Yesterday's post presented an analysis of floor and ceiling levels for the percent of stocks to be held in a rebalanced portfolio. Today's post presents a similar analysis for a portfolio that takes a different strategy. Instead of rebalancing toward a target percentage, it rotates strongly to stocks or to bonds, depending on which asset has recently had better returns. How strongly? Until this post, the working assumption has been to rotate the entire porfolio, going 100% to stocks or 100% to bonds. Today, the topic is whether it's best to rotate stocks to a floor higher than 0% or a ceiling lower than 100%. All these analyses are part of an on-going series that began on June 3, 2019, comparing traditional rebalancing with the alternative strategy of rotation. 

Drawdowns
The chart below summarizes 48 combinations of floor and ceiling values for rotating the portfolio between mostly or entirely stocks and mostly or entirely bonds. (For specifics about the data, see "Some Technical Details" at the end of this post.)

On average, across all floor-ceiling combinations, the trend for rotation was reminiscent of the one reported previously for rebalancing. Going to a floor of 10% in stocks was actually, perhaps counterintuitively, better than going to 0% in stocks. The margin was small, and tended to be better when the ceiling was low (as in the 40% example in the chart) than when it was high (see the 100% example). A floor of 15% was virtually as good as 0%, but above that point, drawdowns tended to accelerate.

Real Returns
​How do similar combinations of floor and ceiling values effect a portfolio's 25-year returns, adjusted for inflation? The next chart illustrates the main results, annualized.

There are two messages here. First, increasing the floor percent in stocks had little effect on annualized returns over a 25-year period. Even raising the floor to 40% reduced real returns by just a fraction of a percent compared to a floor of 0% to 15%. Second, in contrast, raising the ceiling had a big effect. Consistently applying the rotation strategy for 25 years yielded real returns that were about 2% higher when the ceiling was 100% than when it was 40%.

The average in the chart, representing a ceiling near 70%, paid handsome returns of about 6% above inflation when the floor was 10%. That result was quite close to the performance of rotating from a ceiling of 100% to a floor of 40%. As illustrated by these two examples of 70-10 and 100-40, different combinations of floor and ceiling values may produce similar long-term accumulations. They will differ, however, in potential drawdowns. That necessitates an analysis of relative returns, adjusted for drawdown risks.

Relative Returns
The story gets a bit more complicated at this point. The historical evidence indicated that three factors had to be considered together: drawdown risks, potential for real returns, and the window-size for comparing whether recent outcomes had been better for stocks or for bonds. To illustrate these dimensions, the chart below shows examples of relative returns (risk-adjusted) when large-cap stocks and 10-year Treasuries were compared over three-month and twelve-month windows.

To understand this evidence, recall how a relative return is defined (as detailed on June 17). It measures a portfolio's incremental real return, compared to investing 100% in 10-year Treasuries, after compensating for the portfolio's incremental risk of drawdowns. If a portfolio has better raw returns than Treasuries, but also has higher drawdowns, the relative return will be less than the raw increment. In fact, the relative return can diminish to virtually zero if the drawdowns are excessive.

Several points in the chart deserve emphasis:

• The relative returns for rotation portfolios were consistently high, generally above 1%. In contrast, previously reported results for rebalancing ranged from 0.3% to 0.8%. Thus, overall, rotation portfolios in these data-sets produced better risk-adjusted returns than rebalanced portfolios. (As will be noted in future posts, exceptions to this conclusion are rare.)
• Relative returns tended to be higher when the floor percent was lower. On reflection, this result makes sense. The trigger for rotating out of stocks and into Treasuries is that Treasuries, based on recent performance, are giving better returns; furthermore, their drawdown-risk is low. Therefore, reducing stock-exposure by a larger amount at such times should mean a greater reduction of potential losses. And the historical evidence says that it did.
• The best results came from portfolios with a ceiling at 50% in stocks, with a floor of 0% or 10% and a reference window at or near 3 months. Although not shown in the chart, a ceiling below 50% had somewhat lower relative returns. Very high ceilings, such as the 100% example in the chart, stayed close to the average outcome. The sweet spot may be about 50% to 60%.

Takeaways
The lessons to be drawn from these findings depend on your goals as an investor:

• If your main concern is to limit drawdowns, your lower boundary for a rotation portfolio should be 0% to 15%. This finding begs the question: "Which is better? Holding a rebalanced portfolio with a floor at 10%, or rotating a portfolio around low percentages, such as a floor of 0% and a ceiling of 15% to 25%?" My next post will examine exactly this question.
• If your main concern is to maximize real returns, then rotate your portfolio from high exposure to stocks (70% or more) to low exposure (0% to 10%).
• If you prefer a compromise on boosting returns while also limiting drawdowns, your best strategy is to rotate between about 50% to 60% in equities when they are strong, and 0% to 10% when they are weak, with the remainder in bonds. Another question is begged: "How do rotations like 50-to-0 or 60-to-10 compare to rebalancing at, say, 40-60 or 25-75?" As long-term portfolios, historically, all of these offered good risk-adjusted performance. But is any one of them distinctively better than the others for an investor who wants to optimize relative returns? This, too, will be covered in upcoming posts.

