Chapter 21 MACRO-LEVEL REAL ESTATE INVESTMENT ISSUES © 2014 OnCourse Learning. All Rights Reserved.1.

2 "MODERN PORTFOLIO THEORY" (aka "Mean-Variance Portfolio Theory", or “Markowitz Portfolio Theory” – Either way: “MPT” for short)  DEVELOPED IN 1950s (by MARKOWITZ, SHARPE, LINTNER) (Won Nobel Prize in Economics in 1990.)  WIDELY USED AMONG PROFESSIONAL INVESTORS  FUNDAMENTAL DISCIPLINE OF PORTFOLIO-LEVEL INVESTMENT STRATEGIC DECISION MAKING. 21.2 Basic Mean-Variance Portfolio Theory (See text Appendix 21A (or slides at end) for intro/review of portf return statistics.) © 2014 OnCourse Learning. All Rights Reserved.

3 21.2: FOR RIGOROUS QUANTIFICATION, PORTFOLIO THEORY ASSUMES: YOUR OBJECTIVE FOR YOUR OVERALL WEALTH PORTFOLIO IS:  MAXIMIZE EXPECTED FUTURE RETURN  MINIMIZE RISK IN THE FUTURE RETURN © 2014 OnCourse Learning. All Rights Reserved.

4 21.2.1. Investor Preferences & Dominant Portfolios Utility preference surface for return & risk: RISK-AVERSE INVESTOR … RISK RETURN P Q THE CONTOUR LINES (UTILITY ISOQUANTS) STEEPLY RISING IN RETURN OVER RISK: RISK-AVERSE INVESTOR WANTS MUCH MORE RETURN TO COMPENSATE FOR A LITTLE MORE RISK. © 2014 OnCourse Learning. All Rights Reserved.

5 21.2.1. Investor Preferences & Dominant Portfolios Utility preference surface for return & risk: RISK-TOLERANT INVESTOR … THE CONTOUR LINES (UTILITY ISOQUANTS) SHALLOWER: LESS RISK-AVERSE INVESTOR NEEDS LESS RETURN TO COMPENSATE FOR A MORE RISK. RISK RETURN P Q © 2014 OnCourse Learning. All Rights Reserved.

6 “P” DOMINATES “Q”. INDEPENDENT OF RISK PREFERENCES.  BOTH CONSERVATIVE AND AGGRESSIVE INVESTORS WOULD AGREE ABOUT THIS. PORTFOLIO THEORY IS ABOUT HOW TO AVOID INVESTING IN DOMINATED PORTFOLIOS. RISK RETURN P Q DOMINATED BY "Q" DOMINATES "Q" Exh.21-3: PORTFOLIO THEORY TRIES TO MOVE INVESTORS FROM POINTS LIKE "Q" TO POINTS LIKE “ P ". DOMINATES "Q" BOTH INVESTORS WOULD AGREE THEY PREFER POINTS TO THE "NORTH" AND "WEST" IN THE RISK/RETURN SPACE. THEY BOTH PREFER POINT "P" TO POINT "Q". 21.2.2 © 2014 OnCourse Learning. All Rights Reserved.

8 : AT THE HEART OF PORTFOLIO THEORY ARE TWO BASIC MATHEMATICAL FACTS: 1) PORTFOLIO RETURN IS A LINEAR FUNCTION OF THE ASSET WEIGHTS: IN PARTICULAR, THE PORTFOLIO EXPECTED RETURN IS A WEIGHTED AVERAGE OF THE EXPECTED RETURNS TO THE INDIVIDUAL ASSETS. E.G., WITH TWO ASSETS ("i" & "j"): r p = ωr i + (1-ω)r j WHERE  i IS THE SHARE OF PORTFOLIO TOTAL VALUE INVESTED IN ASSET i. e.g., If Asset A has E[r A ]=5% and Asset B has E[r B ]=10%, then a 50/50 Portfolio (50% A + 50% B) will have E[r P ]=7.5%. Making the analysis more formal & rigorous… © 2014 OnCourse Learning. All Rights Reserved.

