Quality Point: A Contemporary Quality Point: A Contemporary Approach to Sales ComparisonApproach to Sales Comparison
Presented to the Fine Appraisers of Eastern Ontario on Behalf of the
Ontario Association – Appraisal Instituteof Canada
by Charlie Abromaitis & George Canning
October 24-25, 2003Peterborough, Ontario
Presentation GoalsPresentation Goals
Outline the current state of practice of the Sales Comparison Approach; is it broken, and if yes how do we fix it?
Discuss the movement to a qualitative analysis, outline the current state of practice, and show why it stops short of its potential.
Present Quality Point as a logical and workable extension of qualitative analysis.
Building ValuationBuilding ValuationModels ...Models ...
What is a Model?What is a Model?
a representation that
captures the essence
of reality.
often a mathematical
expression.
often describes
relationships between
variables
What Did He Mean?What Did He Mean?
“All models are false, some are useful”
George E. P. Box
Direct Comparison ModelsDirect Comparison Modelsas Currently Practicedas Currently Practiced
Two basic approaches - grid estimator and multiple regression analysis (MRA). Both models are based on hedonic theory
Use of approaches polarized - MRA widely employed in assessment appraisal and grid estimator institutionalized in private industry sector
Institutionalized (traditional) Institutionalized (traditional) Direct Comparison Approach Direct Comparison Approach
• Described in Appraisal Literature as far back as the 1930’s
• This approach has had very little modification over the last 70 years
• Essence of approach: differences between the comparables and the subject are made equal through an adjustment grid
Traditional Grid SalesTraditional Grid SalesAdjustment Process - Set TheoryAdjustment Process - Set Theory
The sale price adjustment is an effort to remove the price variation that exists between the comparables and the subject so that they can all become members of the same set. They are adjusted to equality except for random error
Selecting Comparable SalesSelecting Comparable Sales
would the buyer of the comp property have seen the property to be valued as a substitute?
pick sales of properties with the least differences to subject;
seek some comps better and some worse than subject (bracketing).
In an Ideal World, Good Comps In an Ideal World, Good Comps are Restricted to:are Restricted to:
same use, same vicinity, same price band;
similar size;
recent transactions;
and probably many other shared features and conditions of sale.
How Many Comparable Sales?How Many Comparable Sales?
enough to have confidence in predicting value of subject;
a few close comparables are better than lots of dubious ones;
in practice, “3 or 4 good ones” that point to the same value often suffice;
failing this, the search is broadened.
Grid Estimator- Plug inGrid Estimator- Plug inand Playand Play
For each comp, place a value on each difference between comp and subject.
Adjustments Cannot beAdjustments Cannot beDirectly ObservedDirectly Observed
How to find adjustments for the comps is one of the most important issues in the valuation theory of the sales comparison approach
Where Do We Get theWhere Do We Get the Plug In Attribute Prices? Plug In Attribute Prices?
Four Methods to obtain non-observable and, therefore, implied values:
Matched Pairs– find 2 similar comps and
isolate value of a specific item
Cost– depreciated value of items
Survey Regression
The Dichotomy Between The Dichotomy Between Theory and PracticeTheory and Practice
Many appraisals, particularly non-residential, are made in data poor environments. Pulling back the curtain we find:
•lack of attribute pricing data leads to ad hoc implementation of grid method
•ad hoc methods include: all in the head analysis, statement of sales used, written ranking descriptions, qualitative ranking grids, and WAG
“Pay no attention to the man behind the curtain…”
Two Casual Approaches to Two Casual Approaches to AdjustmentsAdjustments
1. The “all in the head” adjustment process (favoured by old-timers).
2. (Mentally) ranking and bracketing the sales prices of comps -
place subject within a sequence of prices of comps
estimate how close subject lies to the comp ranked immediately above and below.
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Example of bracketing
Example – Ranking and Example – Ranking and BracketingBracketing
S1 $140,000 for a 3 bed, 1 bathroom house
S2 $170,000 for a 4 bed, 2 bathroom house
S3 $150,000 for a 4 bed, 1 bathroom house
Subject has 3 beds, 2 bathrooms.
Can you rank Subject?
