Real Estate Price Dynamics and the Value of Flexibility...1 International Meeting of the American...

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International Meeting of the American Real Estate & Urban Economics Association

Amsterdam, July 5, 2017

Real Estate Price Dynamics and the Value of Flexibility

David Geltner, PhDMassachusetts Institute of Technology

MIT Center for Real Estate

Reference:D.Geltner & R.de Neufville,

“Flexibility & Real Estate Valuation under Uncertainty:A Practical Guide for Developers”

Wiley Blackwell, Forthcoming 2018.

Email me [email protected] if you want an academic paper summary of the book & this lecture.

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Topics:

1) Real Estate Price Dynamics

2) The Value of Investment Resale Timing Flexibility

3) A Typology of Real Estate Development Options

4) (time permitting…) Valuing Timing & Product Options in Development

Presenter

Presentation Notes

This topic is taken from my new book, forthcoming from Wiley Blackwell, “Flexibility and Real Estate Valuation Under Uncertainty: A Practical Guide for Developers”, co-authored with MIT Professor Richard de Neufville.

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Empirical Investment Property Asset Price Indices,Numerous Markets in the USA…

Indices based on market transaction prices of repeat-sales of same properties (Source: Real Capital Analytics, Inc.)

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Real Capital Analytics CPPI

National All Types

New York Boroughs Apartment

Manhattan All TypesNYC Apartment

LA CBD West Apartment

Manhattan Apartment

1. RE Price Dynamics

Knowledge of R.E. Price Dynamics Based on:• Historical empirical evidence (Transactions

Prices, Appraisals; Indexes, Residuals)• Economic theory (Capital Mkt theory,

Micro-economic theory)• Common sense

Presenter

Presentation Notes

Granularity of Real Estate Market Prices This slide depicts price indices for over 200 separate Space Markets in the U.S., based on the actual transaction prices of “repeat-sales” of investment properties, that is, properties sold more than once. The price indexes are created by computing the percentage changes of the same property between when it was bought and sold. By observing such changes over continuous time, statistical (econometric) techniques can parse out the market price movements implied for each period of time in a given history. By basing the price index only on the price changes within the same properties, the index avoids an “apples vs oranges” problem of comparing prices of different assets across time. Repeat-sales price indices also directly track the type of price changes faced by property investors, because property investors sell the same properties that they have previously bought, reflecting the same type of price movements as what the repeat-sales price index is based directly on. Price indices like these, and the transaction price databases on which they are based, enable us to study and quantify the nature of investment property price dynamics in great depth and detail. We see that, while the specifics may vary across markets, all property asset price dynamics tend to reflect a few basic common causal or source components. Note that, while the specific movements of the 200 lines in the chart in the slide differ from one to another, the general appearance and “shape” of all the lines appears pretty similar (and, not unlike the simulated lines in we generate artificially).

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Typical Stock Market Price Dynamics:Random Walks (simulated)…

Pricing Factors for Five Future 24-year Scenarios, based on the Random Walk


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Five Independent Random Future Price Histories (Trials): Stock Market Price Dynamics

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

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Presentation Notes

Contrasting Stock Market vs Real Estate Market Price Dynamics Let’s begin with a brief comparison, that may serve to acquaint you with the big picture of what we’re talking about. Let’s compare price dynamics in the stock market with those in the private property asset market. Many students of business or finance are somewhat familiar with price dynamics in the stock market. That market practically originated the idea of “price dynamcis”. We see pictures of indexes of stock prices every day in newspapers and on the television or internet. The lines in those pictures often look roughly something like those in this picture. (And interestingly, it doesn’t really matter whether the time units on the horizontal axis are measured in years, months, days, or even decades!) The picture here is of simulated price histories, randomly generated in a computer (actually, in Excel). They reflect a type of dynamic evolution known as a “Random Walk”. (This type of price dynamic is so famous and ubiquitous in the stock market, we will sometimes simply abbreviate it as “RW”.) The Random Walk is a good model of price dynamics in the stock market. It is not perfect (and it may depend on the frequency of measurement), but it is pretty good. Here’s why… The stock market is very “efficient” in the sense of “informational efficiency”. That is, prices of stocks move very quickly to reflect any news that is relevant to their values. This is because stock markets have high volume of trading of homogeneous shares (each share of the same company has exactly the same claim to value and cash flow) with very low transactions costs and with publicly quoted bid and offered prices and immediate public reporting of trading in what is essentially a double-sided auction market. This makes the market very liquid and highly informed, and enables the observable market prices to almost immediately reflect all the information relevant to their values. Thus, the only thing that could “move” prices (cause them to change over time) would be the arrival of new information, “news”. By definition “news” is not predictable. (To the extent it is predictable, to that extent it is not really “news”.) Thus, the movement of a stock price from its current level will reflect only the arrival of news, and since news is unpredictable, stock price movements must be random, starting from whatever level they were previously at. If we model such a process mathematically, it says that the price next period equals the price this period plus a random disturbance that is uncorrelated with anything in the past: P(t+1) = P(t) + e, where “e” is a random number. This is the definition of a Random Walk. You can easily model it in a computer spreadsheet such as Excel, by using the computer’s random number generator. This is how we have generated the picture in the slide here.

