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4.Ricardo Dias, 2015. Angolan imports fell 25 percent in the second quarter of 2015. Global Agricultural information network 22 (13), 146-147
5. Tregub I.V. Econometrics. Model of real system - монография, М.: 2016. 166 р.
УДК 336.642
Besperstov V. master student International Finance Faculty Financial University under the Government of the Russian Federation
Russia, Moscow Scientific Supervisor: I. V. Tregub REAL ESTATE VALUATION USING SALES COMPARISON METHOD AND MULTIPLE REGRESSION ANALYSIS ON THE EXAMPLE OF RUSSIA
Abstract: Valuation method using multiple regression analysis is widely used across the globe and is seldom used in Russia. The aim of present study is to find the advantages and disadvantages of using Multiple Regression Analysis (MRA) in valuation compared to the application of traditional approach of sales comparison. The procedure of application of MRA involves identifying and listing the factors that influence the value of a house. It is done through literature review of previous researches, published articles, questionnaire survey and interviews of experts in the field. From these attributes, critical house value influencing factors are chosen after thorough statistical analysis of questionnaire survey. In total, samples of fifty three valuation reports have been used & regression has been carried out. The advantage of using MRA method is that it can model the relationship between sale price of a house and housing attributes. MRA regresses each attribute to show how change in each attribute affects the house price. Results obtained from sales comparison method & multiple regression analysis show that, regression gives better accuracy & efficiency in predicting value of property as compared with the traditional approach.
Keywords: Real Estate, property valuation, sales comparison method, multiple regression analysis.
I. Introduction
Real property valuation is a topic of interest for stakeholders for various purposes. Investors are interested to know the purchase price of the property in which they are going to invest. Developers seek to find out the feasibility of selling price for their decision-making. There are risks and uncertainties in property
valuation as it could be subjective [1]. Real estate appraisal, property valuation or land valuation is the practice of developing an opinion of the value of real property. There are no two properties that are exactly identical and have same characteristics. Based on these different characteristics, the appraisal process is important to determine the market value of property [2]. The valuation of properties can be conducted using various methods like comparison method, cost method, residual method, investment method and profit method. The market comparison approach suggests that the indicated value of the subject property equals sales prices of similar properties that have been sold recently and a rein close proximity to the subject property with due consideration to adjustments for dissimilar characteristics. MRA improves over the comparison approach by using many recent sales versus just a few. This statistical analysis decreases the likelihood of human error and the problems of small samples [3]. The present study validates the above statement by predicting value of property by both these approaches of sales comparison & MRA.
Valuation of real estate Valuation of property is required by a number of players in the market place such as real estate agents, appraisers, brokers, property developers, investors, market researchers, analysts, other specialists and consultants [4]. Market value is estimated through the application of valuation methods and procedures. Out of various methods of valuation, sales comparison is the most basic method. In the study of [5], the various adjustment techniques in sales comparison methods such as summative percentage, base percentage and dollar adjustment are considered. Opinion on comparison method by valuers from public sector and private sector shows that the analysis on sequence of elements for adjustment process in comparison method should be tenure, date of transaction, location, physical characteristics, economy condition, zoning, land size, topography and financial term. It states that the comparison method is the best method in determining the market value of property and summative percentage is the best adjustment technique in applying the comparison method. According to [6], appraisers prefer using very few comparable properties in order to sell their expert judgments regarding adjustment and weighting factors. The task of appraisers could be made much easier if they use the academicians' one-price assumption. This helps to reduce the number of adjustment factors and most academicians prefer MRA technique.
Use of MRA in valuation MRA has been implemented by many researchers to study valuation of real estate. [7] cite that MRA is possible for coefficient estimates and factor weight by using a large number of actual sale cases. It offers a very reliable tool to get accurate value for any property. In the study of [3], there are benefits such as less human bias and error when making adjustments for property differences, and easily updated assessment figures. MRA method is most popular because of their established methodology, long history of application, and acceptance among both practitioners and academicians [8]. The problem with MRA method is that it involves human judgment because it relies on functional assumptions to fit the relationships of the variables [9]. Also, multiple regressions have often produced serious problems for
real estate appraisal that primarily result from multicolinearity issues in the independent variables. Absolute error is found out from actual sold price and resulting estimated price by MRA techniques and compare with coefficient of
determination (R2) and Mean Square Error (MSE) values [10].
