Adaptive asset allocation policies

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Adaptive asset allocation policies

  1. 1. Financial Analysts Journal Volume 66  Number 3 ©2010 CFA Institute Adaptive Asset Allocation Policies William F. Sharpe This article proposes an asset allocation policy that adapts to market movements by taking into account changes in the outstanding market values of major asset classes. Such a policy considers important information, reduces or avoids contrarian behavior, and can be followed by a majority of investors.T he third edition of Managing Investment A typical large institutional investor sets an Portfolios: A Dynamic Process states: asset allocation policy after considerable analysis, Strategic asset allocation can be viewed changing it only episodically. According to the as a process with certain well-defined CalPERS (2009) report: steps. Performing those steps produces a CalPERS follows a strategic asset allocation set of portfolio weights for asset classes; policy that identifies the percentage of funds to we call this set of weights the strategic be invested in each asset class. Policy targets asset allocation (or the policy portfolio).1 are typically implemented over a period of several years. This article is about such asset allocation To accommodate disparities between policypolicies. proportions and actual portfolio holdings, most traditional asset allocation policies include accept-Traditional Asset Allocation able ranges around each target weight within which the magnitude of the particular asset classPolicies is allowed to vary. For some investors, the devia-The March 2009 asset allocation report of the tions can become substantial. At the end of MarchCalifornia Public Employees’ Retirement System 2009, the proportions held by CalPERS differed(CalPERS)2 provides the example of a traditional substantially from its policy target (adopted in theasset allocation policy shown in Table 1. A key latter part of 2007 but still in effect at the time), asfeature of such a policy is that the target for each shown in Table 2.3asset class is stated as a percentage of the total valueof the fund, with each asset target between 0 Table 2. CalPERS’ Target and Actual Assetpercent and 100 percent. An asset allocation pol- Allocations, March 2009icy is almost always stated in this manner. I use Policy Current the term “traditional” for such a policy to differ- Asset Class Target Current Targetentiate it from the adaptive policies described Global equity 66% 53.5% 12.5 ppslater in the article. Global fixed income 19 25.2 +6.2 Inflation-linked assets 5 2.5 2.5 Real estate 10 11.4 +1.4Table 1. CalPERS’ Asset Allocation Policy, Cash 0 7.3 +7.3 March 2009 pps = percentage points.Asset Class Policy Target Source: CalPERS (2009).Global equity 66%Global fixed income 19Inflation-linked assets 5 To restore the portfolio by conforming it withReal estate 10 the asset allocation policy, CalPERS would have had to sell some of its holdings in three assetCash 0 classes (global fixed income, real estate, and cash)Source: CalPERS (2009). and purchase additional amounts of two others (global equity and inflation-linked assets). This action was not taken immediately, however,William F. Sharpe is STANCO 25 Professor Emeritus of because the CalPERS board was considering a newFinance, Stanford University, California. asset allocation policy at the time.May/June 2010 www.cfapubs.org 45
  2. 2. Financial Analysts Journal Although statistics are lacking, most large pen- decimal places), indicating close conformance ofsion funds, endowments, and foundations appear the asset proportions with the 60/40 policy.8to have traditional asset allocation policies. Inmany cases, considerable discrepancies between Fidelity Freedom 2020 Fundpolicy and actual asset proportions are allowed todevelop. Some funds actively rebalance holdings to Fidelity Investments offers a series of target-dateavoid substantial discrepancies, whereas others funds. Of those funds at the end of December 2008,allow the proportions to change with market move- the Fidelity Freedom 2020 Fund was the one mostments and then revisit their asset allocation policies used by defined-contribution plans, with assets ofwhen the differences between actual and policy more than $12 billion from such plans.9 The nextweights become large. Relatively few institutional six funds in order of total assets from defined-investors seem to engage in what some might term contribution plans were Fidelity Freedom funds“slavish” adherence to a set of policy asset weights with other target dates.by engaging in frequent rebalancing transactions. An excerpt from the 2008 prospectus for the The majority of multi-asset mutual funds also Fidelity family of funds is instructive:have traditional asset allocation policies. Unlike The following chart [Figure 1] illustrates eachmany institutional investors, however, many such Freedom Fund’s approximate asset allocationmutual funds allow only relatively small devia- among equity, fixed-income, and short-termtions of the actual asset proportions from those funds as of March 31, 2008. The chart also illustrates how these allocations may changespecified in the policy. over time. The Freedom Funds’ target asset Many individual investors invest some or all allocations may differ from this illustration. . . .of their retirement savings in multi-asset mutual [Moreover, the fund’s adviser] intends to man-funds, either directly or through a 401(k) or other age each Freedom Fund according to its targettype of retirement plan. Under the Pension Protec- asset allocation strategy, and does not intend totion Act of 2006, the U.S. Department of Labor4 trade actively among underlying Fidelity fundsincludes only two types of mutual or collective or intend to attempt to capture short-termfunds as “qualified default investment alterna- market opportunities. However, [the fund’stives” (QDIAs): balanced (sometimes called life- adviser] . . . may modify the target asset alloca-stage) and target-date (sometimes called life-cycle) tion strategy for any Freedom Fund and modify the selection of underlying Fidelity funds forfunds.5 At the end of December 2008, 9.1 percent of any Freedom Fund from time to time.10the $1.084 trillion invested in mutual funds offeredby the top 25 providers of such funds to 401(k) A comparison of the allocation for the Fidelityplans was invested in balanced or life-stage funds Freedom 2020 Fund at the end of March 200811 withand 8.9 percent was invested in target-date funds.6 that at the end of March 200912 is shown in Table 3. To illustrate, I provide an example of each As intended, over the course of the year, the percent-type of fund. age of value invested in equity had fallen, providing overall asset allocations extremely close to those called for by the “glide paths” shown in Figure 1.Vanguard Balanced Index Fund Although these funds provide only examples,With $7.5 billion under management in April 2009, their activities suggest that many active and pas-the Vanguard Balanced Index Fund sive multi-asset mutual funds choose to rebalance seeks—with 60 percent of its assets—to track their holdings significantly after major market the investment performance of a benchmark movements in order to minimize differences index that measures the investment return of the overall U.S. stock market. With 40 percent of its assets, the fund seeks to track the Table 3. Fidelity Freedom 2020 Fund’s Asset investment performance of a broad, market- Allocations, 2008 and 2009 weighted bond index.7 Actual, Actual,The Vanguard Balanced Index Fund compares its Asset 31 March 2008 31 March 2009returns with those of a benchmark, with 60 percent U.S. equity 52.6% 52.1%invested in the MSCI US Broad Market Index and Non-U.S. equity 13.7 12.940 percent in Barclays Capital U.S. Aggregate Bond Investment-grade fixed income 25.5 26.1Index. Over the 36 months ended March 2009, the High-yield fixed income 7.6 7.6R2 value for a comparison of the fund’s returns with Short-term funds 0.6 1.3those of the benchmark was 1.00 (rounded to two Source: Fidelity Investments (2008, 2009).46 www.cfapubs.org ©2010 CFA Institute