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Typical Real Estate Price Dynamics:More Complicated (simulated)…


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Five Independent Random Future Price Histories (Trials): Real Estate Price Dynamics


Pricing Factors for Five Future 24-year Scenarios, based on Real Estate Parameters (Random Walk with Autocorrelation, Cyclicality, & Mean Reversion)

Presenter

Presentation Notes

Contrasting Stock Market vs Real Estate Market Price Dynamics Now look at this picture. Here we have similarly created a simple computer model of typical real estate asset price paths, typical real estate market dynamics. Do you see a difference in appearance compared to the stock market-like, Random Walks of the previous slide? These price paths also show some random evolution. After all, real estate markets are not totally inefficient. Real estate market participants also pay attention to news that affects the values of properties, and property prices therefore also move to some extent like a Random Walk. But real estate price dynamics are more complicated, because real estate assets are different from stocks of typical corporations, and because the way private real estate asset markets operate is different from how the public stock exchanges operate. (Incidentally, REIT stocks, the stocks of publicly-traded real estate investment companies, do display price dynamics very similar to most other stocks, largely reflecting the RW process. But here we are focusing on real estate asset prices in the private, direct property market, the price dynamics that are most relevant for micro-level real estate investment.) The simulated real estate price paths shown here reflect a combination of the RW with several additional elements, including autocorreation (inertia), cyclicality, and mean-reversion (tendency to move toward some long-run average level). The following slides will take you in more depth through a “tour” of seven sources or components of real estate price dynamics…

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Five Independent Random Future Price Histories (Trials): Stock Market Price Dynamics


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Same scales…

Both sets are generated from a stochastic process that has 20% annual volatility.

Presenter

Presentation Notes

Contrasting Stock Market vs Real Estate Market Price Dynamics Now look at this picture. Here we have similarly created a simple computer model of typical real estate asset price paths, typical real estate market dynamics. Do you see a difference in appearance compared to the stock market-like, Random Walks of the previous slide? These price paths also show some random evolution. After all, real estate markets are not totally inefficient. Real estate market participants also pay attention to news that affects the values of properties, and property prices therefore also move to some extent like a Random Walk. But real estate price dynamics are more complicated, because real estate assets are different from stocks of typical corporations, and because the way private real estate asset markets operate is different from how the public stock exchanges operate. (Incidentally, REIT stocks, the stocks of publicly-traded real estate investment companies, do display price dynamics very similar to most other stocks, largely reflecting the RW process. But here we are focusing on real estate asset prices in the private, direct property market, the price dynamics that are most relevant for micro-level real estate investment.) The simulated real estate price paths shown here reflect a combination of the RW with several additional elements, including autocorreation (inertia), cyclicality, and mean-reversion (tendency to move toward some long-run average level). The following slides will take you in more depth through a “tour” of seven sources or components of real estate price dynamics…

Eight Sources or Components of R.E. Price Dynamics

These 8 ==> Nature & Magnitude of “Uncertainty”

0. Starting from a known observable price…1. Long-term Trend Rate2. Volatility3. Cyclicality4. Mean-reversion5. Inertia (Autoregression)6. Price dispersion (noise)7. Idiosyncratic drift8. Black swans


Presenter

Presentation Notes

The Difference between Uncertainty and Risk (From the book Appendix…) In common parlance, when thinking about the future of an investment, the words “risk” and “uncertainty” may seem to refer to the same thing. Whether you call it “risk” or “uncertainty,” it reflects the fact that you don’t know for sure what the future will bring, and that can cause your investment to perform differently, possibly worse, than you had expected when you went into it. But economists often distinguish the two terms. In economics terminology, “risk” is quantifiable. Risk can be described by a known probability function. If you know in advance that there is a 20% chance that the bond you are investing in will default and yield a negative 10% return, but otherwise will yield a positive 10% return, then you know your ex ante expected return is: (0.8)X10% + (0.2)X(-10%) = 6%. And you know how much “risk” you face in the investment. This might be referred to as a case of “known unknowns.” You don’t know if the bond will default, but you know the probability that it will happen and the effect of the default if it does happen. In contrast, “uncertainty” is when you cannot quantify the probability; you don’t know how much risk is there. This might be thought of as a case of “unknown unknowns.” Investors are usually much more averse to uncertainty than to risk. But in reality, most investments do face at least some degree of uncertainty. We may have a lot of historical evidence about the nature of stock market returns, but we don’t know for sure what is the probability function that governs their future returns. In this book, we often use the terms “uncertainty” and “risk” interchangeably. The phenomenon we are actually dealing with is uncertainty. But we try to convert uncertainty into risk, in effect, in our simulation models, by positing probability functions that we input into the models. It is in this sense that we quantify something that is in principle not quantifiable, and we can speak of the “magnitude of uncertainty.” We need to do this in order to do quantitative analysis. But we need to be humble. We can never know for sure that our input probabilities are correct. We actually face uncertainty, not mere risk.