9 2) PORTFOLIO VOLATILITY IS A NON-LINEAR FUNCTION OF THE ASSET WEIGHTS: SUCH THAT THE PORTFOLIO VOLATILITY IS LESS THAN A WEIGHTED AVERAGE OF THE VOLATILITIES OF THE INDIVIDUAL ASSETS. E.G., WITH TWO ASSETS:  This is the beauty of Diversification. It is at the core of Portfolio Theory. It is perhaps the only place in economics where you get a “free lunch”: In this case, less risk without necessarily reducing your expected return! e.g., If Asset A has StdDev[r A ]=5% and Asset B has StdDev[r B ]=10%, then a 50/50 Portfolio (50% A + 50% B) will have StdDev[r P ] < 7.5% (conceivably even < 5%). THE 2 ND FACT: s P = SQRT[ w²(s i )² + (1-w)²(s j )² + 2w(1-w)s i s j C ij ] < ws i + (1-w)s j, where: s=StDev, C=correl < ws i + (1-w)s j, where: s=StDev, C=correl WHERE s i IS THE RISK (MEASURED BY STD.DEV.) OF ASSET i. © 2014 OnCourse Learning. All Rights Reserved.

13 Large & Small Stocks (+71% correlation): Each dot is one year's returns. The diversification effect is greater the less correlated are the assets… 21.2.2 Effect of diversification (Exhs.21-4&5…) © 2014 OnCourse Learning. All Rights Reserved.

14 Bonds & real estate (0% correlation): Each dot is one year's returns. The diversification effect is greater the less correlated are the assets… 21.2.2 Effect of diversification (Exhs.21-4&5…) © 2014 OnCourse Learning. All Rights Reserved.

15 Exh.21-5a: For example, a portfolio of 50% large stocks & 50% small stocks would not have provided much volatility reduction during 1970-2010 (from large stk vol 18% & small stk vol 23% to half/half vol 19%) : 1970-2010 Sm/Lg Stk correl = +71% © 2014 OnCourse Learning. All Rights Reserved.

16 Exh.21-5b: Here the portfolio of 50% bonds & 50% real estate would have provided more diversification during 1970-2010, with less volatility than either asset class alone even though a very similar avg total return: 1970-2010 Bd/RE correl = 0% © 2014 OnCourse Learning. All Rights Reserved.

17 Given: Risk that matters to investor is risk in overall wealth, Therefore: Risk that matters in investments (assets) is covariance with overall wealth (contribution to overall wealth volatility); Not the asset’s own volatility (Stdev) per se (e.g., if investor portf primarily stocks & bonds, & if real estate has low correlation with stocks & bonds, then R.E. volatility may not matter to investor; because it may not contribute much to investor's wealth volatility.) KEY POINT THAT YOU CAN ALREADY SEE WITHOUT FANCY MATH… Covariance = Stdev(i)*Stdev(j)*Correl(I,j) © 2014 OnCourse Learning. All Rights Reserved.

18 Everything went down… Much recent bemoaning the lack of diversification between real estate and stocks during the big 2008 crash. 21.2.3 Perceived Role of Real Estate in the Mixed-Asset Portfolio © 2014 OnCourse Learning. All Rights Reserved.

19 Much recent bemoaning the lack of diversification between real estate and stocks during the big 2008 crash. But in the big picture… (“Northeast” & “Southwest” quadrants  Lack of diversification.) Though hard data is lacking, we would probably have to go back a further 30+ yrs to find a third double-down year:  1/30 chance any one year both down… In which quadrant do you care about lack of diversification?...