Model Validation - Checking the Model Validation - Checking the Adjusted PricesAdjusted Prices
1. For consistency– range of adjusted prices
2. For reliability of each comparable sale– minimum value of gross adjustments– minimum number of adjustments– think back to reliability of data
collected.
Re-interpret sales? Find more sales?
Review – Did the Adjustment Review – Did the Adjustment Process Work?Process Work?
Not if the adjusted prices varied by much;
Otherwise, are you confident of the likely selling price?
What’s Wrong with the Ad Hoc What’s Wrong with the Ad Hoc Approach to Adjustments?Approach to Adjustments?
Non-consistent or explicit, therefore, non-reproducible
No testing if correct variables selected or adjustments valid
Not defendable under close scrutiny of courts, reviews
Current State of PracticeCurrent State of Practice
Bipolarized between heavy reliance on WAG method and sparse use of sophisticated models that merge expert intuition with statistical data analysis and techniques from decision science.
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Output from Taurean AVM showing traditional grid approach with attribute pricing supplied by regression analysis.
Letting Go of Old Battle Scarred Letting Go of Old Battle Scarred Adjustment TechniquesAdjustment Techniques
A valuer knows in advance that often the number of sales will be small, the property characteristics will have considerable variance, and the commonly taught methods to equalize the data will not be practically applicable.
Plausible Solutions Would …Plausible Solutions Would …
recognize the competitive business environment that appraisers work in;
at the very least use the market pricing information within the comps employed
allow expert intuition, but recognize that a more analytic rather than intuitive approach to data processing will improve forecasting;
provide some measure of appraisal accuracy in the approach.
Rethinking Comparability …Rethinking Comparability …
Qualitative Comparison: Beyond Traditional Market
Comparison Methods
The Principal of SubstitutionThe Principal of Substitution
A cornerstone of established valuation theory, this principal states a property’s value tends to be set at the cost of acquiring a substitute property with equally desirable utility, assuming that no costly delay is encountered in making the substitution.
What Does Observation of What Does Observation of Transacting Individuals Tell Us?Transacting Individuals Tell Us?
Qualitative comparisons, NOT plus and minus percentage or dollar quantitative adjustments, most reliably replicate the decision making behavior of the majority of real estate market participants.
Qualitative DescriptionsQualitative Descriptions
buyers have personal values they attach to combinations of attributes
by process of evaluation and elimination, buyers match attributes between alternative properties to decide which property provides the most satisfaction relative to cost
application of qualitative comparison requires an inventory and description of the utility attributes of both comps and subject
Principle of Rank SubstitutionPrinciple of Rank Substitution
Donald Wilson refines the Principle of Substitution with the logic of the Principle of Rank Substitution:
“Buyers and sellers do not generally deconstruct the value of alternative properties into price-per-unit attribute adjustments, either systematically or intuitively. They grade and measure the substitute properties on ordinal and cardinal tradeoffs between price and aggregate property attributes … they always grade, measure, compare, rank, and choose among several of the most fitting ones”
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Paper by Donald C. Wilson, The Principle of Rank Substitution, The Appraisal Journal, January 1997.
Traditional Attribute Traditional Attribute DescriptionsDescriptions
appraisers using a qualitative
approach often describe a property’s
relative attributes in words or with
symbols.
quality word descriptors like superior,
inferior, much better, similar or
symbols like ++, -, > are nominal
measurements; they are not
conducive to further analysis.
Qualitative Description by RecodingQualitative Description by Recoding
A statistical thinking approach
suggests nominal data should be
recoded as ordinal data to allow
further quantitative analysis.
Quantitative analysis generally
builds on and works with rigorous
qualitative analysis.
Analysts have to make counts, take
measurements, sort into classes,
and assign ratings.
Value = Utility PremiseValue = Utility Premise
Appraisers infer that transaction price equals utility and that transaction price may be substituted for the value of subject properties with equal utility
The Quality Rating-Price The Quality Rating-Price Comparison ApproachComparison Approach
around for over 30 years in various guises
has received scrutiny from courts and tribunals
taught in land economics courses
described in the appraisal literature
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Bibliography of appraisal literature dealing with traditional sales comparison with the grid estimator and alternative approaches
Why Quality Rating-Price Why Quality Rating-Price Comparison is not MainstreamComparison is not Mainstream
inertia to change in appraisal societies and court and tribunal decisions that tend to enforce traditional methods;
general lack of commitment to lifelong learning on part of busy practitioners due to pressures of commercial practice;
communication barriers hinder crossover of ideas between academics and practitioners.
when everything is going fine and you’re getting your piece of the pie – why risk change?
