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ERP by neuralnetworks

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PRACTICE PAPERS

Estimated realisation price(ERP) by neural networks:

forecasting commercialproperty values

Owen Connellan and Howard James

1. IntroductionThe progress of applying statistical and neural network methods to residentialvaluation by the use of comparables has been reported in the academic press forthe last five years by Do and Grudnitski (1992), Donnelly (1990), Evans, et al.(1992) and Tay and Ho (1991). The results have shown a cautious success, butthere are clearly many a spects of methodology still to be explored andimprovements can still be made. For example, it is known that location is amajor factor in the value of a property, whilst other influencing factors are thesize and quality of the dwelling. All these attributes are considerably inter-related, which presents the analyst with some critical problems of methodology.Nevertheless, the field has been sufficiently well explored as to raise hopes that

a combination of statistical and neural network methods may give rise to usefulprocedures for decision support for the residential valuer: for example seeJames (1994).

The methods of valuation used so far depend on the principle that the priceof a property depends on its attributes, such as age, size, quality, condition andlocation. Various methods are used to determine the extent t o which theindividual attr ibutes contribute to price, such weights being determined bymeans of analysis of known prices for similar properties that have been soldwithin a time period during which the prices have not moved to such an extentas to invalidate the comparison; or some index correction can be made to takeaccount of market movements. We call this kind of analysis cross-sectional. Thework described in this paper concerns the estimation of value in the future, and

thus the behaviour of value over time is the main objective of the study. Thus byanalysing the past behaviour of values, we study the extent to which thesevalues can be extrapolated into the future to obtain a predicted future price. In

Journal of Property Valuation &

Invest ment, Vol. 16 No. 1, 1998,

pp. 71-86. © MCB University Press,

0960-2712

Received November 1996Revised September 1997

The authors wish to thank Dr Angus McIntosh and his colleagues at Richard Ellis, Internat ionalProperty Consultants, for their kind help and assistance with data, without which this work would not have been possible. We also thank our colleagues at the Centre for the BuiltEnvironment at Glamorgan University and t he Department of Land and Constru ctionManagement at the University of Portsmouth for their support and encouragement.



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effect the work is a time series study, and we call this longitudinal analysis, todistinguish the method from the cross-sectional analysis of previous work.However, we are not suggesting that longitudinal methods are a substitute forcross-sectional; they have their special uses a nd may indeed be used incombination.

The field of commercial property appraisal presents more challenges to theanalyst. The valuation of both commercial and residential property can requirethe use of the direct comparison method; the existence of available data relatingto residential properties has resulted in the widely reported applications of cross-sectional methods of analysis allied to property attributes. However,commercial investment properties are not heterogeneous products and there is a

relative scarcity of data which effectively link values with adequate propertyatt ributes. Furt hermore, commercial investment property valuations aregoverned by lease structures and consequently, the methodology inherentlydepends on future cash flows which have to be discounted at appropriate ratesof return over changing periods of time. These complications inhibit cross-sectional analysis by neural networks. A much more rewarding opportunity forneural networks requires an increased emphasis on longitudinal (time-dependent) data analysis. Thus in this work, our aim was to attempt to showhow time series methods can be applied effectively to the problem of analysingcommercial property values and to prognosticate future valuation trends in auseful and applicable manner.

2. T he rationale for longitudinal as against cross -sec tional analysisThe achievement of valuation by comparables requires the existence andavailability of a sufficiency of transactions within a specified market sector ataround the same time, which is a problem in itself. Assuming it were possible,however, to muster sufficient numbers of transactions of suitable commercialinvestment properties to attempt a cross-sectional comparison by neuralnetwork analysis, it would then be necessary to match property attributes toleasing attributes and furthermore to unravel these attributes against thecomplexities of capitalising anticipated cash flows at appropriate defermentrates. Even if these hurdles could be surmounted, the end product wouldamount to a valuation estimation process, at today’s date, using mathematicalmethods to weight property and leasing attr ibutes coupled with var iablecapitalisation factors.

However, such procedures would not necessarily give a key to forecastingfuture trends, whereas the preferred longitudinal analysis that is adopted in thiswork is geared to examining past patterns to give positive indications for thefuture. As this accorded with an achievable aim of the research, the longitudinalmethod was therefore adopted.

