A data-driven look at the power of diversification

Transcription

1 A data-driven look at the power of diversification Renowned asset allocation expert Craig L. Israelsen, a Financial Planning contributing writer, explores how diversification can mitigate portfolio risk and boost investment returns. In three installments, he examines: What a study of correlations reveals about diversification How to get it right when it comes to calculating returns How to build a portfolio for rising inflation

2 Introduction Portfolio diversification is for folks who can t predict the future. Clearly, if we had perfect foresight we would simply pick the stock or mutual fund that would be the best performer by the end of the year and then sit back and watch it happen. It would never cross our mind to diversify. For the rest of us, we diversify. That means the first step toward diversification is admitting that we are not clairvoyant. Having firmly grasped the obvious, we need to be wary of several behavioral issues that may trip us up. The first is failing to appreciate the virtue of average performance. Diversification assures that our overall portfolio will not be the best performer in town but it will also never be the worst. It will be somewhat average, perhaps a tad above. Of course, this may bother investors who like to take big bets on single asset classes or the stock of a single company. When their guess is right, the bragging begins. But when the bets don t pan out, the losses can be very damaging. Investors who understand the mathematics of performance have learned that minimizing the chance of large losses is one of the key benefits of a diversified portfolio. Investors who diversify recognize that a loss of 50% requires a 100% gain to break even. Since gains of 100% don t happen very often, they decide to minimize the chances of big losses. In short, they come to terms with achieving average performance. They accomplish that by diversifying their portfolio. Chasing performance is another problem that can derail a diversifier. When investors chase performance, they tend to load up on last year s best performing asset class and dump the asset classes that have recently underperformed. These investors have acknowledged that they can t predict winners in advance, but still can t resist buying them after the fact a classic example of buying high and selling low. A resolute commitment to diversification would, in fact, have us rebalance our multi-asset portfolio by selling some of last year s better performers and putting that money into last year s underperformers. A key to engaging in this type of courageous sell high/buy low behavior is understanding that a diversified portfolio is assembled with ingredients that have low correlation with each other. It s guaranteed that we will own winners and not-so-winners (or even some losers) at any moment in time. That s because we built a low-correlation portfolio. We don t want to own all winners (as odd as that sounds) or all losers because that would indicate we have a high-correlation portfolio. When a diversified, low-correlation portfolio does its thing, clients shouldn t flip out. They should recognize that s what a low-correlation portfolio does and rebalancing takes advantage of it. Finally, diversifiers need to think long term. For example, we have not experienced serious inflation for over two decades. Some asset classes, such as commodities, are at their best during inflationary periods. When inflation is napping, commodities tend to underperform. Over the past 10 to 15 years, commodities have certainly underperformed. Maintaining a commitment to diversification means that we will not abandon certain asset classes during periods of underperformance. Inflation will certainly be an issue at some point in the future which is precisely why a diversified portfolio maintains a wide variety of body armor or asset classes that benefit during different economic cycles even when some of that body armor seems unnecessary or even a burden. The arrow of inflation can strike quickly and our portfolios need to be ready in advance. Craig L. Israelsen 2

3 What a study of correlations reveals about diversification One of the major aims of asset allocation is to craft a portfolio with ingredients that don t all behave in exactly the same way. This low-correlation stew offers protection against all assets heading south at the same time. But, of course, that downside protection can be a double-edged sword; the portfolio s ingredients are also unlikely to all do well at the same time. While some of your funds will be winners, others will be relative losers. That s the deal with a diversified portfolio; over the long haul, it works out well, but we have to be patient in the short run. A common sentiment heard during the 2008 financial crisis was, All correlations have gone to 1. While not exactly true, it was the case that correlations among a large number of asset classes increased in relation to large-cap U.S. stocks (the S&P 500) during the latter part of We now have sufficient historical perspective to do a look-back and see where we were then and where we are now in terms of correlations among major asset classes. In this analysis, the asset class against which all correlations will be calculated will be large-cap U.S. stocks. The other 11 major asset classes that will be included in this analysis are shown below: As a reminder, the maximum correlation between two things is either +1 or -1. A correlation of +1 indicates that the two parts move up and down at the same time. A correlation of -1 indicates that the two parts behave very differently when one moves up, the other always moves down. 3