Quality Point: An Overview ...Quality Point: An Overview ...
A Quality Rating-Price Comparison ApproachQPQP
What is Quality Point (QP)What is Quality Point (QP) A 2nd generation quality rating/price
comparison model that compares overall utility scores of comps and their sale prices.
A utility score is a composite variable that numerically summarizes as a crisp number the aggregate qualitative attributes of a comp inventoried by the appraiser using a systematic rating process.
relationships between overall utility scores and sale prices can be expressed as a linear function where value = utility. Existing sales directly compared to appraised property supply the needed market pricing information.
Genesis of QPGenesis of QP
This seminar outlines one implementation of the quality rating-price comparison approach called QP that borrows heavily from the work of Richard Ratcliff, James Graaskamp, Gene Dilmore, Halbert Smith, Terry Grissom and Michael Robbins.
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Paper by Gene Dilmore that outlines history of QP and his implementation using a software program written in Basic.
Advantages of QP OverAdvantages of QP OverTraditional Grid - Part 1Traditional Grid - Part 1
eliminates need for “guesstimating” adjustments – a rampant practice, particularly in data starved environments. No need for outside pricing of differences between sales and subject. All information needed to fit QP model extracted from sales as rated by appraiser.
makes comparison analysis explicit, reproducible, and professional.
simple to use for market knowledgeable appraisers.
Advantages of QP OverAdvantages of QP OverTraditional Grid - Part 2Traditional Grid - Part 2
forces appraiser to pay attention to sale details.
QP model validates itself by checking accuracy through prediction of the prices of the comparable sales and their comparison with actual prices.
efficient in valuing multiple properties of like kind. Once a valid model is built, it can be used over and over by the rating of only the subject properties.
approach is general and broadly applicable to many types of properties
Computational AssistanceComputational Assistance
Several software programs have been written to assist appraisers with the computations needed for QP. However, a commercial spreadsheet program provides the linear programming routines needed to fit the weights and can easily implement the necessary simple linear algebra calculations
Making QP Productive: Making QP Productive: Harnessing the SpreadsheetHarnessing the Spreadsheet
QUALITY POINT RATING ANALYSIS GRID
Property/Sale DetailsSale No. 1 2 3 4 5 6Date 12/94 1/93 1/94 4/93 12/92 ListingMunicipality Baden New Hamburg Ingersoll Ailsa Craig Cambridge PetroliaSite Size (Acres) 7.500 26.420 7.614 7.990 10.400 6.500
Sale Price $220,929 $950,000 $275,000 $350,000 $598,000 $230,000Sale Price/Acre(SPACRE) $29,457 $35,958 $36,118 $43,805 $57,500 $35,385
Quantitative AdjustmentsProperty Rights Conveyed 1.00 1.00 1.00 1.00 1.00 1.00Financing Terms 1.00 1.00 1.00 1.00 0.90 1.00Motivation 1.00 1.00 1.15 1.00 1.00 0.90Market Conditions 0.95 0.80 0.90 0.85 0.80 1.00Baseline Adjusted Price/Acre Site(BADJSP) $27,984 $28,766 $37,382 $37,234 $41,400 $31,846Site Size 1.00 1.00 1.00 1.00 1.00 1.00Size Adjusted Price/Acre Site(SADJSP) $27,984 $28,766 $37,382 $37,234 $41,400 $31,846
Quality Point Ratings WEIGHTS
Potential Density 0.28 3 1 3 3 1 3Planning Status 0.06 3 3 3 5 3 3Services Availability 0.42 1 3 5 5 5 5Location 0.24 5 5 1 1 5 1
1.00
Composite Quality Index (CQI) 2.63 2.91 3.37 3.49 3.76 3.37Quality Adjusted Price/Point/Acre(QADJSP) $10,642 $9,879 $11,091 $10,663 $11,024 $9,449Quality Adjustment Factor 1.28 1.16 1.00 0.97 0.90 1.00Total Adjusted Price/Acre(TADJSP) $35,867 $33,296 $37,382 $35,937 $37,154 $31,846
Model ValidationPredicted Unit Price 27500 30452 35247 36519 39275 35247Actual Unit Price (After Adjustment to Baseline) 27984 28766 37382 37234 41400 31846Residual (484) 1,686 (2,135) (715) (2,125) 3,401Residual as % of Actual Unit Price -1.73% 5.86% -5.71% -1.92% -5.13% 10.68%
QP adapts well to the matrix grid of a good spreadsheet program and its built-in linear programming tools like Excel’s Solver
Steps in QP Technique:Steps in QP Technique:
