5.2/15 Real Estate Indices and Unsmoothing Techniques

Question 1

LO 15.1: Demonstrate knowledge of real estate indices and unsmoothing.

Answer 1

For example: • Identify the uses of real estate price indices. • Define unsmoothing and explain the rationale for the process

Question 2

SMOOTHED SERIES

Answer 2

Result of using reported prices or returns that have a lag relative to actual prices or returns. Appraisal method produces this effect because older prices are used to value properties.

Question 3

UNSMOOTHING

Answer 3

Process of removing the effects of smoothing from a data series.

Question 4

LO 15.2: Demonstrate knowledge of the concept of smoothed pricing.

Answer 4

For example:

• Discuss the effect of price smoothing on arbitrage in a perfect market.
• Identify factors that contribute to persistence in price smoothing.
• Recognize problems that can result from price smoothing

Question 5

• Discuss the effect of price smoothing on arbitrage in a perfect market

Answer 5

When prices are delayed (i.e., price smoothing occurs), arbitrage opportunities exist. In a perfect market with zero transaction costs and no trading restrictions, arbitragers will purchase assets after a general rise in prices and short sell assets after prices fall.

Because real estate is not publicly traded, there is generally no opportunity to arbitrage the smoothed prices and, thus, in real estate markets, smoothing may be more pronounced and potentially permanent.

Question 6

• Identify factors that contribute to persistence in price smoothing.

Question 7

• Recognize problems that can result from price smoothing.

Answer 7

• Smoothing = Lower std dev. also lower estimate correlation coefficients, and lower betas. Creates Upward biased SHARPE Ratios.
• Portfolio Optimization models will generate excessive allocation to smoothed asset clases
• Artificially low correlation may lead to incorrect hedge ratios, difficult for risk management.
• Creates Serial correlation or / autocorrelation in the index return series.

Question 8

2 Main Reasons previnting arbitrage profit

Answer 8

1. Prices do not actually represent trading opportunities. Appraisals are estimates and do not represent actual transaction prices.
2. Even if prices represent true buy and sell values, transaction costs may be prohibitive and prevent arbitrage activities. In real estate deals, transaction costs are generally high and the time it takes to trade is often long, making the likelihood of arbitrage small.
3. Markets in different time zones generally exhibit lagged pricing behavior (after one major market has a significant decline in prices, the next market to open will show a large decline as well). This allows for an arbitrage opportunity in open-end international equity mutual funds—which trade at NAV (based on last close—and hence stale data). However, to discourage short-term trading (and therefore profiting from arbitrage activities), many funds have erected barriers, such as early redemption fees.

Question 9

Serial Correlation / Autocorrelation

Answer 9

A return series with serial correlation will have lower volatility and lower correlation with other asset classes, which results in biased riskadjusted perforance measures.

Question 10

LO 15.3: Demonstrate knowledge of models of price and return smoothing

Answer 10

For example:

• Explain how and why current reported prices are modeled as a function of past true prices.
• Explain how and why current reported returns are modeled as a function of past true but unobservable returns.
• Explain how estimated values of true prices can be determined from reported prices using an estimation of the parameter for first order autocorrelation.
• List and discuss four explanations for smoothed prices and delayed price changes in a price inde

Question 11

• Explain how and why current reported prices are modeled as a function of past true prices.

Question 12

• Explain how and why current reported returns are modeled as a function of past true but unobservable returns.

Question 13

• Explain how estimated values of true prices can be determined from reported prices using an estimation of the parameter for first order autocorrelation.

Question 14

• List and discuss four explanations for smoothed prices and delayed price changes in a price index.

Question 15

Formula for most recent true but unobservable price, as a function of current and lagged observable smoothed values

Answer 15

P_t,true = P_t-1,reported + [(1/decay) x (P_t,reported - P_t-1,reported)]

For measuring the true price change, it is just:

[(1/decay) x (P_t,reported - P_t-1,reported)]

Question 16

First Order Autocorrelation Formula jpg

Answer 16

Question 17

First order Autocrrelation: Change in Price formula and Returns formula approximations

Answer 17

Question 18

First-Order Autocorrelation (in return or price series)

Answer 18

Autocorrelation refers to the correlation of a time series with its own past and future values.