4 Finally, a correlation of zero or closer to zero indicates that the behavior between the two portfolio ingredients is random and that is the goal. We re generally happy when the correlation between the ingredients in a portfolio are in the range of to There will clearly be exceptions to that, such as the correlation between large-cap U.S. stocks and mid-cap U.S. stocks (which tends to be quite a bit higher than +0.50). We re generally happy when the correlation between the ingredients in a portfolio are in the range of to Studying correlation makes the most sense when we do it in the context of a diversified portfolio. This analysis utilizes the 12-asset model shown below. Correlations were calculated over rolling 12-month periods starting on Jan. 1, 1998, and going through Nov. 30, CALCULATING CORRELATIONS See the chart Portfolio-Level Correlation. The first 12-month correlation of large-cap U.S. stocks and mid-cap U.S. stocks was calculated from January 1998 through December 1998, and it was The correlation between large-cap U.S. stocks and small-cap U.S. stocks was calculated over the same 12 months, and it was The average correlation between large-cap U.S. stocks and the other 11 asset classes during the first 12-month period was Over the next 12-month period (February 1998 through January 1999), the average correlation in the portfolio was This same calculation was done for all the subsequent 12-month rolling periods through November 2016 (for a total of 216). The average portfolio-level correlation for this 12-asset model was 0.41 over the total 18-plus-year period. It s clear to see that, in the fall of 2008, the average correlation between large-cap U.S. stocks and the other 11 asset classes spiked higher (see circle in graph). In October of 2008, every asset class in this 12-asset model had significant negative monthly returns except for cash. 4

5 WEARING A SEATBELT This serves as a reminder of why we wear seat belts, and why we have cash in a broadly diversified portfolio. October of 2008 was indeed a seismic event in terms of its impact on correlation among the ingredients in this 12-asset portfolio. Consider this: The rolling 12-month portfolio-level correlation was 0.39 as of September Then, one month later, the average correlation of the 11 assets classes to large-cap stocks jumped to This serves as a reminder of why we wear seat belts, and why we have cash in a broadly diversified portfolio. Aggregate correlation within the 12-asset portfolio continued to increase over the next several months, and hit a high point of 0.70 in June and July of Since that time, correlation within the 12-asset model has declined. In September 2015, correlation had declined to As of November 2016, the average correlation of the 11 asset classes to large-cap U.S. stocks was DEEPER VIEW Let s now examine the rolling correlations of each individual asset class with large-cap U.S. stocks for the two years prior to and after October 2008 (see Upward Pull ). It s visually clear that correlations between large-cap U.S. stocks and the 11 other major asset classes were generally lower prior to October 2008 and higher afterwards except for cash. Cash, by virtue of its consistently positive nominal returns, tends to have low correlation with large-cap U.S. stocks. Fixed-income asset classes also tend to have reliably low correlation with large-cap U.S. stocks. In October 2006, the rolling 12-month correlation between large-cap U.S. stocks and U.S. bonds was Correlation was 0.09 with U.S. TIPS, with non-u.s. bonds and with cash. 5

6 By October 2008, the 12-month correlation had become 0.46 between large-cap U.S. stocks and U.S. bonds, 0.46 with TIPS, with non-u.s bonds and 0.22 with cash. By October 2010, the 12-month correlation between large-cap U.S. stocks and U.S. bonds was -0.38, and it was with TIPS, 0.23 with non-u.s. bonds and with cash. We observed some upward fluctuation in the correlation between large-cap U.S. stocks and U.S. bonds and U.S. TIPS, but in general, these fixed-income ingredients maintained their low correlation with U.S. large-cap stocks during this particular four-year period. By contrast, the correlation between large-cap U.S. stocks and the other equity ingredients started fairly high and went higher. Indeed, in October 2006, the 12-month correlation between large-cap U.S. stocks and mid-cap U.S. stocks was 0.84, and it was 0.78 with small-cap U.S. stock, 0.63 with non-u.s. stocks and 0.77 with emerging stocks. In October 2008, the 12-month correlations had jumped to 0.98 with mid-cap stocks, 0.96 with small-cap U.S. stocks, 0.92 with non-u.s. stocks and 0.85 with emerging stocks. As of October 2010, the 12-month correlation between large-cap U.S. stocks and mid-cap U.S. stocks remained high at 0.96, and was 0.91 with small-cap U.S. stocks, 0.90 with non-u.s. stocks and 0.92 with emerging stocks. THE DIVERSIFIERS Among the diversifier asset classes, the 12-month correlations with large-cap U.S. stocks as of October 2006 were relatively low: 0.57 for real estate, 0.34 for natural resources and for commodities. By October 2008, those correlations had risen to 0.84 for real estate, 0.72 for natural resources and 0.53 for commodities. At the end of October 2010, they were even higher: 0.87 for real estate, 0.95 for natural resources and 0.87 for commodities. As of November 2016 (not shown in Upward Pull ), 12-month correlations between large-cap U.S. stocks and the other U.S. equity asset classes were still high (0.96 with mid-cap stock and 0.92 with small-cap stocks). Encouragingly, the correlations between large-cap U.S. stocks and non-u.s. equity have declined somewhat (0.79 between large-cap U.S. stocks and non-u.s. stocks, and 0.68 between large-cap U.S. stocks and emerging stocks). The diversifiers are doing their job better now (0.67 correlation between large-cap U.S. stocks and real estate, 0.64 with natural resources and 0.23 with commodities). Finally, as of November 2016, U.S. bonds had a 12-month correlation with large-cap U.S. stocks of -0.07, and 0.10 for TIPS, 0.10 for non-us bonds and 0.32 for cash. While it s important to consider the correlation of each ingredient with every other portfolio ingredient, we can also get an overall sense of the aggregate portfolio correlation by simply calculating the correlation of each portfolio ingredient with large-cap U.S. stocks. So, did correlations all go to 1 in the fall of 2008? No, not if measuring correlation over rolling 12-month periods at the portfolio level. Just as performance tends to regress to its mean, portfolio-level correlation tends to do the same. One key message from this analysis is that, although portfolio-level correlation increased in 2008 and 2009, that is not a reason to abandon the core investing tenet of diversification. 6

