The Journal of WealTh ManageMenT 49Winter 2016

Javier estrada

is a professor of finance at IESE Business School in Barcelona, Spain.jestrada@iese.edu

Alternatives: How? How Much? Why?Javier estrada

Alternatives are increasingly viewed as assets that investors should at the very least consider when deciding their asset allocation.

Some investors may conclude that what these assets contribute to their portfolios is not worth the trouble of including them; others may decide to include them as a small satel-lite; and yet others may decide to include them with sizable allocations. The ultimate goal of this article is to discuss evidence that may help investors to make this decision.

Obviously, there are many assets that fall within the very broad category of alterna-tives, including hedge funds, private equity, or venture capital, to name but a few; the focus of this article is on commodities and real estate. Exposure to the former is explored by considering gold, the commodity most widely used, and for the longest time, for investment purposes; exposure to the latter is explored by considering real estate invest-ment trusts (REITs), a liquid and popular way to invest indirectly in real estate. Ulti-mately, the research question in this article is whether exposure to these two alternatives—commodities through gold and real estate through REITs—is desirable (and why), and if that is the case, what should their allocation be (and why).

The main results can be summarized as follows. First, portfolio optimization sug-gests that both gold and real estate belong to

optimal portfolios, regardless of whether the goal is to minimize risk, to maximize risk-adjusted return, or to maximize the growth of the capital invested. Second, gold enhances risk-adjusted returns regardless of whether it replaces stocks, bonds, or both; real estate, however, enhances risk-adjusted returns if it replaces stocks, but does the opposite if it replaces bonds. And third, alternatives are generally more effective at reducing risk than they are at enhancing returns; in this regard, replacing stocks with gold leads to the largest reductions in risk.

The rest of the article is organized as follows. The next section examines in more detail the issue at stake and some of the rel-evant contributions on the topic, followed by a discussion of the evidence, and then an assessment. An appendix with tables con-cludes the article.

THE ISSUE

Alternatives in Theory and in Practice

Modern f inancial theory argues that all an investor needs to make an optimal investment decision is two assets, the market portfolio, and the risk-free rate, chosen in the specific proportions that maximize the investor’s utility. In practice, the market portfolio is vastly simplif ied and typically

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50 alTernaTives: How? How MucH? wHy? WinTer 2016

thought of as a diversif ied portfolio of stocks, but in theory, the market portfolio is the collection of all risky assets. Put differently, commodities and real estate do belong to the feasible set of risky assets that investors should hold in their portfolios.

Until rather recently, however, most asset allocation advice focused on the proportions of stocks and bonds (and perhaps cash) an investor was supposed to hold in his portfolio; only in the last few years has considering alternatives as an asset class in asset allocation decisions become widely accepted. Arguably, the increasing use of alternatives by university endowments, pioneered by Yale’s David Swensen, has encouraged other institutional investors, as well as many individual investors, to con-sider them for their portfolios.

Of the many and varied assets considered alterna-tive, two of them—commodities and real estate—are the focus of this article. Investors can gain exposure to the first through options, futures, exchange-traded funds (ETFs), or shares in companies largely exposed to one or more commodities, besides the obvious direct ownership. And they can gain exposure to the second, again, besides direct ownership, through individual REITs or REIT ETFs, the latter being particularly useful to individual investors given their low minimum investment, diversification benefits, high liquidity, and low cost. As already mentioned, of the many ways to include commodities and real estate in a portfolio, expo-sure to the former is explored here by considering gold, and exposure to the latter by considering (a broadly-diversified index of ) REITs.

The Role of Alternatives in a Portfolio

A large amount of literature explores the rea-sons for, and impact of, including gold and real estate in investors’ portfolios. Erb and Harvey [2013] and Emmrich and McGroarty [2013] provide thorough reviews focusing on gold; Hudson-Wilson, Fabozzi, and Gordon [2003] and Clayton et al. [2013] do the same, focusing on real estate. A similar review is not necessary here.

It suffices for our purposes to highlight that the most pervasive argument for investing in commodities (particularly gold) and real estate is their low correla-tion to the stocks and bonds held in most portfolios, and, therefore, the corresponding reduction in risk that ultimately leads to an increase in risk-adjusted return.

The same argument, in fact, has been made more generally for most alternative investments, including hedge funds; see, for example, Mileff, Sonnenberg, and Welch [2012]. That said, a wide variety of other reasons has been given to incorporate gold and real estate into investors’ portfolios.

