CC BY
3
https://www.cbr.ru/press/PR.aspx?file=15072015_190947ik2015-07-15T19_06_47.htm
5. Центральный банк Российской Федерации (Банк России), Пресс-служба, О соответствии нормативной базы Банка России стандартам Базеля II, Базеля 2,5 и Базеля III URL: http ://www.cbr.ru/press/pr.aspx?file=15032016_163316ik2016-03 -15T16_30_17.htm
6. Basel Committee on Banking Supervision, Implementation of Basel standards, A report to G20 Leaders on implementation of the Basel III regulatory reforms, August 2016 URL: http://www.bis.org/bcbs/publ/d377.pdf
7. Bank for International Settlements, Basel Committee on Banking Supervision, Basel III: international regulatory framework for banks URL: http://www.bis.org/bcbs/basel3.htm
8. Banks Financial Data URL: http://kuap.ru/banks/9999/balances/
9. Data on closed banks URL: http://www.banki.ru/banks/memory/?by=PROPERTY_date&order=desc
УДК 336.642
Bibik Yuriy 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 THE METHOD OF CORRELATION AND REGRESSION ANALYSIS Annotation: One of the directions of the formalized scientific approach of methods of mathematics in real estate valuation. The history of development of domestic estimative activities has shown the problems, which exist in this sphere. So, for example, selective check revealed distinction in the cost of the same property estimated by different appraisers. The independent appraiser is urged to resolve this conflict of interest, whose task is to estimate object competently and without prejudice, with deep arguments to convince participants of transaction that the size calculated by it and is that objective cost which reflects object value in the market of time in this place at present. Thus, for the determination of market value of the premises, the correlation and regression model describing interaction of the major factors was constructed.
Key words: Real estate, valuation, regression, correlation, comparative approach, income approach, cost approach, Subject property, object-analogue.
Application of mathematical methods is an essential element of modern economics as well as application of real estate valuation. The contents and the main purpose of valuation - calculation of the most probable price of the object ownership in a free competitive market. The methodological basis of the valuation
are three common approaches: comparative, income and cost. From a methodological point of view, valuation is defined as the scientific field of applied economic analysis, which determine the most probable selling price or the purchase of an asset based on the analysis of the dynamics of the forces of demand for this asset and its supply in the relevant market segment. One of the areas it formalized scientific approach is the use of methods of mathematics in the valuation.
Correlation and regression analysis methodology
According to article 3 of Federal law from July 29, 1998 #135-FL "about appraisal activity in Russian Federation", appraisal activity means a professional activity of the subjects of valuation activity (appraisers) for the purpose of establishing in respect of objects of valuation of the market, cadastral or other value. Most valuations are dedicated to the definition of market value - the most probable price of the object at which the property can be disposed on the open market in a competitive environment where the parties of transaction are reasonable, have all the all the necessary information, and there is no any extraordinary circumstances that reflects on the value of transaction.
In accordance with current legislation in the area of professional valuation activities for the purpose of valuation, the appraiser must use income, comparative and cost approaches or justify refusal of the usage of particular approach. The valuation method is a sequence of procedures, allowing (on the basis of material information for the method) to determine the value of property by one of the approaches.
It is considered that the valuation result obtained by the comparative approach, reflects in the best way the value of estimated market value of the property under the conditions of developed market and sufficient information content about prices, terms of transactions and the characteristics of the objects-analogues. According to that, the obtained value under the comparative approach corresponds to the actual practice of purchase and sale of similar objects, so we obtain market value.
Each of the valuation methods are inherent in limitations to use, advantages and disadvantages. Since the valuation report prepared by a professional appraiser, is a document of evidentiary value, the method of correlation and regression dependence (hereinafter CRD) it is perhaps one of the most objective methods of comparative approach. The calculation under this method is based on the construction of correlation and regression dependence between the sales price (offers) of object-analogues and any one (single-factor model) or more (multi-factor model) parameters. When using other methods of comparative approach, the appraiser should make corrections (adjustments) to the prices of object-analogs, which take into account the existing significant differences from the valuation object (sales comparison method) or assign ranks to each comparison criteria (ranking method). The main disadvantage of these methods is a certain subjectivity of calculations.
