Real Estate Appraisal and Bid Price: An Empirical
Evaluation of Alternative Theories
Carl R. Gwin
Baylor University
Seow-Eng Ong
National University of
Singapore
Andrew C. Spieler
Hofstra University
April 2005
Abstract
Mortgage appraisals are often required before a loan is approved. When
information on the transaction price is available and when mortgagees
(lenders) compensate appraisers for mortgage appraisals, a principal-agent
problem may arise. The effect is that appraisers tend to overstate the true
value of a property because they have an incentive to set the appraised value
to be equal to the transaction price. An earlier paper by Gwin, et al (2000)
examines this principal-agent problem. This paper offers an alternative theory
that provides a different prediction. The alternative theory is predicated on
the updating appraisal process ala Quan and Quigley (1991), and a signaling
modification to Gwin, et al. (2000). In addition, an empirical test to the
theoretical moral hazard model postulated by Gwin, et al. (2000) and the
alternative theory is carried out using appraisal and transaction data from a
lending institution in Singapore.
For presentation at the American Real Estate Society Conference
Santa Fe 2005
Real Estate Appraisal and Bid Price: An Empirical
Evaluation of Alternative Theories
Introduction
Daly (2001) finds that the main priority of valuers in UK, Ireland and
Australia is to confirm the bid price. As one anonymous valuer puts it, “The
mortgagee valuation is a confirmation of bid price.”
Do appraisers acting on behalf of mortgagees exercise independent judgement
in ascertaining the appraised value, or are they influenced by the mortgagees? This
question is relevant since mortgagees require appraisals before mortgages are
approved. The purpose of mortgage appraisal is to ensure the value of the real estate
meets or exceeds a minimum loan to value ratio. The appraiser knows this and a
moral hazard problem can arise if the mortgagee rewards the appraiser with future
business for successful appraisals, i.e., those that result in a loan being made.
This principal-agent problem has been highlighted in Lentz and Wang (1998).
If a representative of the mortgagee is compensated based on loans generated, then the
mortgagee may put pressure on an appraiser to value the real estate at the price agreed
upon by the seller and buyer. On the other hand, a mortgagee concerned about the
number of defaults may be more likely to pressure an appraiser to undervalue real
estate. Smolen and Hambleton (1997) find in a survey that nearly 80% of appraisers
had been pressured by lenders to alter their appraisals. Smolen and Hambleton argue
for regulations to protect appraisers from zealous lenders. Worzala, Lenk, and
Kinnard (1998) find in a survey of appraisers that most of the respondents had
experienced mortgagee pressure to overestimate real estate value. However, they find
no evidence that lender size, the value of the change to the appraisal, or both have any
influence on appraisers.
2
Bid or transaction prices are the product of negotiation between sellers, real
estate brokers, and buyers who may have interests inconsistent with those of a
mortgagee. For example, home buyers/mortgagors have a strong incentive to see
appraisals at their maximum value in order to qualify for as large a loan as possible
and as independent verification of a fair price. Sellers and brokers would happily
accept high appraisals to close the sale and avoid the costs of further marketing the
property. These incentives contribute to the possibility that bid price can be
significantly greater than true value. Unfortunately, a mortgagee may face losses if the
mortgagor defaults on the mortgage and there is insufficient collateral to recover the
face value of the loan. Consequently, mortgagees rely on independent appraisers to
verify the true value of the real estate, but can they?
Gwin, el al. (2000) examine an appraiser’s incentives in conducting an
appraisal. They find that a moral hazard problem can arise if the mortgagee rewards
the appraiser with future business for successful appraisals, i.e., those that result in a
loan being made. An appraiser may be willing to overstate the value of a property if
the lender wants him to do so. This moral hazard problem can lead to real estate
appraisals being equal to bid price.
