Derivatives are used for speculative purposes and to reduce the risks manifested on financial markets. Banking market, due to the high volatility of exchange rate and interest rate derivatives are frequently used to cover the risk associated with lending. Contracts such as options on the exchange rate of national currency, swaps - on interest rate exchange, forward on the interest rate, swaps and options on interest rates, banks enable unbundling credit risk and the funding market and credit risk transfer, and keeping its ownership.derivatives, forward contracts, futures, swaps, options, securitization

Ion NITU

Mihaela SUDACEVSCHI

English

Research Papers in Economics

Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  1
USING THE MARKET MODEL ON ROMANIAN  
STOCK EXCHANGE 
 
  Ph. D. Professor Daniel ARMEANU                         Ph.D. Nataliţa HURDUC 
Master Student Cristina Andreea DOIA          „Athenaeum” University Bucharest 
    Ph.D. Student Andreea NEGRU 
Academy of Economic Studies Bucharest                        
 
 
 
Abstract 
One of the concerns in portfolio management is to anticipate market 
evolution, generally given by a stock index. The market value of a stock is 
connected to the trends of the index; each security follows, more or less, the index 
trend line. This relationship between the return on a financial security and the 
return on a market index outlines the concept of market model. 
 
Key words: market model, systematic risk (market risk), unsystematic risk 
(idiosyncratic risk), volatility, correlation coefficient, etc. 
Clasificare JEL: G11 
 
The relationship between the return on a security and the return on the 
market portfolio generated widespread concern among financial specialists and one 
of the  results of their studies was W. Sharpe’s market model, that came public in 
1970. The model describes the link between the return of an asset and the return of 
the market using  a regression and due to its simplicity and coherence, it became 
very popular, framing at the same time an important starting point for the future 
research in stock market.  
The market model explains the linear relationship between the return on a 
stock, on one hand, and the rate of return for the market index, in the same period 
of time, on the other hand. We mean by market model the regression: 
i M R i i i R ε β α + + =                                                                               (1) 
One of the basic assumptions for this model is the one that says the return of 
a security is described mostly by a single macroeconomic factor, the market’s 
return, respectively. Consequently, the securities’ variability (risk) can be 
explained by the variability of the market’s return, to a great extent, and this gives 
the quantification of the systematic risk (non-diversifiable, market risk. This type 
of risk is linked to the swings in macroeconomic indicators like: gross domestic 
product, inflation rate, average interest rate, exchange rate, etc. The amount of risk 
that cannot be explained by variability in the market’s return is the idiosyncratic Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  2
risk, diversifiable, and refers to the firm-specific risk factors and the economic 
sector to which the company belongs: 
 
2 2 2 2
i M i i ε σ σ β σ + =                     (2) 
The diversifiable risk for each security is given by the variance of the 
residuals,  σεi
2.  This risk can be virtually eliminated  from a portfolio through 
diversification. 
( )
2 2 2 2 2
,
2 1 M i i i M i i σ β σ σ ρ σ ε − = − =                                      (3)               
The systematic risk is measured by beta. 
Beta (βi = the slope of the regression line) is an elasticity coefficient of a 
security return (Ri) with respect to index return (RM). In other words, it measures 
the percentage change βi% in the return Ri when the return RM is increased or 
decreased by 1% (statistically speaking).  
2
M
iM
i σ
σ
β =     where:                        (4) 
 
() ()
1 T
R R R R
σ
M Mt
T
1 t
i it
iM −
− −
=
∑
=                       (5) 
 
()
1 - T
R R
σ
T
1 t
2
M Mt
2
M
∑
=
−
=                         (6) 
 