1. Select comparable sales.
2. Choose appropriate unit of comparison.
3. Adjust sale prices to a common baseline using traditional quantitative methods.
4. Choose value influencing qualitative attributes.
5. Outline the range of utility displayed by comps and subject in the attributes and score on ordinal scale.
6. Find variance minimizing attribute weights using optimizing program (Solver in Excel).
Trad
itional
New
Steps in QP Technique – Cont’d:Steps in QP Technique – Cont’d:
7. If required (reduces variance further), apply size adjustment based on fitting power curve.
8. Evaluate model by using it’s derived mean price/utility function to predict the baseline adjusted prices of the sales. Compare predicted prices with actual comp prices.
9. If model predicts prices of comps within acceptable range of error, score the subject’s utility consistent with the sales.
10. Use the mean price/utility function or regression coefficient to predict price of subject.
New
Circular AnalysisCircular Analysis
part of QP process is a circular analysis
includes checking remaining variation in price not explained by model and error shown by residual price analysis.
feedback of model error guides selection of retained comparables, accuracy of attribute choices and appraiser’s rating judgement.
Quality Point: The Details ...Quality Point: The Details ...
A Quality Rating-Price Comparison ApproachQPQP
Quantitative Property Quantitative Property Characteristics Characteristics
Based on interval data that can be measured and compared in a precise manner.
Sales should be adjusted to a common base prior to the other adjustments
Property Rights Financing Motivation Market Conditions
Multi-attribute Utility AnalysisMulti-attribute Utility Analysis
4 step process for mapping comp and subject utility:
1. determining value influencing attributes for property type appraised
2. mapping utility by defining categories of quality for attributes and assigning ordinal scale
3. rating of comp attributes using defined ordinal scale
4. optimal fitting of rated comp attributes to sale prices through attribute weighting
Qualitative Property Attributes Qualitative Property Attributes
Qualitative property characteristics consists of data that are based on subjective measures, whereby the data tend to fall into nominal or ordinal categories.
They need to be systematically ranked or treated.
Location
Building Quality
Income
Condition etc.
Coding reduces a description to a more manageable size through the use of letters, numbers, or symbols.
In QP applications, descriptions of relevant property characteristics are ultimately reduced to numerical values so that mathematical calculations may be performed.
Mapping UtilityMapping Utility
Mapping Utility with Operational Mapping Utility with Operational Definitions Definitions
Use operational definitions when rating - avoid crude descriptors i.e. good location ranked 5 is near an interchange with the expressway.
Operational definition says good location ranked 5 is no more than 1 block from an interchange with the expressway.
An analogy: the operational definition of a food dish is its recipe and not a description of its smell, color, texture, etc.
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Samples of coding with operational definitions for varied property types.
Qualitative NOT quantitative property characteristics are ranked in a very simple order for easy referencing.
An ordinal scale is the best ranking procedure for this.
1=below average or fair 3=average 5=above average
Ranking Property CharacteristicsRanking Property Characteristics
The ordinal scale point system needs to be able to portray real differences understood by buyers and sellers.
Large scaling systems tend to be more difficult to manage.
Variable or Property Characteristics tend to be either/or with little or no gray areas.
Why is a Simple Scale the Best?Why is a Simple Scale the Best?
Can Nominal Scales Change?Can Nominal Scales Change?
The 1-3-5 ordinal scale is not written in stone.