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Real estate price indexes, & the transaction data they are made from, enable us to identify and quantify eight components of real estate price dynamics or randomness in the way property asset prices evolve over time. Here you can see six of them: (1) The long-term trend rate…


Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Component #1: the long-term trend. As noted in Module 2 (Unit 4), in the U.S. the long-term trend rate in property asset price growth (for the same properties, that is, aging over time) tend to be 1% to 2% less than inflation. This reflects the real depreciation of the building structure, net of capital expenditures (that is, even after or in spite of capital improvements), combine with the fact that the land component of property value averages only about half the total asset value, and land value for commercial property in U.S. cities has not tended to grow much in real terms (net of inflation). There are exceptions, and in some places (and some other countries) where land supply is more highly constrained in the presence of strong lont-term growth in demand for space, the long-term trend growth rate may be higher than this approximate rule of: Inflation minus 1% to 2% per year.

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Real estate price indexes, & the transaction data they are made from, enable us to identify and quantify eight components of real estate price dynamics or randomness in the way property asset prices evolve over time. Here you can see six of them:(1) The long-term trend rate; (2) Short-term volatility (that accumulates)…


Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Component #2: Volatility. This is the component of real estate asset price dynamics that reflects the Random Walk, the current response of property prices to relevant current news. This is the part of real estate price dynamics that is therefore similar to stock market price dynamics. At the broad aggregate level, there is relatively little such volatility, though there is some, because property asset markets are generally well functioning markets that naturally reflect and respond to relevant news, at least, over some time horizon (with some lag). The quantitative measurement of volatility in real estate market prices depends strongly on the frequency at which the returns are computed. As noted in our description of the RW, this type of volatility accumulates in the level of the price index. If the market randomly moves up one period, then its movement in the next period will start from that new level that the index moved to the previous period. In the aggregate index depicted here (the heavy black line) volatility does not show up much. This is because volatility (steadily accumulating risk realization) is largely obscured by Cyclicality (Component #3), Mean Reversion (Component #4), and Inertia (Component #5). (These components of real estate price dynamics will be illustrated in the following slides.) But this obscuration of volatility does not mean that volatility is not present in the real estate price index. It is most certainly present, for the reason noted above, the reflection of the arrival of “news” in the valuation of property assets.

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Real estate price indexes, & the transaction data they are made from, enable us to identify and quantify eight components of real estate price dynamics or randomness in the way property asset prices evolve over time. Here you can see six of them: (1) The long-term trend rate; (2) Short-term volatility; (3) Cyclicality; & (4) Mean Reversion…

Mid-Cycle to Mid-Cycle 2001-1615 yrs


Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Component #3: Cyclicality. Real estate asset prices historically seem to exhibit much stronger cyclicality than we observe in the stock market. The cycle tends to be largely national, and often even international, at least among investment properties that are large and prominent enough to attract international capital. The period of the cycle seems to be pretty long by economic standards, over ten years and more commonly 15 to 20 years. The evidence is that the cycles seem to be pretty regular. What causes such cyclicality? We are not sure, and there may be several causes, and there is no guarantee that the future will be very similar to the past in this regard. One theory is that it is related to the large use of debt financing in real estate investment. Mortgage and other debt or debt-like financing tends to be a larger share of real estate’s capital structure than is true for most stocks. And debt markets tend to be cyclical. The asset market may be, but isn’t necessarily or always, in sync with the space market. There have been times when the asset market was strong when the space market was week (early 1980s, early 2000s). A general economic recession will almost always cause some down movement in the space markets, but not necessarily in the asset market. Component #4: Mean-reversion. This refers to the tendency of prices to revert toward some long-run level or trend. In part, over a long horizon, mean-reversion could describe some aspect of cyclicality. But over the shorter term, prices also seem to revert toward some long-run trend. There is a fundamental economic reason why such mean-reversion would make sense. We have noted that on average, in the U.S., approximately half of the value of the typical investment property reflect the land value component of the property asset value. The other half reflects the value of the built structure. The land component is in some sense like a pure, perpetual capital asset that is of very inelastic supply. Demand for land can rise, or fall, and the price of the land must rise and fall accordingly, as the supply is inelastic. But building structures are produced goods, very long-lived it’s true, but produced goods nevertheless, in this sense not fundamentally different from other produced capital goods like motor vehicles, airplanes, ships, refrigerators… Produced goods prices reflect the price elasticity of their supply. The construction industry tends to be pretty price-elastic. In most countries, an increase in demand for construction does not drive up the price of construction very much or for very long. And vice versa, a decrease in demand for construction tends more to reduce the quantity of construction than to reduce its price. The price of construction reflects the marginal opportunity cost of the inputs into construction: labor, materials. These tend to be pretty elastically supplied most of the time in most places. While it may appear that construction prices rise over time, once you control for general inflation and for improvements in the quality of the construction, in fact the real cost of construction probably does not have much of an upward trend, if any, over the long term. At least, this has been the history. Thus, price elasticity of supply of structures (construction) causes some component of property asset prices to tend to revert toward the long run marginal cost of construction, which tends to be pretty stable in real terms.