CRD method has been widely used in valuation of commercial and
residential real estate, land, plants, equipment and vehicles. Calculations by this method may be implemented by constructing a linear or non-linear model.
In this article, we will analyze the usage of CRD method based on linear multivariable model using MS Excel on the example of commercial premises, located in the Central Administrative District of Moscow.
Applying the CRD method, the appraiser should perform the following
steps:
1. Determine the composition of the pricing factors;
2. Choose analogues objects;
3. Select the type of regression model f (x);
4. Evaluate the model parameters;
5. Build a regression model;
6. Check the adequacy of the model;
7. Calculate the market value of the object of evaluation.
Step 1. On the basis of the analysis of the retail market in Moscow by the appraiser, it was determined that the main pricing factors are: the type of building, total area of the premises, the liveliness of the street, street line, floor location, separate entrance and (or) allocated Parking space, condition of the premises.
Because these factors are the quality characteristics (in addition to the total area), each of them has a significance coefficient. If selected weights do not provide the significance of the regression equation, the coefficients are subject to revision. Table 1 indicates the adopted significance coefficients in terms of pricing factors.
Table 1. Significance coefficients in terms of pricing factors
Pricing factors Characteristic factor Coefficient significance
Building type Administrative 2
Residential 1
Busy street Main 2
Auxiliary 1
house Line First 2
Second 1
Floor location First 2
Resist or plinth 1
Separate entrance Several 3
Yes 2
No 1
Allocated parking No 1
Yes 2
Rooms condition Euro repair or after repair 3
Working 2
Without finishing or repair is required 1
Step 2. The research of analogues is performed according to the proposals of sales of commercial premises located in the Central administrative district of Moscow in electronic databases. All chosen objects-analogues are located in
residential buildings on the first line and do not have an allocated Parking space. Since these pricing factors for all object-analogues and the object of evaluation is identical, they are excluded from the model. Characteristics of objects-analogues and Subject Property are shown in Fig. 1.
Figure 1. Characteristics of objects-analogues
J AB C O E f 0 H 1 Tab!« • Clwctf l>tk«ol o»|«cH-—iatof\i«t_
Analogues Oflet jmce Ofet prie« fo» 1 «1 m Tout area, hj 111 Busy itree! Flora Sejmrale entrance Condition
Objecl I 70 670 000 294 458 240.0 main 1 several operating
Object 2 76 560 000 218 743 350.0 mam {round yea operating
Objecl 3 17 665 000 284 919 62.0 aux 1 DO require repairmen!
Object 1 32 390 000 372 299 87.0 aux around ves euio repaij
Objecl 5 28 860 000 430 "46 67.0 aux 1 several require repairmen!
Objecl 6 47 850000 330000 145.0 maui 1 several operating
Objecl" 26 795 000 243 591 110,0 mam 1 several operating
Objcct 8 68 265 000 371005 184.0 aux 1 several operating
Objects 57 420 000 110 423 520,0 mam 1 no require rqwirment
Object 10 125 880 000 279 733 450.0 aux around yes operating
Object 11 20 900 000 307 $33 68.0 mam 1 vet operating
Objecl 12 13 000 000 325 000 40.0 mam 1 ye« after repairmen!
Objecl 13 l-OOOOOO 220 7*9 77,0 mam 1 no ■equire repamuent
Obiect 14 24 OOO 000 369 231 65.0 mam 1 yes after repairmen!
Object 15 85 860 000 353 333 243.0 main 1 ves after repairmen!
Object 16 33 000 000 289 474 114,0 mam 1 several require repairmen!
Objcct 17 244 395 000 226 082 1 081.0 main 1 several after repairmen!