22 Much recent bemoaning the lack of diversification between real estate and stocks during the big 2008 crash. But in the big picture… “Fat tails” (non-normality) can be represented by “big bear” events (asset class down > -20%). How does R.E. compare?... “Big Bear” Events: > -20% decline 41 yrs history: 5 LgStk, 7 SmStk, 3 RE, 2 LTGBnd; 2 coincide across all

23 “Fat tail” magnitude: Real estate avg “big bear” ≈ 2/3 that of stocks, half the frequency, and more regular (predictable)… Much recent bemoaning the lack of diversification between real estate and stocks during the big 2008 crash. But in the big picture… © 2014 OnCourse Learning. All Rights Reserved.

24 Of the 8 bears listed here, only 2 afflicted all three “risky” asset classes (and actually also bonds too). Two “market-wide” big bears, separated by 33 years. (Clearly the Great Depression, 40 years earlier, also did that.) Much recent bemoaning the lack of diversification between real estate and stocks during the big 2008 crash. But in the big picture… © 2014 OnCourse Learning. All Rights Reserved.

25 “Fat tail” magnitude: Real estate avg “big bear” ≈ 2/3 that of stocks, half the frequency, and more regular (predictable)… Trough-to-Trough history is fair and conservative 35-year period

26 21.2.4 STEP 1: FINDING THE “EFFICIENT FRONTIER” SUPPOSE WE HAVE THE FOLLOWING RISK & RETURN EXPECTATIONS… INVESTING IN ANY ONE OF THE THREE ASSET CLASSES WITHOUT DIVERSIFICATION ALLOWS THE INVESTOR TO ACHIEVE ONLY ONE OF THREE POSSIBLE RISK/RETURN POINTS… © 2014 OnCourse Learning. All Rights Reserved.

27 INVESTING IN ANY ONE OF THE THREE ASSET CLASSES WITHOUT DIVERSIFICATION ALLOWS THE INVESTOR TO ACHIEVE ONLY ONE OF THE THREE POSSIBLE RISK/RETURN POINTS DEPICTED IN THE GRAPH BELOW… IN A RISK/RETURN CHART LIKE THIS, ONE WANTS TO BE ABLE TO GET AS MANY RISK/RETURN COMBINATIONS AS POSSIBLE, AS FAR TO THE “NORTH” AND “WEST” AS POSSIBLE. Exh.21-7a: © 2014 OnCourse Learning. All Rights Reserved.

29 FINALLY, IF WE ALLOW UNLIMITED DIVERSIFICATION AMONG ALL THREE ASSET CLASSES, WE ENABLE AN INFINITE NUMBER OF COMBINATIONS, THE “BEST” (I.E., MOST “NORTH” AND “WEST”) OF WHICH ARE SHOWN BY THE OUTSIDE (ENVELOPING) CURVE. Exh.21-7c: THIS IS THE “EFFICIENT FRONTIER” (IN THIS CASE OF THREE ASSET CLASSES). Exh.21-7c: © 2014 OnCourse Learning. All Rights Reserved.

30 “EFFICIENT FRONTIER” CONSISTS OF ALL ASSET COMBINATIONS (PORTFOLIOS) WHICH MAXIMIZE RETURN AND MINIMIZE RISK. EFFICIENT FRONTIER IS AS FAR “NORTH” AND “WEST” AS YOU CAN POSSIBLY GET IN THE RISK/RETURN GRAPH. (Terminology note: This is a different definition of "efficiency" than the concept of informational efficiency applied to asset markets and asset prices.) A PORTFOLIO IS SAID TO BE “EFFICIENT” (i.e., represents one point on the efficient frontier) IF IT HAS THE MINIMUM POSSIBLE VOLATILITY FOR A GIVEN EXPECTED RETURN, AND/OR THE MAXIMUM EXPECTED RETURN FOR A GIVEN LEVEL OF VOLATILITY. © 2014 OnCourse Learning. All Rights Reserved.