  3. 3. Adaptive Asset Allocation Policies Figure 1. Fidelity Freedom Funds’ Asset Allocations Freedom Freedom Freedom Freedom Freedom Freedom 2050 2040 2030 2020 2010 2000 Freedom Freedom Freedom Freedom Freedom Freedom 2045 2035 2025 2015 2005 Income Weight (%) 100 90 Short-Term Funds 80 Fixed-Income Funds 70 60 50 40 Equity Funds 30 20 10 0 50 45 40 35 30 25 20 15 10 5 0 5 10 15 Years to Retirement Years after Retirement Equity Funds Fixed-Income Funds Short-Term Funds Note: On the x-axis, “0” refers to retirement. Source: Fidelity Investments (2008).between actual and policy asset allocations. Funds Consider an investor who attempts to keep thethat do so follow traditional asset allocation poli- actual asset percentages of a portfolio consistentcies: Balanced funds rebalance to conform with a with a stated asset allocation policy. I define such aconstant asset allocation over time, and target-date strategy as one that follows an asset allocation policyfunds rebalance to conform with an asset allocation by rebalancing a portfolio frequently to conform itthat varies slowly over time as called for by a pre- with a pre-specified set of asset proportionalspecified glide path. values. Assume that our investor rebalances a port- folio to conform it with a stated set of asset propor-The Contrarian Nature of Tradi- tions at the end of every review period (e.g., everytional Asset Allocation Strategies month or quarter). Given n asset classes, the dollarThe term “contrarian” is used in many contexts. amounts initially invested in the assets are X1, . . .,The following definition is closest to the meaning I Xn. The initial value of the portfolio isintend in this article: V0 = ∑ X i , (1) An investment style that goes against prevail- i ing market trends by buying assets that are performing poorly and then selling when they and the initial asset proportions are perform well.13 X1 XFor purposes of this article, I consider investors ,..., n . (2) V0 V0contrarian if they buy assets that perform poorlyrelative to the other assets in the portfolio and sell We assume that these proportions are equal to theassets that perform well relative to the others. investor’s asset allocation policy proportions.May/June 2010 www.cfapubs.org 47
  4. 4. Financial Analysts Journal Now imagine that a period has passed and that tor will sell the asset because Di will be negative.the value relative for asset i (the ratio of the ending Such assets are relative winners. Moreover, the bet-value to the beginning value) is ki. The new dollar ter such an asset’s performance (i.e., the larger itsvalues of the assets are value relative, ki), the greater will be Yi, the amount k1 X1 ,..., kn X n . sold, as a percentage of the current holding. (3) In this setting, an investor who follows an assetThe ending value of the portfolio is allocation policy is undoubtedly a contrarian. To V1 = ∑ ki X i , (4) repeat the obvious: i Rebalancing a portfolio to a previously setand the new asset proportions are asset allocation policy involves selling relative k1 X1 k X winners and buying relative losers.14 ,..., n n . (5) V1 V1We denote the value relative for portfolio Kp as Contrarians All? V1 If I wish to buy a security, someone must sell it to KP ≡ . (6) me. If I wish to sell a security, someone must buy it. V0 Now assume that the investor wishes to pur- Anyone who rebalances a portfolio to conform withchase and sell securities in amounts that will make an asset allocation policy must trade with someone.the new asset proportions equal the initial policy From time to time, companies and other enti-proportions. Let D1, . . ., Dn represent the dollar ties issue new securities and purchase or redeemamounts of the assets purchased (if positive) or sold existing ones. But most security transactions(if negative). The goal is to select a set of positive, involve trades of existing securities between twonegative, and possibly zero values for D1, . . ., Dn investors, which raises the question, can all inves-such that tors be contrarians? The answer is no. I illustrate with a simple example. Each of four ki Xi + Di Xi investors follows an asset allocation policy with = (7) V1 V0 positive proportions of four asset classes, althoughfor every asset i. This step requires that the proportions differ. A period has passed, and the assets have performed differently. In Table 4, the ( Di = K p − ki X i .) (8) assets are numbered in terms of their performance Also of interest is the amount of an asset pur- (i.e., k1 > k2 > k3 > k4). The investors differ in theirchased as a proportion of the value before the trans- initial allocations and thus have different overallaction. We can denote this amount as Yi : portfolio returns (Kp values). Each investor wishes to make transactions to rebalance the portfolio to Di Kp Yi ≡ = −1. (9) the particular asset allocation policy. In Table 4, a ki X i ki minus sign indicates an asset to be sold and a plusIf an asset underperforms the portfolio as a whole, sign one to be purchased. The last three columns(Kp  ki) will be positive. As Equation 8 shows, the show the number of investors wishing to sell aninvestor will purchase the asset because Di will be asset, the number wishing to buy, and the differ-positive. Such assets are relative losers. Moreover, ence between the two.the poorer such an asset’s performance (i.e., the Because every investor holds the best per-smaller its value relative, ki), the greater will be forming asset, every portfolio return will be belowYi , the amount purchased, as a percentage of the the return of the best performing asset. Hence,current holding. every investor will wish to sell shares of Asset 1. Conversely, if an asset outperforms the portfo- Conversely, every portfolio return will be greaterlio as a whole, (Kp  ki) will be negative. The inves- than the return of the worst performing asset, and Table 4. Asset Allocation Trades for Four Investors Assets in Decreasing No. of No. of Net No. Order of Return Investor A Investor B Investor C Investor D Sellers Buyers of Sellers 1 – – – – 4 0 4 2 – – – + 3 1 2 3 + + – + 1 3 2 4 + + + + 0 4 448 www.cfapubs.org ©2010 CFA Institute
