Uniwersytet Ekonomiczny

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1 Uniwersytet Ekonomiczny George Matysiak Introduction to modelling & forecasting December 15 th, 2014 Agenda Modelling and forecasting - Models Approaches towards modelling and forecasting Forecasting commercial property markets Yields Case study: forecasting a local office market Reading office rents Forecast accuracy Commercial property markets consensus views Models and forecasts 1 Forecasts are necessary because of implementation lead times e.g. it takes time to execute buying/selling decisions or to develop! Forecasts are used in order to reduce uncertainty and risk in decision making Increasingly being demanded, and used, in real estate applications George Matysiak 1

2 Models and forecasts 2 An abstraction or representation of a real system or problem in hand Models can be used to explain or predict e.g. yields, capital values, rental growth, construction costs Models can be deterministic or probabilistic values certain values uncertain probability distributions Models and forecasts 3 Models and forecasts permit an explicit analysis makes underlying model/relationship explicit makes underlying assumptions clear permits analysis of potential impact of different variables on property market variables Sensitivity analysis impact of changes in input values Uncertainty can be quantified Provide a basis for informed decision making Deterministic and statistical models There are two types of relationships: deterministic or exact relationships statistical relationships which have uncertainty associated with the values of a dependent variable Statistical relationships are specified in probabilistic terms Regression analysis commonly used in estimating statistical models George Matysiak 2

3 Probability Distributions The set of all possible values that a random variable can take and its associated probabilities is called a probability distribution Used to determine the degree of confidence (uncertainty) one has in a forecast A simple forecasting model Is there really a 50 % chance of getting it right? Approaches to modelling and forecasting George Matysiak 3

4 Forecasting approaches FORECASTING METHODS use historical data as the basis of estimating future outcomes QUANTITATIVE METHODS use the assumption that it is possible to identify the underlying factors that might influence the variable that is being forecast QUALITATIVE METHODS incorporate intuitive judgements, opinions and subjective probability estimates TIME SERIES METHODS CAUSAL FORECASTING METHODS JUDGEMENTAL METHODS Forecasting Methods Approaches to forecasting Qualitative Forecasting - gives the expected direction of variables of interest Expert Opinion Surveys Indicators Quantitative Forecasting quantifies the expected direction and magnitude Deterministic models Stochastic models (random component) George Matysiak 4

5 Time series forecasting Weights historical observations to forecast future values of the series Extrapolates by projecting past patterns into the future many types of models available Assumes past patterns will continue i.e. underlying structure remains unchanged Techniques for average forecasts Naïve forecasts - the forecast for any period equals the previous period s actual value Moving Averages - technique that averages a number of recent actual values, updated as new values become available Exponential Smoothing - weighted averaging method based on previous forecast plus a percentage of the forecast error Naïve forecast Naive Forecast F t+1 = A t Method best when there is no trend, only random error Graphs of sales over time with and without trends s s F F s s F F No Trend s s Trend F George Matysiak 5

6 Moving Average Forecasting A smoothing forecast method for data that jumps around Best when there is no trend 3-Period Moving Av. F t+1 = [A t + A t-1 + A t-2 ]/3 Dependent Variable * * * * * Forecast Line TIME Time-Series Patterns Horizontal Trend Seasonal Cyclical Trend Analysis and Projection Linear Trend Analysis: Assumes a constant unit change in an important variable over time Growth Trend Analysis: Growth trend analysis assumes constant percentage change in an important economic variable over time George Matysiak 6

7 Extrapolative Methods The History Forecast Recognising a pattern in the past data history - assuming the same pattern applies to the future Now Time Extrapolative methods Dependent Variable Yt??? T o TIME Y t = Trend +Cyclical + Seasonal + Random Noise Time series components Time Series is a time-ordered sequence of observations taken at regular interval over time Trend - long-term movement in data Cycles - wavelike variations lasting more than one year Seasonality - short-term regular variations in data Irregular variations - caused by unusual (one off) circumstances Random variations - caused by chance George Matysiak 7

8 Can capital values (yields) be explained by a pattern?????, Matysiak June 2007 Pure time series approach Advantages Best in immediate or short-term Simple techniques easy to understand and communicate Need data on only one variable for univariate techniques Disadvantages Vulnerable to changes in structure Black box --no theory! Poor in predicting cyclical turning points Cannot be used for what if (different assumptions) simulations Econometric models Application of statistics to economic/property data in order to establish relationships/models Models are causal relationships George Matysiak 8