The model in Gwin, et al. (2000) lends itself to empirical testing in that the
prediction of the incentive to set an appraised value equal to the bid/transaction price
is demarcated under different market conditions. Specifically, the prediction is for a
lower incentive to set an appraised value equal to the bid/transaction price under a
bear market. Under a bear market, the appraiser is more likely to set an appraised
value lower than the bid/transaction price. This paper, in contrast, draws on the Quan
and Quigley (1991) framework and reworks the moral hazard model in Gwin, et al.
(2000) to formulate an alternative theory that predicts an increased incentive to set an
3
appraised value equal to the bid/transaction price under a bear market. In addition,
this paper provides an empirical test of the competing theories by way of a probit
model that examines the effect of a bear market on the likelihood to set an appraised
value equal to the bid/transaction price.
The next section outlines the theoretical models and provides a signaling
modification to the moral hazard model in Gwin, et al. (2000). In the following
section, a testable hypothesis is formulated to evaluate the competing models. The
data from a loan cooperative in Singapore is then used to empirically test the theories
and the results are reported. The empirical findings provide support for an alternative
theory predicated on the Quan and Quigley (1991) appraisal updating framework and
a signaling modification to the Gwin, et al. (2000) moral hazard model.
Theoretical Models
A Moral Hazard Model
The theoretical model postulated by Gwin, et al., (2000) is essentially a moral
hazard model where the appraiser considers the effects of his appraisal on (1) the
likelihood of securing a mortgage for the lender and (2) the probability of future
default. One key assumption is that the appraiser does not know the amount of loan
applied for, but he knows the maximum loan-value ratio that the mortgagee will lend.
It is also assumed that the mortgagor will ruthlessly default if the value of the house
falls below the loan outstanding at some future time. In addition, the lender will
penalize the appraiser if the mortgagor defaults within a reasonably short time period.
The appraiser evaluates the probability of default conditioned on the appraised
value and the state of the real estate market. The appraiser compares the probability of
default if the appraised value (A) is equal to the transaction price (Po) and that if A <
Po. Interestingly, the state of the real estate market, which is indicative of the future
4
price trend, has a significant impact on the appraiser's evaluation. If the trend of
property prices is rising, then the probability of a default by the mortgagor is low. So
the appraiser finds it optimal to choose A = Po. If the market is on a downtrend, then
the appraiser is likely to choose A < Po in order to protect against future loss in
business. See the Appendix for a summary of the model in Gwin, et al. (2000).
The above predictions provide a testable hypothesis - in a bear market, the
probability of appraisal being less than the transaction price is likely to increase and
that the probability of appraisal being equal to the transaction price is likely to
decrease.
An Alternative Model
An alternative hypothesis can be drawn from the framework in Quan and
Quigley (1991). Quan and Quigley (1991) show that the appraised value in period t
(At) is a function of the transaction price in period t (Pt) and the appraised value in
period t-1 (At-1). In other words,
At = KPt + (1 − K ) At −1 ,
(1)
where K is a function of the variances of the transaction price and appraisals.
Although Quan and Quigley (1991) is silent on the formation of the appraised
value under different market conditions, we contend that in a bearish market, the prior
appraised value is not a good indicator of true value. The motivation is as follows:
When the market is bearish, the appraiser knows with a high degree of certainty that
the prior appraised value (in period t-1) is too high. In addition, if the proposed
transaction value Pt is lower than the prior appraised value, At-1, it would be difficult
for the appraiser to attach a positive weight to At-1. In contrast, given that that buyer
5
has agreed to purchase at Pt, the appraiser would attach a higher weight to the agreed
price as being the true market value in a bearish market.
By this reasoning, the appraiser tends to attach a low weight on the appraised
value from the previous period and a higher weight to the agreed transaction price; so
(1 − K ) → 0 when the market is bearish. As such, At = Pt (to maintain consistency
with the previous notation, A = Po ). This tendency does not hold when the market is
stable or bullish. Consequently, the alternative hypothesis is in contrast with that in
Gwin, et al. (2000).