  5. 5. Adaptive Asset Allocation Policiesthus every investor will wish to buy shares of Asset Thus:4. With regard to the best and worst performing Not all investors can follow traditional assetassets, every investor is indeed a contrarian, and allocation policies.15the group as a whole must find some investors More pragmatically, for a large number ofwho do not follow asset allocation policies with investors to be able to follow traditional asset allo-whom to trade. cation policies, a large number of other investors Note that in each investor’s column, minus must be willing to take the other sides of the requi-(sell) signs come first, followed by plus (purchase) site trades. Investors in the latter group must pur-signs because each investor will wish to sell all chase assets that have performed well (relativeassets with performance (ki) greater than that of the winners) and sell assets that have performedportfolio (Kp). Investor asset allocations, like port- poorly (relative losers). As I discuss later in thefolio returns, will differ, however, so the points at article, such a strategy will prove superior if secu-which minus signs stop and plus signs begin will rity price trends persist; therefore, investors whovary—all of which leads to a key characteristic of pursue such a strategy are often termed trend fol-the last column: The net number of sellers (number lowers. To oversimplify, for every contrarian thereof sellers  number of buyers) will be smaller, the must be a trend follower. Not only is it impossiblepoorer an asset’s performance. for all investors to follow contrarian strategies, but To keep the example simple, I assume that each it is also impossible for those with a majority ofinvestor’s portfolio performance differs from that capital assets to do so.of each asset. This assumption, however, need not Identifying investors who have traditionalbe the case. If an asset’s performance equals that of asset allocation policies is easy. As indicated ear-an investor’s portfolio, the investor will not wish to lier, there are many such investors. But identifyingbuy or sell shares in it—a situation that could be investors who pursue trend-following policies isrepresented with a zero in the table. harder. This fact raises a more practical question: We could make another modification that How many investors actually follow an asset allo-would increase the realism of the example. Some cation policy? The answer might well be relativelyinvestors may have an asset allocation policy that few. Although many investors have asset allocationcalls for zero exposure to one or more assets. This policies, relatively few are likely to follow theirsituation could also be represented with a zero in policies by rebalancing their portfolios frequently.the table because no trades will be required. As suggested earlier, multi-asset mutual funds Taking such possibilities into account would appear to be a major exception: They rebalancemodify the characteristics of the table only slightly. their portfolios frequently by buying relative losersThe net number of sellers will either decrease or and selling relative winners.stay the same, the lower an asset’s performance. We should not read too much into this result.Although the net number of sellers will not increase Why a Contrarian Strategy?the lower an asset’s return, the difference between Why might an investor wish to adopt a contrarianthe dollar value of shares offered for sale and the strategy? There are two possible reasons. The inves-dollar value of shares desired to be purchased by tor might believe that markets are efficient and thatthe group of investors that follows asset allocation the preferences and/or positions of the ultimatepolicies may not share this characteristic because of beneficiary or beneficiaries of a fund differ suffi-differences in the values of an asset’s holding across ciently from those of the average investor to war-portfolios. Put somewhat differently, the relation- rant such a strategy. Alternatively, the investorship between (1) the net number of shares offered might believe that markets are inefficient and thatand (2) asset return may not be completely mono- the majority of investors do not realize that a con- trarian strategy can provide a better combinationtonic, especially for assets with returns close to that of risk and return than can conventional trend-of the overall market. following strategies. Despite this caveat, those attempting to rebal-ance portfolios to asset allocation policies will, as a Efficient-Market Views. Perold and Sharpegroup, wish to sell shares of the best performing (1988) documented a key relationship betweenasset and purchase shares of the worst performing market returns and the performance of differentasset. This fact alone leads to two conclusions that asset allocation policies. They compared the pay-should seem obvious at this point: offs provided by following a traditional asset allo- Not all investors can be contrarians. cation policy with those obtained by following aMay/June 2010 www.cfapubs.org 49
  6. 6. Financial Analysts Journalbuy-and-hold strategy. Assuming investments in only if they are less concerned than the averagetwo asset classes (bills and stocks), they defined investor about inferior returns in very bad or veryconstant-mix strategies as those that “maintain an good markets. This scenario seems an unlikely oneexposure to stocks that is a constant proportion of for the typical small investor, for whom most bal-wealth” (p. 18). They noted: anced and target-date funds are designed. In general, rebalancing to a constant mix From late 2007 through early 2009, returns on requires the purchase of stocks as they fall in stock markets around the world were dismal, with value . . . and the sale of stocks as they rise in many markets posting losses of 50 percent or more value . . . where, strictly speaking, changes in in real terms. Sobered by these results, some value are measured in relative terms. (pp. 19–20) analysts changed their assumptions about stock Perold and Sharpe (1988) further showed that returns. In some cases, positive serial correlations ofthe desirability of rebalancing to constant propor- returns were assumed. This assumption increasedtions of wealth depends on the movements of the probabilities of trends and thus extreme long-market prices: term returns. In other cases, some other process was In general, a strategy that buys stocks as they included to provide a distribution with a “fat left fall and sells as they rise will capitalize on tail,” which increased the probabilities of large neg- reversals. The marginal purchase decisions will ative returns. Some analysts included both features turn out to be good ones, as will the marginal in their models. In models with such assumptions, sell decisions. A constant-mix strategy will extreme markets are more likely, making traditional thus outperform a comparable buy-and-hold strategy in a flat (but oscillating) market asset allocation policies even less appropriate for precisely because it trades in a way that funds designed for small investors. exploits reversals. . . . [But] a constant-mix approach will underperform a comparable Inefficient-Market Views. Many advocates of buy-and-hold strategy when there are no rebalancing rationalize their position by assuming reversals. This will also be the case in strong that markets are inefficient and that other investors bull or bear markets when reversals are small with whom they can trade do not fully understand and relatively infrequent, because most of the marginal purchase and sell decisions will turn the nature of asset returns. As Arnott and Lovell out to have been poorly timed. . . . (1990) opined: Cases in which the market ends up near its How many investors permit their asset mix to starting point are likely to favor constant-mix drift with the whims of the markets (assuring strategies, while those in which the market ends overweighting at market highs and under- up far from its starting point are likely to favor weighting at the lows). . . . Simple rebalancing buy-and-hold strategies. . . . Neither strategy can provide the necessary measure of control