Erb and Harvey [2013] argue that some of the arguments advanced to add gold to a portfolio include that gold is an inf lation hedge; a currency hedge; an attractive alternative to assets with low real returns; a safe haven in times of stress; a potential return to the gold standard; and the suggestion that gold is under-owned. Hudson-Wilson, Fabozzi, and Gordon [2003], in turn, summarize some of the arguments advanced to add real estate to a portfolio, which include to reduce risk; to enhance returns above the risk-free rate; to hedge against unexpected inf lation or def lation; to hold a portfolio that reasonably ref lects the investment uni-verse; and to generate strong cash f lows.

In their book on alternative investments, Stein and DeMuth [2011] advocate to add both commodi-ties and real estate to investors’ portfolios, in order to diversify risk exposure and gain some protection. They recommend, at least as a f irst step, that inves-tors reduce their equity allocation by 10% and allo-cate that portion of the portfolio to equal allocations to these two alternatives. Hence they argue that if an investor holds a 60-40 stock–bond portfolio, he should reduce his exposure to equity by six percentage points (10% of 60%), and add three percentage points of com-modities and another three percentage points of real estate, thus replacing a 60-40 stock–bond portfolio by a 54-40-3-3 portfolio of stocks, bonds, commodities, and real estate.

The evidence discussed in this article is partly con-sistent with this recommendation. On the one hand, the results here do show that, at least as far as risk reduc-tion is concerned, the best outcomes are obtained when alternatives, particularly gold, replace stocks rather than bonds. On the other hand, the results here indicate that the combined allocation to gold and real estate should perhaps be larger than 6%. In fact, portfolio optimization suggests a combined allocation between 15% and 35%, depending on the criterion considered; an evaluation of risk–return trade-offs further suggests that a combined allocation of 5%–10% may not make much of a differ-ence to the risk-return profile of a 60-40 portfolio, and a higher allocation may be desirable.

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The Journal of WealTh ManageMenT 51Winter 2016

EVIDENCE

Data

The sample considered here consists of four assets, namely, stocks, bonds, commodities, and real estate. Stocks are represented by the S&P 500 Index; bonds by an index of 10-year U.S. Treasury Notes; commodities by the price of gold; and real estate by the FTSE NAREIT All REITs Index. All returns are monthly, nominal, and account for both capital gains/losses and cash f lows (divi-dends or coupons). The sample period starts in December 1971 and ends in December 2014. Exhibit A1 in the appendix summarizes some characteristics of these four assets over the whole 43-year sample period.

The benchmark against which all other portfo-lios are evaluated consists of a 60% exposure to stocks and a 40% exposure to bonds. This asset allocation is often called the “industry standard” and throughout this article is referred to as the 60-40 portfolio. Over the whole sample period, this allocation had an annual-ized return, volatility, and downside volatility of 9.9%, 10.0%, and 5.9%, with a beta of 0.61.1

Portfolio Optimization

The first step of the analysis consists of exploring whether an optimal portfolio would include gold and real estate. To this purpose, three optimization criteria are considered: minimizing risk, maximizing risk-adjusted return, and maximizing the geometric mean return. This last criterion, sometimes referred to as the Kelly criterion or geometric mean maximization, aims to maximize the growth of the capital invested, and, therefore, wealth at the end of the holding period; see Estrada [2010] and De Santiago and Estrada [2013]. Exhibit 1 summarizes the results of the analysis.

Panel A of Exhibit 1 shows the optimal allocations to stocks, bonds, gold, and real estate. When the goal is to minimize the risk of the portfolio (MinSD), with risk measured as volatility, the optimal allocations to gold and real estate are 10.9% and 3.9%, for a combined weight of just under 15%; the rest of the portfolio is allo-cated 15.7% to stocks and 69.5% to bonds. Panel B shows that this portfolio has an expected annualized return of 8.7%, with volatility of 7.1% and a Sharpe ratio of 0.26.

A less conservative criterion than minimizing risk is maximizing a portfolio’s risk-adjusted return

as measured by the Sharpe ratio (MaxSR). As Panel A shows, this goal yields a higher allocation to both gold (13.0%) and real estate (6.8%), for a combined weight of just under 20%. As Panel B shows, this port-folio has a slightly higher expected annualized return (9.1%), volatility (7.3%), and Sharpe ratio (0.27) than the MinSD portfolio.