MRA relies on econometric modeling i.e. fluctuation in market value which reproduces the market behavior based on probability framework. Rough Set Theory (RST) is not based on behavior modeling. MRA has less Mean Absolute Percentage Error (MAPE) and shows better performance than RST and MRA is better if small data sets are run. While results also depend on the functional specification of MRA, MRA still performs better when small samples are used [11].
Identification of factors
There are two categories of variables involved in regression modeling namely dependent and independent variables. The dependent variable is a market value, which can be represented by rents, sale price or owner's estimated price. The second category consists of the independent variables namely locational, structural and environmental factors. In structural attributes, variables such as size of plot, floor area, age of building, number of rooms, number of stores, level of unit and housing fixtures are often used. Variables such as accessibility to amenities or facilities and other public facilities represent the locational traits. Neighborhood traits can be explained by variables such as quality of amenities and / or facilities, road quality, environment quality and view from property [12]. Study by [13] measured the effect of location on residential house prices. The attributes considered in their multiple regression model were sale price, date of sale, age of property, size, number of bedrooms and bathrooms, number of garages, type of central heating, condition. The finding was that location and structural characteristics are the key determinants of residential property values. [14], concluded that the contribution of housing characteristics have not changed over time. Only the age coefficient was affected by time and the effect was negative. [1] & [15] cite that the number of bedrooms has the highest weight in their study and helps to create a good quality of life that command on higher prices. More rooms mean higher construction costs, thus the higher the value of the property. According to [1], the bigger the land size, higher the value of a property and the bigger land size implies a potential for further improvement & land subdivision and generally households pay more for a property close to a school, particularly one with a high reputation. The access to schools is an important determinant [16].
Based on the literature survey and discussion with experts located across Russia, a total of fourteen variables have been finalized for further analysis. These seventeen variables are as shown in Table 1 below.
Table 1. Variables identified for the study
SrNo. Variable Variable code Value
1 Built up area X1 Quantitative
2 Plot shape X2 Qualitative
3 Location X3 Qualitative
4 Zoning X4 Qualitative
5 Age of building /property as on the date of valuation X5 Quantitative
6 Number ofstoresin building X6 Quantitative
7 Condition of property X7 Qualitative
8 Type of construction X8 Qualitative
9 View from property X9 Qualitative
10 Access road width X10 Qualitative
11 Parking facilities X11 Qualitative
12 Nearness to amenities X12 Qualitative
13 Nearness to facilities X13 Qualitative
14 Internal transport facilities X14 Qualitative
Data conversion
Valuation report is usually a written statement of the valuer's opinion about fair market value of a subject property as on the specified date. It is a conclusion which results from the process of research and analysis of actual and relevant data. It contains general information namely purpose of valuation, date of valuation, name of owner, street & warden, zoning of property, classification of locality and proximity to civic amenities, like school, hospitals, offices, cinema etc. and means & proximity to surface communication. It also focuses on technical details of property namely built up area, number of floors & height of each floor, year of construction, condition of property, view from property, parking facility, estimated future life, type of construction, number of lifts, and specifications of doors & windows, flooring, finishing, internal wiring, plumbing and painting etc. For analysis of these factors through MRA, the factors should be converted in quantitative manner. The variables are identified by classifying factors and their corresponding meaning in numerical value in such a fashion that, built up are defined as a measure of floor area. It is measured quantitatively in square meters. For regular and irregular plots have the value given is 1 and 2 respectively as location is classified as superior, good and poor with poor as areas of low income, good as areas of middle class and superior as areas of high income group. House in superior location is referred as 1, good awarded a 2 and poor location is represented by a 3. Likewise all the variables have been given quantitative value as per possible situations.