3. The principles of neural networksNeural networks are a recently developed type of adaptive computer programwhich can learn patterns in data, mimicking the action of the human brain. The




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data are applied to the program in a process called “training”, during which theprogram learns by example the underlying patterns in the data. When thetraining process is complete, the program acts as a model of the data which canbe used to forecast the outcome of new events which conform to the patterns inthe training data. Our preference for using neural networks in this investigationwas motivated by their increasing use by academic and commercial analysts inthe task of recognition of complex patterns in multivariate data. Their ability toidentify non-linear underlying patterns as shown by Cybenko (1989), de Grootet al. (1991), Funahashi (1989) and Hornik et al. (1989) is a strongrecommendation for their use in the interpretation of commercial property datain which there are numerous and complex interactions of influences and the

distinct possibility of the existence of non-linear patterns. If the patterns areindeed non-linear, then neura l networks are able to model them. Neuralnetworks are regarded by many authoritative commentators as a usefuladdition to standard statistical techniques, and are in fact themselves based onstatistical principles: see Bishop (1995).

4. A ss es sment of the available dataIn order to pursue the research effectively, a fairly large data bank of expertvaluations over several years was needed. It is well recognised in valuationresearch that, because of the paucity of commercial market transactions and thelack of supporting information, it is necessary to rely on valuation expertiserather than the limited empirical evidence of achieved commercial prices. This

view is backed by Cullen (1994) of IPD who argued that valuations are muchmore accurate than has been suggested. We were thus very fortunate to begiven access to past valuations from Richard Ellis over some eight years. Theproperties comprise a range of office investments in the City of London and theWest End which are regularly re-valued on a monthly basis. This data sourcegave a continuum of valuation expertise involving over 90 separate valuationsfor each property – a veritable treasure trove! However, what is more importantare the most recent valuations which revealed an over-renting situation runningback about three or four years. This clearly was having a major influence on thevaluations, and accordingly it was decided to disregard data prior to the over-renting period.

Using spreadsheets it was possible to summarise and analyse the RichardEllis valuat ions, property by property. This spreadsheet analysis, usingiterative techniques to test equivalent and all-risks yields, enabled a checkingand consistency programme to operate throughout the recorded life of eachproperty. In discussion with Richard Ellis, a number of issues relating to thevaluations were clarified. As a result, the spreadsheets contained completerecords of the detailed inputs, month by month, of all the numerical data used toachieve the Richard Ellis valuations of each property. The valuation methodadopted by Richard Ellis is a standard practice used with over-rented properties(freehold) of capitalising the estimated rental value in perpetuity at an all-risksyield to which is added the capital value of the amount of over-renting for a



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restricted period, capitalised at a higher rate of return in step with the long-termbond market.

Having obtained th is spreadsheet format , we next had t o focus on thenecessary process to find patterns within these data which would support aforecasting role for artificial neural networks. What we were looking for weregeneral economic influences (i.e. outside factors) which could be linked to avaluer’s interpretation of property market yields and cash flow expectations.

In a testing process, the linkage of various external economic factors (i.e.other than property market statistics) such as inflation, equity yields and thebond market were considered. For the period of the valuation data beingexamined (that is 1991 to 1996) perhaps due to the over-renting nature of many

properties, it was apparent that long-dated gilt interest rates had an importantinfluence over the movement of valuat ions. Such over-renting meant that thecapital values were substantially attributable to the covenant of the lessee topay the rent (a quasi-bond situation) notwithstanding that the market rentalvalue was lower. Hence there was a logical and experimental foundation for theinclusion of long-term gilts as a contributory var iable in determining ourcapital estimates and predictions; a view also proposed by Baum who pointedout “…(the) wholly rational but poorly recognised lagged relationship betweenbond yields and yields for property with long-term bond-like cash flows”(Baum, 1995), which connection we surmised to apply to the rent overagesituation existing under most of the leases. It was possible to show that giltshave an effect on capital valuations by measuring the linear correlation between

capital values and current and past gilts. These correlations were significantback to a year before the capital valuations and so we conclude that gilts are aleading indicator of the movement of property valuations.

Having accepted the hypothesis that 15 year gilts are indeed a major externalinfluence on valuations, it was decided to model the property valuations as adouble time series of the valuations and the 15 year gilts. The outcome of thework was to simulate these previous valuations for the time series usingproperty indices relevant to the locational zones of the properties, a process wehave termed “backtracking”, rather than the Richard Ellis valuations.