dominates the other. A constant-mix policy over a drifting mix. It is worthwhile if properly tends to be superior if markets are character- managed. (pp. 13, 18) ized more by reversals than trends. A buy-and- Note the reference to “market highs . . . and lows.” hold policy tends to be superior if there is a The statement suggests that one can tell when an major move in one direction. (pp. 21–22) asset is at its market high or low before the Ultimately, the issue concerns the preferences fact—hardly an efficient-market concept. of the various parties that will bear the risk and/or enjoy the reward from investment. Although Arnott, Burns, Plaxco, and Moor There is no reason to believe that any particular (2007) took a more nuanced approach, they still type of dynamic strategy is best for everyone seemed to suggest that rebalancing can take advan- (and, in fact, only buy-and-hold strategies tage of market inefficiency: could be followed by everyone). (p. 26) Not rebalancing may mean holding assets that Roughly speaking, an efficient-market view have become overpriced, offering inferiorholds that an investor is best served by adopting the future rewards. A commitment to rebalance toaverage opinion of investors about the probabilities the strategic asset allocation offers an effectiveof possible future combinations of returns. Among way to dissuade clients from abandoninginvestors who accept this premise, the return distri- policy at inauspicious moments. (p. 702)bution associated with a rebalancing strategy will To buttress their view, Arnott et al. (2007)appeal to only a minority, with another group of reported the results of an empirical test that usedinvestors taking the other sides of the rebalancing monthly rebalancing from 1973 to 2003, whichtrades of the first group. Absent superior knowl- showed that a rebalanced portfolio would have pro-edge about the return-generating process, investors vided a greater average return with a smaller stan-should follow a traditional asset allocation policy dard deviation than would a “drifting mix.” As50 www.cfapubs.org ©2010 CFA Institute
  7. 7. Adaptive Asset Allocation Policiesdiscussed earlier, rebalancing to a constant mix typ- undesirable. An investor who adopts a traditionalically outperforms a buy-and-hold strategy when asset allocation policy and rebalances frequently toreversals are more common than trends. In periods conform with it must either (1) have an unusual setwith more trends than reversals, the comparison is of preferences for returns in different markets (aslikely to yield the opposite conclusion. As is fre- described earlier) or (2) believe that markets will bequently the case, the outcomes of empirical tests inefficient in this sense more often than not over awith past data can be highly period dependent. period of several years. When adopting an investment strategy, one I believe that the majority of institutionalmust make an assumption about the nature of investors who adopt traditional asset allocationfuture security markets. If one believes that mar- policies do so for neither of those two reasons.kets are inefficient, taking advantage of investors Rather, they adopt a policy designed to reflect bothwho do not realize that this is so makes sense. their preferences for risk vis-à-vis return and theirNonetheless, the task can be daunting, as Arnott special circumstances when they adopt a policy. As(2009) argued: time passes and markets change, the policy no At its heart, rebalancing is a simple contrarian longer serves its original purpose. But neither a strategy. In ebullient times, this means taking traditional rebalancing approach nor a “drifting money away from our biggest winners. In the mix” is appropriate. I suggest two possible alterna- worst of times, the process forces us to buy more of the assets that have caused us the tives later in the article. First, however, let us see greatest pain. Most investors acknowledge it as how far a traditional policy can diverge from its a critical part of the successful investor’s original position. toolkit. But recognition and action are two different things. Surrounded by bad news, pulling the trigger to buy securities down 50 Bond and Stock Values in the percent, 75 percent, or even 90 percent is United States exceedingly difficult for even the staunchest of rebalancers. Many lose their nerve and blink, Consider a simple asset allocation policy that letting a healthy portion of the excess returns involves only U.S. bonds and U.S. stocks. Assume slip from their grasp. (p. 1) that the former are represented by the Barclays Arnott’s argument reflects some of the points Capital (formerly Lehman) U.S. Aggregate BondI have made thus far. It recognizes that rebalancing Index and the latter by the Wilshire 5000 Totalis, in fact, a contrarian strategy. It acknowledges Market Index.17 Now, consider a balanced mutualthat such action involves buying losers and selling fund that has chosen an asset allocation policy withwinners. It suggests that most investors believe 60 percent invested in U.S. stocks and 40 percent inrebalancing is desirable but that many “lose their U.S. bonds and that uses these two indices asnerve and blink.” And it reflects Arnott’s view that benchmarks. Its goal is to provide its investors withmarkets are sufficiently inefficient that by failing to a portfolio representative of the broad U.S. marketrebalance, investors let “a healthy portion of the of stocks and bonds. Investments in each asset classexcess returns slip from their grasp.” are made via index funds in order to track the underlying returns closely. The similarity of this fund to the VanguardAsset Allocation Policy and Balanced Index Fund is not coincidental. The twoMarket Efficiency differ only with respect to the indices used for U.S.The vast majority of those who adopt an asset allo- stock returns, but the two alternatives are highlycation policy heed the following recommendations: correlated. The expectations involved in strategic asset Figure 2 shows the ratio of (1) the total market allocation are long term. “Long term” has capitalization of the stock index to (2) the sum of different interpretations for different investors, the total market capitalizations of the bond and but five years is a reasonable minimum refer- stock indices over the period January 1976–June ence point.16 2009. More succinctly, it shows the value of U.S. Are markets efficient in the long run? That stocks as a percentage of the value of U.S. stocksdepends on what is meant by the term “efficient.” and bonds over 33.5 years.In the current context, we need merely ask whether As Figure 2 shows, the relative values of U.S.an investor wishes to assume that significant num- stocks and bonds have varied substantially. Thisbers of investors are foolish enough to take the finding is not an exception—in other countries,other side of contrarian trades when doing so is security values have also varied substantially.May/June 2010 www.cfapubs.org 51