7 Get it right when it comes to calculating returns Many advisers seldom if ever take the time to determine the return of investments on their own. Often, they will rely on third-party calculations for the average annualized performance of funds and stocks. That isn t necessarily a problem, because high-quality data providers always use the geometric mean when showing average annualized returns. The problem may arise when you are called upon to calculate an average return of an investment over a multi-year period. Here s a bold statement for all advisers: If you are called upon to calculate the average return of an investment, make sure you use the geometric rather than the arithmetic mean. Doing the math wrong means your clients will not fully understand their investment returns and it s adviser jail time for you. okay, jail time may not happen. But, misrepresenting performance can certainly result in a fine. Here s why. The calculation for the arithmetic mean is simply the sum of all the numbers divided by total number count. It can never be an accurate guide for investment returns over the years, unless there is zero volatility, which is a next-to-impossible scenario. The geometric mean, on the other hand, takes into account compounding the returns compound upon each other. The arithmetic mean ignores compounding. In other words, 7

8 the geometric mean recognizes the process by which investments actually grow or decline, which is geometric in nature, not arithmetic. You must calculate the geometric mean to get a truly precise look at how a fund or stock has performed over time. Here s how it works. THE WHY AND HOW The following statements are found in the Global Investment Performance Standards Handbook, 3rd Edition, 2012, published by the CFA Institute: Section 2: Calculation Methodology (page 15) 2.A.2. Firms must calculate time-weighted rates of return that adjust for external cash flows. Both periodic and sub-period returns must be geometrically linked. Section 3-5 Provision 5.B.2.d (page 204) Annualized returns represent the geometric average annual compound return achieved over the defined period of more than one year. Annualized performance is only permitted for periods of one year or more. Annualized Return (%) = {[(1 + R)1/n] 1} 100, where R is the cumulative return for the period, which is calculated by geometrically linking the sub-period returns during the period, and n is the number of years in the period. Not recognizing the difference between an arithmetic mean and a geometric mean is where the problem begins. 8

9 INDEX PERFORMANCE Let s consider the returns of the S&P 500, the MSCI Emerging Markets Index and the threemonth Treasury bill from 2000 through 2016 (see Three Asset Classes ). Per the chart, the correct 17-year average annualized return (or geometric mean) for the S&P 500 is 4.51%, whereas the incorrect arithmetic average return is the significantly higher 6.16%. The next column displays the annual growth of $10,000. The terminal value by the end of 2016 is $21,167. The correct growth rate (or average annualized percentage return) that turns the $10,000 into $21,167 is 4.51%, not 6.16%. 9