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Index of Long-term History of U.S. Institutional Commercial Real Estate Same-property Transaction Prices: 2000 = 100 (nominal $)

This longer term historical price index shows the cycles in commercial (investment) property more completely…

Pk-Pk 1971-8716 yrs

Pk-Pk 1987-200720 yrs

Trgh-Trgh 1975-9217 yrs

Trgh-Trgh 1992-200917 yrs


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Real estate price indexes, & the transaction data they are made from, enable us to identify and quantify eight components of real estate price dynamics or randomness in the way property asset prices evolve over time. Here you can see six of them : (1) The long-term trend rate; (2) Short-term volatility; (3) Cyclicality; & (4) Mean Reversion;& (5) Inertia (momentum, Autoregression: AR(1))…


Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Component #5: Autoregression (inertia). This refers to the tendency of prices to display momentum. Once they start moving in one direction, they tend to continue to move in that direction for a while. The returns, or changes in the price levels, tend to reflect in part the previous period’s return. That is, the returns have “memory”. This is the opposite of the Random Walk type of process. What causes autoregression or inertia in real estate prices? It is the lack of perfect informational efficiency that distinguishes real estate markets from stock markets. When news arrives relevant to asset market values, nobody knows right away exactly what that means for the values of specific individual assets. In the face of such uncertainty, it is rational for investors to react conservatively, to minimize the amount by which they revise their “reservation prices” (the private valuations at which they would be willing to trade). If bad news arrives, sellers will only slightly or slowly revise downwards the prices at which they are willing to sell, though buyers may tend to more quickly and substantially reduce the prices at which they are willing to buy. The market may display a greater reduction in trading volume than in the prices observed of transactions that do get consummated. Essentially, the news does probably eventually get fully incorporated into transaction prices, but it happens gradually, with a little bit of the news getting incorporated each period, for some time. This creates autocorrelated returns, serial correlation. The return in one period tends to be positively correlated with the return in the previous period.

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Summarizing up to here:1) Mkt Trend ≈ 1-2%/yr < Infla (real depr in structures) Secular trends, Real Growth, Deprec, Infla.2) Mkt Volatility ≈ 10-15%/yr. Mkt Informational Efficiency, News Arrival.3) Mkt Cycle ≈ 10-20 yrs, amplitude 50% of mean. Sup/Dem (space), Capital Flows (asset mkt).4) Mean Reversion ≈ 0.2-0.4 . Bldg structure is produced good (supply elasticity), Fdtl real values.5) Mkt AR(1) ≈ 0.2-0.4 (annual freq). Lack of perfect info efficiency, Sluggish price discovery.

Mid-Cycle to Mid-Cycle 2001-1615 yrs

Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Let’s summarize up to now. We have introduced five components of private real estate market returns. All five of these components apply systematically to all properties, hence, they apply to aggregate market returns, the types of returns that are reflected in price indexes (such as, in the thick black line in the chart in the slide, the aggregate index). This slide summarizes the sources or causes of these five components of property market price dynamics, as we have discussed in preceding slides. The remaining two components of property price dynamics are non-systematic across individual properties, that is, they apply to how individual property prices move differently than or separately from each other and from the market wide average…

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We can quantify: 48% ≈ exp(sqrt(2*.15^2 + 6*.12^2))-1(Mkt (index) volatility is 15%/yr. The values 2*.152 & .122 are intercept & coefficient from regression of repeat-sales model residuals-

squared onto time-between-sales. Deal noise twice: once each at buy & sell.)

Preceding are features of the market as whole (aggregate prices). A sixth type of uncertainty, primarily in individual assets or metro markets: Idiosyncratic drift of individual assets or market cumulatively away from overall average…


Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Component #6: Idiosyncratic Drift. This refers to accumulating volatility that is specific to individual assets, uncorrelated with volatility or other price movements in other assets, and hence, uncorrelated with the market index. Over time, this causes individual property price paths to diverge from the market index. It is difficult, almost impossible to accurately depict the true price paths of individual properties (repeat appraisals of the same property tend to be strongly anchored to the previous appraisal). But we can observe the cumulative drift in their price paths by the dispersion in the individual repeat-sales pairs as a function of the time between their sales. Here for illustrative purposes we are depicting something that probably looks similar to individual property idiosyncratic drift by noting the cross-sectional dispersion in the individual 100+ granular price indices in this depiction of the Real Capital Analytics market indices. In fact, by analyzing the individual repeat-sales pairs dispersion, we can quantify the approximate typical magnitude of idiosyncratic drift. It is surprisingly large, on the order of 12% per year in terms of standard deviation of the individual property return differences from the market index. Other analysis indicates that the idiosyncratic drift is not exactly a Random Walk. There seems to be a limit to how far individual property values can usually deviate from the market trend in which they are located. Individual properties can only do “so well” or “so poorly”, compared to the market average. To borrow terminology from the stock market, in real estate the “shooting stars” can only shoot so high, and the “fallen angels” can only fall so far. Still, as you can glean from this depiction of granular market drift, cumulative idiosyncratic drift is likely to be quite significant for investment performance at the micro-level of individual properties. Another thing that we observe is that individual property idiosyncratic performance tends to occur largely in the first few years after acquisition, either doing well or poorly compared to the market average, and they their returns tend to revert toward the market average return, before the property is re-sold again. Idiosyncratic investment performance no doubt partly reflects “luck”. But surely it also reflects the relative skill and diligence of some property investors compared to others. For this reason, idiosyncratic performance should be of particular interest to micro-level property investors. There is not much you can do about the market your property is in. But there may be a lot you can do about your particular property within that market.

