Real Estate Finance and Investments: Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]

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Introduction

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]* *_____* (Introduction) Thus far, our discussion of risk and required rates of return has stressed a methodology or an approach that should be used when evaluating a specific project or mortgage financing alternative. In this chapter, we provide some insight into the measurement of return and risk for various real estate investment vehicles and investment portfolios. We will apply concepts and methodologies based on financial theory and demonstrate possible applications to real estate investments... Also, many portfolio managers are interested in knowing how well investment portfolios perform when real estate investments are combined with other securities.

Comparing Risk Premiums

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Computing Holding Period Returns*... *Comparing Investment Returns*... *_____* (Comparing Risk Premiums) In addition to returns, risk premiums may be calculated for each investment class relative to T-bills. Risk premiums may also be calculated for each investment relative to all other investments. For example, during the 1985 - 2014 period, EREITs earned an average risk premium of 1.71 percent per quarter, in excess of T-bills (2.66% - 0.95%)... When compared to the NCREIF Index, which provided returns of 1.90 percent compounded quarterly, EREIT returns were higher by 0.76 percent. We should recall, however, that the NCREIF Index is compiled on an unleveraged basis; that is, the properties in the index were purchased on an all-cash basis, or "free and clear" of debt.

HPRs and Inflation

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Computing Holding Period Returns*... *Comparing Investment Returns*... *_____* (HPRs and Inflation) All returns shown in Exhibit 22-4 may also be compared with the quarterly rate of inflation, as represented by the CPI, which was 0.69 percent. The comparison with the CPI provides some insight into whether returns from each investment category exceeded the rate of inflation (thereby earning real returns).

Comparing Investment Returns

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Computing Holding Period Returns*... *_____* (Comparing Investment Returns) We can now begin to compare total returns for the various investment categories contained in Exhibit 22-4... The geometric mean returns (also called time-weighted returns by many portfolio managers) show that from 1985 to 2014, stocks constituting the Standard & Poor's 500 Index (S&P 500) produced quarterly returns of 2.71 percent.

arithmetic mean return

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Computing Holding Period Returns*... Although the values of the arithmetic mean and geometric mean are sometimes very close, this will not always be the case, particularly if values in the series rise and fall sharply or the series is longer than the sample shown in the exhibit... _____s are simple averages (not compounded) and are widely used in statistical studies spanning very long periods of time... Exhibit 22-4 contains summary statistics for various investments that we have chosen to include in the chapter.

geometric mean return

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Computing Holding Period Returns*... An example of how holding period returns are calculated for a hypothetical security index is demonstrated in Exhibit 22-3... An alternative way of considering these return data is to calculate the _____. This return is calculated by finding the nth root of the product of each quarterly HPR in series multiplied together, minus 1 (see bottom of Exhibit 22-3). The _____ was equal to .89 percent, a measure of the quarterly compounded rate of return that an investor would have earned on $1 invested in the index during the period.

Holding Period Return (HPR)

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Computing _____s* While the cumulative total returns shown in Exhibit 22-2 are useful information, additional insight into the risk-return characteristics of each security can be obtained by examining returns over shorter time periods. The most fundamental unit of measure used by portfolio managers to measure investment returns for individual securities, or a class of securities in a portfolio, is the _____. This is generally defined as follows: _____ = (P_sub_t - P_sub_(t - 1) + D_sub_t) / P_sub_(t - 1) where P_sub_t is the end-of-period price for the asset, or value of an index for an investment, or index representing a class of investments, whose performance is being assessed; P_sub_(t - 1) is the beginning-of-period value; and D represents any dividends or other cash payouts that may have occurred during the period over which the _____ is being measured.

Correlation (ρ)

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Elements of Portfolio Theory*... *Portfolio Risk*... *Covariance and _____ of Returns: Key Statistical Relationships*... Two statistics provide a numerical measure of the extent to which returns tend to either move together, in opposite directions, or have no relationship to one another. These statistics are the covariance and _____ between the two return series... While the covariance measure is useful, it is somewhat difficult to interpret because it is an absolute measure of the relationship between returns... Because of this problem, we need a method to gauge the importance of the statistic on a relative scale of importance. The coefficient of _____ is used to obtain this relative measure or the extent to which one set of numbers moves in the same or opposite direction with another series. The formula for the _____ statistic _____ is ______sub_(ij) = COV_sub_(ij) / (σ_sub_i σ_sub_j)... The _____ statistic may only range between +1 and -1; therefore, it is a much easier way to interpret the extent to which returns are related.