II. Application of multipleregression analysis
Regression analysis is defined as a statistical tool for the investigation of
relationships between variables. It is used to find casual effect of one variable upon another. For example, in real estate appraisal the price of property depends on the location and the question is what the relationship between them is and how to quantify it [7]. MRA is a technique that allows additional factors to enter the analysis separately so that the effect of each can be estimated. It is valuable for quantifying the impact of various simultaneous influences upon a single dependent variable. MRA is a statistical methodology that utilizes the relationship between two or more independent variables and a dependent variable. The dependent and independent variables are regressed using properties of known prices to determine the established relationships (coefficients) between the two types of variables. The determined coefficients are then used for the prediction of prices of unsold properties in the same stock. MRA determines the coefficients with the least possible error. Multiple regression is carried out to establish the effect of all independent variables working together on sale price. The regression equation proposed is as follows [12]:
P= a0+ b1X1+ b2X2+ b3X3.......bnXn+ e
P is the dependent variable i.e. house price/value (dependent variable -P), a0 is the regression constant , X1, X2, X3...Xn are predictor or independent variables, b1,b2,b3...bn = are regression coefficients and e is the error term. The regression constant (a0) is the Y intercept (i.e. value of Y when X=0). The regression coefficients (b1-bn) are value of each independent variable. They indicate how much value will change for a unit change in each characteristic, where other characteristics are constant. The error term (e) indicates the difference between the observed value and the predicted value of the depended variable. It is used for accuracy and reliability of the MRA model [12].
Regression is carried out in Microsoft Excel (version 2010) using trial and error method. Converted data of total fifty three valuation reports are fed to the software in transposed form in such a way that the first column contains the observations on the dependent variable i.e market value and then the other, adjoining columns contain the observations on all the seventeen independent variables.
_Table2. Regression Statistics
Regression Statistics
MultipleR 0.998
R Square 0.997
Adjusted RSquare 0.995
StandardError 2.269
Observations 53.000
Table3. ANOVA table
df SS MS F Significance F
Regression 14 58824.08 4201.71984 816.0478 1.34728E-42
Residual 38 195.6569 5.148864588
Total 52 59019.73
As shown in table 2, the multiple regression is 0.998. This indicates that the correlation among the independent and dependent variables is positive. The coefficient of determination, from the regression results is 0.997, showing that the combined influence of fourteen variables explains 99.7% of all house price variations. The R2 range should be within 0 < R2< 1. The adjusted R-square, a measure of explanatory power, is 0.995. This statistic is not generally interpreted because it is neither a percentage (like the R2), nor a test of significance (such as the F-statistic). The standard error of the regression is 2.269, which is an estimate of the variation of the observed home prices.
Table3 shows ANOVA analysis of variance information which provides the breakdown of the total variation of the dependent variable i.e. house prices. The F-statistic is calculated using the ratio of the Mean Square regression (MSR regression) to the Mean Square residual (MSR residual). If the value of significance F is over than that of value F then the test is said to be significant. In above case, the significance F value is very small as compared to value F hence test is said to be significant.
Table4. Final Regression Table
Coefficients StandardErr or t Stat P-value Lower95% Upper95 %
Intercept 72.80 4.07 17.88 0.00 64.56 81.04
Built up area in Sq.ft 0.02 0.00 60.18 0.00 0.02 0.02
Plot shape -9.08 2.08 -4.37 0.00 -13.29 -4.87
Location -7.39 0.73 -10.18 0.00 -8.85 -5.92
Zoning 6.17 0.49 12.58 0.00 5.18 7.16
Age of building/property s on the date of valuation 0.08 0.03 2.50 0.02 0.01 0.14
Number of storey in building -4.16 0.31 -13.55 0.00 -4.78 -3.54
Condition of property -7.32 0.61 -12.10 0.00 -8.55 -6.10
Type of construction -13.96 1.08 -12.89 0.00 -16.16 -11.77
View from property -5.00 0.33 -14.99 0.00 -5.68 -4.33
Access road width 8.41 0.35 24.38 0.00 7.72 9.11
Parking facilities -3.74 0.17 -22.00 0.00 -4.09 -3.40
Nearness to amenities -3.55 0.29 -12.18 0.00 -4.15 -2.96
Nearness to facilities -8.42 0.43 -19.59 0.00 -9.30 -7.55
Internal transport facilities 15.15 0.52 28.96 0.00 14.10 16.21
Table 4 shows the coefficients of each independent variable. The T-statistic is calculated using the ratio of the coefficients of variable to the standard error of variables. The intercept value 72.80 is the value of Y when values of all the independent variables are zero. For hypothesis testing, if we consider 95% of confidence level then P should be less than 0.05 of output variable. If output variable has P>0.05 then the intercept value is not significant showing that these variables are not going to affect dependent variable. If the P-values of output variables have 95% of confidence level then only these variables are accepted for further regression analysis. For present study, all variables are having P<0.05 values (table 4), all 14 variables are significant in regression analysis.