The scale 1-3-5-7 is another scale
The squaring of these scales may be useful in explaining non-linear variance in selling price.
1-9-25 or 1-9-25-49.
These exponential scales will be dealt with in the seminar.
Ockham’s Razor
It’s a Subjective Process – So It’s a Subjective Process – So What?What?
True objectivity in data analysis is unattainable
The appraiser is not a neutral passive reader of the market
Any appraiser brings a set of prior knowledge, experience, capacities, and intentions to each valuation that is unlikely to be the same as the set of another appraiser
Both quantitative and qualitative analyses are interpretive – making meaning from data
Fitting a QP Model to SalesFitting a QP Model to Sales
attribute weights are the optimum combination of weights. Optimum is the least remaining model explained variation in comp prices decided by iterative (trial & error) routine.
goal is to derive overall composite utility scores for comps that result in function coefficients between the composite scores and sale prices.
Weighting: The Old ApproachWeighting: The Old Approach
weights are assigned to attributes to reflect their relative importance in explaining the variance in comp prices
to determine appropriate weights, various sets of weights for the attributes are tried, with the resulting coefficient of variation (COV) noted.
by trial and error the analyst may determine the weights that will minimize the COV.
this approach does not guarantee that one obtained the optimal (i.e., the best) because the possibilities are enormous to try all.
Weighting: An Automated Weighting: An Automated Contemporary ApproachContemporary Approach
obtaining weights for attributes is a linear programming optimization problem.
a computerized software approach is needed to replace a tedious and lengthy manual approach that requires an iterative process of best guesses.
For QP, the "best" or optimal solution means the weights that minimize the variation in the sale prices per quality point per unit.
Excel’s Solver Add-inExcel’s Solver Add-in
one of many computerized software approaches to finding optimum solutions for problems like the QP weighting problem.
provides optimal solution in step-by-step approaches called optimization solution algorithms.
algorithm is a series of steps that will accomplish a certain task.
aim of process is to find optimal solution values for variables that minimize or maximize the objective function while satisfying the constraints.
Using Solver in QPUsing Solver in QP
In QP, Solver will find weight values for the property attributes that satisfy the all weights = 100% constraint while minimizing the objective.
The objective is some function that depends on the attributes.
The objective in QP is the coefficient of variation (COV) of the distribution of the prices per point per unit, a function we use to measure the remaining variation in sale prices.
The QP COV is a ratio of the standard error of the sale prices per point per unit, our measure of spread, and the mean, our measure of centre.
Weighting ConstraintsWeighting Constraints
constraints play a key role in determining what weights can be assumed by the decision variables, and what sort of objective value can be attained.
a key general constraint in QP is that the percentages allocated to the attributes must sum up to 100%.
a heuristic constraint of a minimum weight (say 5%) insures that each attribute plays some part in the determination of the model.
we can constrain the chosen attributes to be greater than or equal to some small positive quantity to avoid any attribute being totally ignored in minimizing variation in sale price.
The Additive Weighting Process The Additive Weighting Process (Sale No. 1):(Sale No. 1):
Attribute Attribute Weight
Rating Weighted Rating
Location 0.59 3 = 1.77 Access/Visibility 0.05 7 = 0.35 Physical 0.05 3 = 0.15 Use Restraints 0.05 7 = 0.35 Site Preparation 0.26 1 = 0.26 Composite Quality Score
1.00
2.88
Using the QP Model to AppraiseUsing the QP Model to Appraise
In this implementation of QP, the rating and valuation of the subject property is conducted last, separately from fitting and weighting the comps.
SUBJECT RATING AND VALUATIONAttributes WEIGHTS RATING Model Summary & Subject ValuationPotential Density 0.28 3 Mean 10457.94Planning Status 0.06 3 Standard Error 267.74Services Availability 0.42 5 Remaining Price Variation 2.56%Location 0.24 1 Site Area (Acres) 6.500
PER UNITComposite Quality Index 1.00 3.37 Point Estimate of Value $229,000 35,247Size Adjustment Function (1=None) 1 Value Range $223,000 to 34,345
$235,000 36,150
Size – A Special CaseSize – A Special Case
Lack of good comps often leads to use of sales data with wide disparities in size
Adjusting for size difficult because relationship between size and price is often non-linear – principal of marginal utility
Size adjustments can be derived by fitting curves to find the “pattern”
QP calculates size adjustments (if required) using power curves
Theory suggests size adjustments to be applied last, after all other explanations of price variation exhausted
Curve Fitting for Size Curve Fitting for Size AdjustmentAdjustment
90% Curve
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QP Derived FunctionQP Derived Function
a function is a variable so related to another that for each value assumed by one there is a value determined for the other.