10 As clearly illustrated, the geometric mean is the rate of return that correctly expresses the growth of $10,000. The arithmetic mean dramatically overstates the actual annualized growth rate of $10,000. For this reason, the arithmetic mean is always incorrect when expressing the rate at which invested money grows over time. Also worth noting is the fact that the gap between the incorrect arithmetic mean and the correct geometric mean widens as the standard deviation of return increases. For example, the difference between the two means is very small for the 3-month Treasury bill (1.69% arithmetic mean vs. 1.67% geometric mean). But the standard deviation of the 17 annual T-bill returns is also very small, at 2%. By contrast, the fluctuation of returns for the MSCI EM Index is huge, as evidenced by the standard deviation of 32.6%. Accordingly, the difference between the arithmetic mean (11.09%) and geometric mean (6.18%) is quite large. CASE STUDY ONE Now we will examine two case studies to illustrate how to calculate the correct average return of an investment. Our first simple example will illustrate the problem of representing the arithmetic mean as the average return. 10

11 CASE STUDY TWO The case of the missing three-year average annualized return for the Zippy Fund. The Zippy Fund had a cumulative return of % over the three-year period. With that calculated, we now can compute the three-year average annualized return (or the geometric mean). To invoke a driving metaphor, the cumulative percentage return represents the total distance traveled over three years, whereas the average annualized percentage return is the rate of speed traveled per year. The correct geometric mean will always be smaller than the incorrect arithmetic mean precisely because the geometric mean is taking compounding into account, whereas the arithmetic mean fails to do so. To make matters worse, the arithmetic mean becomes more wrong as the annual returns of the asset being analyzed are more volatile, as we observed in Three Asset Classes. USING EXCEL TO CALCULATE THE GEOMETRIC MEAN If you choose to perform this type of calculation in Excel, you can calculate the average annualized percentage return directly without first calculating the three-year cumulative percentage return. 11

12 The first step is to convert the raw returns into a format that Excel will accept when using the Geomean formula. You will need to divide each raw return by 100 and then add 1, as follows: (using the returns of the Zippy Fund): This transformation of the raw annual return data allows the Geomean function to work correctly, inasmuch as the Geomean function in Excel cannot work with negative numbers. To solve this, we express the negative return of % in year two as Thus, in this transformed format, positive annual returns will be represented by a number over 1 (such as ). A return of 0% will be represented as 1 exactly, and negative annual returns will be transformed into a number less than 1. Now you are ready to use the Geomean function in Excel. In cell B4, you would enter the following formula: = Geomean (B1:B3)-1. The result will display as If you change the cell format to %, the result will display as 4.23%. The bottom line, no matter which method you use, is this: When you re tempted to calculate an average return, always, always, always think geometrically. Use any other method and you ll be wrong. A portfolio for rising inflation What effect does inflation have on a portfolio, and what kind of portfolio is better built to withstand it? In recent years, inflation has been on the lower end of the scale. Of course, that will change eventually, and, if the past 47 years are any guide, when inflation ticks back up, we may see a distinct shift in the performance of various asset classes. So how might advisers adjust their clients portfolios as inflation rises again? First, a bit of background. From Jan. 1, 1970, through Dec. 31, 2016, the 47-year average annual inflation, as an arithmetic mean, has been 4.07%, whereas the 47-year median CPI has been 3.27%. The average annualized growth rate of inflation (the geometric mean) between 1970 and 2016 was 4.03%. Here we will focus on the 3.27% rate. Doing so will facilitate the analysis of asset class performance during the years of both low and high inflation. The median rate of inflation during the 23 years with below-average CPI was 2.09%; it was 4.54% during the 24 years with an equalto-or-above median CPI. Please see Inflation: Low Years and High Years for an illustration. 12

13 As shown below in Annual Inflation, the most recent year with inflation above 3.27% was 2007, when it increased by 4.08%. 13

14 Since then, through 2016, we have experienced very modest levels of inflation: 2008 at 0.09%, 2009 at 2.72%, 2010 at 1.50%, 2011 at 2.96%, 2012 at 1.74%, 2013 at 1.50%, 2014 at 0.76%, 2015 at 0.73% and 2016 at 2.09%, using the U.S. BLS CPI All Urban non-seasonally adjusted data. In fact, since 1990, there have only been five years in which the annual rate of inflation was over 3.27%. A LONGER LOOK We will now review inflation and asset performance over the 47-year period from 1970 through The performance of seven major asset classes will be reviewed during the 23 years of low inflation, as well as the 24 years with higher inflation. The seven asset classes include large-cap U.S. stocks, small- cap U.S. stocks, non-u.s. stocks, U.S. bonds, U.S. cash, real estate and commodities. Large-cap U.S. equities are represented by the S&P 500, while the performance of small-cap U.S. equities was captured by using the Ibbotson Small Companies Index from 1970 to 1978, and the Russell 2000 from 1979 to The performance of non-u.s. equities is represented by the Morgan Stanley Capital International EAFE Index (Europe, Australasia, Far East). U.S. bonds were represented by the Ibbotson Intermediate Term Bond Index from 1970 to 75, and the Barclays Capital Aggregate Bond Index from 1976 to