The size of βi compared to market beta βM (which, by default, is equal to one: 
βM = 1) classifies the securities by their systematic risk in:  
•  more volatile securities(with βi > 1); 
•  volatile securities (with βi = 1)  
•  less volatile securities (with βi < 1).  
The securities with βi = 0 are an exception to the rule of market model, 
meaning that their return is completely independent of RM. The securities with βi < 0 
are not very common, in negative correlation with the stock market. The knowledge 
of βi size is useful in estimating the expected return  of the securities [E(Ri)] and in 
active portfolio management (buying volatile stocks when the market is in expansion 
or less volatile stocks when the market is in contraction). 
The correlation coefficient (ρiM) between Ri and RM measures the strength of 
the linear dependence between Ri and RM. Its significance is complementary to βi 
because: 
i
M
i iM σ
σ
β ρ =  or: 
M
i
iM i σ
σ
ρ β =                                (7) Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  3
Consequently, 
• a coefficient βi  > 1 will be accompanied by a significant correlation 
coefficient 0,5 ≤ ρiM < 1; 
• a βi < 1 will have a ρiM  which emphasizes a low intensity correlation  i R
~
 ~ 
M R
~  (0 ≤ ρiM < 0,5). 
The fraction of the variance in Ri that is explained by RM in a linear 
regression analysis is synthesized by the coefficient of determination R
2, which is 
the square of the correlation coefficient: R
2 = ρ
2.  
The intercept αi for the linear regression is the difference between the 
average  i R  and the average return explained by the average market return  M R : 
M i i i R R β α − =                          (8) 
This symbolizes the return Ri when the retun RM is zero. The intercept αi can 
vary between positive and negative values, depending on the stock market 
instability. 
Study case 
In the table below we gave an exemple of the correlation that exists between 
each security and the market portfolio using the least squares method. For the 
market portfolio we used BET index, as it is a free float weighted capitalization 
index of the most liquid 10 companies listed on the BVB (Bucharest Stock 
Exchange) regulated market. 
 
Table 1. Components of market model for 13 stocks 
 
  σiM  βi  αi  σi
2  βi
2×σM
2  σεi
2  ρiM  Ri
2 
ALU  0,000240  0,654777  0,000312  0,000838  0,000157  0,000681  0,433222  0,187682 
ALR  0,000263 0,717088  0,001719 0,001202 0,000189 0,001013 0,396189 0,156966 
ATB  0,000241  0,655560  -0,000435  0,000629  0,000158  0,000472  0,500539  0,250539 
AZO  0,000304 0,827473  0,001200 0,001156 0,000251 0,000905 0,466112 0,217261 
BRD  0,000032  0,088422  0,003115  0,000661  0,000003  0,000658  0,065883  0,004341 
TEL  0,000110 0,299607  0,002306 0,002281 0,000033 0,002249 0,120154 0,014437 
TUFE  0,000245  0,668877  -0,000105  0,000804  0,000164  0,000640  0,451773  0,204099 
RRC  0,000348 0,947452  0,000716 0,000905 0,000329 0,000575 0,603343 0,364023 
SIF3  0,000418  1,137997  -0,000100  0,001043  0,000475  0,000568  0,674992  0,455614 
SNP  0,000397 1,080940 -0,000332 0,000668 0,000429 0,000239 0,801303 0,642087 
SOCP  0,000167  0,455653  0,000313  0,001020  0,000076  0,000944  0,273268  0,074676 
TLV  0,000378 1,030670 -0,000286 0,000688 0,000390 0,000298 0,752837 0,566764 
TRP  0,000145  0,396491  0,001447  0,000848  0,000058  0,000791  0,260744  0,067987 
  
BET  0,000367  1  0  0,000367  0,000367  0  1  1 Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  4
In the table above we notice that the most volatile stocks are SIF 3, SNP and 
TLV, all the others being less volatile, with a βi < 1. Among the least volatile stocks 
we can mention BRD, SRT and TRP. For SIF3, SNP and TLV with beta greater 
than one, the correlation coefficient has the following values 0.67, 0.8, 0.75, 
respectively. 
Next we will give an exemple for the market model using SNP. For this 
purpose, we had the regression: 
RiSNP=αiSNP + βiSNP * RiM + εi                                                                                                                      (9) 
Using the least squares estimation, we got the results: 
 
Table 2. Statistical results 
 
Dependent Variable: SNP 
Method: Least Squares 
Variables Coefficient Std.  Error    t-Statistic Prob. 
Intercept (α) -0.000332 0.000996 -0.332896 0.0395 
BET 1.080940 0.051351 21.05021 0.0000 
R-squared  0.642087     Mean dependent var  0.003017 
Adjusted R-squared  0.640638     S.D. dependent var  0.025892 
S.E. of regression  0.015522     Akaike info criterion  -5.485167 
Sum squared resid  0.059507     Schwarz criterion  -5.456914 
Log likelihood  684.9032     F-statistic  443.1113 
Durbin-Watson stat  2.226704     Prob(F-statistic)  0.000000 
 
The coefficient for the BET’s return has the value βSNP = 1.08094.   
The intercept’s αSNP value is αSNP = -0.000332, significant with a confidence 
level of 95%. 
The estimation is:      
RSNP = -0,000332 + 1,080940*RM 
 
Considering the value of the coefficient βSNP  (1.080940) > 1, we can say that 
SNP is very volatile, which means that a +/- 1% change in the market index will 
generate changes greater than +/- 1%, and those changes consist of  +1.080940% in 
the return of SNP.  
 