  8. 8. Financial Analysts Journal Figure 2. The Ratio of the Value of U.S. Stocks to U.S. Stocks plus Bonds, January 1976–June 2009 Ratio (%) 80 70 60/40 60 50 Actual 40 75 80 85 90 95 00 05 10 Over the entire period, the proportion of value cent. It is no longer representative of the market’sof stocks averaged 60.7 percent—close to that of a risk and return; instead, the fund is riskier, presum-traditional 60/40 strategy with monthly rebalanc- ably with a higher expected return.ing, as shown in the figure. The average increase in Figure 2 shows that from January 1976 throughthe value of bonds was larger than that of stocks. June 2009, our fund varied from being significantlyBut the total return on stock investments averaged riskier than the U.S. bond plus stock market tomore than that on bond investments, as one might being considerably less risky. At the end of Marchexpect over the long run as a reward for the greater 2000, the proportion of market value in stocks wasrisk of stock investments. 75.06 percent, leading to the lowest relative risk for Table 5 shows the annualized monthly the fund in the entire period. At the end of Februaryaverages18 of the total returns, the percentage 2009, the situation was just the opposite: The pro-changes in market value, and the differences portion of market value in stocks fell to its nadir ofbetween the two. Overall, investors neither 43.18 percent, making the fund, at 60 percent, muchextracted large amounts of cash from the bond and riskier than the overall U.S. bond plus stock market.stock markets nor invested substantial amounts of In sum, our fund failed to meet its goal ofnew cash. They did, however, invest in new bonds providing a strategy representative of the overallin amounts that were close to the sum of coupon U.S. bond and stock markets except in the very longpayments received from bonds and the dividends run. And, as Keynes (1923) taught us, “in the longpaid by their stocks. run we are dead” (ch. 3). To accomplish its goal, our fund needs to adapt its allocation policy. Let us now consider twoTable 5. Returns and Changes in Market approaches that an investor might use: (1) optimi- Value of U.S. Bonds and Stocks, zation based on reverse optimization and (2) an January 1976–June 2009 approach that I call an adaptive asset allocation Change in policy. We will assume that the investor is con- Return Market Value Difference cerned with only the return on assets (ruling outBonds 8.20% 10.82% 2.62 pps cases in which liabilities are taken into account) andStocks 11.27 8.96 2.31 that the managed fund constitutes the entire port-pps = percentage points. folio (ruling out the use of balanced or target-date funds as components of a larger portfolio). Assume that our balanced fund opened its Optimization Based on Reversedoors in February 1984, when the value of U.S.stocks was 59.62 percent of the total value of stocks Optimizationand bonds. At the time, the fund with 60 percent in Many asset allocation policies are chosen afterstocks well represented an investment in the U.S. extensive analyses designed to determine a set ofbond and stock markets and should have had a optimal strategies with different combinations ofsimilar risk and expected return. Fast-forward to risk and return. In some cases, the analysis uses aOctober 1990. The market value of stocks is now standard Markowitz mean–variance approach. In47.99 percent of the total, but the fund has been others, the goal is to maximize an investor’srebalanced to maintain its policy target of 60 per- expected utility. In many cases, these optimization52 www.cfapubs.org ©2010 CFA Institute
  9. 9. Adaptive Asset Allocation Policiesanalyses are conducted with constraints on asset The inevitable conclusion is that an investor’sholdings that are designed to reflect liquidity asset allocation, expressed in the traditional man-requirements or other factors. Moreover, the chosen ner as percentages of total value in each assetpolicy may differ to some extent from the analyti- class, should change over time to reflect changingcally “optimal” asset mixes. market values, even if the investor’s characteris- Whatever the process, asset allocation policies tics are unchanged. This conclusion is the keyare set after considering estimates of the risks and tenet of this article.returns of major asset classes and the correlations Note that such an approach may not requireamong their returns. More generally, the relation- substantial transactions over and above those asso-ship can be characterized as follows: ciated with reinvesting dividends, interest pay- ments, and other cash received from security Asset allocation t = issuers. Moreover, there is no reason to expect that (10) f ( Investor characteristicst , Market forecastst ) . such an approach will involve selling relative win- ners and buying relative losers, as must be done toThe subscripts indicate that the appropriate asset conform with a traditional asset allocation policy.allocation at time t depends on the investor’s char- Equation 12 also shows that a formal systemacteristics and the forecasts for asset returns and could be set up to revise an investor’s asset alloca-risks at the time. The notation f () should be read as tion policy frequently by conducting a reverse opti-“is a function of” the items in parentheses. mization analysis followed by optimization. This Consultants and others who make market fore- process, however, requires complex models incasts typically consider historical returns and some order to accommodate real-world aspects21 and isaspects of economic theory. Some forecasters, but apparently used by relatively few organizations.22by no means all, consider the current market values To provide an alternative, I offer a procedureof major asset classes. The following rather crude that can be used to periodically adapt an organiza-equation represents the preferred approach: tion’s asset allocation policy in light of asset market Market forecasts >t = values without requiring actions that are clearly contrarian in nature. The procedure is simple and f (History <=t , Economic theoryt , (11) can be implemented easily. Although I make no Market valuest ) . claim that it is the best possible approach, it should be better than either strict conformance with a tra-The subscripts indicate that market forecasts for ditional asset allocation policy or the adoption ofoutcomes occurring after time t are based on histor- such a policy followed by subsequent actions (orical information for periods up to and including lack thereof) that treat the policy as irrelevant.time t and on economic theory and market valuesat time t.19 Why should market values inform forecasts? Adaptive Asset AllocationBecause an asset’s current market value reflects the Policiescollective view of the probabilities of future pros- The term “adapt” can be defined as follows:pects. This information is valuable and should be To adjust oneself to different conditions,taken into account when managing a portfolio. environment, etc.23 Analytic approaches for making market fore- In this case, the “different conditions, environment,casts in this manner are generally termed reverse etc.” are new asset market values.optimization.20 Mean–variance approaches assume Imagine that a fund investing in U.S. stocksthat capital markets provide unbiased estimates of and bonds established an asset allocation policy offuture prospects (Sharpe 1974, 1985) or incorporate 80 percent stocks and 20 percent bonds at the endviews about deviations from such estimates (Black of February 1984, with the Wilshire 5000 Total Mar-and Litterman 1991). A comparable approach has ket Index representing stocks and the Barclays Cap-been suggested for making forecasts to be used in ital U.S. Aggregate Bond Index representing bondsexpected utility analyses (Sharpe 2007). (as shown in Figure 2, the market proportions were Combining Equations 10 and 11 gives the fol- 59.62 percent and 40.38 percent, respectively).lowing important relationship: Assume that this information was taken into Asset allocation t = account in the study that led to the 80/20 policy. A traditional approach would hold that the f (Investor characteristicst , History<=t , (12) policy calls for adjustments in holdings to achieve Economic theoryt , Market valuest ) . an 80/20 allocation no matter what the subsequentMay/June 2010 www.cfapubs.org 53