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Actual Sale Price Minus TBI Predicted Value (% of Sale Price)

Histogram of TBI Sales Price Prediction Error

Std Dev = +/- 15%Avg Absolute Diff = 11.1%

A seventh type of uncertainty in individual assets: Price Dispersion of actual prices around predicted price…

TBI model is very good predictor of asset prices… Starts out with professional appraisal of each property, then improves on that with regression model of actual transaction prices to eliminate appraisal lag…


Presenter

Presentation Notes

Eight Components of R.E. Asset Price Dynamics Component #7: Price Dispersion (“noise”). This brings us to the last of the seven components of property price dynamics. In a sense, this is not really a “dynamic” component. No one can know the exact market value of any given property at any given time. The transaction price in any given deal will be the result of, effectively, of a search and negotiation process between one buyer and one seller, neither of whom knows the exact market value. Even if there is an auction process (and investment properties in the U.S. are often sold by way of a two-stage sealed-bid auction), the process still largely represents two individuals “finding each other”, with neither knowing very exactly the market value. The result is that actual sale prices are distributed randomly around the (unobservable) “true market value” (which by definition equals the mean of the ex ante probability distribution of the sale price). This type of random dispersion in observable prices differs from the “volatility” that has been previously described (in Components 2 & 6) in that price dispersion, or “noise”, does not accumulate over time. It occurs only if and when a property is sold. Still, we need to consider this aspect of real estate prices if we are going to simulate the property price dynamics that matter for investors.

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Actual Pct Change Dispersion Around Index

Histogram of CPPI Individual Properties Round-Trip (avg 6 yrs hold) Price Cumulative % Change Dispersion Around Market (Index)

Std Dev = +/- 48%Avg Absolute Diff = 33%

This histogram reflects a combination of the sixth and seventh sources of uncertainty: Pricing Noise & Idiosyncratic Drift.

Quantification: 48% ≈ exp(sqrt(2*.15^2 + 6*.12^2))-1(Mkt (index) volatility is 15%/yr. The values 2*.152 & .122 are intercept & coefficient from regression of repeat-sales model residuals-

squared onto time-between-sales. Deal noise twice: once each at buy & sell.)


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aka “fat tail” events:e.g., Financial crisis of Oct 2008-Mar2009…

The eighth type of uncertainty: “Black Swans,” Unpredictable major jumps affecting all assets…


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Reviewing the Types of Uncertainty seen in the History of REIT share prices…

(1) Long-term avgdrift rate

(8) “fat tail” events:e.g., Financial crisis of Oct 2008-Mar 2009…


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(2) MktVolatility





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(3) Long-run cycle &(4) Mean-Reversion

(2) MktVolatility





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(7)IdioDrift

+ (5) Inertia & (6) Dispersion not depicted here as does not exist in stock mkt (but does in priv mkt)



(3) Long-run cycle

(2) MktVolatility



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Topics:





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Presentation Notes


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Expected Cash Flows: Totals: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11

Projected Operations (Realistic Assumptions):Potential Gross Income (PGI) 100.00 102.00 104.04 106.12 108.24 110.41 112.62 114.87 117.17 119.51 121.90Vacancy Allowance 5.00 5.10 5.20 5.31 5.41 5.52 5.63 5.74 5.86 5.98 6.09Effective Gross Income 95.00 96.90 98.84 100.81 102.83 104.89 106.99 109.13 111.31 113.53 115.80Operating Expenses 35.00 35.70 36.41 37.14 37.89 38.64 39.42 40.20 41.01 41.83 42.66Net Operating Income (NOI) 60.00 61.20 62.42 63.67 64.95 66.24 67.57 68.92 70.30 71.71 73.14Capital Improvement Expenditures 10.00 10.20 10.40 10.61 10.82 11.04 11.26 11.49 11.72 11.95 12.19Net Cash Flow from Operations (PBTCF) 50.00 51.00 52.02 53.06 54.12 55.20 56.31 57.43 58.58 59.75 60.95PBTCF from Reversion 1218.99PBTCF Total (Including Reversion) 50.00 51.00 52.02 53.06 54.12 55.20 56.31 57.43 58.58 1278.75Time 0 PV @ OCC 1000.00Projected IRR @ Mkt Val Price 7.00% -1000.00 50.00 51.00 52.02 53.06 54.12 55.20 56.31 57.43 58.58 1278.75

The Starting Point:The classical 10-year DCF Valuation Pro-forma…

(Only make it realistic – no )Here, a simple rental property:

Key ideas:• Start from ubiquitous existing practice;• Practitioners have good knowledge about ex ante likely future

cash flows (once you give “haircut” to make realistic);• This “Base Case” or “original pro-forma” is realistic and

unbiased, hence, good estimates of means (prob expectations) of future CFs.

• Classic is “single-stream” (just one future…)

Pro-forma PV = $1000 (=MktVal); Going-in IRR = 7.00% (=OCC)

2. Value of Resale Flex

24

Represent possible future ex post deviations from ex ante projection (single-stream) by use of

“Pricing Factors”…Ratio by which we multiply the original pro-forma cash flow expectation to arrive at a future cash flow outcome in a given scenario

Future Scenario Cash Flow Outcome = (Classical Pro-Forma Cash Flow) X (Pricing Factor)

Example:Base Case Pro-forma Year “t” CF = $100.Optimistic Scenario Year “t” CF = $110.