Covariance, Correlation

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Elements of Portfolio Theory*... *Portfolio Risk*... *___1___ and ___2___ of Returns: Key Statistical Relationships* One important aspect of individual investment returns to consider is how the return on a prospective new asset will vary with returns on an existing portfolio. Clearly, if the asset is producing returns that move up and down in a pattern that is very similar to movements in portfolio returns, the inclusion of that asset in the portfolio will not reduce total variation (risk) by very much... Two statistics provide a numerical measure of the extent to which returns tend to either move together, in opposite directions, or have no relationship to one another. These statistics are the ___1___ and ___2___ between the two return series.

Covariance

Covariance and Correlation of Returns: Key Statistical Relationships

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Elements of Portfolio Theory*... *Portfolio Risk*... *_____* (Covariance and Correlation of Returns: Key Statistical Relationships)... What are some other important relationships at this point? It should be clear that if two investments are highly positively correlated, the reduction in the variance in portfolio returns hence, risk) is likely to be smaller than if there is no correlation or negative correlation because, in the latter case, the distribution of two returns will be either unrelated or negatively related, and the interaction between returns will not be reinforced... Consequently, it should be stressed that anytime the correlation between returns on two assets is less than +1 some reduction in risk (standard deviation) may be obtained by combining investments, as opposed to holding one investment (or one portfolio) with higher standard deviation than the prospective investment... Based on the foregoing analysis, it should be clear why the standard deviation of portfolio returns in our example is not equal to a simple, weighted average of the standard deviation of the two individual investment returns. Further, if variation in security returns is a reasonable representation of risk to investors, then it should become apparent that there may be some benefit, in the form of risk reduction, by diversifying an investment portfolio to include assets with returns that are negatively correlated, or assets with returns showing little or no correlation. Of course, the other critical dimension that has to be considered is how the mean return of the portfolio will be affected when the individual securities are combined. For example, if two securities have the same positive mean returns and these returns are perfectly, negatively correlated (e.g., -1) then it may be inferred that an investor can earn a positive portfolio return with zero risk if both investments are purchased (the standard deviation of the combined returns is zero).

Calculating Portfolio Returns

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Elements of Portfolio Theory*... *_____* (Calculating Portfolio Returns) To demonstrate an approach that may be used to answer these questions, we will assume that both stocks i and j were weighted equally in one portfolio at the beginning of the period. We will then compute the mean return and standard deviation for the combined portfolio (see Exhibit 22-5). The mean return for the portfolio, HPR_sub_p [with a line on top] is calculated as HPR_sub_p [with a line on top] = W_sub_i (HPR_sub_i [with a line on top]) + W_sub_j (HPR_sub_j [with a line on top])... where W represents the weights that securities i and j represent as a proportion of the total value of the portfolio (i.e., W_sub_i + W_sub_j = 1.0). Based on this calculation, we see that the portfolio return would have been 2.34 percent quarterly, which is less than what would have been earned on stock j alone. However, we cannot really conclude much from this result until we consider how portfolio risk have been affected when the two investments were combined.

Portfolio Risk

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Elements of Portfolio Theory*... *_____* (Portfolio Risk) To consider how total portfolio risk would have been affected by the addition of stock i to an existing portfolio consisting only of stock j, the standard deviation of the new portfolio returns is calculated (see Exhibit 22-5)... However, it is important to note that unlike the mean HPR for the portfolio, the standard deviation of portfolio returns for the two indexes is not equal to the simple weighted average of the individual standard deviations of the two indexes; that is, [(.5)(6.24%)] + [(.5)(9.33%)] does not equal the standard deviation of the portfolio returns... In other words, there is interaction between the two returns in the sense that the pattern, or direction of movement, in each of the individual HPR's is not the same in each period.