Object 18 19 885 000 375 189 53.0 mam 1 several operating
Objcct 19 43 750 000 397 727 110.0 aux. 1 yes operating
Object 20 17 500 000 236 486 74.0 mam ground several operating
Subject Profwrtv 212.0 mala 1 yes operating
Source: Student's calculations
Step 3. The unknown function f(x) in the vicinity of the point corresponding to the average levels of each factor can be represented by a segment of the power series. Because the intervals of variation of factors is small, we can use linear approximation in the form of polynomial model. The multiple linear regression equation is described by the formula:
y — value of the resulting sign, obtained by substitution of the corresponding values of factor variables in a regression equation; x1, x2, ..., xn — factorial indicators; a1, a2, ..., an — model parameters (model coefficients);
Step 4. In table 1 the composition of the main pricing factors is given, and the values of the coefficients significance, estimating qualitative characteristics of analogues. If the object - analogue is superior to the Subject property on any parameter, it is assigned a greater weighting and Vice versa. On the basis of the qualitative evaluation of the object and objects- analogues, a table given below shows a summary of characteristics of analogues, expressed by the quantitative values of the coefficients of importance (Fig. 2)
Figure 2. Scoring characteristics of object-analogues.
1 Table won» £ fkinrtfrtitlti o( ob|«rlmalognri
2 Aualopies Offer price Ofct price for 1 sq til, with discount rate at 1?". Total area, sq m. Busv street Floor Separate entrance Coodmon
} Object 1 294 458 250 289 240.0 2
4 Object 2 218 743 185 932 350,0 2
5 Object J 284 919 242 181 62,0 1
6 Object 4 372 299 316454 87.0 1
7 Object? 430 746 366 134 67,0 1
» Object 6 330 000 280 500 145.0 2
9 Object 7 243 591 207 052 I 110,0 2
10 Object 8 371 005 315 354 I 184.0 1
11 Object 9 110 423 93 860 I 520.0 2
12 Object 10 279 733 237 773 450.0 I
13 Object 11 307 533 261 403 6S.0 2
14 Object 12 325 000 276 250 40.0 2
15 Object 13 220 779 187 662 77.0 2
16 Object 14 369 231 313 846 65.0
17 Object 15 353 333 300 333 243,0
18 Object 16 289 474 246053 114,0
1» Object 1T 226 082 192 170 1 081.0
20 Object 18 375 189 318911 53,0
21 Object 19 397 727 338 068 110.0 1
12 Object 20 236 486 201 013 74,0 -y
23 Subject Proper« 212.0 2 j
24
2b Talik rtfre«sk>* statistics
26 43950 2-615 32301.03-51 5~T36-3866T 83565 9-395 100.91429 155584 8513
27 11380 76666 10259 65943 1925992609 16627.25)52 30 56202374 50122,74377
2« 0.823722452 32202-92564 =KJ eHJ *H 1
29 13,08404213 14 ««a «HJ "HI
30 «7842617648 14518397873 »HJ •HJ "HO, "HJ
Source: Student's calculations
The asking prices are used in the calculations, not sales data, i.e., price at which retail premises were offered in the market. Information collected for calculations on not yet completed transactions, then the bid prices used discount at negotiable rate of 15%.
The dependent variable in this case is the value of the market value of 1 sq. m. of analogues. Independent data are quality characteristics.
Step 5. To build a multiple linear regression you should use the built-in function LINEST. As a result, the function fills the block of cells A26:F30 (Fig. 2). In reference to the function of the sense of its application and interpretation of the obtained results can be explained quite well. However, it was decided to show in table 2 in what order additional regression statistics returns.