Finally, a more aggressive criterion than the pre-vious two is to maximize the growth of the capital invested, which amounts to maximizing a portfolio’s geometric mean return. An unconstrained optimization (MaxGM-U) yields a short position in bonds (-88.1%), which is perhaps not surprising given the stated goal. If the optimization is constrained to nonnegative weights (MaxGM-C), then Panel A shows allocations to gold and real estate of 10.6% and 23.2%, thus adding up to just over a third of the portfolio, with the rest (66.2%) allocated to stocks. Panel B shows that this portfolio has an expected annualized return of 10.7%, with volatility of 13.2% and a Sharpe ratio of 0.19.

Three conclusions are worth highlighting from this analysis. First, all three optimization criteria sug-gest that gold and real estate belong to an optimal port-folio. Second, portfolio optimization calls for combined allocations to gold and real estate that range, roughly, from 15% (MinSD) to 35% (MaxGM-C). And third,

e x h i b i t 1Optimal Allocations

This exhibit shows, in Panel A, the optimal allocations to stocks, bonds, gold, and real estate given the goals of minimizing risk (MinSD), maxi-mizing the Sharpe ratio (MaxSR), maximizing the geometric mean return unconstrained (MaxGM-U), and maximizing the geometric mean return subject to a no-short-selling constraint (MaxGM-C). Panel B shows the expected performance of the four portfolios based on the annualized geometric mean return (GM), volatility (SD), and Sharpe ratio (SR). The data are described in Exhibit A1 in the appendix. All figures (except Sharpe ratios) are in %.

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52 alTernaTives: How? How MucH? wHy? WinTer 2016

although the more conservative criteria (MinSD and MaxSR) suggest an allocation to gold roughly twice as large as that to real estate, the more aggressive criterion suggests just the opposite.

Risk-Adjusted Returns

As already mentioned, the most pervasive argu-ment for including gold and real estate in a portfolio is their low correlation to stocks and bonds, and, there-fore, their positive impact on risk-adjusted returns. Three issues related to this argument are explored in this section. First, whether in the sample considered here it is indeed the case that introducing gold and real estate enhances risk-adjusted returns; second, whether this enhancement holds regardless of the definition of risk (volatility, downside volatility, or beta); and third, whether this enhancement is independent of the asset (stocks, bonds, or both) that gold and real estate replace in the portfolio.

Exhibit 2 reports the results of the analysis con-sidering three measures of risk-adjusted return. Panel A displays results for the ratio between mean return and volatility (RAR-SD); Panel B, for the ratio between mean return and downside volatility (RAR-SSD); and Panel C, for the ratio between mean return and beta (RAR-Beta). The first column of the exhibit reports these three risk-adjusted return measures for the 60-40 portfolio, and the rest of the columns for six portfolios with allocations between 2.5% and 15% to gold, real estate, and both gold and real estate in equal proportions.2 These alternatives may enter the portfolio from the allo-cation to stocks, the allocation to bonds, or the allocation to both stocks and bonds in equal proportions.

The top third of Panel A (labeled “Gold”) shows that when gold is introduced in proportions between 2.5% and 15% by replacing stocks, bonds, or both, RAR-SD increases monotonically with the allocation to gold. The only minor exception is when gold increases from 12.5% to 15% of the portfolio replacing bonds, in which case there is a very small (and statistically non-significant) decrease in RAR-SD.3

The middle third of Panel A (labeled “Real Estate”) shows that when real estate replaces stocks, RAR-SD increases monotonically with the proportion of real estate. When it replaces bonds, or both stocks and bonds, however, RAR-SD decreases monotonically with the allocation to real estate.

Finally, the bottom third of Panel A (labeled “Both”) shows that when both gold and real estate replace stocks, or both stocks and bonds, RAR-SD increases monotonically with the allocation to alternatives. When alternatives replace bonds, however, there is a slight (and statistically nonsignificant) decrease in RAR-SD when the allocation to alternatives increases beyond 10%.

Although not identical, the results just discussed for RAR-SD are generally similar in Panel B (RAR-SSD) and Panel C (RAR-Beta), where the measures of risk-adjusted return are based on the semideviation and beta. In fact, three general results follow from Exhibit 2. First, introducing gold generally increases risk-adjusted returns, largely regardless of whether the allocation comes out of stocks, bonds, or both. Second, introducing real estate generally increases risk-adjusted returns when the allocation comes out of stocks, and decreases risk-adjusted returns when the allocation comes out of bonds or both stocks and bonds. And third, introducing both gold and real estate generally increases risk-adjusted returns when the allocation comes out of stocks or both stocks and bonds.