Portfolio Weighting: Trading Off Risk and Return

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Elements of Portfolio Theory*... *_____* (Portfolio Weighting: Trading Off Risk and Return) In our hypothetical example, we have seen that adding stock i to a portfolio containing stock j would have reduced portfolio risk (standard deviation) by a lesser amount (%) than the reduction in portfolio mean return... However, in our computations, we assumed that both assets were equally weighted. Could a more optimal portfolio, that is, one containing some other combination of stocks that would have either increased returns relative to an increase in risk or maintained returns while decreasing risk, been attained by varying the weight (proportion) of the two securities in the portfolio? To answer this question, we first consider the sample of NCREIF and S&P 500 returns from Exhibit 22-4, or those returns that comprised the period 1985 - 2014... The correlation between both return series was 0.1344 (see Exhibit 22-7). Because the correlation coefficient was less than 1, some reduction in risk would have been possible by combining the two assets... Second, we want to understand the importance of weighting securities in a portfolio. To determine the optimal weighting, all combinations of both assets must be considered... The result is shown in Exhibit 22-8... Hence, the curve in the exhibit shows the trade-off between return and risk for the portfolio as the two asset classes are combined in varying proportions... Note that even though the NCREIF Index had a lower mean HPR during this period, when compared with the S&P index (see Exhibit 22-4), diversification benefits may be realized by combining assets as opposed to holding only S&P 500 or NCREIF properties. This is illustrated in Exhibit 22-8. In Exhibit 22-8, note that having a portfolio of 100 percent NCREIF has a lower return but greater risk than holding some S&P with NCREIF... The portion of the curve with a positive slope (returns increase as risk increases) is known as the efficient frontier. It represents the most efficient combination of securities that provides investors with maximum portfolio returns as portfolio risk increases. Returns below the efficient frontier (or in the interior of the ellipse) are inferior because there is always a better combination of securities that will increase returns for a given level of risk.

Diversification by Property Type and Location

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Diversification by Property Type and Location) We have seen that when individual properties are combined in a portfolio, the risk of the portfolio is reduced when the properties are not correlated... Similarly, properties in different locations are affected by different economic fundamentals affecting the economic base of the area. Exhibit 22-11 shows the returns for office, retail, industrial, and apartment properties from 1979 through 2014... Exhibit 22-12 shows the performance of five selected MSAs. We see that different metropolitan areas behaved differently over time.

Example - Swap Office for Retail

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Example - Swap Office for Retail) To illustrate the use of derivatives to hedge portfolio risk, consider the following example. ABC Investors decided to enter into a derivative transaction on January 1, 2000, that swapped office returns for retail returns. That is, it agreed to pay the return on the NCREIF office index but receive the returns on the NCREIF retail index... Retail returns outperformed office returns over this particular five-year period... Note that the investor is not taking the risk of the returns on real estate as reflected by the NCREIF Index in this case. The investor is taking the risk related to the relative performance of retail versus office - in this case, betting that retail will outperform office.

Global Diversification

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Global Diversification) In recent years there has been an increasing interest among investors, especially large institutional investors, to invest on a global basis. There are several reasons for this. First, the number of investment opportunities around the globe is increasing... Exhibit 22-13 shows a breakdown of the global real estate market, and Exhibit 22-14 shows the countries with the largest commercial real estate markets and the size of the market... Second, indexes measuring the historic returns for commercial real estate are being developed in other countries, allowing investors to have a benchmark for the performance of real estate in those countries like we have with the NCREIF index in the United States... A third reason for investing globally is that there are diversification benefits that result from including real estate from other countries in a portfolio... Exhibit 22-15 shows the performance of real estate in several countries... We see that there are differences in the performance of real estate in different global cities... Exhibit 22-16 shows the correlations between the returns for the different global cities and the US for both private and public markets.

Portfolio Diversification: EREITs and Other Investments

Public versus Private Real Estate Investments

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Public versus Private Real Estate Investments) We saw previously that the performance of private real estate as reflected in the NCREIF Index and the performance of REITs as reflected in the NAREIT Index were quite different in terms of historic returns, standard deviations, and correlations with other assets... One explanation for this might be that the NCREIF Index does not capture all of the variability of returns because it is based on appraised values, as discussed earlier. An alternative explanation, however, is that when real estate is owned by publicly traded REITs, it takes on more of the risk of public markets in general. As we saw in Exhibit 22-7, REITs have a much higher correlation with the S&P 500 than NCREIF. Also, we saw that the NCREIF Index has a much higher correlation with the CPI, indicating it may be a better inflation hedge than REITs. There is likely to be truth in both arguments - that appraisals reduce the variance of the true returns in the NCREIF Index but publicly traded REITs take on additional variance because they trade in more active markets that are influenced more by short-term flows of capital into and out of the stock market. To see what the difference in variability is between NCREIF and NAREIT, we have plotted the historic returns for each in Exhibit 22-10... Although some people argue about which index is a better indication of the performance of equity real estate, it is quite possible that the conclusion should be that both private real estate investments (represented by the NCREIF Index) and public real estate investments (represented by the NAREIT Index) could play a role in a portfolio.