Some Technical Details
These analyses aggregated statistics and data from a large number of observations, which could be categorized in several ways:

1. Four countries: the U.S., Japan, Germany, and Australia. For all these countries, public monthly data was obtainable for (a) the total return, including reinvested dividends, for an index of large-cap stocks going back at least 25 years in local currency; (b) at least 25 years of dividend history for country-specific, constant-maturity, 10-year Treasury bonds in local currency; and (c) at least 25 years of inflation history as measured by a country-specific index of consumer prices.
2. Seven 25-year periods. Four quarter-centuries were available for the U.S., between April 1919 and March 2019, and one each in Japan, Germany, and Australia from April 1994 to March 2019.
3. Different reference windows. Generally, the analyses presented here are averages from comparing bond-returns and stock-returns over windows of three months or twelve months. Unless otherwise noted, the results were the same for these two windows. Other analyses, not presented here, also considered windows varying from one to twelve months, plus combinations of multiple window-sizes.
4. Floor-ceiling settings. The results in this post are from 48 pairs with floors of 0%, 10%, 15%, 20%, 25%, 30% or 40% in stocks and ceilings of 40%, 50%, 60%, 70%, 80%, 90% or 100% in stocks. These seven floors and seven ceilings generated 49 possible combinations. However, one of them, 40% floor and 40% ceiling, is really a rebalancing strategy, not rotation, and was therefore excluded.

​All together, the seven sets of 25-year periods for different countries, the two reference windows, and the 48 floor-ceiling settings generated 672 observation points, each of which had multiple statistics such as annualized nominal and real returns, maximum 25-year downdowns, worst-month drawdowns, and more, both for the large-cap indexes and for country-specific Treasuries.

Primary data-sources were the St. Louis Federal Reserve for Treasuries, inflation, and some stock indexes; Yahoo Finance for the historical total returns of other stock indexes; and older historical data for the U.S. as published by Robert Shiller. Data published directly by index-providers, such as the Deutsche Borse and MSCI, was sometimes used for verification  or to fill gaps.

My recent posts analyzed two investment strategies, in several countries and across various 25-year periods. One strategy rebalanced a portfolio that aimed for 60% in large-cap stocks and 40% in 10-year Treasuries; the other was invested either 100% in stocks or 100% in Treasuries, depending on which of the two assets had recently given better returns. An obvious question is "Why these percentages?" Maybe 60-40 is not optimal for rebalancing, although it is often proposed as if it were. And perhaps rotating between other boundaries (say, 80-20 and 20-80) would be better than going all-or-none. This week's posts address the question by seeking the best floor and ceiling values for the percent invested in stocks.

The chart above is a starting point. It is for one strategy, rebalancing, and one boundary, the floor. The chart is for a hypothetical investor who asks, "What type of rebalanced portfolio would minimize my risk of suffering drawdowns?" Naively, one might assume that, given a choice between large-cap stocks and 10-year Treasuries, the lowest risk would go to a portfolio invested entirely in Treasury bonds. In the chart, that portfolio is at the extreme left. Moving to the right, other portfolios add more and more large-cap stocks, and they pay for it with bigger drawdowns.

Back in the low-risk area at the left edge of the chart, it turns out, perhaps surprisingly, that investing 10% in stocks and 90% in Treasuries is better than going all-in on Treasuries. Nearly as good is a portfolio that rebalances 15% in stocks against 85% in Treasuries. This finding is robust across all the data-sets in last week's analyses, which covered the most recent 25 years in Germany, Japan, and Australia, and the last century in the U.S. The result is also broad in another sense. It is the aggregate pattern across three types of drawdowns: the maximum drawdowns over 25-year periods, the worst single month in 25-year periods, and the average loss for all months that experienced a drawdown.

​Although the advantage of putting 10% in large-cap stocks may seem small, it was very consistent over time and geography. Perhaps the reason is that the growth potential of equities is needed to counteract the vulnerability of Treasury bonds to be drawn down when central banks keep interest rates excessively low or when inflation first erupts.