A Signaling Modification
Although at first sight, the alternative model ala Quan and Quigley (1991)
may produce conflicting results from Gwin, et al. (2000), it can be shown that the
model in Gwin, et al. (2000) can be modified to produce a consistent result. The
insight is that the appraised value can be regarded as a signal of value to the buyer. In
particular, we need to consider how a buyer would act when he receives a report
(signal) that the appraised value is less than the intended transaction price when the
market is bearish.
Following the same notation as in Gwin, et al. (2000) (see Appendix), suppose
A < P0 when the market is bearish. Po is the price that the seller and buyer have
negotiated. When the buyers observes A < P0 , his reaction would be that he has
overpaid for the property. In most countries, the appraisal (A) is revealed to the buyer
before the final completion of the purchase. At this point in time, all the buyer has
paid is an option to purchase and he has the right not to proceed with the purchase
(Ong, 1999). Given that the signal that the true value is lower than the contracted
6
price, the buyer has every incentive to break off the purchase, or negotiate for a lower
price.
In either case, the mortgage application is unlikely to proceed, which results in
a loss of business for the mortgagee. As noted in Gwin, et al. (2000), if the appraisal
is less than the price, then the mortgagee rejects the loan application. The appraiser
knows this and consequently, the loss of business for the mortgagee may be severe
enough to offset against a future but uncertain loss should the mortgagor default.
This reasoning would change the original prediction in Gwin, et al. (2000) in
that it would be optimal for the appraiser to choose A = P0 even in a bearish market
environment.
Methodology and Hypotheses Testing
To test the two theoretical models, this paper posits a probit model that defines
the probability of appraisal being equal to transaction price. The dependent binary
variable yi, which can be either 0 (failure) or 1 (success), depends on a vector of
independent variables, denoted as xi. The dependent variable is defined as taking a
value of 1 if the appraisal value equals transaction price. So y1i = 1 if A=Po.
Among the explanatory variables is a dummy variable to indicate a bear
market. Under the first hypothesis ala Gwin, et al. (2000), we expect the coefficient
on the bear market dummy variable to be negative, but under the alternative
hypothesis, we expect the bear market dummy variable coefficient to be positive.
In addition, we define a second dependent variable that takes the value of 1 if
the appraised value is less than the transaction price. So y2i = 1 if A<Po. We expect the
coefficient on the bear market dummy variable in the regression on y2i to be positive
under the hypothesis postulated by Gwin, et al. (2000).
7
A general specification is that the probability of observing 1 for yi is
Pr( y i = 1) = F ( β ' x i ),
(2)
for i=1, 2,..., N and F is an appropriate distribution function.
We shall define two specifications for F, vis-à-vis the probit and logit models
by specifying F=Φ and F=Λ, respectively, where
β 'x
Φ( x) =
∫ (2π )
−1 / 2
−∞
⎛ 1 ⎞
exp⎜ − t 2 ⎟dt ,
⎝ 2 ⎠
(3)
and
Λ ( x) =
exp( β ' x)
.
1 + exp( β ' x)
(4)
It is well accepted that the probit and logit models can be estimated by
maximizing the likelihood function:
N
L = ∏ [F ( β ' x i )] i [1 − F ( β ' x i )]
y
1− yi
.
(5)
i =1
Data
The data for this study comes from the National Trade Union Cooperative
(NTUC) of Singapore, a cooperative association that has been issuing mortgages since
1983. Although mortgage financing comprises a relatively small part of NTUC’s loan
portfolio, NTUC exercises very prudent lending requirements. For example, NTUC
will issue loans only if the loan is no more than 5 times the borrowers’ total annual
income. In comparison, some local banks issue loans much higher than 5 times annual
income. In addition, NTUC tends to exercise more restraint in the setting of its
mortgage rates while other banks tend to be extremely aggressive in lowering rates to
8
gain a competitive edge. Consequently, their loan portfolio consists mainly of
“genuine” homebuyers instead of speculators.