It is interesting to note that the highest RAR-SD (0.334), RAR-SSD (0.602), and RAR-Beta (0.018), in bold in Exhibit 2, are all found when an allocation of 15% to gold comes entirely from the portfolio’s alloca-tion to stocks.4 This result begs the question whether even higher allocations to gold, coming out of the allo-cation of stocks, would further improve risk-adjusted returns. Exhibit 3 explores this issue.

All portfolios in Exhibit 3 have a 40% allocation to bonds, and trade-off between gold and stocks, with the allocation to the former (between 0% and 60%) carved out of the allocation to the latter. To clarify, if the allo-cation to gold is 0%, the resulting portfolio is allocated 40% to bonds and 60% to stocks; if the allocation to gold is 60%, the resulting portfolio is allocated 40% to bonds and 60% to gold, with no stocks. As the exhibit shows, RAR-SD and RAR-SSD peak at allocations to gold of 20% and 25%, respectively. Beta-RAR, in turn, peaks at the maximum allocation to gold (60%), simply because the resulting portfolio, which holds no stocks, is essentially uncorrelated to the stock market (the correla-tion is 0.02), and therefore its beta to the stock market is basically 0 (0.02).

Arguably, a 40-60 bond–gold portfolio does not seem very “reasonable” for an investor to hold and is the result of this particular definition of risk-adjusted

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The Journal of WealTh ManageMenT 53Winter 2016

return, which rewards lack of correlation to the stock market. Furthermore, although RAR-SSD peaks at an allocation to gold of 25% (0.620), it has essentially the same value at an allocation to gold of 20% (0.619).

Therefore, Exhibit 3 suggests that a portfolio with an allocation of 40% to bonds, 40% to stocks, and 20% to gold would provide investors with an ideal trade-off between risk and return. The performance of this

e x h i b i t 2Risk-Adjusted Returns

This exhibit shows three measures of risk-adjusted return (RAR) expressed as the ratio between a portfolio’s arithmetic mean return and three measures of risk, volatility (SD), downside volatility (SSD), and beta, for a portfolio consisting of 60% stocks and 40% bonds (60-40), as well as for portfolios con-sisting of allocations between 2.5% (2.5) and 15% (15.0) to gold, real estate, and equal proportions to both gold and real estate. The portfolio’s allocation to alternatives is carved out of stocks, bonds, or equal proportions of both stocks and bonds. The data are described in Exhibit A1 in the appendix.

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54 alTernaTives: How? How MucH? wHy? WinTer 2016

particular portfolio during periods of financial turmoil will be further explored below.

Risk–Return Trade-Offs

An assessment of risk-adjusted returns implies, by definition, assessing the trade-off between risk and return. However, the most typical variables used in risk-adjusted return ratios, volatility, downside volatility, or beta, are just three of the many that could be consid-ered. Investors do assess risk in many other, and widely different, ways. In fact, Warren Buffett disavows the use of volatility and beta as measures of risk and focuses on the likelihood of losing purchasing power over the intended holding period instead; see Estrada [2013].

Using “unconventional” measures of risk has both pros and cons. It is clear that investors assess risk in some ways that may be diff icult to build into a neat model, or even to quantify, and yet these risk measures should not be ignored in a realistic analysis.5 Hence, on the positive side, exploring the implications of assessing risk with variables other than volatility, downside vola-tility, or beta makes the analysis more comprehensive. On the negative side, assessing a risk–return trade-off

with “unconventional” risk measures turns the inquiry into a more subjective evaluation than it would be if it were based on an objective comparison of Sharpe ratios, Sortino ratios, or Treynor ratios.

Exhibits 4, 5, and 6 evaluate the trade-off between risk and return with three different measures of risk, namely, the probability of an n-month loss (PL-nM), the average n-month loss over all n-month periods with losses (AL-nM), and the worst n-month return (WR-nM), in all cases for n equal to 12, 36, and 60.6 These three exhibits consider six portfolios with allocations between 2.5% and 15% to gold, real estate, or both gold and real estate in equal proportions, coming out of the allocation to stocks (Panels A), to bonds (Panels B), and to both stocks and bonds in equal proportions (Panels C). These six portfolios are evaluated against the benchmark 60-40 portfolio. Summary statistics for all the portfolios con-sidered are reported in Exhibit A2 (focusing on gold), Exhibit A3 (focusing on real estate), and Exhibit A4 (focusing on both gold and real estate) in the appendix.