Real Estate Performance and Inflation

Risks of Global Investment

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Risks of Global Investment) We have found that there are many reasons to consider investing on a global basis. However, this approach carries with it certain risks that are not necessarily reflected in the measures of portfolio risk we have discussed in this chapter. First, there is currency risk because exchange rates may change in a way that makes the dollar worth less relative to the currency of the country where the investment is located... Second, although indexes and information sources are developing in many countries, the data may not be as reliable in all cases or as extensive as in the United States... Third, there are different tax laws and property rights to deal with when investing globally... Fourth, there could be political instability in the country, which may increase risk because of uncertainty as to how the political situation will affect attitudes about foreign investment in the country. Fifth, there are the obvious communication barriers and cultural differences. To try to mitigate many of these risks, U.S. investors often try to find a joint venture partner based in the country where they want to invest.

Up Shares and Down Shares

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Up Shares and Down Shares) Another approach was recently introduced by the Global Index Group (www.globalindexgroup.com) in the US based again on the NCREIF Property Index. Their approach is to create two related securities - one called Up Shares and one called Down Shares. As their name might suggest, the up shares benefit if the NCREIF Index goes up in value more than expected and the down shares benefit if the NCREIF Index goes down in value more than expected. Exhibit 22-17 illustrates how the Up Share Value and Down Share Value can change depending on what happens to the index... There are many ways that derivatives or "synthetic securities" can be created based on indices like the NCREIF Property Index. We have just illustrated two: the use of swaps and the use of up and down shares. In both cases, they provide investors with additional tools to adjust the risk and diversification of their portfolios.

Use of Derivatives to Hedge Portfolio Risk

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification*... *_____* (Use of Derivatives to Hedge Portfolio Risk) In recent years we have seen the introduction of derivatives based on the NCREIF Property Index, discussed previously in this chapter. Derivatives allow investors to take a position in real estate or hedge a position without actually buying or selling properties. They receive or pay a return based on the performance of the NCREIF Property Index or an index based on one of the property types shown earlier in the chapter. Derivatives can be used as a way to enter the real estate market for the first time... At the same time, another pension fund or perhaps a hedge fund that already has a real estate portfolio might decide that they are overexposed to the commercial real estate market but don't want to sell any of their properties because they feel that they can earn above average returns relative to the risk. They could sell, or "short," the NCREIF index to reduce their exposure to real estate. This reduces their risk while allowing them to capture any return that they can achieve above the return on the NCREIF Index. (In the next chapter we will refer to this as earning alpha.) Another important use of derivatives is to adjust exposure to different property types.

diversification benefits

coefficient of variation

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Risk, Return, and Performance Measurement*... *Risk-Adjusted Returns: Basic Elements* Given that the combined effects of the sources of risk described above will be reflected in the variability in investment returns, one way of taking into account investment risk when evaluating performance is to consider the variability of returns... One approach that may be used to consider risk and returns is to compute the _____ of the returns. This is defined as the standard deviation of returns divided by the mean return (this can be based on either the arithmetic or geometric mean returns for a given investment or investment index). This concept is sometimes referred to as a risk-to-reward ratio and is intended to relate total risk, as represented by the standard deviation, to the mean return with the idea of determining how much return an investor could expect to earn relative to the total risk taken if the investment was made. For example, if an investor holds a portfolio containing securities with a mean return of 2 percent and a standard deviation of 3 percent, the _____ is 1.5. This may be interpreted as taking 1.5 units of risk for every unit of return that is earned. An interesting comparison may now be made between the investment performance of EREITs and the NCREIF Index. Recall from Exhibit 22-4 that the NCREIF produced a lower mean return compared with EREITs. However, when mean returns for both investment categories are risk-adjusted, the NCREIF Index appears to have outperformed the EREIT index on a risk-adjusted basis... A lower _____ suggests less risk relative to the return. Or conversely, higher return relative to the risk - thus, a higher risk-adjusted return. It has already been pointed out that the NCREIF Index (1) does not include the effect of leverage in investment returns and (2) property values used to compute the NCREIF Index are based largely on quarterly appraisals plus a relatively small number of actual sale transactions... If property appraisals (1) differ significantly from actual market values and (2) affect the variation in the index, then the NCREIF Index may not be representative of true real estate returns or volatility in those returns. For example, results in Exhibit 22-4 for EREITs indicate that the geometric mean return was 2.66 percent and the standard deviation of returns was 9.29 percent, resulting in a 2.99 _____. This compares to a mean return of 1.90 percent and a standard deviation of 2.99 percent for the NCREIF Index and a _____ of 1.15. These results indicate a material difference in both return and risk for the two indexes... Further, equity REIT shares are bought and sold in an auction market with continuous trading, whereas the individual properties that make up the NCREIF Index are bought and sold in a much more limited, negotiated market between parties.