The data from NTUC mortgages comprises the transaction price (Po),
appraised value (A), loan amount (LOAN), term of mortgage (TERM), household
income (HHINC), age of oldest mortgagor (AGE), number of mortgagors (NB) and
the transaction date (PDATE). The data set spans a period from 1983 to April 1999.
Most of the loans are issued over the last 5 years. The real estate market in Singapore
underwent a severe bear spell from 1997 through late 1998 as a consequence of the
Asian economic crisis. A bear market dummy variable (BEAR) is created that takes
the value of 1 if the transaction is originated over this period, 0 otherwise.
Exhibit 1 summarizes the data. A total of 559 residential mortgages were
sampled. This represents almost half of NTUC’s mortgage loan portfolio. 1 The
average age of the oldest owner (AGE) is 38. The average annual household income
(HHINC) is S$99,000, but the range is rather wide. In terms of loan-specific
information, we see that the average loan amount (LOAN) is S$334,000. The loan-tovalue ratio (LV) averages 0.55, with a maximum of 0.88. On average, buyers pay a
1% premium over valuation. The highest premium is 5% over valuation. The mean
loan term (TERM) is 20.8 years; some terms can be as short as 5 years and the
maximum is 30 years. 2 The annual household income-to-property price ratio
(HHINCOV) averages 17.3%.
Of the 559 observations, 469 loans (84%) were made when the property
market is bearish. Of these, the appraisal is equal to the transaction price in 399 loans.
1
Mortgages comprising the other half of the loan portfolio (that is omitted for this
analysis) were issued within less than 6 months of the date of data extraction.
2
A 30-year maximum loan term is the norm in Singapore.
9
The appraisal is higher than the transaction price in 41 cases, and lower than the
transaction price in 119 cases.
Exhibit 2 shows the margin (computed as the difference between the
transaction price and appraised value the normalized by the price) plotted against the
loan-value ratio (LV). The distribution shows that there is a lot of clustering around a
margin of zero. In other words, in a majority of cases, the appraised value is equal or
nearly equal to the transaction price. This result can be viewed as another validation
of the observation that appraisers often set the appraised value close or equal to the
transaction price.
Empirical Results
The distribution of appraised values relative to transaction prices is
summarized in Exhibit 3. The distribution is also computed under bear market
conditions, and non-bear market conditions. When the market is bearish, the
proportion of cases in which the appraised value is equal to the transaction price is
0.80, compared to 0.71 in the full sample. By contrast, this proportion falls to 0.24 in
non-bear markets. It is clear from the results in Exhibit 3 that prima facie evidence
exists to support the hypothesis that appraisers are more likely to appraise at the
transaction price in a bear market.
Exhibit 4 shows the results of the probit model 3 where the dependent variable
is y1i where it takes the value of 1 if A=Po, 0 otherwise. The independent variables are
BEAR, NB, LV, HHINCOV and AGE. To differentiate between the different
theoretical models, the variable of interest is BEAR for reasons highlighted in the
3
Results for the logit model are qualitatively the same as that for the probit model,
and are thus not reported.
10
previous section. The coefficient on BEAR is positive and significant. This means
that the probability of observing an appraisal that is equal to the transaction price
increases when the market is bearish. This result is supportive of the alternative theory
that appraised value tends to be equal to the transaction price in a bear market.
Exhibit 5 shows the results of the probit model where the dependent variable
is y2i where it takes the value of 1 if A<Po, 0 otherwise. The coefficient on BEAR is
negative and positive. Again, the result is contrary to the prediction in Gwin, et al.
(2000), but is consistent with the alternative theory and the signaling modification to
the moral hazard model.
Interestingly, the results in Exhibit 4 show that the likelihood of appraised
value being equal to the transaction price is increasing in the loan-value ratio and
number of mortgagors (NB). Put differently, the higher the loan amount and the larger
the number of borrowers, the higher the tendency for the appraiser to match the
transaction price. Age and household income are not significant variables.