9 Econometric models Single equation models Focus on forecasting a single variable (can ignore simultaneity issues) Structural models Recognize simultaneity issues (e.g. RICS City office market model) Econometric/explicit approach:advantages Logical and explicit framework enabling relationships to be investigated May have a well-developed body of theory and existing empirical evidence to draw upon Possible to investigate hypothesised relationships Permit an understanding of relationships and subsequent modification when underlying dynamic structure changes Alternative modelling methodologies/strategies which can be referred to Permits a simplified representation of the real world to be postulated to any degree of dis-aggregation Econometric/explicit approach:advantages (cont) Influence of each variable in a relationship may be assessed (simulation) Whole battery of statistical tests available Possible to trace and reproduce the causes of both successful and inaccurate forecasts when outcome known Identification of turning points Policy simulations possible Forecast best in the long run George Matysiak 9

10 Econometric approach:issues Prone to "data mining" Data problems e.g. measurement/revision Unobservable variables e.g. expectations No consensus about relationships Simultaneity problems Wide margins of uncertainty. Implies that true relationship may be little understood A "good fit" on past data is no guarantee of continuing relationship Non-constant parameters i.e. changing relationships Inadequate sample sizes Omitted variable bias (missing variables) Regression models, cause and effect When we formulate a regression model relating the inputs X to the output Y, we often think of the model as describing a cause and effect relationship between the inputs and outputs Because of the ease of use of modern statistical software, regression analysis has become grossly abused by naïve users who postulate regression models that are virtually meaningless and sometimes downright hilarious (to those understanding the limits of regression modeling) Many examples of regression models being suspect correlation/significant regression results does not imply causation or meaningful relationship apply common sense tests, not just statistical tests! Modelling & Forecasting Property Markets George Matysiak 10

11 Links between property variables and the economy Rental growth is a function of economic growth - different sectors have different growth expectations Inflation affects rental growth Interest rates affect corporate profit/demand & cost of supply Target rates are based on returns in other capital markets Discount rates reflect Government Bond/SWAP rates/yield curve + risk premia Example: office market modelling framework The Space Market determination of demand/supply and development of office space relationships The Capital Market property pricing relative to other assets (investors supply finance capital) Modelling linkages between the two markets important short run and long run (equilibrium) considerations Occupier Market, Capital Market & Property Market Rent Occupier Market Space S D Risk Rent Property Discount Rate Property Cap Value Risk Free Rate Risk Premium Capital Market Construction Costs Property Development Finance & Funding George Matysiak 11

12 City of London Office Model Equation 4 Equation 7 Planning Policy Expected Real Effective Rents Starts Equation 2 Interest Rates Equation 6 Expected Capital Gains Equation 5 Equation 3 Completions Depreciation/ Withdrawals Equation 1 Stock/Space City Employment Market Share Economic Growth Equation 10 Equation 8 Real Effective Rents Rent Free Periods General Price Level Equation 9 Headline Rents Yield considerations Property Yields Investment performance, rate of return, is driven by rental growth and changes in yields Do you think that property markets are currently over-priced, fairly priced or under-priced? Why? George Matysiak 12

13 Why model & forecast yields? Investment performance, rate of return, is driven by rental growth and changes in yields Framework for analysis: DCF profile 2 c c(1 g) c(1 g) V (1 ) (1 ) (1 ) r r r if r > g k = r-g cap rate (market info/comparables) r and g are anticipated future values c V ( r g) Unbundling the all risks yield k = Rf + Rp + E(d) - E(g) Rf = risk free rate of return Rp = risk premium E(d) = expected depreciation E(g) = expected rental growth What are these values? Explicit DCF framework (one approach) short term/long term value distinction Market view v intrinsic (fundamental) assessment George Matysiak 13

14 Modelling yields in theory The initial yield (cap rate) can be expressed as: k = RF + RP - g + d A change in the yield can be the result of a change in any of these Thus, modelling yields requires a link to the investment market (through the risk free rate) as well as occupier market An approach to yield determination Combination of technical forecasts fundamental values (equilibrium values) Reversion of modelled (technical) forecasts towards fundamental values Yield assessment Short-term weight of money impact Long-term fundamental risk premium reduction/re-pricing? George Matysiak 14