NAREIT

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Sources of Data Used for Real Estate Performance Measurement*... *REIT Data: Security Prices* One of the two sources of data used to produce investment returns on real estate in this chapter is based on REITs. The National Association of Real Estate Investment Trusts REIT Share Price Index (_____) is a monthly index based on ending market prices for shares owned by REIT investors... The data used in this chapter are based on only those REITs that own real estate, or equity REITs.

NCREIF

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Sources of Data Used for Real Estate Performance Measurement*... *_____ Property Index: Property Values* The _____ Property Index measures the historic performance of income-producing properties either (1) acquired by open-end or commingled investment funds that sell investment units owned by qualified pension and profit-sharing trusts, or (2) acquired by investment advisors and managed on separate account bases. The data incorporated in the _____ Index are based on the performance of properties managed by members of the National Council of Real Estate Investment Fiduciaries (_____). Quarterly rates of return are calculated for all properties included in the index and are based on two distinct components of return: (1) net operating income less capital expenditures and (2) the quarterly change in property market value (appreciation or depreciation). The _____ Index contains data on five major property categories: apartment complexes, office buildings, industrial (warehouses, office/showrooms/research and development facilities), retail properties (including regional, community, and neighborhood shopping centers as well as freestanding store buildings), and hotels... To obtain changes in value, quarterly appraisals are made, and when sales occur, actual transaction prices negotiated by the buyer and seller are a part of the index.

Data Sources for Other Investments

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Sources of Data Used for Real Estate Performance Measurement*... *_____* (Data Sources for Other Investments) In contrast to the scarcity of real estate return data, data on financial assets are plentiful and easy to obtain. In this chapter, we will also develop measures of investment performance for common stocks from the Standard & Poor's 500 Index of Common Stocks (S&P 500), U.S. Treasury bills (T-bills), longer term U.S. Treasury bonds, and long-term corporate bonds contained in the Barclays Capital U.S. Aggregate Bond Index. These Indexes (see Exhibit 22-1) are generally computed daily, weekly, monthly, quarterly, and annually and are published regularly in the financial press.

Hybrid and Mortgage REITs

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *Sources of Data Used for Real Estate Performance Measurement*... *_____* (Hybrid and Mortgage REITs) A mortgage REIT investment return series and a hybrid REIT return series are also shown in Exhibit 22-1... Hybrid REITs operate by buying real estate and by acquiring mortgages on both commercial and residential real estate.

Conclusion

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (Conclusion) This chapter has introduced the measurement of investment performance and the basic elements of portfolio theory... We have stressed that the nature of real estate investment return data is very limited and may not be representative of a broad measure of real estate returns... Results from the portfolio simulations conducts and reported in the last part of the chapter indicate that there appeared to be significant gains available from portfolio diversification into real estate during the period 1985 - 2009 based on these limited data sets.

Cumulative Investment Return Patterns

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (Cumulative Investment Return Patterns) A series of historic total return indexes (see Exhibit 22-2) have been developed to begin the discussion of real estate equity investment performance. We have included three equity indexes: the S&P 500, EREIT (equity REITs), and NCREIF Property Index. Debt securities are represented by indexes for T-bills and government bonds (For sources, see Exhibit 22-1)... The patterns indicate that $100 invested from the end of 1985 through 2009 would have produced the greatest total return (based on quarterly price changes and reinvestment of all dividends, interest, or income) if it had been invested in securities comprising the S&P 500 index. Total return rankings of the other indexes were as follows: Equity REITs, NCREIF Index, Bond Index, and T-Bills. We stress, however, that although these return patterns are informative, it should not be implied that each investment is equivalent in risk.

