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lead to a concept that is relevant in the context where the term normally is used. A definition of market value should be such that market value ‐ so defined ‐ will be of interest for potential buyers and sellers thinking about a future transaction, or for measuring the wealth of a company in the balance sheet.

2.4 Problem 1: ‘Estimated Price’ or ‘Most Probable Price’?

      As there always are uncertainty about the price that is possible to fetch when selling a specific property at a specific point in time, the formulation ‘most probable price’ seems to be the best as this uncertainty then is clear. In IVSC (2019 , p. 18), ‘the estimated amount’ is also explained in terms of ‘the most probable price reasonably obtainable in the market’, even though it is not clear what ‘reasonably obtainable’ adds to the formulation.

This does not, however, solve all problems. Suppose that there are 10 observations from recent transactions of very similar properties. Should the most probable price refer to the mean value or to the median value? If the observations are skewed, there can be rather large differences between the mean and the median. As valuers usually are suspicious against ‘outliers’, the median should perhaps be the most relevant concept.

      The next question is how ‘most probable’ should be interpreted in the context of property valuation. As discussed in Lind (1998 ), there are at least two definitions of probability, or two different ways of looking at the concept of probability.

      The first is the frequency interpretation of probability. In this interpretation, saying, for example, that the probability is 1/6 to get the number 3 when throwing a dice would simply mean that if the dice is thrown a large number of times, then the result would be a number 3 in 1/6 of the throws.

      This interpretation is, however, rather meaningless in a real estate valuation context as it is not practically possible to sell the same property a large number of times during a short period of time. Even in a rather homogenous market, there is a limited number of transactions. Defining the most probable price as the average of the observed prices would be the same as saying that the probability of getting a number 3 is not 1/6 because the frequency of getting number 3 differed from 1/6 in the first 10 throws. With a frequency interpretation of probability, it would therefore not be possible to present convincing evidence whether a certain price is the most probable or not.

      A second interpretation of probability is the logical interpretation, where probability measures the degree of confidence that is rationally justified by the available evidence. This interpretation seems very suitable in a property valuation context. When a valuer, for example, asserts that the value is 100, it would in this interpretation mean that given the available evidence it is more rational to believe in a price around 100 than to believe in a price around 90 or around 110. Controversies about the value of a specific property can also typically be seen as controversies about the interpretation of the relevant evidence. A valuation method is from this perspective a method to collect and analyse evidence in order to arrive at rational belief about what the price will be if the property is sold.

      The conclusion in this section is then that the formulation ‘most probable price’ is the best one and that it can be explained further by saying that it refers to the price for which there is the strongest arguments, or for which there is the strongest evidence.

2.5 Problem 2: Shall the Definition Refer to a Competitive Market?

      A special feature of the Appraisal Institute definition is that it refers to the price in ‘a competitive market’, while there is no such reference in the IVSC definition.

Here, we would side with the IVSC definition, primarily with reference to the criteria that a good definition should be relevant for actors on the market. Actual property markets differ in size and in the number of actors on the market and can be evaluated as more or less competitive. Independently of the level of competition, actors can be expected to be interested in the probable price if a property is to be sold or bought. The conclusion must then be that market value should be defined in such a way that it is applicable independently of how competitive the specific market is. It should be possible to discuss the market value of a unique property and of a property on a thin market, and this means that a reference to ‘a competitive market’ should not be included in the definition of market value.

      Including such a condition would also create methodological problems. If market value is defined as the probable price on a competitive market and the current market is not so competitive, there is no observable evidence about the price on the competitive market. Observed prices could not be used directly to make inferences about the market value and that is a big problem as valuation should be based on observable evidence.

2.6 Problem 3: Should the Definition Refer to Prudent and Knowledgeable Actors?

      The condition that parties had acted knowledgeably and prudently is clarified in the following way in IVSC (2019 , p. 19–20):

      presumed that both the willing buyer and the willing seller are reasonably informed about the nature and characteristics of the asset, its actual and potential uses, and the state of the market as the valuation date… . the prudent buyer or seller will act in accordance with the best market information available at the time.

There are two problems with including this kind of formulation. First, it raises empirical problems. What is the state of the market? What is the best market information at that time? How can the valuers know what is the best market information available – and what it means to act in accordance with this information? Some actors in the market rely on intuition and gut‐feeling, and is such behaviour inconsistent with being prudent? And if comparative sales are used during the valuation process, how should the valuer find out whether these sales fulfil the conditions that the parties had acted prudently and knowledgeable? We would suggest that there can be large differences in opinion about those issues, both among actors in the market, valuers and followers of the market, especially during boom periods. Robert Shiller argued in a famous book (Shiller 2000 ) that share prices in the late 1990s was based on ‘irrational exuberance’. Some would probably say the same about the property market in many countries during the late 1980s or during the period before the financial crises around 2009. If transactions were carried out by people with ‘irrational exuberance’, those transactions would not be relevant for evaluating the market value at that point in time – if the market value is defined as the expected price given knowledgeable actors. Some of the problems that this leads to will be discussed also in Chapter 5 when the concept mortgage lending value is discussed.

      The second argument against including reference to prudent and knowledge actors is the same as the argument against including a reference to competitive markets. In reality, the prudence and knowledge differ between actors, between markets and over time, and the market value concept should be applicable independently of the characteristics of the actors on the market. Adding references to prudence and knowledge reduces the relevance of the market value so defined, especially when a valuation is done for transaction purposes.

      The conclusion would therefore be that the conditions about prudence and knowledgeability should not be included in the definition. The valuer should look at the current market as it is and should not have to evaluate whether the actors in this market are rational or not, given a certain interpretation of rationality. It should also be remembered that the market value definition refers to the most probable price, and if there now and then are (especially) stupid actors on the market – paying too much or selling to cheap compared to other transactions at the same time – those prices would simply not be rational to expect and should therefore not be given great weight when the market value is estimated. This means that the valuer might need to evaluate what lies behind certain transactions with deviating prices, but

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