 
 
 Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  5
The coefficient β also gives the slope for the scatter plot: 
 
Graph 1. Correlation SNP against BET 
-.08
-.04
.00
.04
.08
.12
-.08 -.04 .00 .04 .08
BET
S
N
P
 
The global risk of the security, by its components, will be: 
 
                           σ
2
SNP = β
2
SNP*σ
2
SNP + σ
2
εSNP                                                               (10) 
 
and can be described as: Global riskSNP = Market risk + Firm-specific risk 
⎪
⎩
⎪
⎨
⎧
  0,00024   =  
+
= ∗
= =
risk   specific - firm  
                 
risk market     00043 , 0
00067 , 0
2
2
2
ε σ
σ β
σ
BET SNP
2
SNP  
This decomposition outlines that the market risk is greater than the firm – 
specific risk, the explanation consisting of the high level volatility of the security 
sensitive to the market swings. 
For measuring the intensity of the relationship between the two returns, we 
computed the correlation coefficient  8 . 0
,
, =
∗
=
M SNP
M SNP
M SNP σ σ
σ
ρ   and its value 
indicates a directly proportional and highly correlated dependence between SNP 
andi BET. 
R
2 = ρ 
2
SNP,M, having a value of R
2 = 0.64, that says that 64% of the changes 
in SNP’s return is caused by the market changes. 
 
The stability of the coefficients obtained from the estimation was analysed 
with a forecast for the return on SNP using the market model: 
 Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  6
Graph 2. Return on SNP forecast using market model 
-.15
-.10
-.05
.00
.05
.10
.15
250 275 300 325 350
SNP (forecast)
Forecast: SNP
Root Mean Squared Error  0.014562
Mean Absolute Error       0.010238
Mean Abs. Percent Error  81.24216
Theil Inequality Coefficient  0.267808
      Bias Proportion         0.002134
      Variance Proportion  0.024902
      Covariance Proportion  0.972964
 
One of the dorecast evaluators is the Mean Absolute Percent Error, and 
indicates the average percentage deviations of the forecast from the actual, with the 
formula: 
100
| ' | 1
1
⋅
−
−
= ∑
+ =
T
p t t
t t
y
y y
p T
MAPE ,                               (11) 
where:  T = total number of observations; 
   p = number of observations used for modelling;   
      p+1 = indicator for the first forecast value (16.04.2010). 
 
According to the forecast results, the forecast returns on SNP differ 81% by 
the actual returns. 
 
Graph 3. Correlation actual against forecast returns on SNP 
-.12
-.08
-.04
.00
.04
.08
.12
-.2 -.1 .0 .1 .2
SNP
S
N
P
(
f
o
r
e
c
a
s
t
)
 Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  7
Theil’s coefficient is a forecast evaluator with values in the interval (0,1); the 
closer to 0 the value is, the better the adjustment is. In our case, the value for this 
coefficient is pretty low, around 0.26. 
Next we created a line chart using the actual return on SNP series and the 
forecast series for the following period of time:  
 
Graph 4. Actual and forecast return on SNP 
-.15
-.10
-.05
.00
.05
.10
.15
SNP SNP (forecast)
16.04.2010
 
 
Conclusion 
As a result of using the market model for 13 securities on the Romanian 
stock market, we noticed that the idiosyncratic risk is greater than the systematic 
risk, with two exceptions (SNP and TLV), risk that can be diversified away to 
smaller levels in a portfolio. 
Having picked BET index as the whole capital market for Sharpe’s market 
model leads to 64% reliability on the model (according to the coefficient of 
determination R
2), in the case of SNP, but for the other securities the numbers lead 
to the conclusion that the market return is not given by the BET index. 
Applying the market model for SNP using BET index shows out its 
efficiency in forecasting expected returns, but it still has his boundaries given by 
the stability of α and β. 
  
 
 Internal Auditing & Risk Management     _________________      Anul V, Nr.4(20), Decembrie 2010 
 
  8
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THE INNOVATIONS ON THE FINANCIAL MARKETS USING DERIVATIVES FOR BANKING MARKET RISK COVERAGE

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THE INNOVATIONS ON THE FINANCIAL MARKETS USING DERIVATIVES FOR BANKING MARKET RISK COVERAGE

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