Conclusion
In conclusion, this paper is an attempt to empirically test the likelihood of an
appraiser setting an appraised value that equals the bid or transaction price. The extant
literature has highlighted this issue (Smolen and Hambleton, 1997; Rudolph, 1998;
Lentz and Wang, 1998; Worzala, et al. 1998; Finch, et al., 1999). Gwin, et al. (2000)
provide an interesting moral hazard model that examines the appraiser's incentives in
conducting an appraisal. In particular, the focus is on an appraiser that acts on behalf
of the mortgagee and is thus remunerated by the mortgagee for current and future
businesses (see Lentz and Wang, 1998).
The model in Gwin, et al. (2000) lends itself to empirical testing in that
predictions of the incentive to set an appraised value equal to the bid/transaction price
11
is demarcated under different market conditions. Specifically, the prediction is for a
lower incentive to set an appraised value equal to the bid/transaction price under a
bear market. This paper, in contrast, draws on the Quan and Quigley (1991)
framework and reworks the moral hazard model in Gwin, et al. (2000) to formulate an
alternative theory that predicts an increased incentive to set an appraised value equal
to the bid/transaction price under a bear market.
Utilizing mortgage data from a loan cooperative in Singapore, we empirically
test the likelihood of appraised value being equal to the transaction price in a probit
model. The results find support for the alternative theory.
12
References
Daly, J. (2001) “Economic Sustainability in Real Estate Markets: Implications no a
Federal State” Fourth Sharjah Urban Planning Sympsium.
Finch, J. Howard; Fogelberg, Larry; and Weeks, Shelton. (April 1999). “The Role of
Professional Designations as Quality Signals.” The Appraisal Journal, 67(2), pp. 14346.
Gwin, Carl R., Ong, S. E. and Maxam, Clark. (2000) “Why Do Real Estate Appraisals
Nearly Always Equal Bid Price? A Theoretical Justification.” ENHR/International
AREUEA conference, Gavle, Sweden, June 2000.
Lentz, George H. and Wang, Ko. (1998). “Residential Appraisal and the Lending
Process: A Survey of Issues.” Journal of Real Estate Research, 15(1/2), pp. 11-39.
Ong, S. E. (1999). “Aborted Property Transactions: Seller Under–compensation in the
Absence of Legal Recourse,” Journal of Property Investment and Finance, 17(2), 126
– 144.
Quan, Daniel C. and Quigley, John M. (June 1991). “Price Formation and the
Appraisal Function in Real Estate Markets.” Journal of Real Estate Finance and
Economics, 4(2), pp. 127-46.
Rudolph, Patricia M. (1998). “Will Mandatory Licensing and Standards Raise the
Quality of Real Estate Appraisals? Some Insights from Agency Theory.” Journal of
Housing Economics, 7, pp. 165-79.
Smolen, Gerald E. and Hambleton, Donald Casey. (January 1997). “Is the Real Estate
Appraiser’s Role Too Much to Expect?” The Appraisal Journal, 65(1), pp. 9-17.
Worzala, Elaine M.; Lenk, Margarita M.; and Kinnard, William N. (October 1998).
“How Client Pressure Affects the Appraisal of Residential Property.” The Appraisal
Journal, 66(4), pp. 416-27.
13
Exhibit 1: Descriptive Statistics
The variables are: transaction price (Po), appraised value (A), bear market dummy variable
(BEAR), number of mortgagors (NB), loan amount (LOAN), loan to value ratio (LV), annual
household income (HHINC), annual household income-to-property price ratio (HHINCOV) and
age of mortgagor (AGE).