Table 5. Data conversion of valuation reports
Valuation Reports R1 R2 R3 R4 R5 R6 R7 R8 R9 R10
Market value(inLac.) 33.85 16.11 41.28 31.77 28.38 28.67 102.67 171.54 15.14 80.61
Built up are in Sq.ft 1687.16 827.42 2500 1644 1215 882.16 2373 4210 1594 4433
Plot shape 1 1 1 1 1 1 1 1 1 1
Location 1 1 2 2 1 2 2 1 2 2
Zoning 3 5 3 3 3 3 5 3 3 3
Age of building /property as on the date of 0 6 23 17 5 1 2 10 2 16
valuation
Number of
storey in building 2 5 2 1 1 3 2 2 2 2
Condition of property 1 1 2 1 1 1 1 1 2 1
Type of construction 2 2 2 2 2 2 2 2 2 2
View from property 2 3 3 3 2 3 1 1 3 1
Access road width 2 1 2 4 1 2 4 3 3 1
Parking facilities 7 2 7 8 3 3 2 1 7 2
Nearness to amenities 1 2 2 4 2 5 1 1 2 2
Nearness to facilities 2 3 1 4 3 3 1 1 3 4
Internal 1 1 1 2 1 3 1 3 1 1
transportfacilities
Conversion of data from valuation reports has been carried out and it is used for regression model. The same for ten valuation reports is shown in table 5. Value is calculated using the estimated model factors and respective characteristics of the subject property. Using the coefficients (table 4) model obtained is as follows:
Y=b0 +b1*X1 +b2*X2+ b3*X3+ b4*X4+ b5*X5+ b6*X6+ b7*X7+ b8*X8+ b9*X9+ b10*X10+ b11*X11+ b12*X12+ b13*X13+ b14*X14
Based on this standard equation, for the present study, the model used would
be:
Y=72.80+0.02*X1-9.08*X2-7.39* X3+6.17*X4 +0.008* X5-4.16* X6-7.32*X7 -13.96*X8.-5.00* X9+8.41*X10 -3.74*X11 -3.55* X12-8.42*X13 +15.15*X14
Where Y= Market value
72.80= the regression constant (a0) is the Y intercept (i.e value of Y when
X=0).
X1= Built up area, X2= Plot shape, X3= Location, X4= Zoning, X5= Age of
building, X6= No of story, X7= Condition of property, X8= Type of construction, X9= View from property, X10= Access road width, X11= Parking facility, X12= Nearness to amenities, X13= Nearness to facilities and X14= Internal transport facility.
Results of MRA
The accuracy of the above valuation model is tested by comparing the actual sale values of fifty three valuation reports with the predicted market values from MRA. The predicted values for the sampled houses are calculated using the house value model above and their results are shown in Table 6.
Table 6. Comparing actual versus predicted value for MRA
Valuation Reports Actual Market value(In Lac.) PredictedMa rket value (In Lac.) Valuation Reports Actual Market value(In Lac.) PredictedM arket value (In Lac.)
R1 33.85 34.99 R27 29.08 27.26
R2 16.11 16.20 R28 107.03 112.48
R3 41.28 41.72 R29 15.84 15.50
R4 31.77 32.11 R30 14.85 12.71
R5 28.38 29.17 R31 13.2 13.17
R6 28.67 29.80 R32 16.14 16.75
R7 102.67 106.43 R33 4.35 3.95
R8 171.54 163.12 R34 10.21 9.04
R9 15.14 14.24 R35 10 10.03
R10 80.61 80.78 R36 18.18 20.44
R11 17.92 17.57 R37 20.47 20.21
R12 30.75 30.01 R38 8.45 7.22
R13 29.65 28.91 R39 11.61 12.25
R14 83.45 84.31 R40 19.31 17.38
R15 88.34 88.91 R41 30.67 31.92
R16 93.75 97.07 R42 14.06 15.02
R17 105.09 106.00 R43 22.14 24.24
R18 58.87 56.84 R44 9.63 10.88
R19 20.27 19.88 R45 30.49 30.83
R20 19.37 20.80 R46 19.27 21.01
R21 52.93 52.12 R47 29.57 28.90
R22 17.55 17.67 R48 11.35 11.69
R23 60.27 58.71 R49 10.22 10.36
R24 12.55 13.19 R50 9.65 7.18
R25 43.82 42.59 R51 9.6 10.61
R26 21.78 21.38 R52 14.12 12.86
R53 14.12 15.11
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Figure 1. Comparison of actual and predicated market value
Results of MRA for 14 factors show that predicted market values are within ±5% of actual market value. From table 6 and the line graph shown in Fig.1 above, it can be seen that the predicted values are very close to the actual values.