31 SUMMARY UP TO HERE: DIVERSIFICATION AMONG RISKY ASSETS ALLOWS:  GREATER EXPECTED RETURN TO BE OBTAINED FOR ANY GIVEN RISK EXPOSURE, &/OR;  LESS RISK TO BE INCURRED FOR ANY GIVEN EXPECTED RETURN TARGET. (This is called getting on the "efficient frontier".) PORTFOLIO THEORY ALLOWS US TO:  QUANTIFY THIS EFFECT OF DIVERSIFICATION  IDENTIFY THE "OPTIMAL" (BEST) MIXTURE OF RISKY ASSETS (It also allows to quantify how much it matters.) © 2014 OnCourse Learning. All Rights Reserved.

32 MATHEMATICALLY, THIS IS A "CONSTRAINED OPTIMIZATION" PROBLEM ==> Algebraic solution using calculus ==> Numerical solution using computer and "quadratic programming". Spreadsheets such as Excel include "Solvers" that can find optimal portfolios this way (via numerical search algorithms). Remember: Milton Friedman told Harry Markowitz in 1956 (HM defending his PhD dissertation): “This is not economics.” What is it?... “Optimal control”, a branch of Operations Research or “Engineering Systems. © 2014 OnCourse Learning. All Rights Reserved.

33 Example: Given following expectations: Assuming weights: (1/2)Stocks, (1/3)Bonds, (1/6)RE, Portf mean (expected) return is: Portf variance is the sum across the 9 cells: (1/2)(1/2)(.15)(.15)(1.00)(1/2)(1/3)(.15)(.08)(0.30)(1/2)(1/6)(.15)(.10)(0.25) (1/2)(1/3)(.15)(.08)(0.30)(1/3)(1/3)(.08)(.08)(1.00)(1/3)(1/6)(.08)(.10)(0.15) (1/2)(1/6)(.15)(.10)(0.25)(1/3)(1/6)(.08)(.10)(0.15)(1/6)(1/6)(.10)(.10)(1.00) 0.00560.00060.0003 0.00060.00070.0001 0.00030.00010.0003 = 0.0086SUM SQRT(0.0086) = 9.26% = Portf Volatility

34 MATHEMATICALLY, THIS IS A "CONSTRAINED OPTIMIZATION" PROBLEM Set the problem up in Excel ® as on the previous slide. Invoke the Excel Solver so as to: Find the weights ( w ST, w BD, w RE ) such that they: Are all positive, Are all positive, Sum to 1, Sum to 1, Produce portf mean return r P = target return, and Produce portf mean return r P = target return, and They minimize the portfolio volatility. They minimize the portfolio volatility. Repeat for various different target return points to trace out the efficient frontier. © 2014 OnCourse Learning. All Rights Reserved.

35 Portf Volatility Portf Expexted Return Min-vol asset class Max-vol asset class Min-vol portf You want this. Not this. For starting point (left-hand edge of “area chart”) Let optimizer (e.g., Excel “Solver”®) find the portfolios (asset class shares) that trace out this frontier… by specifying target returns, then minimize portf vol. © 2014 OnCourse Learning. All Rights Reserved.

38 21.2.6 Major Implications of Portfolio Theory for Real Estate Investment Exh.21-9: Core real estate assets typically make up a large share of efficient (non-dominated) portfolios for conservative to moderate return targets. MinVar Portf Retn © 2014 OnCourse Learning. All Rights Reserved.

39 21.2.7 EXPAND PORTFOLIO CHOICE SET BY ADDING ADDITIONAL SUB-CLASSES OF ASSETS… For example, suppose we add the following expectations for an additional sub-class of stocks (small stocks) and an additional sub-class of real estate (REITs)… Exh.21-10a: © 2014 OnCourse Learning. All Rights Reserved.