Elements of Portfolio Theory

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (Elements of Portfolio Theory) The preceding section dealt with one approach that may be used to compare investments by considering the investment's mean return and the standard deviation of those returns... In addition, investors must consider the extent to which the acquisition of an investment affects the risk and return of a portfolio of assets. This question is very important because of the interaction between returns when investments are combined in a portfolio... When investors add to an existing portfolio, it is important to understand how the acquisition of new assets may impact the return and risk of the entire portfolio. Building a portfolio by considering the return and standard deviation of returns for individual investments will not always ensure that an optimum portfolio will be obtained. Indeed, any new asset that is being considered as an addition to a portfolio should be judged on the grounds of "efficiency," that is, whether its addition to an existing portfolio will increase expected portfolio returns while maintaining, or lowering, portfolio risk. Alternatively, an investor may also judge whether the portfolio efficiency of an asset will lower portfolio risk while maintaining or increasing the expected portfolio return. To illustrate how the interaction between investment returns occurs, we consider the data in Exhibit 22-5... Assuming that an investor was holding a portfolio composed only of stock j at the beginning of the investment period, the question to answer is, how would the addition of another investment (as represented by real estate stock i) affect the quarterly mean portfolio return and its standard deviation?

Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification) From the preceding analysis, it should be clear that there are many different assets that have the potential to be combined efficiently in a portfolio that will provide an optimal risk-return relationship for investors... Exhibit 22-7 is a correlation matrix, or table, that contains the coefficient of correlation for returns on all securities listed in Exhibit 22-4. The purpose of calculating these coefficients is to consider how various investment vehicles might be combined efficiently with various other assets when building a portfolio. We can gain some insight into the question of whether portfolios containing certain securities would be more efficient if real estate investment vehicles were added. We will focus on this more narrow question, because to consider the question of what the optimum portfolio should contain would have to include an examination of the risk and returns for the global, or worldwide, set or securities and assets available to investors... An efficient frontier, such as the one shown in our two-investment case in Exhibit 22-8, would also exist for this larger, diversified market portfolio... In this section, we consider the question of portfolio performance, diversification, and real estate.

Risk, Return, and Performance Measurement

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (Risk, Return, and Performance Measurement) While comparing investment returns is an important starting point in evaluating investment performance, it represents only one part of the analysis. We know from material presented earlier that investments that produce higher returns usually exhibit greater price volatility and are generally riskier than investments that produce lower returns. In cases involving individual real estate investments, such risks may be a function of the type of property, its location, design, lease structure, and so on. Those attributes, and the attendant risks associated with those attributes, can be thought of as a type of business risk. Another source of risk occurs when real estate investments are leveraged. In these cases, default risk is present. Finally, because of the relative difficulty and time required to sell property, liquidity risk is certainly present... One way of considering this risk-return relationship is to compute risk premiums, as we did above... Another way of looking at the risk-return relationship is to think about the way in which business, default, and liquidity risks affect the pattern of returns that investors expect to earn. Over time, returns (dividends and price changes) on investments with more of these risks present are likely to exhibit more variation than investments with fewer of these risks... The assumption that variability in asset returns represents risk and that premiums over what could be earned on a riskless investment represent the price of risk is the foundation of modern finance theory.

Sources of Data Used for Real Estate Performance Measurement

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (Sources of Data Used for Real Estate Performance Measurement) In this section, we provide information on two sources of real estate data that are used to a limited extent when measuring real estate investment performance. We also consider investment returns from data that are available on common stocks, corporate bonds, and government securities. Exhibit 22-1 summarizes the data available for these investments. We rely on two sources for real estate returns in this chapter. The first is security prices as represented by real estate investment trust (REIT) shares. The second data source is based on estimates of value of individual properties owned by pension plan sponsors. Note that the primary differences in these data is that one source is based on real estate-backed securities and the other is based on estimates of individual properties.

The Nature of Real Estate Investment Data

*Real Estate Finance and Investments*... *Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]*... *_____* (The Nature of Real Estate Investment Data) When measuring the investment performance of something as broadly defined as real estate, one must keep many things in mind... Because of these limitations, current attempts to measure real estate investment performance are based on limited data that are made available from a few select sources. The available data may not be representative of (1) the many types of properties, (2) the many geographic areas in which commercial real estate is located, or (3) the frequency of transactions indicative of real estate investment activity in the economy as a whole.

Real Estate Finance and Investments: Chapter 22: Real Estate Investment Performance and Portfolio Considerations [4/27/20]

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