15 Yield drivers Considerations: DCF components Sentiment/weight of money Random component Are there differences in yields between property types? Are there differences in yields across locations? Can we get a fix on the risk premium? historic returns profile may provide some insights yield assessment Short-term rental growth outlook required return/risk premium weight of money impact Long-term fundamentals risk premium risk free rate rental growth Relative importance? Scenario 1:Equal annual discount and growth rates Percentage 70.0% 60.0% 50.0% 40.0% 30.0% Percentages of Total Value All discount rates 9% risk free 5% risk premium 4% rental growth 2% In excess of 5 years represents 70% of value 20.0% 10.0% 0.0% Year 1 Year 2 Year 3 Year 4 Year 5 Sum 5 >5 Years Years George Matysiak 15

16 Scenario 2: First five years risk premium increased by 1% Percentage 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% Percentages of Total Value LT discount rate 9% risk free 5% risk premium 4% rental growth 2% Short-term discount rate 10% risk free 5% risk premium 5% rental growth 2% In excess of 5 years represents 69.4% of value Change in value = -3.6% 0.0% Year 1 Year 2 Year 3 Year 4 Year 5 Sum 5 >5 Years Years Scenario 3: LT risk premium increased by 1% Percentage 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% Percentages of Total Value LT discount rate 10% risk free 5% risk premium 5% rental growth 2% Short-term discount rate 9% risk free 5% risk premium 4% rental growth 2% In excess of 5 years represents 67.1% of value Change in value = -8.8% 0.0% Year 1 Year 2 Year 3 Year 4 Year 5 Sum 5 >5 Years Years Modelling and forecasting Reading office rents George Matysiak 16

17 A rental modelling approach Modelling methodology may distinguish between long run rental levels and short run dynamic (rental growth) changes. (Analogy with house price levels and growth in house prices) Link rental levels with fundamental driver variables e.g. retail rental levels may depend on retail turnover/sales Capture short-term movements in rental levels In long term reversion towards underlying fundamental rental values Technically known as an error correction mechanism Space Variables AVAILABILITY TAKE_UP Source: Strutt & Parker Fundamental link: rental indices ERV IPDALLOFFICEINDEX ERV READINGOFFICEINDEX George Matysiak 17

18 Rental Growth % l a u n A IPD ALL OFFICE RENTAL GROWTH READING OFFICE RENTAL GROWTH Rental Growth & Availability READING AVAILABILITY READING OFFICE RENTAL GROWTH Source: IPD, Strutt & Parker Rental Growth & Take-Up READING TAKE UP READING OFFICE RENTAL GROWTH Source: IPD, Strutt & Parker George Matysiak 18

19 Anorak s corner: Estimated Long-Run Relationship Variable Coefficient Std. Error t-statistic Prob C IPD Office Rental Index R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) 0 Anoraks corner: Estimated Rental Growth (Dynamic) Relationship Variable Coefficient Std. Error t-statistic Prob. C ERV_Growth(-1) Availability -5.35E E Take-up 6.61E E Correction Term Anorak s corner: Some summary regression statistics for growth equation R-squared 0.87 Adjusted R-squared 0.83 S.E. of regression 2.85 George Matysiak 19

20 Schematic of regression-based forecasting Econometric model Dependent Variable Independent variables Independent variables Regression Regression Coefficients Point forecast Interval Forecast Residuals Forecast errors Past Data Forecast Forecast rental growth % % - 6.6% Base Forecast Upper limit Lower limit...a large standard error can imply next to useless forecasts! George Matysiak 20

21 Stages in the modelling/forecasting process Define forecasting problem Look at relevant theory & techniques Collect and analyse data Define/specify and estimate the model test robustness/diagnostics, forecast and evaluate Present initial forecasts and revise on feedback Distribute final forecast Monitor and evaluate the forecasts when actual values are know! An important basic assumption underlying forecasts Past patterns or underlying behaviour/relationship will continue into the future can we do better than this? George Matysiak 21

22 Investment Property Forum: Profile of Annual Consensus Forecasts IPF Survey data IPF surveys undertaken in February, May, August and November A changing sample of real estate organisations involved in real estate brokerage/advisory, institutional fund management and investment banking Publicly available by category and consensus Individual forecasts provided on a confidential basis Targets Rental growth, capital growth and total return, to match end of calendar year performance as recorded by the IPD All Property Index Forecasts up to three years ahead The target becomes easier to hit as the calendar year progress over the year, informed by reported IPD monthly performance figures George Matysiak 22

23 IPF: Distribution of rental growth forecasts IPF: Distribution of rental growth forecasts IPF: Evolution of consensus UK rental growth forecasts for 2011 George Matysiak 23

24 IPF: Distribution of capital growth forecasts Range of views for total return Range of views for London offices rental growth George Matysiak 24

