed in the NSE from 1990 to 2017.  By means of multiple regressions analysis of stock 

price to sensitivity of the price changes, liquidity changes, interest rate and exchange risk. From the findings of the 

study, we conclude that price risk and liquidity risk have positive effect on stock prices while interest rate risk and 

exchange rate risk have negative effect in stock prices. From the regression summary, we conclude that systemic 

risk significantly affects stock prices in Nigeria.  We make the following recommendations:  

1. The management of the capital market should ensure that the operating environment is risk minimum to 

ensure appreciable stock prices by developing strategies and policies aim at managing the systematic risk in 

the operating environment and engage a regular environmental impact assessment on systemic risk, to avert 

its negative effect on stock prices. 

2. Liquidity risk can be properly managed by formulating optimal liquidity strategy, therefore the study 

recommends the need for management to ensure optimum liquidity that balance cash inflow and cash 

outflow and policies should be formulated to manage the systematic risk within the operating environment 

to enhance good stable stock price. 

3. Exchange rate risk can be managed by formulating policies that will leverage the firms the challenges of 

depreciating Naira exchange rate.  Therefore the study recommend that the macroeconomic factors that 

results in depreciating Naira exchange rate should be well managed and financial policies should be 

formulated by the regulators of the Nigerian capital market to manage equity price risk of the 

manufacturing firms. 

 

REFERENCES 

Aduda, J. (2012). The determinants of stock market development: the case for the Nairobi stock exchange. 

International Journal of Humanities and Social Science, 2(9), 2221-0989. 

Afego, (2012). Weak form efficiency of the Nigeria capital market. An Empirical Analysis (1984-2009).  

Choudhary, K., & Choudhary, S. (2010). Testing Capital Asset Pricing Model: Empirical  Evidences from Indian 

Equity Market.  Eurasian Journal of Business and Economics, 3(6), 127-138 

Dupernex, S. (2007). Why might share prices follow random walk? Student Economic Review, 21, 167-179. 

Granger, C.W.J. (1969). Investigating causal relations by econometric models and cross spectral methods. 

Econometrica 37, 24-36. 

Gujarai,D.N.,(2003)Basic econometrics, fourth edition,Irwin/McGrawHILL. New York 

Inegbedion, H.E. (2009). Efficient market hypothesis and the Nigerian capital market.  An Unpublished M Sc. Thesis 

written in the Department of Business Administration, University of Benin, Nigeria. 



www.acseusa.org/journal/index.php/aijbms     American International Journal of Business and Management Studies   Vol. 1, No. 1; 2019 

19 

 

Bollerslev, T., Osterrieder, D., Sizova, N.,  & Tauchen, G. (2011). Risk and return: Long-run relations, fractional 

cointegration, and return predictability. Journal of Financial  Economics,108(2), 409-424 

Pollet, J. Jegadeesh,  N., & Kräussl R., (2009).The Risk and Return Characteristics of Private Equity Using Market 

Prices. Working paper, NO 45. 

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive 

models. Econometrica, 59 (6), 1551-1580. 

Johansen, S., (1995). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 

12(2), 231–254. 

Lintner, J. (1965b). Security prices, risk, and maximal gains from diversification. The Journal of Finance, 20(4), 

587-615. 

Lo, A.W. &  MacKinlay A.C. (1989). The size and power of the variance ratio test in finite samples. A Monte Carlo 

investigation. Journal of Econometrics, 40, 203-238. 

McCurdy, T. H., & Morgan I. G. (2011). Intertemporal risk in the foreign currency futures basis. Canadian Journal 

of Administrative Sciences / Revue Canadienne des Sciences de l'Administration 16(3) 172-184. 

Moessner, R.(2010). Central bank swaps line effectiveness during the euro area sovereign debt crisis. Journal of 

International Money and Finance 35, 167-178. 

Mossin, J, (1966). Equilibrium in a capital asset market. Econometrica,  34(4), 189-211 

Nelson, C.R. and C.I. Plosser, (1982). Trends and random walks in macroeconomic time series: Some evidence and 

implications. Journal of Monetary Economics, 10, 139- 162. 

Nier, (2009).  Market discipline, disclosure and moral hazard in banking. Journal of Financial Intermediation 15, 

333–62. 

Pandey, I.M (2005). Financial management (9th ed.). New delhi: Vikas Publishing House PVT Ltd 

Sharpe, W.F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of 

Finance. 

Zigrand, J.-P. (2014). Systems and systemic risk in finance and economics. Systemic Risk Centre Special Paper, 

1(3), 109-126. 

 

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Copyright for this article is retained by the author(s), with first publication rights granted to the journal. This is an 

open-access article distributed under the terms and conditions of the Creative Commons Attribution license 

(http://creativecommons.org/licenses/by/4.0/). 

 