Exhibit 4, which focuses on gold, shows that increasing the allocation to this commodity has the big-gest impact on returns when it replaces bonds, which increases the annualized return of the 60-40 portfolio (9.9%) by 50 basis points to 10.4% at an allocation of 15%. The impact on returns is rather negligible when gold replaces stocks (a maximum of 10 basis points), and slightly higher when it replaces both stocks and bonds (a maximum of 30 basis points).

From the perspective of risk, replacing stocks with gold has a clearly positive impact. As the allocation to gold increases, the probability of losses, the average loss decrease, and the worst returns are mitigated sub-stantially; in fact, for allocations to gold 5% or larger, the worst returns become positive. Introducing gold, however, is not as beneficial when it replaces bonds. In this case, although the probability of losses decreases slightly, the impact on the average loss and the worst return is less clear. When gold replaces both stocks and bonds, the impact on all three risk variables is positive but to a lesser degree than when it replaces just stocks.

Exhibit 5 reports a similar analysis, in this case considering different allocations to real estate. Introducing real estate has no impact on returns when it replaces stocks, and a maximum impact of 40 (20) basis points when it replaces bonds (both stocks and bonds) at a 15% allocation. In terms of risk, when real estate replaces stocks, the impact is rather negligible, with a

This exhibit shows three measures of risk-adjusted return (RAR) expressed as the ratio between a portfolio’s arithmetic mean return and three measures of risk, volatility (SD), downside volatility (SSD), and beta, for a portfolio with a 40% allocation to bonds and allocations to gold between 0% (the 60-40 stock–bond portfolio) and 60% (a 40-60 bond–gold portfolio), with the allocation to gold carved out of stocks. The data are described in Exhibit A1 in the appendix.

e x h i b i t 3Risk-Adjusted Returns—An Expanded View

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The Journal of WealTh ManageMenT 55Winter 2016

small positive impact in the probability of losses, and a small negative impact on the average loss and the worst returns. When real estate replaces bonds, however, the impact is clearly negative on all three risk variables, and particularly on the worst returns; and when it replaces both stocks and bonds, the impact is generally negative on all risk variables.

Finally, Exhibit 6 reports once again a similar anal-ysis, in this case considering different allocations to both gold and real estate in equal proportions. In terms of returns, the largest impact is observed when alternatives replace bonds; there is a rather negligible impact when they replace stocks, and an intermediate impact when they replace both stocks and bonds. In terms of risk, the

This exhibit shows the annualized return (GM) of a portfolio consisting of 60% stocks and 40% bonds (60-40), as well as for portfolios consisting of allocations to gold between 2.5% (2.5) and 15% (15.0), carved out of stocks (Panel A), bonds (Panel B), and equal proportions of both stocks and bonds (Panel C). It also shows the proportion of 12/36/60-month periods with losses (PL-12M, PL-36M, and PL-60M); the average loss over all the 12/36/60-month periods with losses (AL-12M, AL-36M, AL-60M); and the worst return over all 12/36/60-month periods (WR-12M, WR-36M, WR-60M). The data are described in Exhibit A1 in the appendix.

e x h i b i t 4Risk–Return Trade-Offs—Gold

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56 alTernaTives: How? How MucH? wHy? WinTer 2016

best results are observed when alternatives replace stocks, with a positive impact on all three risk variables. The impact on risk is generally negative when alternatives replace bonds, and mildly positive when they replace both stocks and bonds.

In short, the overall results that emerge from Exhibits 4–6 suggest the following. First, alternatives

tend to enhance returns most when they replace bonds, have a rather negligible impact when they replace stocks, and a small impact when they replace both stocks and bonds. Second, alternatives tend to reduce risk most when they replace stocks, have little or nega-tive impact when they replace bonds, and a mixed impact when they replace both stocks and bonds.