"So what?" you might say, if you are more interested in your portfolio's potential for long-term gains than its exposure to reversible losses. In that case, consider the chart above. For the same data-sets, it shows annualized returns over 25 years, adjusted for local inflation. Not surprisingly, real-returns increased as the percentage of equities rose in a rebalanced portfolio. Notice, however, that above 80% the curve levels off. For the countries and time-periods in this analysis, on average, rebalancing at 80% to 90% in stocks was virtually as good as holding nothing but stocks.

At this point in the analysis, we have a floor (about 10%) for investors concerned about minimizing drawdowns and a ceiling (near 90%) for those concerned about maximizing gains. What if you care about both? Then, in the jargon of finance, you aim to optimize your risk-adjusted returns. Or, in lay terms, you are willing to expose your portfolio to some increase in drawdowns, provided that you are paid back, in equal measure, with better returns.

​Taking guidance from a method proposed by Franco and Leah Modigliani, I calculated a relative return that adjusted the real return to compensate for the risk of drawdowns. It was calculated as benefit times penalty, where:

• benefit = portfolio's real return minus the real return of 10-year Treasuries
• penalty = average drawdown of 10-year Treasuries divided by the average drawdown of portfolio

In this formulation, big drawdowns will cause the penalty to be a small fraction that decrements any incremental returns. The next chart shows this risk-adjustment for the same rebalanced portfolios.

The best relative returns for rebalanced portfoflios, in this analysis, occurred in the range of 20% to 40% invested in stocks and the rest in bonds. These allocations paid about 0.6% to 0.8% more than 10-year Treasuries, after accounting for inflation and drawdowns. Investors concerned about earning good returns with tolerable drawdowns may find portfolios in this range to be their preferred choice.

That said, even a rebalanced portfolio with a large allocation to stocks would be a winner. In the right hand portion of the chart, the curve remains in positive territory. These portfolios do, therefore, provide an incremental benefit over Treasuries, even after adjusting for their exposure to drawdowns. The risk-adjusted benefit just happens to be rather modest.

My next post will use the same three-step method to analyze the strategy of rotation:

• What is the best floor to minimize drawdowns, 0% or some other value?
• What is the best ceiling to maximize returns, 100% or something else?
• What combination of floor and ceiling values gives the best relative returns?

Earlier posts this week compared rebalancing and rotation across time in a single country: 100 years in U.S. markets. Today's post takes a turn, pivoting to hold time steady while examining a varied set of countries. Time is constrained to the last 25 years; the countries are Germany, Japan, and Australia. While not having the last word, recent experience in these global markets closes one important chapter in the story that began on June 3 when I asked, What Now: Sell, Rebalance, or Rotate?

At first glance, the averages over the three countries seem familiar. The biggest drawdowns were for large-cap stocks; the smallest ones, for local 10-year Treasuries. Smoother results came from rebalancing 60% in stocks and 40% in Treasury bonds, while tempered drawdowns and the best inflation-adjusted returns were definitive for 100-or-0 Rotation. Underneath the averages, however, investors in the three countries had very different experiences in the last quarter-century.

Of the three, Germany most closely resembled the U.S. from 1994 to early this year. Stocks rose overall, though the German DAX had a deeper drawdown (-68%) than did the American S&P 500 (-51%). Bonds were more competitive with stocks in Germany, enabling a portfolio that rebalanced 40% local Treasuries against 60% local stocks, all in local currency, to keep pace with an all-stocks portfolio. While these strategies took their different paths to similar destinations, 100-or-0 Rotation ultimately found a way to take investors even farther in Germany (8.7% annualized, adjusted for local inflation) than did the same strategey in the U.S. over the same years (7.4%).

Japan's experience was sadly unique. Stocks were mostly underwater for the last 25 years. Though inflation was low, the Nikkei 225 barely kept up with it, even with dividends reinvested. Bonds and the 60-40 portfolio managed to finish about 3% and 2% above inflation, respectively, in their characteristic ways:  paddle-boarding with local Treasuries behind the harbor breakwall; and boogie-boarding to catch big surf the 60-40 way, not quite so daring as air-freaking stocks. Outmanuvering all others, once again, was 100-or-zero Rotation, which rode the good waves and avoided the rest.

Yet another distinctive pattern transpired in Australia. Nominal interest rates for local 10-year Treasuries were higher in Australia (averaging 5.7% from 1994 to 2019) than in the other countries (3.9% in Germany, 1.9% in Japan, and 4.4% in the U.S.). Had Australian investors appreciated that local inflation was tepid (2.5%), they would have been wise to prefer their Treasuries, whose 25-year run exceeded both the AX 200 index of stocks, with reinvested dividends, and a 60-40 rebalanced portfolio. The strategy of 100-or-0 Rotation was sometimes the worst, though not by much. In the end it eaked out a small victory.