41 GENERAL QUALITATIVE RESULTS OF PORTFOLIO THEORY 1) OPTIMAL REAL ESTATE SHARE DEPENDS ON HOW CONSERVATIVE OR AGGRESSIVE IS THE INVESTOR; 2) TYPICALLY, REAL ESTATE IS A SIGNIFICANT SHARE. (COMPARE THESE SHARES TO THE AVERAGE U.S. PENSION FUND REAL ESTATE ALLOCATION WHICH IS LESS THAN 5%. THIS IS WHY PORTFOLIO THEORY HAS BEEN USED TO TRY TO GET INCREASED PF ALLOCATION TO REAL ESTATE.) 3) REAL ESTATE APPEAL IN PORTF DUE TO LOW CORRELATION WITH STOCKS & BONDS. (INPUT ASSUMPTIONS IN THE ABOVE EXAMPLE DID NOT INCLUDE A HIGH RETURN OR LOW VOLATILITY FOR R.E. THUS, LARGE R.E. SHARE IN OPTIMAL PORTF MUST NOT BE DUE TO SUCH ASSUMPTIONS.) © 2014 OnCourse Learning. All Rights Reserved.

42 Another Role for Real Estate On the Asset Side: –Real Estate is a diversifier : Reduces asset volatility On the Liability Side (of a defn ben PF): –Real Estate is an inflation hedge Reduces exposure to inflation risk (COLAs, CPI-salary creep). Can explicitly integrate the two sides by applying MPT to Net Assets (assets net of PV of anticipated liabilities). –But tricky to properly include inflation risk. © 2014 OnCourse Learning. All Rights Reserved.

45 Expected Return Volatility 5% 10% 7.5% 5%10% < 7.5% A B i.e., we don’t have this anymore (if A is riskless): P e.g., where P is { (1/2)A & (1/2)B }… This is now 0% (not 5% anymore) Red line is now straight (on top of green) © 2014 OnCourse Learning. All Rights Reserved.

51 THE GRAPH BELOW SHOWS THE EFFECT DIVERSIFICATION IN THE RISKY PORTFOLIO HAS ON THE RISK/RETURN POSSIBILITY FRONTIER. THE FRONTIER IS STILL A STRAIGHT LINE ANCHORED ON THE RISKFREE RATE, BUT THE LINE NOW HAS A GREATER “SLOPE”, PROVIDING MORE RETURN FOR THE SAME AMOUNT OF RISK, ALLOWING LESS RISK FOR THE SAME EXPECTED RETURN. © 2014 OnCourse Learning. All Rights Reserved.

Commercial real estate (CRE) is a large share of total investable wealth ($Trillions) © 2014 OnCourse Learning. All Rights Reserved.59 12% of total investable wealth 21.4: Some Broader Considerations in Portfolio Allocation

$15 Trillion U.S. Pension Fund Assets… Defined Benefit (DB): $6.6 trillion Defined Contribution (DC): $8.6 trillion & growing. DB plans often fall short of their stated CRE targets DC plans need new vehicles for making CRE investments. Why do U.S. Pension Funds Invest So Little in Real Estate?... 60

Problems with investing in private real estate… Illiquidity Large transactions costs Large investment management costs Large capital outlay requirements Difficulty measuring asset values Infrequent return measurement Impossibility of short positions 62© 2014 OnCourse Learning. All Rights Reserved.

Uncertainty is a bigger impediment than risk (uncertainty is inability to know or quantify the risks) PFs feel disadvantaged relative to information and ability to execute, relative to local entrepreneurial players Investment mgrs take large fees and may have conflicts of interest 63 Why do U.S. Pension Funds Invest So Little in Real Estate?... © 2014 OnCourse Learning. All Rights Reserved.