Question 19

4 Primary causes of smoothed prices and delayed price changes (i.e. for first-order autocorrelation):

Answer 19

1. Olrd or stale prices used for index components that have not traded recently
2. professional appraiser may observe prices on delayed basis and generate smoothed returns - due to Anchoring (give higher weight to previous observations).
3. When different properties rise quickly, maybe bias to trade only lower price properties, and artificially lower the pricing of properties that have increased in value faster than the low priced properties.
4. In RE, there is delay between setting the price and reporting the transaction.

Question 20

LO 15.4: Demonstrate knowledge of the process of unsmoothing a price or return series

Answer 20

For example:

• • Explain the process of unsmoothing a return series using first-order autocorrelation.
• • Describe the three steps of the unsmoothing process.
• • Describe the process of unsmoothing a return index based on a model of smoothed price changes rather than returns.
• • Explain the process for unsmoothing returns with higher-order autocorrelation.

Question 21

Formula for True Return based on Reported/Smoothed returns (approximation)

EXAM FOCUS! (most important formula from this topic)

Answer 21

Question 22

Requirements for unsmoothing reported return series

Question 23

• Describe the three steps of the unsmoothing process. (15.4)

Answer 23

Step 1: Specify the form of autocorrelation (first order or higher orders)

Step 2: Esimate the parameters of the assumed autocorrelation process - often the first-order autocorrelation parameter, p (rho). this parameter is the correlation coefficient between each observation and the proceeding observation. (eqution attached)

Step 3: insert the estimated correlation coefficient (p) in the true return eqution we previously covered and solve for the true but unobservatble return. (2nd eqution attached).

Question 24

• Describe the process of unsmoothing a return index based on a model of smoothed price changes rather than returns. (15.4)

Answer 24

Step 1: Use a cumlative wealth index (including compounding) to convert returns to a price index.

Step 2: Use subtraction to convert index to series of price changes.

Step 3: Estimate the correlation Co-eff (p) using Pi,j = σi,j / ( σiσj)

Step 4: Estimate true price changes using the return equation (with price change rather than returrns) (attached)

Step 5: Use true price changes to form a price index

Step 6: Convert true price index back to returns.

Question 25

LO 15.5: Demonstrate knowledge of the application of the unsmoothing process.

Answer 25

For example: * • Explain the process of unsmoothing a historical return series. * • Describe how the first order autocorrelation coefficient can be estimated. * • Explain how the estimated autocorrelation coefficient can be used to calculate the volatility and the beta of an unsmoothed return series. * • Describe the relationship between the variances of true and reported returns. * • Describe the relationship between the betas of true and reported returns. * • Interpret the results of unsmoothing a return series.

Question 26

Risk with smoothed returns, from mean-variance optimization approach

Answer 26

* Overallocate due to artivicially low volatility of smoothed return * overallocate due to understated correlation coefficients with other asset classes.

Question 27

Estimate Formulas for True Variance, and True Beta, using p (first-order autocorrelation paramenter)

Answer 27

Question 28

LO 15.6: Demonstrate knowledge of noisy pricing.

Answer 28

For example: • Discuss the types of noise in transaction prices and appraised values of real estate properties, explanations for the noise, and problems created by noisy pricing.

Question 29

Real Estate property values from transactions are measured with error / **transaction noise**

Answer 29

* True Mkt values are unobservable; transaction pricing is outcome of negotiations. True mkt value should be between buyer's **reservation price**, and seller's reservation price. this measurement error is **purely random error.** * **Temporal lag bias** results because of lag between negotiation & reporting of a RE transaction. *

Question 30

**Appraisal Error**

Answer 30

* differences between a property's true value and appraised value * may not be centered around true value * appraisal errors can be reduced by using more data (but must include stale data), reduces random noise but increases temporal lag.

Question 31

Formula for how using "n" more transactions for appraisal affects original appraisal error

Answer 31

Question 32

LO 15.7: Demonstrate knowledge of appraisal-based real estate indices.