III. Application of sales comparison method The sales comparison approach is of interest because it is widely regarded by most appraisers as the approach that produces the most reliable estimate of the value of a subject property, especially when there are many recently sold properties comparable to the subject property. But, appraisers do not make use of a particularly large number of these comparable properties. Usually, appraisers combine their expert judgment with a relatively small number of comparable sales to arrive at a final estimate of value [6]. The sales comparison approach is dependent upon the availability, accuracy and period of sale transaction data. Information sources include government records and appraiser's local contacts. The comparison method is the most common approach used by the professionals. The data consists of the actual transaction prices of residential buildings having market period of two years, covering 2013 to 2014. Total 53 valuation reports of residential buildings have been collected from practicing government valuers. These valuation reports are considered for studying sales comparison method.
Results of sales comparison method Out of 53 properties, 10 properties namely R1, R2, R3, R5, R17, R47, R26, R14, R19, and R45 have been considered for application of sales comparison approach. Choice of property from the dataset is on the basis of location and each of the selected properties have been chosen from different locations to cover larger area. Table 7 shows comparison of actual versus predicted market value of selected properties that have been assessed by sales comparison method.
Table7. Comparing^ actual versus predicted value for sales comparison method
Valuation ActualMarke Market Value
Reports t value (In by Sales
Lac.) comparison (In Lac.)
R1 33.85 35.45
R2 16.11 16.35
R3 41.28 46
R5 28.38 33.45
R17 105.09 115.6
R47 29.57 35.28
R26 21.78 30.62
R14 83.45 88.58
R19 20.27 35.07
R45 30.49 30.9
Market value by sales comparison of properties under consideration show more value as compared to actual market value (Table 7).
Property value by ready reckoner rates Ready reckoner is an official document prepared by government authorities in Russia which has rates for land and property mentioned in it for different parts of a city for a particular financial year. Stamp duty calculation is generally done on the basis of ready reckoner rates. The rate given in ready reckoner can be the least rate a particular property can have. There are ready reckoner rates for the year 2014 taken from Federal State Statistics Service of Russia to derive value. Table 8 gives rates and corresponding value of property if ready reckoner rate is considered.
Table8. Property value by ready reckoned rates (Index:2014)
Valuati on Reports Property area (in Sq.m) ActualMa rketvalue (In Lac.) Readyreckonerrates ofproperties(Year 2014) Propertyvalue by ready reckonerrates (In Lac.)
Land Cost (Rs/Sq.m) Construction cost(Rs/Sq.m) Total cost (Rs/Sq.m)
R1 156.80 33.85 1140 13,557 14,697 23.04
R2 76.89 16.11 3443 10,000 13,443 10.34
R3 232.34 41.28 2216 9684 11,900 27.64
R5 112.91 28.38 3228 8608 11,836 13.36
R17 477.32 105.09 1291 10,760 12,051 57.52
R47 121.18 29.57 3873 16,140 20,013 24.25
R26 73.18 21.78 4660 20,982 25,652 18.76
R14 362.82 83.45 1721 16,678 18,400 66.75
R19 177.72 20.27 1140 6456 7596 13.50
R45 65.93 30.49 2216 14,526 16,742 11.04
IV. RESULTS AND CONCLUSION
Actual market value of property, predicted market value from MRA and
market value by sales comparison are considered for the comparison. The difference between actual market value & predicted market value from MRA of properties R1, R2, R3, R5, R17, R47, R26, R14, R19, R45 shows less difference as compared with the difference between actual market value & predicted market value by sales comparison method. Table 9 shows comparison of results of MRA, sales comparison method and value by ready reckoner. Observing the difference between actual and predicted values by all methods (table 9), it can be concluded that the results obtained from MRA method shows small variation as compared to results obtained from sales comparison method. Also, ready reckoner value is on lower side as compared with values by all other methods. Ready reckoner value can be considered as basic value of a property as decided by government which forms the basis for calculating stamp duty.