This exhibit shows the annualized return (GM) of a portfolio consisting of 60% stocks and 40% bonds (60-40), as well as for portfolios consisting of allocations to real estate between 2.5% (2.5) and 15% (15.0), carved out of stocks (Panel A), bonds (Panel B), and equal proportions of both stocks and bonds (Panel C). It also shows the proportion of 12/36/60-month periods with losses (PL-12M, PL-36M, and PL-60M); the average loss over all the 12/36/60-month periods with losses (AL-12M, AL-36M, AL-60M); and the worst return over all 12/36/60-month periods (WR-12M, WR-36M, WR-60M). The data are described in Exhibit A1 in the appendix.

e x h i b i t 5Risk-Return Trade-Offs—Real Estate

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The Journal of WealTh ManageMenT 57Winter 2016

Third, of all the possibilities explored, risk decreases most when gold replaces stocks; in fact, it is the only case of all those considered in which all risk mea-sures monotonically decrease as the proportion of gold increases (and that of stocks decreases), at least until it reaches the maximum 15% considered in these three exhibits. And last but certainly not least, alternatives

seem to be more effective at reducing risk than at enhancing returns.

Performance during Crises

As already discussed, one of the most pervasive arguments in favor of adding alternatives, particularly

e x h i b i t 6Risk–Return Trade-Offs—Gold and Real Estate

This exhibit shows the annualized return (GM) of a portfolio consisting of 60% stocks and 40% bonds (60-40), as well as for portfolios consisting of equal (total) allocations to both gold and real estate between 2.5% (2.5) and 15% (15.0), carved out of stocks (Panel A), bonds (Panel B), and equal proportions of both stocks and bonds (Panel C). It also shows the proportion of 12/36/60-month periods with losses (PL-12M, PL-36M, and PL-60M); the average loss over all the 12/36/60-month periods with losses (AL-12M, AL-36M, AL-60M); and the worst return over all 12/36/60-month periods (WR-12M, WR-36M, WR-60M). The data are described in Exhibit A1 in the appendix.

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58 alTernaTives: How? How MucH? wHy? WinTer 2016

gold, to a portfolio is to enhance risk-adjusted returns. The evidence discussed here fully supports this argu-ment, and further highlights that the increase in risk-adjusted return stems more from a reduction of risk than from an increase in return. Hence, it is interesting to assess, during periods of financial turmoil, the perfor-mance of a 60-40 stock–bond portfolio relative to that of a portfolio that is partly invested in alternatives.

The results of the previous section suggest that relative to a 60-40 stock–bond portfolio, reducing the allocation to stocks by 15 percentage points and increasing the allocation to gold by the same amount would provide investors with the largest risk reduction. In addition, Exhibit 3 suggests that risk-adjusted returns would be further enhanced by allocating 20% (rather than 15%) to gold, replacing an equal proportion of stocks in the portfolio. Hence, Exhibit 7 compares the performance of a 60-40 stock–bond portfolio to that of a 40-40-20 stock–bond–gold portfolio during two recent periods of market turbulence. The performance of an all-stock portfolio is also considered for additional perspective.

The first turbulent period considered is between the end of August 2000 and the end of September 2002 (Crisis 1), which is the bear market that followed the Internet bubble. During this 25-month period, the S&P 500 fell 46.3% (44.7% considering dividends). The second turbulent period is between the end of October 2007 and the end of February 2009 (Crisis 2),

which is the bear market during the relatively recent global f inancial crisis. During this 16-month period, the S&P 500 fell 52.6% (50.9% considering dividends).

As Exhibit 7 clearly shows, the addition of gold to a portfolio was highly beneficial during both crises. Risk as measured by the standard deviation, the semidevia-tion, and beta, was lower for the 40-40-20 portfolio than for both the all-stock and the 60-40 portfolios. With a minor exception, the 40-40-20 portfolio also had a beneficial impact on the probability of monthly losses, the average monthly loss during months with losses, and the worst loss. And last, but certainly not least, although $100 fully invested in stocks at the beginning of each crisis period turned into $55.3 ($49.1) during the first (second) crisis, the same $100 invested in the 40-40-20 portfolio turned into $98.0 ($90.6), thus limiting the losses to only 2.0% (9.4%).

ASSESSMENT

For many years, alternative investments have been an important asset for institutional investors, and more recently for individual investors as well. This broad asset class encompasses assets as widely different as hedge funds, private equity, venture capital, commodities, and real estate. This article focuses on the last two, and more precisely on gold and REITs, and its ultimate goal is to help investors decide whether they need alternatives in their portfolios, and if so, why.

e x h i b i t 7Impact of Introducing Gold During Financial Crises

This exhibit shows the monthly geometric mean return (GM), standard deviation (SD), semideviation for a 0% benchmark (SSD), and beta during the August 2000–September 2002 (Crisis 1) and October 2007–February 2009 (Crisis 2) periods, for a portfolio fully invested in stocks (S&P 500), another invested 60% in stocks and 40% in bonds (60-40), and another invested 40% in stocks, 40% in bonds, and 20% in gold (40-40-20). It also shows the proportion of months with losses (PL), the average monthly loss in months with losses (AL), and the worst monthly loss (WL) during the same crisis periods, as well as the terminal value of $100 invested at the beginning of each period (TV). The data are described in Exhibit A1 in the appendix.