Variable
Po ($)
A ($)
BEAR
NB
LOAN ($)
LV
HHINC ($)
HHINCOV
AGE (years)
Mean
616,592
613,094
.8390
1.97
333,916
0.550
99,318
0.167
38.4
Std Deviation
296,461
292,120
0.3678
0.50
174,173
0.159
85,904
0.121
6.95
Minimum
136,000
120,000
0
1
47,000
0.05
9,800
0.021
24
Maximum
3,350,000
3,350,000
1
6
1,264,000
0.882
1,235,461
1.615
64
Exhibit 2: Distribution of Margin by Loan-Value Ratio
MARGPCT = (Po-A)/Po
LV = LOAN/Po
.5
MARGPCT
.0
-.5
-1.0
-1.5
-2.0
-2.5
.00
.25
.50
LV
.75
1.00
14
Exhibit 3: Distribution of Appraised Values relative to Transaction Prices (proportions)
Variables are: Transaction price (Po) and Appraised value (A),
A=Po
A<Po
A>Po
Sample size
Full Sample
0.7138
0.2129
0.0733
559
Bear Market
0.8038
0.1364
0.059
469
Non-bear market
0.2444
0.6111
0.1444
90
Exhibit 4: Likelihood of Appraised Value equal to Transaction Price
Dependent variable y1i =1 if A=Po; 0 otherwise. Independent variables are bear market
dummy variable (BEAR), number of mortgagors (NB), loan to value ratio (LV), annual
household income-to-property price ratio (HHINCOV) and age of mortgagor (AGE).
Variable
Constant
BEAR
NB
LV
HHINCOV
AGE
Log likelihood function
Number of observations
Coefficient
-1.9916
1.5137
0.3641
0.8071
-0.2617
0.0058
Std Error
0.5433
0.1619
0.1259
0.3966
0.4123
0.0093
t-statistic
-3.666
9.350
2.891
2.035
-0.635
0.629
p-value
0.0002
0.0000
0.0038
0.0419
0.5255
0.5295
-275.23
559
Exhibit 5: Likelihood of Appraised Value less than Transaction Price
Dependent variable y2i =1 if A<Po; 0 otherwise. Independent variables are bear market
dummy variable (BEAR), number of mortgagors (NB), loan to value ratio (LV), annual
household income-to-property price ratio (HHINCOV) and age of mortgagor (AGE).
Variable
Constant
BEAR
NB
LV
HHINCOV
AGE
Log likelihood function
Number of observations
Coefficient
1.4597
-1.3589
-0.3164
-0.6286
-0.2293
-0.0053
Std Error
0.5577
0.1555
0.1308
0.4106
0.2720
0.0096
t-statistic
2.617
-8.737
-2.419
-1.519
-0.843
-0.547
p-value
0.0089
0.0000
0.0155
0.1289
0.3990
0.5841
-242.08
559
15
Appendix
The model in Gwin, et al. (2000) is predicated on the setup in Quan and Quigley
(1991) where the buyer’s reservation price is P r and the seller’s ask price is P a . It is
assumed that the buyer’s reservation price includes an appraisal fee ( f ) and that the
seller’s ask price includes any transaction or search costs associated with matching a
seller to a buyer. Given any potential match where P r ≥ P a , a non-cooperative
bargaining game is used to split the surplus P r − P a using Rubinstein's (1982)
bargaining model such that the seller gets share ω of the surplus and the buyer 1 − ω ,
where ω is a function of the buyer's and seller's discount factors ( ρ b and ρ s ,
respectively):
1− ρb
(A-1) ω =
.
1− ρbρ s
(
)
Thus the transacted price P0 at time t = 0 is a weighted average of P r and P a :
P0 = ωP r + (1 − ω) P a .
Consider now the observed transacted price in a buyer’s market. Typically
when the market is falling, buyers are few and are able to exert greater bargaining
power. That being the case, the buyers can literally wait forever, and ω = 0 . In
contrast, when the market is rising, a seller’s market exists where sellers are few and
far in between, and buyers are likely to chase prices. In this instance, ω = 1 . So the
transacted price is likely to be closer to the seller’s bid price in a seller’s (rising)
market ( P0 → P a ) and is likely to be closer to the buyer’s reservation price in a
(A-2)
buyer’s (falling) market ( P0 → P r ).