Table 9. Comparison of results of MRA & sales comparison method
Valuati ActualMarket Propertyv PredictedMa Market Differenc Differenc Difference
on value (In Lac.) alue by rket value by Valueby ebet ebet bet Actual
Report ready MRA Sales Actual Actual MV &
s reckonerr (In Lac.) compariso MV & MV & Market
ates n(In Lac.) value by Predicted value by
(In Lac.) ready reckoner rates (In Lac.) MV by MRA (In Lac.) Sales compariso n(In Lac.)
R1 33.85 23.04 34.99 35.45 10.81 1.14 1.6
R2 16.11 10.34 16.20 16.35 5.77 0.09 0.24
R3 41.28 27.64 41.72 46 13.64 0.44 4.72
R5 28.38 13.36 29.17 33.45 15.02 0.79 5.07
R17 105.09 57.52 106.00 115.6 47.57 0.91 10.51
R47 29.57 24.25 28.90 35.28 5.32 -0.67 5.71
R26 21.78 18.76 21.38 30.62 3.02 -0.40 8.84
R14 83.45 66.75 84.31 88.58 16.7 0.86 5.13
R19 20.27 13.50 19.88 35.07 6.77 -0.39 14.8
R45 30.49 11.04 30.83 30.9 19.45 0.34 0.41
It can be thus concluded that qualitative characteristics of property are difficult to identify and measure. To overcome this problem MRA method is very accurate method. MRA allows more factors to enter the analysis separately and to estimate effect of one variable upon another. Sales comparison being traditional approach can be used for properties with lesser value or it can be used to have a quick judgment of range of value for a property. It can be used for approximate valuation. Ready reckoner rate gives a basic value of property and it is generally not considered as the actual value of any property.
MRA makes possible the coefficient estimates and factor weightings using a large number of realized sales. It offers a very reliable tool to get accurate assessment value for any property. Sales comparison method is dependent on the basis of judgmental values. MRA requires proper identification of variables affecting property value & data conversion. Reliability of results of MRA can
improve with more number of cases as input. Results of sales comparison can improve with more number of sales instances with higher degree of similarity. Also, experience of valuer affects results of sales comparison. MRA when compared with sales comparison method, gives results with lesser error thus is more acceptable.
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УДК 330.43
Dashkina A.K.
1st undergraduate course Financial University under the Government of the Russian Federation
Russia, Moscow Academic advisor: Chuvahina L. G.
Дашкина А.Х. студент магистратуры
1 курс
финансовый университет при Правительстве Российской
Федерации Россия, Москва
Научный руководитель: Чувахина Л.Г. , к. э. н., доцент ИССЛЕДОВАНИЕ ЗАВИСИМОСТИ КУРСА ДОЛЛАРА США К КАНАДСКОМУ ДОЛЛАРУ ОТ ЦЕНЫ НА НЕФТЬ THE INVESTIGATION OF U.S. DOLLAR EXCHANGE RATE DEPENDENCE FROM CANADIAN DOLLAR OIL PRICE Аннотация: В статье описана методика расчета курса доллара США по отношению к канадскому доллару в зависимости от цены на нефть марки Брент.
Annotation: This paper illustrates the method of calculation of the U.S. dollar exchange rate to the Canadian dollar, depending on the oil price of Brent.
Ключевые слова: курс доллара США к канадскому доллару, метод наименьших квадратов, однофакторная параболическая модель
Key words: U.S. dollar exchange rate to Canadian dollar, least square method, univariate parabolic model
The U.S. dollar exchange rate to the Canadian dollar (USD/CAD) as a function of the value of oil is in the following form:
_ К = f(BRi)
where: Yt is the calculated value of the US dollar to Canadian dollar; BRi - the price of oil.
Figure 1. shows the field correlations of the US dollar exchange rate to Canadian dollar to the price of oil.
Based on the field correlation, (for the General combination) it is possible to hypothesize that the relationship between all possible values of the USD/CAD exchange rate (Fj) and the cost of oil (BRt) is parabolic in nature.