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The Journal of WealTh ManageMenT 59Winter 2016

Brunel and Elmes [2012] suggest that alternative assets are not a must in any portfolio owing to their lower liquidity, more complex investment processes and instruments, higher counterparty risks, lower transpar-ency, and higher fees. Their argument focuses on hedge funds, but the challenges they highlight also apply to other alternative assets. That said, the two assets con-sidered here, gold and REITs, are arguably among the least affected by these shortcomings.

From the evidence discussed in this article, sev-eral findings are worth highlighting. First, three very different optimization criteria—minimizing risk, maximizing risk-adjusted returns, and maximizing the growth of the capital invested—all suggest that gold and REITs do belong to optimal portfolios. The optimal exposure ranges between 15% and 35% of a portfolio, depending on the optimization criteria considered.

Second, although real estate enhances risk-adjusted returns when it replaces stocks, and does the opposite when it replaces bonds, gold enhances risk-adjusted returns regardless of whether it replaces stocks, bonds, or both. This is the case under three different definitions of risk-adjusted return, based on three dif-ferent definitions of risk, namely, volatility, downside volatility, and beta.

Third, alternatives seem to be more effective at reducing risk than at enhancing returns; in this regard, the largest reductions in risk are obtained when gold enters the portfolio by replacing stocks. This is the case regardless of whether risk is assessed with conventional variables (such as volatility, downside volatility, or beta) or less conventional variables (such as the probability of losses, the average loss over periods with losses, and the worst return).

Finally, during the two most recent bear markets, a portfolio invested 40% in stocks, 40% in bonds, and 20% in gold, clearly outperformed both an all-stock portfolio and a 60-40 stock–bond portfolio. During these two crises, the introduction of gold reduced portfolio risk as measured by both traditional (standard deviation, semi-deviation, and beta) and nontraditional (probability of losses, average loss during period with losses, and worst loss) measures of risk. As a result, the capital invested fell much less when the portfolio contained gold than when it did not.

All in all, the evidence discussed here suggests that individual investors should follow the lead of institu-tional investors and seriously consider alternatives, at

least gold and REITs, in their regular asset allocation decisions. This advice is particularly easy to imple-ment in the current marketplace, which features a wide variety of highly liquid, low-cost ETFs that provide direct exposure to these assets.

a p p e n d i x

This exhibit shows, for the series of monthly returns over the January 1972–December 2014 period, the arithmetic mean return (AM) and geometric mean return (GM), standard deviation (SD), semideviation for a 0% benchmark (SSD), beta, lowest return (Min), and highest return (Max). Betas and correlations are estimated with respect to stocks. All returns are nominal, in dollars, and account for capital gains/losses and cash f lows. All figures are (except beta) in %.

e x h i b i t a 1Summary Statistics

e x h i b i t a 2Introducing Gold

(continued )

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60 alTernaTives: How? How MucH? wHy? WinTer 2016

ENDNOTES

The author would like to thank an anonymous ref-eree for valuable comments. Patricia Palgi provided valuable research assistance. The views expressed herein and any errors that may remain are entirely his own.

1Downside volatility is calculated for a benchmark return of 0%. For a practical introduction to this measure of risk, see Estrada [2006].

2When both gold and real estate are added to a port-folio, they are included in equal proportions and the sum of the two allocations is equal to the labels in the top row. To illustrate, an allocation to both gold and real estate of 2.5% implies a 1.25% allocation to each asset.

3All statements based on the significance of differences in RAR-SD are based on the Jobson–Korkie–Memmel test, at the 5% level of significance; see Memmel [2003].