64 Chapter 21 Summary: MPT & Real Estate... The classical theory suggests a fairly robust, substantial role for the real estate asset class in the optimal portfolio (typically 25%-40% without any additional assumptions), either w or w/out riskless asset. The classical theory suggests a fairly robust, substantial role for the real estate asset class in the optimal portfolio (typically 25%-40% without any additional assumptions), either w or w/out riskless asset. This role tends to be greater for more conservative portfolios, less for very aggressive portfolios. This role tends to be greater for more conservative portfolios, less for very aggressive portfolios. Role is based primarily on diversification benefits of real estate, somewhat sensitive to R.E. correlation w stocks & bonds. Role is based primarily on diversification benefits of real estate, somewhat sensitive to R.E. correlation w stocks & bonds. Optimal real estate share roughly matches actual real estate proportion of all investable assets in the economy. Optimal real estate share roughly matches actual real estate proportion of all investable assets in the economy. Optimal real estate share in theory is substantially greater than actual pension fund allocations to real estate in U.S. Optimal real estate share in theory is substantially greater than actual pension fund allocations to real estate in U.S. Optimal R.E. share can be reduced by adding assumptions and extensions to the classical model: Optimal R.E. share can be reduced by adding assumptions and extensions to the classical model: Correct for appraisal-smoothing, private mkt lag, variable liquidity (as in HW3). Extra transaction costs, illiquidity penalties; Long-term horizon risk & returns; Net Asset-Liability portfolio framework; Investor constrained to over-invest in owner-occupied house as investment. But even with such extensions, optimal R.E. share often substantially exceeds existing P.F. allocations to R.E. (approx. 3% on avg.*) But even with such extensions, optimal R.E. share often substantially exceeds existing P.F. allocations to R.E. (approx. 3% on avg.*) © 2014 OnCourse Learning. All Rights Reserved.

65 Appendix 21A

66 "Picture" of 1st and 2nd Moments... First Moment is "Trend“. Second Moment is "Deviation" around trend. Food for Thought Question: IF THE TWO LINES ABOVE WERE TWO DIFFERENT ASSETS, WHICH WOULD YOU PREFER TO INVEST IN, OTHER THINGS BEING EQUAL?... Asset A?,… or Asset B? Actual asset value: 1 st & 2 nd moments of return L.R. trend of asset value: 1 st moment only of return © 2014 OnCourse Learning. All Rights Reserved.

67 "Picture" of 1st and 2nd Moments... First Moment is "Trend“. Second Moment is "Deviation" around trend. Food for Thought Question: IF THE TWO LINES ABOVE WERE TWO DIFFERENT ASSETS, WHICH WOULD YOU PREFER TO INVEST IN, OTHER THINGS BEING EQUAL?... Asset A?,… or Asset B? Line B: G-Mean/Yr = 8.9% A-Mean/Yr = 8.9% Ann. Vol. = 0% Line A: G-Mean/Yr = 8.9% A-Mean/Yr = 12.2% Ann. Vol. = 18% © 2014 OnCourse Learning. All Rights Reserved.

68 "Picture" of 1st and 2nd Moments... First Moment is "Trend“. Second Moment is "Deviation" around trend. Food for Thought Question: IF THE TWO LINES ABOVE WERE TWO DIFFERENT ASSETS, WHICH WOULD YOU PREFER TO INVEST IN, OTHER THINGS BEING EQUAL?... Asset A?,… or Asset B? Line B: G-Mean/Yr = 6.4% A-Mean/Yr = 6.4% Ann. Vol. = 0% Line A: G-Mean/Yr = 6.4% A-Mean/Yr = 9.7% Ann. Vol. = 18% © 2014 OnCourse Learning. All Rights Reserved.

69 S&P500 LTG Bonds Private Real Estate Mean (arith) 13.2%9.6%10.0% Std.Deviation17.5%12.5%10.9% Correlations: S&P500100%3%12% LTG Bonds 100%-4% Priv. Real Estate 100% Historical statistics, annual periodic total returns: Stocks, Bonds, Real Estate, Annual-frequency statistics 1975-2009 (trough-to-trough)… PORTFOLIO THEORY IS A WAY TO CONSIDER BOTH THE 1ST & 2ND MOMENTS (& INTEGRATE THE TWO) IN INVESTMENT ANALYSIS. 1 st Moments 2 nd Moments © 2014 OnCourse Learning. All Rights Reserved.

Chapter 21 MACRO-LEVEL REAL ESTATE INVESTMENT ISSUES © 2014 OnCourse Learning. All Rights Reserved.1.

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