Answer 32

For example: * • Discuss three primary approaches to appraising real estate, and identify the two primary advantages and three primary disadvantages of appraisal-based models. * • Describe NCREIF and key characteristics of the NCREIF Property Index (NPI). * • Describe the comparable sales method of appraisals. * • Describe and apply the discounted cash flow analysis method (a.k.a. income approach) of appraisals.

Question 33

Three approaches for Appraising

Answer 33

1. **sales comparison approach** based on recent comps. include adjustments for differences between characterstics of specific property and those of comps, such as age, location, condition, and size. 2. **income appraoch** - estimates property values by PV of expected future cash flows, or by dividing NOI by discount rate. 3. **cost approach -** estimates replacement cost of property. Add value of land to current replacement cost of new building less adjustments for estimated depreciation and obsolescence. Better for newer buildings, as those estimates can be tricky.

Question 34

2 Advantages of Appraisal-Based Models

Answer 34

1. Small sample size not a problem (it is a problem for repeat - sales method) 2. Appraisals can be frequent (but costly)

Question 35

3 Disadvantages of appraisal-based models

Answer 35

1. Appraisals are backward looking (inputs are past transaction prices) and subjective. In some cases, not all properties are reappraised each quarter - stale pricing 2. appraisals result in price smoothing for indices, which results in understated volatility. 3. appraisals usually rely on comps, appraisal errors can be large for unique properties, or if comp data is stale.

Question 36

NCREIF Property Index (NPI)

Answer 36

* heavily based on appraisals * most properties receive annual appraisals, some every 2 or 3 years. * properties sold on average every 6-7 years * published quarterly * *value-weighted index* *

Question 37

RE return calculations

Answer 37

**Income Return (cap rate) -** NOI / adjusted beginning property value **Capital Value Return (**capital appreciation return) : (Change in Property value during period + partial sales - capital improvies) / adjusted beginning property value **Adjusted beginning property value -** begining prop value adjusted for capital improvements, partial sales, and reinvestment of the NOI. **Total Return -** Income return + Capital Value Return

Question 38

LO 15.8: Demonstrate knowledge of transaction-based real estate indices.

Answer 38

For example: * • Identify the key characteristics of transaction-based real estate indices. * • Discuss the repeat-sales method (RSM) for estimating transaction-based price indices, including two key advantages and three key disadvantages, and apply the process for using the RSM to construct an index. * • Discuss the hedonic pricing method (HPM) for estimating transaction-based price indices, including its five key advantages and six key disadvantages, and apply the three-step process for calculating a hedonic price index. * • Compare and contrast RSM and HPM indices. * • Describe sample selection biases associated with transaction-based indices.

Question 39

**Transaction-Based Index**

Answer 39

* based wholly on reported sale prices in RE transactions * can have derivatives based on the index, if it is accuracte * For accuracy, * must have sufficient data * adjust for property characterstics * minimal unexplained variation * Primary methods used to construct are **repeat-sales method** & **hedonic pricing method**

Question 40

**Repeat-Sales Method (RSM)**

Answer 40

* based on changes in the values of properties over an observation period based on at leasted two reported transactions * Use properties that have transacted at least twice to infer price changes for all properties. * observed percentage price changes are regressed onto time-dummy variables.

Question 41

Advantages of RSM (Repeat-Sales Method)

Answer 41

*

Question 42

**Drawbacks of RSM**

Answer 42

* only captures value info from small sample of peroperties with multiple sales during the measurement window. Ignore properties that sold only once during window * Prices may reflect more than returns - such as improvements. captured by index but may not represent true market gain * Updates to RSM results in "backward" adjustments - when a property is sold, the holdigng period return is allocated to all the periods intervening since hte property was previously bought (returns are backfilled). *