Represent by Price Factor = 1.10:Optimistic Yr.t CR = BaseCase*PF = $100*1.10 = $110.


25

Model realistic real estate pricing factors this way, Represent possible future “scenarios” (outcomes)…

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Pricing Factors for Five Future 24-year Scenarios, based on Real Estate Parameters (Random Walk with Autocorrelation, Cyclicality, & Mean Reversion)


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• Each future scenario we randomly generate (using probability based Pricing Factors) is an equally possible “future history” (a “trial” in MC terms).

• In the real world, as the future happens (becoming the present fleetingly and then the past permanently), there is only one actual history.

• Prior to the future happening, as far as we know in the present, there are many possible futures that could happen.

• They are governed by our estimated probability distributions and pricing dynamics assumptions. This is the nature of uncertainty.

Monte Carlo Simulation to represent uncertainty in future ex post DCF Property Valuation (ex ante)…


27

Monte Carlo Simulation to represent uncertainty in future ex post DCF Property Valuation (ex ante)…• Each future scenario we randomly generate (using

probability based Pricing Factors) is an equally possible “future history” (a “trial” in MC terms).

• Generate many such scenarios (we use 10,000 for teaching purposes in Excel; you could do more).

• Integrate across all (e.g., 10,000) outcomes.• Relative frequency of simulated ex post outcomes

(fraction of 2000) is “sample probability” density.• It’s an estimate of actual underlying outcome

probability distribution, hence, estimate of:• Ex Ante Probability of Outcomes (quantification of

uncertainty: turning “unknown unknowns” into “known unknowns”, replacing “uncertainty” with “risk”).


28

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Time 0 PV @ OCC

PV Frequency Distribution Function(across 2,000 simulated project outcomes

Inflexible PV Distn Inflexible Mean PV Pro-forma PV

Effect of Uncertainty, Without Flexibility:Risk in property’s Time 0 PV

(ex post, discounted to Time 0 @ OCC)

Monte Carlo E[PV(CFs)] = PV(E[CFs]) Pro-forma“PV is a Linear Function of CFs”

E[PV] = $1000 = Pro-forma PV


29

Risk in property’s Time 0 IRR (ex post, @ $1000 price at Time 0)

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Realized IRR

IRR Frequency Distribution Function(across 2,000 simulated project outcomes)

Inflexible IRR Distn Inflexible Mean IRR Pro-forma ex ante IRR

E[IRR] < 7% = Pro-forma IRR


Ex Post IRR is symmetric probability distribution (not skewed), butIRR is Concave Function of PV E[IRR(CFs)] < IRR(E[CFs])

30

-5%

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IRR

Inflexible Ex Post PV Outcome

IRR by Ex Post PV @ $1000 Price, Inflexible Case


Ex Post IRR is symmetric probability distribution (not skewed), butIRR is Concave Function of PV E[IRR(CFs)] < IRR(E[CFs])

Presenter

Presentation Notes

PV is a linear function of CFs. If IRR is concave over PV, it is also concave over CFs.

31

PV has skewed distribution but unbiased in Proforma.IRR has symmetric distribution but biased in Proforma.

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PV Frequency Distribution Function(across 2,000 simulated project outcomes

Inflexible PV Distn Inflexible Mean PV Pro-forma PV

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Realized IRR

IRR Frequency Distribution Function(across 2,000 simulated project outcomes)

Inflexible IRR Distn Inflexible Mean IRR Pro-forma ex ante IRR

Uncertainty Without Flexibility…2. Value of Resale Flex

32

Modeling flexibility in resale timing:Can sell before 10 yrs, or after…

“Stop-Gain” Flexible Resale Decision Rule:Sell as soon as market prices are >= 20% above Base

Case (pro-forma) projection for any given year.

This type of rule is sometimes proposed for stock market investments, but it is controversial and does not systematically work well in simulations, because stocks follow Random Walk.But real estate has Momentum & Cycles & Mean-Reversion…

Example:Base Case Pro-forma Year “t” CF = $100.

In a given random future scenario Year “t” CV = $121.Then Sell! (not before or after).


33

• Don’t be “too greedy”.

• Mean-reversion: If it goes up, it’s got to come down.

• Cyclicality: If it goes up, it’s got to come down…

What is the idea behind the Stop-Gain Rule?2. Value of Resale Flex

34

Flexible ReSale Timing with Stop-Gain @ 20% over Base Case:Typical Cumulative Sample Probability Function, Target: PV

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PV Cumulative Distribution Function: Stop-Gain Rule @ Input Price Factor

(across 2,000 simulated project outcomes)

Flexible PV Distn Flexible Mean PV Inflexible PV DistnInflexible Mean PV Pro-forma PV

E[PV] ≈ $1250 = 25% grtr than

MktVal (pro-forma DCF) or Inflex


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Realized IRR

IRR Cumulative Distribution Function: Stop-Gain Rule @ Input Price Factor

(across 2,000 simulated project outcomes)

Flexible IRR Distn Flexible Mean IRR Inflexible IRR DistnInflexible Mean IRR Pro-forma ex ante IRR

Flex E[IRR] ≈ 14% > 6.6% ≈ Inflex E[IRR]Versus 7% pro-forma OCC

Flexible ReSale Timing with Stop-Gain @ 20% over Base Case:Typical Cumulative Sample Probability Function, Target: IRR


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PV Frequency Distribution Function(across 2,000 simulated project outcomes.) Note: Compare shapes & locations, not integral areas.