25 Accuracy of consensus forecasts One-year ahead rental growth forecasts One-year ahead capital growth forecasts George Matysiak 25

26 One-year ahead total return forecasts Two-year ahead rental growth forecasts Two-year ahead capital growth forecasts George Matysiak 26

27 Two-year ahead total return forecasts Observations & Conclusions Interpolation vs Extrapolation When using a regression model for prediction, only predict within the relevant range of data Relevant range for interpolation House Price ( 1000s) Square Feet Do not try to extrapolate far beyond the range of observed X s George Matysiak 27

28 How can forecasts go wrong? Values of input variables System shock/surprises Model errors; model is not perfect Adjustments to pure model generated output Structural breakdown/model failure the world has changed! Forecasts outside range of experience Thin market - little or very specific evidence is sample evidence representative? Random component Always look at prediction interval (range)! Model failure? Forecasts can (will) go wrong! Model stability Data revisions Assumptions Subjective adjustments Random component George Matysiak 28

29 A pro-forma for forecasts Assumptions should be made clear Judgemental adjustments should be made clear Interval/scenario forecasts i.e forecast uncertainty in addition to point/base case forecasts UK property market total return forecasts: scenarios Source: Gerald Eve, Invbrief Spring 2009 UK rental growth forecasts: scenarios Source: Gerald Eve, Invbrief Spring 2009 George Matysiak 29

30 Rental growth City offices: scenarios Source: Gerald Eve, Invbrief Spring 2009 Observations 1 The shorter the time frame, the greater the attraction of simple time series models The longer the time frame, the greater the attraction of causal modeling, such as regression analysis Parsimony principle: other things equal, simple models are preferable to complex models Observations 2 Simple models can be more effective than complex ones A sophisticated or elaborate model does not imply that it is more likely to perform better than a simple forecasting rule (more can go wrong!) Market based knowledge should be used to inform model generated forecasts George Matysiak 30

31 it s only a forecast The forecasts usually represent most likely ( base ) outcome will (most likely) turn out to be wrong! But, understanding the process is valuable how did we get here? Think in terms of scenarios (alternative outcomes)...true but... Keep it all in perspective! Forecasting is the art of saying what will happen, and then explaining why it didn t! Some things are so unexpected that no one is prepared for them The market can stay irrational longer than you can stay solvent J.M Keynes George Matysiak 31

32 Model plus random component! Appendix Measuring forecast accuracy: metrics Evaluating forecasts Statistical Measures - based on the error Error = Actual Forecast (1 period ahead) The Naive Forecast if you can't beat it, try again (or give up) Value to decision makers cost of 'errors' effect on decisions Monitor Forecast Error George Matysiak 32

33 Definition of the forecast error Error (e) of a forecast is measured as a difference between the actual (A) and forecasted values (F), that is, e=a-f, or, in a relative form: e=100% (A-F)/A. The error can be determined only when actual (future) data are available. Some measures of forecast accuracy 1. Mean Error (ME) 2. Mean Absolute Error (MAE) 3. Mean Percentage Error (MPE) 4. Mean Absolute Percentage Error (MAPE) 5. Mean Squared Error 6. Root Mean Squared Error Forecasting Performance Measures 1 MFE n 1 MAD n n t1 n t1 100 MAPE n 1 MSE n n t1 ( D t F ) D t F t n t1 Dt Ft D ( D t F ) t t t 2 George Matysiak 33

34 Mean Error ME ( A F ) t n where A t = Actual value in period t F t = Forecast value in period t n = Number of forecast periods t Mean Absolute Error MAE A F t n where A t = Actual value in period t F t = Forecast value in period t n = Number of forecast periods t Mean Percentage Error ( At Ft ) / At MPE n where A t = Actual value in period t F t = Forecast value in period t n = Number of forecast periods 100 George Matysiak 34

35 Mean Absolute Percentage Error ( At Ft ) / At MAPE n where A t = Actual value in period t F t = Forecast value in period t n = Number of forecast periods 100 Mean Squared Error MSE ( A F ) n where A t = Actual value in period t F t = Forecast value in period t n = Number of forecast periods t t 2 Root Mean Squared Error RMSE ( A F ) where A t = Actual value in period t F t = Forecast value in period t n = Number of forecast periods t n t 2 George Matysiak 35

36 Uniwersytet Ekonomiczny George Matysiak Introduction to modelling & forecasting December 15 th, 2014 George Matysiak 36