Eg. apartment buildings are selling for 8 times gross income is a function.
QP function extracted from information within the sales combined with analyst’s heuristic intuition; outside pricing information not needed.
QP derived function can be applied to value a subject property.
The Quality-Price FunctionThe Quality-Price Function
If we measure the aggregate utility of a comp as a number and relate this number to its sale price, we can derive a function that can be used to predict the price of a property.
One approach is to express a comps price as dollars per point of utility score per comparison unit by dividing the price per unit by the total weighted score.
Another route is to perform a simple regression analysis of price per unit against the weighted scores.
The Function: PriceThe Function: Priceper Point per Unitper Point per Unit
total score for each sale - a weighted average composite index of a property’s utility.
collective scores divided into the sale prices of comps is valuation model
average price per point per unit of sales is coefficient or function that convert the subject’s composite utility score into a price forecast.
small variation in score/price coefficients means much of price variation within sales explained by the composite utility scores
QP Function by Linear QP Function by Linear RegressionRegression
QP function is the relationship between a comp’s composite utility score and its price. In a perfect world relationship between composite utility scores and unit prices of set of sales may look like
this:
8.00
10.00
12.00
14.00
16.00
18.00
20.00
22.00
3.0 4.0 5.0 6.0 7.0 8.0
Composite Utility Score
Sal
e P
rice
Per
Un
it
Valuing With Regression Valuing With Regression FunctionFunction
8.00
10.00
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20.00
22.00
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Composite Utility Score
Sal
e P
rice
Per
Un
it
•graphed function is 2.5 or the 8 sales are selling for $2.50 per quality point per unit.
•say subject has rated composite utility score of 6.4.
•predicted sale price is 2.5 6.4 = $16.00 per unit.
Model ValidationModel Validation
Validation is the process of comparing the model's output with the behavior of the phenomenon.
Confirmation of the model's behavior is essential. How else can one determine if a useful model has been built.
Same function from model used to predict subject price is used to predict prices of comps.
Residual AnalysisResidual Analysis
Price predicted for comp compared to sale price (after quantitative adjustment to baseline)
Difference between predicted price and actual sale price is residual or error
Model that predicts sales with little error is considered a useful model
Model Summary: Case Study #1Model Summary: Case Study #1
QP Model Building Stage
Average Remaining
Price Variation %
Change %
Unadjusted Sales 45
After Quantitative Adjustments to Baseline
35 -22
After Qualitative Rating (equal weights) 22 -37
After Attribute Weighting 10 -54
After Quantitative Size Adjustment 3 -70
Between Unadjusted and Final -93
Model Summary: Case Study #2Model Summary: Case Study #2
QP Model Building Stage
Average Remaining
Price Variation %
Change %
Unadjusted Sales 45
After Quantitative Adjustments to Baseline
35 -22
After Qualitative Rating (equal weights) 22 -37
After Attribute Weighting 10 -54
After Quantitative Size Adjustment 3 -70
Between Unadjusted and Final -93
QP Pitfalls and InefficienciesQP Pitfalls and Inefficiencies
Avoid intricate models (Occam’s Razor).
Avoid Black Box view – partly computerized so it must be right.
Residual validation test is not omnipotent – predicting inside model always performs better than predicting outside the model.
Weights for attributes are reflective of the sales and their common interactions and not necessarily the market in general.
Wrap-up & HousekeepingWrap-up & Housekeeping
Future hands-on seminar on using QP
Seminar evaluation form
Recertification credits document
Keeping in touch
www.valuationscience.comHANDOUT REFERRAL ...
Bibliography for further reading on the state of practice of sales comparison, QP, and size adjustments.