Flexible PV Distn Flexible Mean PV Inflexible PV Distn Inflexible Mean PV Pro-forma PV

E[PV] ≈ $1250 = 25% grtr than MktVal (pro-forma DCF)

Flexible ReSale Timing with Stop-Gain @ 20% over Base Case:Typical Sample Probability Density (Frequency) Function, Target: PV


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Flex E[IRR] ≈ 14% > 6.6% ≈ Inflex E[IRR]Versus 7% pro-forma OCC

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IRR Frequency Distribution Functions on Same Scale(across 2,000 simulated project outcomes)

Flexible IRR Distn Flexible Mean IRR Inflexible IRR Distn Inflexible Mean IRR Pro-forma ex ante IRR

Flexible ReSale Timing with Stop-Gain @ 20% over Base Case:Typical Sample Probability Density (Frequency) Function, Target: IRR


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PV Simulation ResultsFlex Inflex

Mean $1,265 $1,00095%ile $1,656 $1,424

Median $1,255 $9605%ile $884 $702

Std Deviation $228 $228mean/Std Deviation 5.55 4.40

Mean Holding Period (yrs) 9.28 10.00Proportion Inflex>Flex 0.19Proportion Flex>Inflex 0.76

Std Err of Difference 6.95

IRR Simulation ResultsFlex Inflex

Mean 14.34% 6.58%95%ile 34.70% 11.50%

Median 10.75% 6.46%5%ile 5.90% 2.09%

Std Deviation 9.10% 2.92%mean/Std Deviation 1.57 2.26

RiskPrem/DnSideStdDev 2.43 1.79Proportion Flex<Inflex 0.15Proportion Flex>Inflex 0.80

Typical Simulation Output Statistics:2. Value of Resale Flex

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Flexible Resale does not always beat Inflexible 10-yr(But it usually does…)

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Inflexible PV Outcome

Flexible Minus Inflexible PV Outcomes Difference As Function of Inflexible PV

Scatterplot: Each dot is one of 10,000 outcome scenarios


Downward shape of the cloud ==> Flexibility helps most in downside outcomes.

40Scatterplot: Each dot is one of 2000 outcome scenarios

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Flexible Minus Inflexible IRR Outcomes Difference As Function of Inflexible IRR


Flexible Resale does not always beat Inflexible 10-yr(But it usually does…)

Downward shape of the cloud ==> Flexibility helps most in downside outcomes.

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2. Value of Resale FlexStabilized Asset Flexible Resale Timing Effect:

Sensitivity Analysis of Various Price Dynamics and Decision Rule Assumptions on the Mean Valuation & IRR Outcomes

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Analysis Input Parameter Values

Resale Timing: Ex Post Mean Present Value Ratio Flexible / Inflexible

1: Vol & Noise

2: Auto & Revert

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5: Cyc Period

6: Cyc Phase

7: Trigger

9: StkMktVol

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Resale Timing: Ex Post Mean IRR Difference: Flexible - Inflexible

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2: Auto & Revert

3: Cyc Ampli

4: All Four

5: Cyc Period

6: Cyc Phase

7: Trigger

9: StkMktVol

10: StkMktTrig

Valuation finding appears pretty unbiased and robust.

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• Can you for sure commit to, implement Stop-Gain @ 20%?

• Will you have sufficient information?

• What if you care more about the IRR Std Dev?

• Simulation valuation is relevant for “Private Value”(or “Investment Value” ) of particular Decision Maker.

• Distinct from “Market Value” (MV).

Why is Mkt Val $1000, not $1250?...What is the $1250 PV if not Mkt Val?...


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Expected Cash Flows: Totals: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11

Projected Operations (Realistic Assumptions):Potential Gross Income (PGI) 100.00 102.00 104.04 106.12 108.24 110.41 112.62 114.87 117.17 119.51 121.90Vacancy Allowance 5.00 5.10 5.20 5.31 5.41 5.52 5.63 5.74 5.86 5.98 6.09Effective Gross Income 95.00 96.90 98.84 100.81 102.83 104.89 106.99 109.13 111.31 113.53 115.80Operating Expenses 35.00 35.70 36.41 37.14 37.89 38.64 39.42 40.20 41.01 41.83 42.66Net Operating Income (NOI) 60.00 61.20 62.42 63.67 64.95 66.24 67.57 68.92 70.30 71.71 73.14Capital Improvement Expenditures 10.00 10.20 10.40 10.61 10.82 11.04 11.26 11.49 11.72 11.95 12.19Net Cash Flow from Operations (PBTCF) 50.00 51.00 52.02 53.06 54.12 55.20 56.31 57.43 58.58 59.75 60.95PBTCF from Reversion 1218.99PBTCF Total (Including Reversion) 50.00 51.00 52.02 53.06 54.12 55.20 56.31 57.43 58.58 1278.75Time 0 PV @ OCC 1000.00Projected IRR @ Mkt Val Price 7.00% -1000.00 50.00 51.00 52.02 53.06 54.12 55.20 56.31 57.43 58.58 1278.75

The Starting Point:The classical 10-year DCF Valuation Pro-forma…

(Only make it realistic – no )

Here, a simple rental property:

For management purposes (not just Mkt Val estimation), does this “single-stream” DCF look pretty lame compared to explicit

consideration of both uncertainty and flexibility?...