  10. 10. Financial Analysts Journalmarket proportions might be. But as I have argued, Consider a world in which changes in assetthis course is unlikely to be a wise one. Instead, the market values result only from changes in securitypolicy proportions should be adjusted as market prices and reinvestment of cash flows from eachvalues change. I propose instead a procedure that asset in the same class. An investor who makes noI call an adaptive asset allocation (AAA) policy. withdrawals or additional investments and Table 6 and Table 7 show the required calcu- chooses to reinvest all cash flows from each assetlations for the appropriate allocation at the end of class in the same class will be in compliance withOctober 1990, when stocks were a substantially the particular adaptive policy at all times and willsmaller portion of overall market value. not need to transact with other investors. This sce- nario follows from the fact that the value of theTable 6. Market Values of U.S. Bonds investor’s holdings of each class will change by and Stocks, February 1984 and precisely the same percentage as the value of the October 1990 market (ki) will change. In such a setting, AAA Stocks Bonds policies are macro-consistent in the sense that all ($ billions) ($ billions) % Stocks investors can follow such strategies.Vim,0 (Feb. 1984) 1,648.19 1,116.49 59.62 Of course, the investment world is extremelyVim,t (Oct. 1990) 2,652.92 2,875.69 47.99 complex. New issues of securities, buybacks, andki = Vim,t/Vim,0 1.6096 2.5757 redemptions occur frequently. Moreover, the total values of these transactions for an asset class rarelyTable 7. Adaptive Policy Allocations, net to zero. Public companies go private and vice February 1984 and October 1990 versa. Some investors have positive net cash flows Stocks Bonds Sum that require purchases of new assets, whereas oth-AAif,0 80.00% 20.00% ers must sell assets to raise cash. Despite these com-(AAif,0 )(ki ) 128.77 51.51 180.28% plications, a group of investors that follows AAA(AAif,0 )(ki )/Sum(AAif,0)(ki ) 71.43 28.57 policies is unlikely to need to make large purchases or sales of assets with investors who do not follow Table 6 shows the total outstanding market such policies. This situation contrasts starkly withcapitalizations for each of the two indices at the two the situation of investors who attempt to complydates (February 1984 [time 0] and October 1990 with traditional asset allocation policies; such inves-[time t]) and the ratios of the ending values to the tors must frequently purchase assets that are rela-beginning values (denoted ki, as before). Table 7 tive losers and sell those that are relative winners.shows the calculations for the new asset allocation. Tables 6 and 7 use the following formula toFor each asset, the initial proportion in the fund is compute the proportion invested in asset i in fundmultiplied by the ratio of the new total market (f) at time t:value of the asset class as a whole to the old value.In this case, the outstanding values of both assets X if , t = ( X if , 0 Vim, t Vim,0 ) . (13)increased substantially. Hence, the sum of theadjusted proportions for the fund is much greater ( ∑ X if , 0 Vim, t Vim,0 i )than 100 percent, as shown in the third column. To Here, Vim,t and Vim,0 are the total outstanding mar-compute the new asset value proportions for the ket values of asset i at times t and 0, respectively.fund, the figures in the second row are divided by The proportion invested in asset i at time 0 is Xif,0 ,their sum, which gives the new asset allocation and the proportion to be invested at time t is Xif,t.shown in the last row. Note that the total market value of asset i at In this case, stocks fell from representing close time 0 equals its proportion of total value (Xim,0)to 60 percent of total market value to slightly less times the total value of all assets at the time (Vm,0).than 48 percent. Thus, the fund’s asset allocation A similar relationship holds for time t. Thus,policy changed from one with 80 percent investedin stocks to one with 71.43 percent so invested. Vim,0 = X im, 0Vm,0 Why is this procedure likely to be preferred to (14) Vim, t = X im, tVm, t .a traditional approach? Because it need not requirethat investors who have such policies transact with Substituting these relationships in Equation 13other investors whenever market prices change, as and canceling terms gives a formula for calculatingdo traditional asset allocation policies. the new proportion for the fund to invest in asset i54 www.cfapubs.org ©2010 CFA Institute
  11. 11. Adaptive Asset Allocation Policiesas a function solely of the proportions at time 0 and With this interpretation, we can straightfor-of the ratios of the proportions for the market port- wardly apply the adaptive approach to a wide rangefolio at the two periods: of investments. I illustrate with three prototypical types of funds. X if , t = ( X if , 0 X im, t X im,0 ) . ( ∑ X if , 0 X im, t X im,0 i ) (15) Institutional FundsTable 8 shows the computations for February 1984 As indicated earlier, most pension funds, endow-and October 1990. ments, and foundations conduct asset allocation studies that lead to the selection of a policy asset mix, which can be considered the base policy (Xf,0).Table 8. Adaptive Policy Allocations with Presumably, this asset allocation was considered Asset Proportions, February 1984 appropriate given the market conditions (Xm,0) at and October 1990 the time, whether or not these market values were Stocks Bonds Sum used explicitly when determining asset prospects.Xim,0 59.62% 40.38% Under this assumption, the asset allocation policyXif,0 80.00 20.00 can be converted to an adaptive policy by simplyXim,t 47.99 52.01 applying the adaptive formula (Equation 15) in(Xif,0)(Xim,t )/Xim,0 64.39 25.76 90.15% subsequent periods.Xif,t 71.43 28.57 As with the traditional approach, allowable deviations from the policy targets may be selected. In this example, the initial asset allocation set For example, these deviations could be set to equalat time 0 is assumed to have been appropriate, the currently allowed deviations of the holdings ingiven the market values of the asset classes at the each asset class. If the fund makes few, if any,time. This allocation is typically the case when an trades, the resulting ranges are less likely to beinstitutional investor selects an asset allocation pol- violated under an adaptive policy than under aicy. The adaptive formula (Equation 15), however, traditional approach.can be applied in other contexts. Key is the state- Undoubtedly, many institutional funds wouldment of an asset allocation policy in terms of base consider the conversion from a traditional to anvalues for (1) the policy and (2) the market. A adaptive asset allocation policy too dramatic topossible example would be the following: accept overnight. At the very least, I would suggest The fund’s Asset Allocation Policy is to have that the required computations for an adaptive asset 80 percent invested in stocks and the remain- allocation policy be performed periodically so that der in bonds when the market value