Let A be the appraised value at time t = 0 . If the appraisal is greater than or
equal to the price, then the mortgagee approves the loan. If the appraisal is less than
the price, then the mortgagee rejects the loan application. Let θ ∈ [0,1] represent the
probability that the transaction is completed between the seller and buyer. The
probability of a completed transaction (subsequent to an agreement on price between
the seller and buyer) is given by
(A-3)
θ = Pr[A ≥ P0 ].
We assume that an appraisal that results in a rejection of the mortgage
application ( A < P0 ) cannot result in a renegotiation of the contracted price. In a
buyer’s market P0 → P r , therefore an appraisal less than price cannot be resolved
with a reduction in price. In a seller’s market, the price is determined by bargaining.
Thus, price does not depend on the appraisal.
Mortgagees set a maximum loan-value ratio ( LV ). The appraiser knows LV
and P0 , but not the amount of the loan that the mortgagor is applying for. However, it
is assumed that the appraiser expects a maximum loan.
Given the above framework, Gwin, et al. (200) show that the probability of
default if the appraiser values at 1) greater than or equal to the bid price and 2) below
the bid price.
Case 1: A ≥ P0 . The probability of default is given by
(A-4)
[
]
λ = Pr PT < mT = LV × P0 .
16
Rewriting equation (4) as
⎡ PT
⎤
< LV ⎥,
⎣ P0
⎦
it can be seen that the probability of default is low if the market trend is rising. So
λ → 0 when the market is bullish.
λ = Pr ⎢
(A-5)
Case 2: A < P0 . The probability of default is given by
(A-6)
⎡P
⎤
λ' = Pr ⎢ T < LV ⎥ < λ,
⎣A
⎦
since A < P0 .
The risk of default is lower, but the trade off is that the probability that the
application is unsuccessful is increased. This may not good for the bank, and may
result in a loss of business. In particular, Gwin, et al. (2000) shows that under certain
conditions, it can be shown that in a rising market trend, the appraiser always chooses
A = P0 . When the market is falling, it can be shown (following the same reasoning
above) that it is optimal for the appraiser to choose A < P0 to protect against loss in
future business when the mortgagor defaults.
Consider the appraiser’s problem in a rising or seller’s market. He knows that
the transacted price is likely to be closer to the seller’s ask price ( P0 → P a ). If his
appraisal value ( A ) is higher than the transacted price, the loan amount will still be
based on the transacted price). If A < P0 , the buyer would not be able to obtain the
loan and may not be able to close the transaction. Since it is a seller’s market, the
seller can easily find another buyer. This translates to a loss in business for the
mortgagee. In other words, in a rising market, the appraiser trades off the risk of
default by setting A > P0 and the loss of business for the mortgagee by setting A < P0 .
The probability of default in a rising market tends to zero. So the appraiser is inclined
to choose A = P0 in a rising market.
Even if the market is stable, and the probability of default is higher than that in
a rising market, the fact that the loan is based on the minimum of appraisal and
transacted price would mean that the appraiser would optimally choose A = P0 .
(Recall that the bank’s loan policy is public knowledge.)
Now consider the appraiser’s problem in a falling market. It has been
established earlier that the transacted price is likely to be closer to the buyer’s
reservation price ( P0 → P r ) in a buyer’s market. As equation (A-6) shows, the
probability of default when A < P0 ( λ ′ ) is lower than that if A = P0 ( λ ), the
appraiser is better off choosing A < P0 . This is simply because a default would result
in a loss in future business for the appraiser. If the buyer is unable to close the deal
when A < P0 , the buyer is not necessarily worse off since prices are falling (in fact,
the buyer may be better off). So the loss in business for the mortgagee if the buyer is
unable to secure the purchase is not necessarily severe enough when considered
against a future loss should the mortgagor defaults. Hence, the appraiser chooses
A < P0 .
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