5. Preliminary exploratory workThe next section of the work was therefore concentrated on examining the effectof gilts on the valuations. The initial work laid the basis for the methods whichare described in this paper by showing that for the London commercialproperties studied, there were two influences on the development of capitalvaluations with time: current and lagged 15 year gilts and variables relating tothe properties themselves. Particularly important were overage period, rentalvalue and rent received. In view of the fact that capital valuation fluctuationsare influenced mainly by external economic factors and variables relating to theindividual building and its lease structure, it was decided that these factors andvariables would be incorporated by using a double time series of gilts andcapital values. The gilt time series encapsulated the economic influences on the




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valuation, and the capital valuation time series contained the influence of thevariables relating to the individual properties: not only overage, rental valueand rent received, but any other variables which were not immediately availableas specific numbers but which were embedded in the time series nevertheless(Farmer and Sidorowich, 1988; Takens, 1981). Thus according to the Takenstheory, a time series can include the contributory variables (Box et al., 1970;Cottrell, 1995; Moore II et al., 1994).

The question may arise as to why forecast property yields and forecast rentindices were not used in addition to gilt returns to project the subject valuationforward. It was considered that the inclusion of such property indices was notnecessary because they were all implicit in the time series of the capital values.

Thus the expected influences on valuation movements from both economic andproperty indices were all taken into account by the double time series of laggedgilts and capital valuations. Furthermore, there are distinct advantages in thelagging process, i.e. using past data series as inputs. By using the data in thislongitudinal format, any forecast errors would be mitigated by the influence of the lags. Consequently, we felt there would be a good chance of the forecasts of the valuat ions being within reasonable bounds, a hypothesis which wasultimately supported by the results. In addition, the incorporation of additionaltime series would have increased the number of inputs t o the model sodrastically as to make it impossible to find the underlying general patternswhich are necessary in order to predict the series into the future. This is knownto mathematicians as the “curse of dimensionality” (Bishop 1995).

6. The “backtracking” technique: creating a valuation historyThe actual history of Richard Ellis valuations was certainly a very worthwhilebonus in examining valuation trends in a defined market over a period of time,permitting longitudinal analysis in some depth. However, such a bonus is a rarephenomenon and what was being sought was an all-purpose model forvaluation forecasting that would operate independently of such a recordedvaluation history. The possibility of creating a simulated history was proposed,taking as a base an actual valuation at the current date, or a transaction thatcould be analysed into an acceptable valuation format. This simulated historywas named “backtracking” and consisted of creating historical valuations forindividual properties by relating variations in valuations back in t ime to factors

specific to the par ticular property, and to property indices applying to thelocation and type of investment. Further arguments for using backtrackingrather than valuation history, in addition to data availability issues are:

• An actual valuation history will contain all abrupt changes in valuationbrought about by part icular unique circumstances applying to theproperty in the past , e.g. physical changes to the building and tenantlease changes. Such changes, though important , are not necessarilyrelevant to the future trend of valuations (i.e. short-term forecasts). Whatare more relevant are the physical state of the property and the tenant



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lease status as revealed by the construction of the valuation (or analysisof the transaction) in the adopted base data (i.e. from today’s open marketvalue – OMV);

• A simulated valuation history which is backtracked from today’s OMVadopts all the attributes of the current valuation such as the physicalstate of the property and the tenant lease status, and thus establishes arequisite pat tern of valuations in the past derived from the base data.Such a pattern is necessary to enable any forecasting technique such asneural networks to learn underlying patterns in a longitudinal series of valuations, so providing the requisite key to short-term forecasting, as issubsequently described. What is also significant for the verification of the method of backtracking is t hat when comparing backtr ackedvaluations with actual valuation histories, there is a reasonably closecorrelation, although the figures are not identical because of variouschanges to valuations of individual buildings which do not influence thegeneral trend.

The process of backtracking is tantamount to valuing with the benefit of hindsight – a very exact science! By “hitching” a current valuation to historicand recognised indices of property yield and rental levels, plus historic 15-yeargilt yields, a “smoothed” pattern of valuations can be produced backwards intime. We began with the premise that at the start of the forecasting period therewould be either a sale price (which could be analysed into an acceptable

valuation) or a detailed valuation. With this initial input it was possible tobacktrack the valuation over a considerable period of time at monthly intervalsusing Hillier Parker figures for Average Yields and Rent Index (as benchmarksfor the valua tion series). The gilt pr ices for any overage situa tion werehistorical, as were the rents passing and any previous changes due to rentreviews. The structure of the lease (in each case) is sacrosanct and the rentpayable under the lease is a contractual cash flow running through to varioustermination dates.