Table 2. The procedure for the return of the additional regression statistics
a5 a4 a3 a2 a1 a0
se5 se4 se3 se2 sel se0
R2 sev — — — —
F df — — — —
sspee. ssocm. — — — —
a0, a1, ...,a5 are the coefficients corresponding to each independent variable.
se0, sel, ... ,se5 standard error values for the coefficients
R2 - determination coefficient;
F - observed value of the coefficient Fischer;
df - degrees of freedom;
sspez. regression sum of squares;
ssocm.. - the residual sum of squares
The function syntax: LINEST (known_y's., [known_x's], the [const], [stats]). Option the "known_y's" is a required argument that represents a range of cells with values of the dependent variable. The parameter "known_x's" is an optional argument that reflects the values of the independent variable. Parameters intercept and "statistics" are also optional. If the parameter intercept is omitted or set to TRUE (as in the example), then the regression is calculated in the usual way. If this parameter is set to zero, then cut regression force is set to zero. If for parameter "stats" TRUE is set (as in the example), then additional regression statistics should be calculated. Otherwise, only the intercept and the angular coefficient (slope).
Formula LINEST is entered as an array formula, therefore, its application should highlight the area of cells. In our case A26:F30 (Fig. 2). Choice of the cell's size shall be guided by the fact that the number of rows for this function is 5, and the number of columns is equal to xn+ 1. You must then enter the formula itself the function =LINEST(C3:C22;D3:H22;;TRUE)) and press the key combination <Ctrl+Shift+Enter>.
Step 6. The basic criterion describing the adequacy of the regression model is the coefficient of determination — R2.
The value of this index indicates the percentage of variance is known to market data is explained with the help of regression. The value of the determination coefficient close to 1.0 indicates that the model explains almost all variability of relevant variables.
In the practical task assessment of the quality of the model in terms R2 is considered to be very high, if the values reach values of 0.9 and above, and sufficient when values of 0.7 and above.
In accordance with calculations in Fig. 2, the connection between the prices of supply of similar projects, and basic pricing factors satisfies the criterion of sufficiency. According to the scale of Chedoca the obtained value of coefficient of determination equal to 0.82 in (cell A28, Fig. 2) indicates a strong direct relationship.
To determine whether the result R2 is random, the F-statistics (Fischer ratio) should be performed. Supposing that in fact there is no relationship between the variables, and was just selected rare counterparts, for which the statistical analysis brought a strong interdependence. The Fisher ratio is used to indicate the probability of the erroneous conclusion that there strong interdependence. If F-observed is greater than F - critical, then the relationship between the variables exists. F-critical can be obtained from table F-critical values in any reference book
on mathematical statistics.
The observed value of the coefficient Fischer, is equal of 13.08 (cell A29 Fig. 2) more than critical, which value is 4.46 at a significance level of 0.95. Consequently, the resulting regression equation is useful for calculating the estimated value of commercial premises.
Step 7. Getting coefficients of regression dependence, the value of the cost of 1 sq. m area Y for the Subject property (cell B3) can be calculated by substituting in the formula multiple linear regression the values of x1, x2,..., xn, corresponding to the characteristics of the evaluated premises specified in the table in Fig. 2. The calculation of the market value of the Subject property is shown in Fig. 3.
Table 3. Calculation of Subject Property market Value
Indicator Value
Market value of the Subject property, rub for 1 sq. m 235 034
Total area of the Subject Property, sq. m 212,0
Market value of the Subject property, rub 49 827 309
Market value of the Subject property roundly, rub 49 830 000
Source: Student's calculations
Based on the analysis and calculations, the value of the Subject property can be reasonably estimated at (rounded): RUB 49,830,000.
References:
1. Tregub I. V. Evaluating the effectiveness of social investment with the use of correlation and regression analysis // Management Sciences. 2014. № 4. p. 62-66.
2. Sternik. Development of real estate valuation comparative approach based on the methodology of the discrete space-parametric analysis of the market, and modeling / Sternik // Audit and financial analysis. - 2009. - № 5. - p. 130-137.
3. Siwiec, Construction and practical application of multi-hybrid model of valuation of commerical real estate / Siwiec // Questions of evaluation. - 2011. -№ 4. - pages 27-36.
4. On the requirements for the number of comparable facilities in the evaluation of real estate comparative approach / I. Anisimova // Questions of evaluation. -2013. - № 1. - pages 2-7.
5. Gribovsky, Barinov, Anisimova. On improving the reliability of the evaluation of the market value using comparative analysis // Problems of valuation. 2012 1191.