of stocks key decision makers could evaluate the fund’s hold- is 60 percent of the total value of stocks and ings in terms of both the traditional approach and bonds, with the proportions to be determined this alternative approach. In time, such an exercise each period by using the adaptive asset might lead to a greater acceptance of the latter. allocation formula.Table 9 shows this asset allocation policy in termsof the formula (Equation 15). Balanced Funds As previously discussed, multi-asset mutual funds are likely to make transactions that areTable 9. An Asset Allocation Policy required by their traditional asset allocation poli- Stocks Bonds cies. To a considerable extent, a multi-asset mutual Xim,0 60% 40% fund’s asset allocation policy will drive its invest- Xif,0 80 20 ments, which makes the choice of the type of policy especially important. More generally, we can denote the mixes of Typically, a balanced fund is designed to pro-market and fund assets as vide a mix of two or more asset classes with a con- ( X m,0 = X1m,0 , X 2m,0 ,..., X nm,0 ) (16) stant level of “conservatism” or “aggressiveness.” Although some may think of these terms as abso-and lute, a more pragmatic approach is to interpret them ( ) as relative. In this view, an “aggressive” fund should X f , 0 = X1 f , 0 , X 2 f , 0 ,..., X nf , 0 , (17) provide more risk than the market as a whole,where there are n assets and Xm,0 and Xf,0 are whereas a “conservative” one should provide less.vectors representing the base market and fund asset A “representative” fund could be designed to pro-allocations, respectively. vide the same risk as the market as a whole.May/June 2010 www.cfapubs.org 55
  12. 12. Financial Analysts Journal Constructing an adaptive representative fund Target-Date Fundsis easy. It would have the market proportions of the As discussed earlier, a target-date fund has a policyasset classes in every period. At the time of forma- “glide path” that indicates the appropriate assettion, the actual proportions (Xf,0) would be set to allocation at each time in the future until the dateequal the market proportions (Xm,0). The adaptive at which money in the fund is to be transferred toformula (Equation 15) would subsequently lead the another vehicle. In effect, the fund has a base allo-fund manager to hold assets in market proportions cation for every period, which can be straightfor-at each period. For example, a balanced fund wardly accommodated in the adaptive assetdesigned to represent the U.S. stock and bond mar- allocation formula. Let Xib,t represent the “base”kets would follow the curve rather than the hori- allocation for time t as specified in the currentzontal line in Figure 2. policy. This allocation replaces the constant alloca- An aggressive fund would begin with an asset tion given by Xif,0 in Equation 15:mix that had greater risk than that of the market atthe time and would then adjust its holdings by X if , t = ( X ib, t X im, t X im,0 ) . ( ) (18)using Equation 15. Figure 3 shows the actual pro- ∑ X ib, t X im, t X im,0 iportions for a fund that wishes to hold an 80/20 mixof U.S. stocks and bonds when the market propor- Equation 15 is more general than Equation 18,tions are 60/40. which can be considered a special case in which As intended, the fund remained more aggres- Xib,t = Xif,0 for every period t.sive than the market throughout the period. Nev- Figure 4 illustrates an adaptive target-dateertheless, the ratio of the fund’s proportion in fund. It assumes that the fund was started in Janu-stocks to that of the market varied, beginning at ary 1976 with a glide path calling for 90 percent in stocks initially, with the allocation decreasing by a1.333 (80 percent/60 percent) and ranging between constant percentage each month until it reaches 101.18 and 1.55. percent in June 2009. Figure 4 shows the base allo- Not surprisingly, at the four times when the cations that would be implemented by a traditionaltotal market value of stocks was close to 60 percent target-date fund, as well as the market proportions.of the total value of stocks and bonds, the fund’s To convert this traditional fund to an adaptiveasset allocation policy dictated a value close to the target-date fund, we assume that the original glideintended 80/20 mix. In this example, although the path was chosen as appropriate when the marketfund was started when the market mix was 60/40, proportions in stocks and bonds are 60 percent andit could have been started at any time with a policy 40 percent, respectively. Using these proportionsstated in terms of a “normal mix” (Xf,0) when mar- for the Xim,0 values in Equation 18, we can see thekets are “normal” (Xm,0). allocations for the adaptive target-date fund. This scenario suggests a simple way to convert Because the glide path is assumed to be optimalan existing balanced fund to an adaptive one. The when the market proportions are 60/40, the adap-stated policy (Xf,0) need only be augmented by the tive proportions and the policy glide path coincide“normal” market conditions (Xm,0) for which it is when stocks are 60 percent of the total value ofappropriate. The asset allocation policy for any bonds and stocks. Whenever the market propor-period can then be determined by using the adap- tion of stocks is below 60 percent, the fund’s allo-tive formula (Equation 15). cation to stocks is below that specified by the glide Figure 3. Asset Allocations: Market and an Aggressive Balanced Fund Ratio (%) 100 90 80 Fund 70 60 50 Market 40 75 80 85 90 95 00 05 1056 www.cfapubs.org ©2010 CFA Institute
  13. 13. Adaptive Asset Allocation Policies Figure 4. Asset Allocations: Market and an Adaptive Target-Date Fund Ratio (%) 100 90 Fund 80 Market 70 Glide Path 60 50 40 30 20 10 0 75 80 85 90 95 00 05 10path. Conversely, when stocks represent more have proposed. If more investment managersthan 60 percent of the value of the market, the adopt my proposed procedure, market value datafund’s allocation to stocks is greater than that may become more widely available.called for by the glide path. I cannot easily understand why funds do not routinely compare their asset allocations with cur-Conclusion rent market proportions in order to ensure that any differences are commensurate with differencesIf my arguments have merit, a number of changes between their circumstances and those of “theshould be made by the investment industry. average investor.” Yet this comparison is rarely First and foremost, more data will need to be done. Perhaps the lack of easily obtained data onmade available about the market values of the secu- market values is the cause, with the absence ofrities in each of the benchmarks designed to repre- such comparisons the effect. Alternatively, the sit-sent major asset classes. Most such indices are uation may be the reverse, with the lack of avail-computed by third parties. For example, Barclays able data on market values caused by insufficientCapital and Wilshire Associates calculate the two investor interest.indices used in this article. Recent and historical I would hope that readers of this article wouldmonthly returns for most popular indices may be request (or demand) that those who provide bench-difficult but not totally impossible to obtain from mark indices make the corresponding market valuessuch providers.24 But obtaining data for the market equally available. For publicly offered mutual fundsvalues of the securities in an index is much harder. or exchange-traded funds, this provision could