The method of valuation adopted at the date of valuation (or method of analysis of a current capita l transaction) was used to take the valuationbackwards in t ime; thus consistency is achieved whilst the relevant leaseparameters obtain. This “smoothed” valuation trail contains within it all thefactors (consistent with hindsight) that go to relate a valuation figure to everyincremental point on the time scale. It was then for the neura l network tounravel and weight the inherent patterns. The neural network uses laggedvaluations from this valuation trail and a lagged economic indicator (15 yeargilts) to process the network, and there was little difficulty in obtaining anaccurate fit to such a backward t ime series of valuations.

The question of the comparison of the backtracks with the actual historicvaluations was examined in the course of the investigation. Over the historicalperiod covered by the investigation, which was 53 months prior to January1996, the backtracks did actually correspond reasonably well to the actual RE




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valuations, except that the backtracks were smoother than the real valuations.Over the period of the work, however, the discrepancy between the two was low,and gave us the confidence that backtracking was a good, smoothapproximation to the real past values.

The next step was a forward one. The backward time series was then relatedto the gilts to produce a model which was tested for it s prediction ability.However, there was a need to make a forward prediction of the 15 year gilts tosupport the forecasting method. Notwithstanding t he fact that the giltpredictions may introduce certain errors, these errors were not criticallyimportant because the main influence on the property values was the combinedlags of the known historic gilts, thereby mitigating any discrepancies in the

forward gilt predictions. The precise methods are described in the next section.

7. Experimental procedureThe methods used for the modelling of time series by neural networks havebeen widely reported in the literature (Azoff 1994) and in fact are a developmentof the autoregressive methods well established and reported in the statisticalliterature, e.g. Kendall and Ord (1990). In essence, a single time series has onlyone dimension, i.e. the successive values of the series, monthly in thisinvestigation. A higher dimensionality (i.e. number of inputs) is required toenable a model to take into account the various multiple factors that influencethe values of the time series. This dimensionality is achieved by consideringthat a current value of the series depends on previous values, so that the inputs

to the model are the past values of the series going back perhaps six to 12months from the current value. This is known as a time lag window, and thiscan be moved over the historical data of the series to produce data cases uponwhich to adjust the parameters of the model. In this case, the parameters of themodel are the weights in the neural network. In the case of statistical models,they are the coefficients in the autoregressive series.

The prediction procedures described in this paper commenced in January1996. This was taken as the first base month for the work. At this time, the 15year gilt values and the Richard Ellis valuations for the properties for Januarywere known. The valuations were used to produce the backtracked capitalvaluations, going back at least 53 months, to provide sufficient data to enablethe neural networks to find patterns in the data.

There were two phases in the prediction procedure. The first was to predictthe 15 year gilts for six months ahead, based on the time series of the gilts forthe preceding months and for this, a neural network was trained on gilts databackwards from, and including, January 1996. The training set used toproduce consisted of 40 data cases, each case consisting of 13 consecutivemonthly gilt figures. This t he first case consisted of the gilt figures forJanuary 1996, December 1995, November 1995 and so on back to January1995. The second case consisted of the gilt figures for December 1995 back toand including the gilt result for December 1994. Each successive case differedfrom the previous one by a shift of one month back in t ime. This set of



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training cases was presented as the training set to the neural network, inorder to determine the correct weights for modelling the historic patterns inthe data. The neural network consisted of 12 input nodes and one output node;the output was the most recent gilt value window whilst the remaining giltvalues for the preceeding months were the 12 inputs. The algorithm used fortraining was back propagation and the network had two “hidden” or internalnodes which allow the network to respond to non-linear patterns in the data.The training was carried out for 850 case presentations presented in randomorder.

When training had finished, the neural network was used to predict onemonth ahead, using as input the January 1996 gilts value and the preceeding11 months’ gilt values. Thus the first forecast of the network gave a predictionof the gilt for February 1996. To obtain the forecast for March 1996, the inputsto the trained network model were its own prediction for February 1996 andthe remaining 11 months prior to that . The process was repeated until sixsteps ahead were predicted. This enlarged gilts data set of 40 cases plus sixnew ones containing the predictions was used as the input set for part of themain predictive network as described next. The gilt forecasts are given inFigures 1 and 2 along with the actual values. Comments on these appear inSection 8.