4This may be, at least in part, because gold has a slightly lower correlation to stocks (-0.01) than to bonds (0.03), and

This exhibit shows, for the series of monthly returns, the arithmetic mean return (AM) and geometric mean return (GM), standard deviation (SD), semideviation for a 0% benchmark (SSD), and beta, for a portfolio con-sisting of 60% stocks and 40% bonds (60-40), as well as for portfolios consisting of allocations to real estate between 2.5% (2.5) and 15% (15.0), carved out of stocks (Panel A), bonds (Panel B), and stocks and bonds in equal proportions (Panel C). The data are described in Exhibit A1. All figures are (except beta) in %.

e x h i b i t a 3Introducing Real Estate

This exhibit shows, for the series of monthly returns, the arithmetic mean return (AM) and geometric mean return (GM), standard deviation (SD), semideviation for a 0% benchmark (SSD), and beta, for a portfolio con-sisting of 60% stocks and 40% bonds (60-40), as well as for portfolios consisting of equal (total) allocations to gold and real estate between 2.5% (2.5) and 15% (15.0), carved out of stocks (Panel A), bonds (Panel B), and stocks and bonds in equal proportions (Panel C). The data are described in Exhibit A1. All figures are (except beta) in %.

e x h i b i t a 4Introducing Gold and Real Estate

This exhibit shows, for the series of monthly returns, the arithmetic mean return (AM) and geometric mean return (GM), standard deviation (SD), semideviation for a 0% benchmark (SSD), and beta, for a portfolio con-sisting of 60% stocks and 40% bonds (60-40), as well as for portfolios consisting of allocations to gold between 2.5% (2.5) and 15% (15.0), carved out of stocks (Panel A), bonds (Panel B), and stocks and bonds in equal proportions (Panel C). The data are described in Exhibit A1. All figures are (except beta) in %.

e x h i b i t a 2 (continued )Introducing Gold

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The Journal of WealTh ManageMenT 61Winter 2016

both are lower than the correlations between real estate and stocks (0.59) and real estate and bonds (0.11).

5An obvious example is political risk, which is difficult to define, difficult to assess, and even more difficult (if at all possible) to quantify.

6The probability of an n-month loss is estimated as a historical frequency. To illustrate, PL-36M is the number of 36-month (rolling and overlapping) periods in which a portfolio lost value divided by the total number of 36-month periods in the sample.

REFERENCES

Brunel, J., and J. Elmes. “Alternative Assets: Are They Still Worth It?” The Journal of Wealth Management, Vol. 15, No. 2 (2012), pp. 49-61.

Clayton, J., F. Fabozzi, M. Giliberto, J. Gordon, Y. Liang, G. MacKinnon, and A. Mansour. “Portfolio Strategy and Structure Take Center Stage: ‘How, What, Where, and When?’ Replace ‘Why?’” The Journal of Portfolio Management, Vol. 39, No. 5 (2013), pp. 12-20.

De Santiago, R., and J. Estrada. “Geometric Mean Maximi-zation: Expected, Observed, and Simulated Performance.” The Journal of Investing, Vol. 22, No. 2 (2013), pp. 106-119.

Emmrich, O., and F. McGroarty. “Should Gold Be Included in Institutional Investment Portfolios?” Applied Financial Economics, Vol. 23, No. 19 (2013), pp. 1553-1565.

Erb, C., and C. Harvey. “The Golden Dilemma.” Financial Analysts Journal, Vol. 69, No. 4 (2013), pp. 10-42.

Estrada, J. “Downside Risk in Practice.” Journal of Applied Corporate Finance, Vol. 18, No. 1 (2006), pp. 117-125.

——. “Geometric Mean Maximization: An Overlooked Portfolio Approach?” The Journal of Investing, Vol. 19, No. 4 (2010), pp. 134-147.

——. “Are Stocks Riskier than Bonds? Not If You Assess Risk Like Warren Buffett.” Journal of Asset Management, Vol. 14, No. 2 (2013), pp. 73-78.

Hudson-Wilson, S., F. Fabozzi, and J. Gordon. “Why Real Estate?” The Journal of Portfolio Management, Vol. 29, No. 5, (2003), pp. 12-25.

Memmel, C. “Performance Hypothesis Testing with the Sharpe Ratio.” Finance Letters, Vol. 1, No. 1 (2003), pp. 21-23.

Mileff, R., N. Sonnenberg, and S. Welch. “Alternative Life-style: The Evolution of Alternative Investments.” The Journal of Wealth Management, Vol. 15, No. 1 (2012), pp. 27-40.

Stein, B., and P. DeMuth. The Little Book of Alternative Invest-ments. Hoboken, NJ: John Wiley & Sons, 2011.

To order reprints of this article, please contact Dewey Palmieri at dpalmieri@iijournals.com or 212-224-3675.

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