beClearly, the index provider has such information.25 encouraged or required by regulatory authorities.In cases where returns for the index are computed Second, it would be useful if institutionalby using a subset of the securities in the represented investors, armed with appropriate market valueuniverse, the provider should still have sufficient data, would at least compute the asset allocationsinformation to provide an estimate of the total mar- that would result from an adaptive policy of theket value of the class. type described here. These computations could It is unclear whether the lack of widespread inform discussions between staff members andavailability of asset class market values is a result those charged with oversight, such as the membersof providers’ desires to recover the costs of obtain- of investment committees and boards. In time,ing such information through subscription fees, a more investment organizations could become suf-lack of sufficient interest on the part of investors ficiently comfortable with adaptive procedures toand investment managers, or both. Of course, the substitute them for the contrarian policies associ-thesis of this article is that asset market values are ated with the traditional approach.highly relevant for any decision concerning asset Third, some mutual fund companies mightallocation, whether made episodically or adjusted offer adaptive balanced funds and/or adaptiveroutinely by using a procedure such as the one I target-date funds. In time, such vehicles mightMay/June 2010 www.cfapubs.org 57
  14. 14. Financial Analysts Journalattract enough investors to represent a significant be convinced of the merit of these arguments topart of the market. A good first step would be to lead to changes in investment practice.offer a balanced index fund designed to truly repre-sent the mix of stocks and bonds in the United States. I thank Geert Bekaert of Columbia University, StevenAs shown in Figure 2, such a fund would differ Grenadier of Stanford University, Jesse Phillips of thesignificantly from such offerings as the Vanguard University of California, Eamonn Dolan of C.M.Balanced Index Fund. If successful, a representative Capital, Carlo Capaul of Julius Baer, and John Watsonbalanced fund might pave the way for additional and Robert Young of Financial Engines, Inc., for theirfunds to follow adaptive asset allocation policies. helpful comments. Although some will find the arguments in thisarticle obvious and others will consider them radi- This article qualifies for 1 CE credit.cal, I hope that a sufficient number of readers willNotes1. Maginn, Tuttle, Pinto, and McLeavey (2007, p. 231). 15. That is, policies with non-negative asset proportions.2. CalPERS (2009). 16. Maginn, Tuttle, Pinto, and McLeavey (2007, pp. 233–234).3. CalPERS (2009). 17. Throughout the article, I use the “full-cap” version of the4. U.S. Department of Labor (2009). index rather than the “float-adjusted” alternative that uses5. More specifically, the pertinent regulation provides for weights for the securities based on estimates of the number four types of QDIAs: of shares likely to be available for trading. (1) A product with a mix of investments that takes into 18. Each annualized monthly average is equal to 12 times the account the individual’s age or retirement date (an corresponding monthly average value. example of such a product could be a life-cycle or 19. For an early discussion of the need to account for changes targeted-retirement-date fund); (2) an investment ser- in market values when making forecasts, see Rosenberg and vice that allocates contributions among existing plan Ohlson (1976). options to provide an asset mix that takes into account 20. An excellent example is described in EnnisKnupp (2009). the individual’s age or retirement date (an example of such a service could be a professionally managed 21. A meanvariance approach could be designed in which the account); (3) a product with a mix of investments that asset allocation policy is characterized by a given ratio of takes into account the characteristics of the group of the investor’s risk tolerance to that of the market as a whole. employees as a whole, rather than each individual (an I explored this possibility earlier (Sharpe 1990). To be prac- example of such a product could be a balanced fund); tical, the reverse optimization procedure needs to be con- and (4) a capital preservation product for only the first sistent with an equilibrium in which there are restrictions 120 days of participation (an option for plan sponsors and/or costs associated with negative holdings—an issue wishing to simplify administration if workers opt out that I have previously discussed (Sharpe 1991). of participation before incurring an additional tax). 22. Full disclosure: I co-founded an investment management See U.S. Department of Labor (2009). and advisory company (Financial Engines, Inc.) that uses6. Appell (2009, pp. 11, 14). asset market values and reverse optimization at least once7. Vanguard (2009). a month to adjust forecasts of risks, returns, and correlations8. Vanguard (2009). for such investment vehicles as mutual funds, followed by9. Appell (2009, p. 12). optimization analyses to make any appropriate changes in10. Fidelity Investments (2008, pp. 40–41). investor portfolios. Although no asset allocation policy per11. Fidelity Investments (2008, p. 11). se is involved, the underlying philosophy is similar.12. Fidelity Investments (2009). 23. Dictionary.com, s.v. “Adapt” (http://dictionary.classic.13. Investopedia.com, s.v. “Contrarian” (www.investopedia. reference.com/browse/adapt; retrieved 8 June 2009). com/terms/c/contrarian.asp). 24. Some returns for the Barclays Capital U.S. Aggregate Bond14. This observation is true under the assumption made Index can be obtained on the websites of mutual funds and throughout the article that no asset proportions are nega- exchange-traded funds that use it as a benchmark. Returns tive. Funds with policies involving negative proportions for the Wilshire 5000 Total Market Index can be obtained at (e.g., leverage) may buy relative winners and sell relative www.wilshire.com/Indexes/calculator. losers. For example, consider a fund with a policy of invest- 25. On its website, Wilshire (www.wilshire.com/Indexes/ ing 150 percent in stocks and 50 percent in short-term Broad/Wilshire5000/Characteristics.html) provides tables bonds (loans). Assume that the initial position is $150 in that include the total market values of the securities in its stocks and $50 in bonds, giving a net worth of $100. If the U.S. equity index at the end of the most recent month, but value of the stock portfolio doubles, the new position will no historical data on market values are provided. The equal $300 in stocks and $50 in bonds, giving a net worth Barclays Capital website does not provide any data on the of $250. The new proportions will be 120 percent in stocks market values of the securities in the U.S. Aggregate Bond and 20 percent in bonds. To restore the fund to its policy Index. I am grateful to both organizations for providing me proportions will require purchasing more stocks and sell- with the historical data used in this article. ing more bonds (i.e., borrowing more money). Such a fund 26. Fundamental Index is a registered trademark of Research will thus purchase relative winners and sell relative losers. Affiliates, LLC.58 www.cfapubs.org ©2010 CFA Institute
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