The main predictive neural network for the valuation forecasts consisted of 26 inputs, consisting of 13 consecutive monthly gilt values, the latest being theoutput month of the neural network. The remaining 13 inputs consisted of consecutive values of the backt racked capital va luations for the subjectproperty, the most recent being the base month for the predictions which is onemonth behind the gilt series. The output of the neural network was the next

Figure 1.Forecast of 15 yearGilts. F1 is the Januarybased forecast forFebruary to June, F2 isFebruary based for theMarch to July forecastsetc.

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month, corresponding to the month of the most recent value in the gilt seriesbecause this had already been predicted by the gilt forecasting proceduredescribed above. The neural network was trained for 850 cycles on 40 vectors,using the same parameters that were used for the gilts, including one hiddenlayer of two nodes. The trained network was then used to predict six steps

ahead using predicted values as inputs after the first step ahead prediction.These procedures were repeated for all the 16 properties, as well as a separatenetwork to predict the whole portfolio.

The predictive processes as described above were carried out for each monthfrom January to May 1996; thus the January base was used to make predictionsfor February to July inclusive, the February base for March to August inclusive,and so on, ending with the May base for the June to November predictions. Allthe predictions were compared with the Richard Ellis valuations for the subjectproperties as they became known throughout the prediction period. The graphsin Figures 3 to 10 present the Richard Ellis valuations (up to July) and each of the five forecasts made designated F1 to F5 in date sequence. For ease of comparison, the graphs are all expressed as indices with the January 1996Richard Ellis valuations as 100. All valuation predictions were made in advancewithout knowledge of the actual subsequent Richard Ellis valuations. On theother hand, our predictions were not made known to the Richard Ellis valuationteam – a double-blind procedure!

8. Discus sion of the resultsAs time moved forward and the base month moved from January 1996 to May1996, there were clearly some multiple predictions for some months. Wherethese were available, the medians for these months were considered, rather thanthe arithmetic mean. The median is a measure of central tendency regardless of

Figure 2.Medians of 15 year

gilt forecastsJAN 96 FEB 96 MAR 96 APR 96 MAY 96 JUN 96 JUL 96

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extreme individual values, whereas the mean would include outliers whichcould distort the forecasting picture (IAAO, 1990).

Prior to any property forecasting, it was necessary to predict forward the 15year gilts. Figure 1 shows the spread of the forecasts whereas Figure 2 matchesthe median of the forecasts to actual gilt returns. Bearing in mind that gilts areconsidered to be an efficient market, it is not surprising that there are variationsbetween real and predicted returns, but the lagging principle, i.e. propertyvaluat ions depend mainly on lagged gilts va lues, minimises the effects of inaccuracies as previously discussed.

Figure 3.Forecasts of the totalled16 portfolio properties

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Figure 4.Neural network forecasts of the totalportfolio

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Consider now the forecast ing of the whole portfolio which in value t ermsexceeds £700 million in total and comprises 16 office investment properties in

the City and West End of London. The results were obtained in two ways: oneby merely totalling the 16 individual property forecasts, and the second by a

separate neural network which predicted forward from a base of the sum of allthe separate 16 backtracked valuations. The results are given in Figures 3 and

4. They demonstrate a reassuring similarity to each other which gives

confidence in the methods. Furthermore, they demonstrate the expectedwidening of the prediction band with the lengthening of the prediction period.

Figure 5.Medians of the summed

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As to accuracy compared with the Richard Ellis valuations, forecasts F2 to F5

pick up the impending overall downward trend of the portfolio valuat ion with a

maximum divergence of 1.0 per cent in the very las t forecast of F1 in July.

Moreover, the close correlation of the forecasts with the Richard Ellis valuations

is portrayed particularly well by plotting the median forecast for each month of

F1 to F5 inclusive. Indeed, the maximum error is approximately 0.6 per cent

around May – see Figures 5 and 6.

Figure 7.Forecasts of capitalvaluations for aproperty in the City of London

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We now examine the separate characteristics of the portfolio as represented bysome individual City and West End properties. Figure 7 is a typical example of a City property which had no fundamental changes in property status over theforecasting period. Again there is the widening of the prediction band with timeand an indication of a continuing downward trend which does not conflict withthe latest Richard Ellis valuations showing a maximum divergence in F2 in Julyof approximately 1.4 per cent. Again, a closer correlation can be demonstratedby plotting the medians of the forecasts for each month (Figure 8) which showsa maximum error of 0.3 per cent from the Richard Ellis valuations in March.