15 Cash was represented by three-month Treasury bills. The performance of real estate was measured by using the annual returns of the NAREIT Index from 1970 to 1977, and the annual returns of the Dow Jones U.S. Select REIT Index from 1978 to Finally, the historical performance of commodities was measured by the Goldman Sachs Commodities Index. As of Feb. 6, 2007, it has been known as the S&P GSCI. In addition to the seven individual asset classes, we will also review the performance of two portfolios. The first portfolio is composed of all seven asset classes in equal allocations of 14.28%, and was rebalanced annually. The second portfolio consists of 60% large-cap U.S. stocks and 40% U.S. bonds the classic 60/40 portfolio. As shown in Asset Performance, large-cap U.S. stocks had an average nominal annual return of 12.70% during the 23 years when inflation was low. By comparison, they had an average real return of 10.42% during the same time period. Both performance figures are impressive. Now, let s turn the tables and look at performance during the 24 years in which there was higher inflation. We observe that large-cap U.S. stocks had an average nominal return of 10.82%, but an average real return of just 4.70%. These results clearly do not support the notion that large-cap U.S. stocks have been a standout performer during inflationary times. The performance of small-cap U.S. stocks has been better than large-cap U.S. stocks during years with low inflation (refer back to Asset Performance ). The average nominal return for U.S. small stocks was 13.73%, whereas the average real return was 11.41%. When looking at performance during years with higher inflation, the superiority of U.S. smallcap stocks versus U.S. large-cap stocks increases; the average nominal return was 12.61%, compared to 10.82%. Even more dramatic is the difference in average real returns during years with higher inflation rates: 6.26% for small-cap U.S. stocks versus 4.70% for large-caps. If inflation protection is your goal, U.S. small-caps have been a better defender than U.S. large caps. But the real story here is commodities. Very simply, broad-based commodity indexes suffer when inflation is low. When inflation is high, commodity indexes and funds perform admirably. This is very likely precisely because energy and commodity prices have gone higher, thus effectively creating inflation. 15

16 The average nominal return for commodities during the 23 low-inflation years was -2.31%, compared to a 21.98% nominal return during the 24 years when inflation was higher. The average real performance of commodities was -4.36% during low-inflation years and 15.13% during high-inflation years. Commodities serve as a protector against inflation and, in that role, completely dominate any other asset class. The next-closest performer using real returns is real estate, at 6.93%. As we have been in a low-inflation environment in recent decades, it s not surprising that commodities have performed relatively poorly. This will change. MODEL PORTFOLIO PERFORMANCE Inasmuch as advisers don t generally build one-asset portfolios for clients, it s important to consider how a multi-asset portfolio performs during periods of low and high inflation. Toward that end, we can evaluate two different portfolios: a seven-asset portfolio and a two-asset portfolio. The equally weighted seven-asset portfolio underperformed the 60/40 portfolio during periods of low inflation, both in nominal and real terms. The average nominal return for the seven-asset portfolio was 8.06%, with a 5.87% average real return, during the 23 years with low inflation nearly all of those years being recent. The two-asset 60/40 portfolio had an average nominal return of 10.23% and an average real return of 8.01%. The two-asset model did not have commodities dragging it down. If you believe inflation will rear its ugly head again, it would be wise to build a portfolio that has demonstrated an ability to defend itself against inflation. Now, let s turn our attention to the years when there was higher inflation. The seven-asset model had an average nominal return of 12.35%, compared to 10.10% for the two-asset portfolio. More important, the seven-asset portfolio had an average real return of 6.08%, compared to 4.02% for the two-asset portfolio. Commodities, real estate and U.S. small-cap stocks all missing in the two-asset model were helpful contributors in the seven-asset portfolio during inflationary years. As an adviser, if you believe inflation will remain low forever, stay with a two-asset portfolio. However, if you believe inflation will rear its ugly head again, it would be wise to build a portfolio that has demonstrated an ability to defend itself against inflation. This will require a wider variety of asset classes including real estate, commodities and small-cap U.S. stock. In short, over the long term, it s beneficial to build a broadly diversified portfolio. 16