Pro-forma PV = $1000 (=MktVal); Going-in IRR = 7.00% (=OCC)


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Topics:





Presenter

Presentation Notes


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Typology of RED Flexibility Options

1. Project Delay Option: Choose when to start project (land value call option, may equally be viewed as “put”).

2. Buildout Modular Production Timing Option: Start & stop (pause) project at any time and recommence later (or abandon).

3. Phasing Option: Parallel (independent) or Sequential. Once started, phase must be completed, but start of any phase can be delayed indefinitely (or ultimately abandoned).

4. Product Mix Switching Option: Build alternate real estate “products” (style, type, tenure; e.g.: 1Br vs 2BR, Apt vs Hotel, Rental vs Condo), substitute one for another.

5. Expansion Options: Horizontal (requires land bank), or vertical (requires design & permitting features).

3. Typology of Dvlpt Options

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Def

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Ch.15 Target Curves Characteristic of Puts & Calls…D

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Off

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InO

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Tim

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In next section consider these three only…



3.


5.

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Topics:





Presenter

Presentation Notes


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Central Tendencies of Simulated Ex Post Development Project Present Value & IRR,Comparison of Three Types of Flexibility Individually & in Combination…


Performance Metric:NPV Percent of

Land Value Internal Rate of ReturnMean Completion

Delay (Yrs)Start Delay Flexibility Only 21.5% 8.2% 1.9

Buildout Delay Flexibility Only 13.0% 7.8% 5.3Switch Option Only 13.6% 5.8% 0.0Start+BldOut Only 21.4% 9.0% 6.2Start+Switch Only 33.8% 12.0% 1.5

BldOut+Swicth Only 25.7% 11.1% 4.1All Three Options 33.9% 12.4% 4.8

Simulated Ex Post Mean Performance Differential, Flexible Minus Inflexible:

Main Results:Flexibility…• Adds 13-34% to project value (land bid-price)• Timing (delay) options are redundant within themselves• Timing & product (delay & type-switching) options are

additive• Modular production delay option (after project start)

may add significantly to project completion time.

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Right-shift in left-hand tail ==> Downside protection.Average 21% project value (land bid-price) improvement, 1.9 yr completion delay.


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Ex Post NPV @ Given Discount Rate (USD 000s)

NPV Frequency Distribution Function Net of $200M Land Price(across 10,000 simulated project outcomes.)

NPV - Start Delay Only NPV - No Flexibility Pro-forma PV

Mean NPV - Start Delay Only Mean NPV - No Flexibility

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Realized Future IRR @ Given Land Price

IRR Frequency Distribution Function at $200M Land Price(across 10,000 simulated project outcomes)

IRR - Start Delay Only IRR - No Flexibility Pro-forma IRR

Mean IRR - Start Delay Only Mean IRR - No Flexibility

Simulated Ex Post Distributions of Development Project Present Value & IRR,Comparison of Start Delay Flexibility Only (blue) versus Inflexible Base Plan (orange)

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Simulated Ex Post Distributions of Development Project Present Value & IRR,Comparison of Modular Buildout Delay Flexibility Only (blue) versus Inflexible Base

Plan (orange)

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NPV - BldOut Option Only NPV - No FlexibilityPro-forma PV Mean NPV - BldOut Option OnlyMean NPV - No Flexibility

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IRR - BldOut Option Only IRR - No FlexibilityPro-forma IRR Mean IRR - BldOut Option OnlyMean IRR - No Flexibility

Right-shift in left-hand tail ==> Downside protection.Average 13% project value (land bid-price) improvement, 5.3 yr completion delay.

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Right-shift in both tails & center ==> Downside protection + Upside opportunity.Average 14% project value (land bid-price) improvement, 0 yr completion delay.


Simulated Ex Post Distributions of Development Project Present Value & IRR,Comparison of Switching Option Only (blue) versus Inflexible Base Plan (orange)

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IRR - Switch Option Only IRR - No FlexibilityPro-forma IRR Mean IRR - Switch Option OnlyMean IRR - No Flexibility

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Right-shift in both tails but especially left ==> Both downside protection & upside opportunities, but especially downside protection.

Average 34% project value (land bid-price) improvement, 4.3 yr completion delay.


Simulated Ex Post Distributions of Development Project Present Value & IRR,Comparison of All Three Options Together (blue) versus Inflexible Base Plan (orange)

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IRR - All 3 Options IRR - No Flexibility Pro-forma IRR

Mean IRR - All 3 Options Mean IRR - No Flexibility

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NPV - All 3 Options NPV - No Flexibility Pro-forma PV

Mean NPV - All 3 Options Mean NPV - No Flexibility

Real Estate Price Dynamics and the Value of Flexibility...1 International Meeting of the American...

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