Figure 9.Forecasts of capital

valuations for aproperty in the West

End of London

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Figure 10 .Medians of forecasts for

a London West EndpropertyJAN 96 FEB 96 MAR 96 APR 96 MAY 96 JUN 96 JUL 96

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Figure 9 is a similar example of a West End property which similarly had nofundamental changes in property st atus over the forecasting period. Thewidening prediction band however indicates an upward direction, which againis not contradicted by the latest Richard Ellis valuations, with a maximumdivergence of approximately 0.7 per cent of F3 in May. The plotting of themedians of the forecasts for each month (Figure 10) demonstrates this trend andshows a maximum error of approximately 0.5 per cent in May compared withthe Richard Ellis valuation figures.

At t he end of this exercise it had to be considered whether the resultsobtained, in terms of accuracy when compared with the subsequent REvaluat ions, would be acceptable to a valuer (or perhaps more importantly to the

client!). To get an overview, one should regard the figures emerging for the totalportfolio and we would hope that the overall mean divergence of approximately0.6 per cent achieved in this work is something that most valuers and clientscould accept.

The importance of forecasting is now becoming more relevant to the valuerbecause of the requirement of the RICS in the new Red Book for the valuer toproduce an estimate of realisation price (ERP) when required by a client:

The new definition of estimat ed realisat ion price (ERP) moves the marketing period, as

assumed in open market value (OMV), from prior to the valuation date to a reasonable periodrunning from it, the duration of the marketing period being determined by the value… In

most cases, the valuer is likely to assess OMV and then consider what further changes in the

market are likely during the marketing period which precedes the exchange of contracts at the

resulting price. Indeed, the revisions to ERP… now specify – some may feel unwisely – thatthe valuer must do this. Changes dur ing this period may be in external factors such as yields,interest ra tes, the quality of the location, reduction in void properties in the locality, and/or

changes in the subject property, such as the outcome of rent reviews (Lovell and French, 1995).

In view of the new Red Book requirements we suggest that our techniques couldbe used as a decision-support aid for the valuer, particularly in thecircumstances envisaged by Crosby et al. (1993).

Whilst we are cautiously encouraged with the level of correlation betweenour predictions and the actual Richard Ellis valuations, further work is beingpursued aimed at developing our techniques and researching the variousinfluences on capital valuation movements over time.

9. Conclusions

The work concludes that it is possible to find underlying patterns in historicalor backtracked capital valuations, and that the patterns are inter-related to 15year gilts in the market under examination, working over monthly incrementaltime periods in the case of over-rented properties. It is then possible to model theunderlying patterns in neural networks using a double time series (lagged) of capital valuations and 15 year gilts, and then to project these values forward intime for a period of five months with reasonable accuracy. These forecasts maybe useful as a decision-support tool for assessing Estimated Realisation Price(ERP) and also in consideration of the new definition of “Forecast of Value”




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recently introduced by an amendment to the RICS Appraisal and Valuation Manual (The Red Book ) (1995).

10. Epilogue: quo vadis?

Prediction is a dangerous practice. “Never prophesy, par ticularly about thefuture” (Sam Goldwyn attrib.) Subsequent shocks in the market can upset allthe best laid schemes of analysts and valuers. At the moment, our researchsuggests that there is an overall downward trend in the London office market (atleast as revealed by this important portfolio) which conflicts with theanticipated recovery reported in the Chartered Surveyor Monthly (CSM)January 1996 “Despite recent indications of limited confidence in theoccupational commercial property market, capital va lues are forecast toincrease by 6 per cent in 1996 and 7 per cent in 1997, according to the latestcommercial property model forecast by the RICS and London Business School”.However, as the Director of Research Consultancy in Richard Ellis (McIntosh,1995) states “Although long-dated UK government yields have fallen in the lastsix months from around 8.5 per cent to almost 7.5 per cent, we predict thatproperty investment yields are unlikely to fall substantially during 1996”. Timewill tell and our research continues!

References

Azoff, E.M. (1994), Neural Network Time Series Forecasting of Financial Markets , John Wiley,

Chichester.

Baum, A. (1995), “Can foreign real estate investment be successful?”, Real Estate Finance, pp. 81-9.

Bishop, C.M. (1995), Neural Networks for Pattern Recognition, Clarendon Press, Oxford.

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(Owen Connellan is an External Research Fellow at the Centre of Research in the BuiltEnvironment at the University of Glamorgan, UK. Howard James is a Senior Research Fellow atthe University of Portsmouth, UK.)

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