Question 43

**Hedonic Pricing Method (HPM)** and steps

Answer 43

Based on observed transaction data, discrete attribute value approach (sum total of the value of attributes that properties possess). Steps: 1. Specify characterstics of properties that are related to value (e.g. location, square footage, parking, quality of anchor stores). 2. use prices of recent transactos to fit parameters of valuation model 3. Use the estimated model parameters to value other, nontransacted properties. Example regression model for valuting retail RE properties: ln(value) = 3.457 + (0.022 × size) – (1.2268 × age) + (0.16 × sales) *need to use e function to get rid of ln (natural log).*

Question 44

RSM vs Hedonic Pricing Model

Answer 44

The primary differences between the two methods is that HPM is sales based (use all individual transactions) and RSM is change in price based (require two sales for sample). * the hedonic indices include all properties that have sold at least once, while RSM indices include data only on properties that have sold multiple times. * Also, hedonic price indices use price levels on some properties to infer price levels on other properties. RSM uses price changes on some properties to infer price changes on other real estate. * The accuracy of the pricing model is critical to the success of either of these approaches.

Question 45

Advantages of HPM (Hedonic Pricing Method)

Answer 45

* HPM uses all transaction data - especially important when sample is small * veratile and can account for important internal and external property attributes * allows for analyzing teh contribution of individual attributes in value determination that may otherwise be difficult to value (school quality, air pollution) * marginal contribution of individual attribute can be dtermined * No backward adjustment is necessary under HPM *unlike RSM*

Question 46

Disadvantages of HPM:

Answer 46

* Requires large sample size, which may be costly * suffers from sample selection bias --model estimates are only based ona ctual transactions (same as RSM) * Potential for **specification error** (may not include all important attributes when building model) * assumes parties to the transaction not only agree on the same attributes as value determinantes but also on the value of said attributes * often suffers from **multicollinearity** (when specified attributes are highly correlated) *

Question 47

NCREIF Transaction Based INdex (TBI)

Answer 47

* utilizes HPM, but also has some similarity to repeat sales method * uses both appraisal values from the NPI (NCREIF Property Index) and transaction prices from NPI. * TBI is published quarterly *

Question 48

LO 15.9: Demonstrate knowledge of major real estate indices

Answer 48

* Recognize popular global real estate indices and their key characteristics. * • Discuss residential real estate property indices. * • Describe the NCREIF Farmland Index and the NCREIF Timberland Index. * • Describe market-traded real estate vehicles (typically classified as real estate investment trusts [REITs]). * • Describe real estate mortgage (or debt) indices

Question 49

S&P/Case-Shiller Home Price Index | (Housing/Residential Index)

Answer 49

* repeat-sales method * Sales pairs are created by combining the new sales price with the previous sales price. * Price differences in a particular region are then used to infer changes in the level of the index.

Question 50

NCREIF Farmland Index

Answer 50

* quarterly index * appraisal method to estimate prices * includes income-generating properties that have been acquired solely for investment purposes * Pension Funds are primary investors

Question 51

NCREIF Timberland Index

Answer 51

* measures performance of institutional timber investments * property must be m2m at least once per year to be included in index * annual return series more reflective of changes in market than quarterly return, as properties are generally not appriased quarterly

Question 52

**Public Real Estate Equity Indices** | (Think REITs)

Answer 52

* **FTSE NAREIT U.S. Real Estate Index Series -** includes several indices that focus on the performance of REITs, includes both equity and mortage REITs * **S&P U.S. REIT Composite Index** * **Dow Jones Wilshire Real Estate Investment Trust Index** * **Dow Jones Wilshire Real Estate Securities Index)** * **MSCI U.S. REIT Index.** * **FTSE NAREIT U.S. Mortgage REIT Index -** Mortage REIT indices.

Question 53

LO 15.10: Demonstrate knowledge of the historical performance of real estate indices.

Answer 53

* Evaluate the historical performance of real estate indices. * Evaluate the historical performance of mortgage REITs. * Evaluate the historical performance of equity REITs

Question 54

• Evaluate the historical performance of real estate indices.

Answer 54

15 years 2000 to 2014, equity and mortage REITs outperformed world equities, global bonds, US high yield, and commodities - however strong volatility, and actually had lower sharpe ratio than global bonds. correlations between equity and mortgage reits and other four asset classes were low - indicates diversifcation is helped by REITs