Good as it was overall, 100-or-0 Rotation exhibited at least one consistent vulnerability. For the worst-month metric, it always finished in third place, better by far than stocks, but outdone both by bonds and by rebalancing. There's a simple explanation, and it has a clear message. If a strategy is 100% invested in stocks when stocks fall suddenly and dramatically in a very short period, as on Black Monday in October 1987 and in the flash-crash of 2010, then the portfolio gets the full effect. However, a portfolio invested partly or completely in Treasuries will partly or completely escape the damage. Furthermore, Treasuries will very likely rise in value at such times.

The natural question to ask is whether a better rotation would stay below some ceiling, never going to 100% in stocks. A related question might be whether 0% is, in fact, the best floor. Happily, the data of the last 100 years in U.S. markets and the last 25 internationally have clear answers for both questions. Next week's posts will show how the answers are derived.

Yesterday's post showed how four investment strategies handled two consecutive 25-year periods between 1944 and 1994, for stocks and bonds in the U.S. Today I'll examine the same strategies over two additional 25-year periods, bookending the previous ones and thus spanning a full century. The first period, 1919 to 1944, had the Great Depression; the second, 1994 to 2019, had the dot-com crash and the Great Recession. Truly, those were stress-tests for any portfolio.

The two charts below capture the main points of interest. (Or, to follow the story-line from the beginning, go back to my June 3 post, What Now: Sell, Rebalance, or Rotate?)

Had you held the S&P 500 (or something similar) throughout the bull market of the 1920's, the dreadful 1930's, and much of World War II, you would have suffered two big drawdowns. The killer, exceeding -80%, took three excruciating years from 1929 to 1932. Another, in 1937, was swifter and, at -41%, must have felt almost as frightful. Look, too, at 60-40 rebalancing! It offered no shelter, hugging the all-stocks portfolio as if in numbed desperation.

Treasury bonds, by comparison, gave an astoundingly smooth ride, perhaps because the bond-market was less mature than it is now or, more likely, because the U.S. Treasury controlled interest rates in a much different manner than the Federal Reserve has done since the 1950's. Yet, as good as the all-Treasury portfolio might have been, it was easily surpassed by 100-or-0 Rotation, a strategy that went all-in on stocks when their recent trend was better than 10-year Treasuries, and all-in on those same Treasuries when they had lately been the better of the two options. In this analysis, "lately" means, very simply, not last month, but the last several.

A half-century later, remarkably similar patterns began to emerge, like old music found in tattered manuscripts and replayed on new instruments. From 1994 to 2009, stocks had a bull market whose brassy boasting was soon silenced by a da capo of drawdowns. For its part, a 60-40 rebalanced porfolio held close to the rhythm of stocks. Treasuries made steady progress, while moving to a subdued drumbeat. Once again, a portfolio of 100-or-0 Rotation avoided firm commitments and, charmingly fickle, danced with each month's better partner. Doing so, it largely side-stepped the worst moments and outdid all others.

Taken together, the four 25-year periods shown in today's and yesterday's posts constitute a statistical sample. Averaging measurements across the four intervals generates an estimate of the outcomes one might expect in future quarter-centuries. For example, an average of the four maximum drawdowns will estimate the expected maximum drawdown in any future 25-year period.

Estimating in this way is more useful than simply calculating the maximum drawdown over the past 100 years. You and I won't be investing for 100 years.  The expectation for any 25-years, based on an admittedly small sample of four, is statistically more reliable and pragmatically more relevant than an expectation for 100 years, based on an even smaller sample of one.

Accordingly, the summary chart below shows several expected outcomes for future quarter-centuries. It also compares expectations across the four investment strategies.

Were you to invest entirely in the S&P 500 over the next 25 years, you should brace for a drawdown of about -48% at some point, plus a bad month with a paper loss of -19%, as you march toward an eventual inflation-adjusted annual return of 7%. In short: nice gains, big pains. Investing entirely in 10-year Treasuries would likely have much smaller drawdowns  of -9% at the low point and -5% in the worst month, but your gains would be correspondingly reduced to about 2% or 3% more than inflation. A typical plan of 60-40 Rebalancing would reduce the pain of drawdowns, compared to the S&P 500, while also sacrificing some gains. Best of all, however, would be 10-or-0 Rotation, which could be expected to generate better gains than the S&P 500 and smaller drawdowns.

My next post will apply the same four portfolios to countries outside the U.S., for the most recent 25-year period.

Historically, you would have gotten good returns by simply holding a target percentage of your portfolio in stocks over many years, keeping the rest in 10-year bonds, and rebalancing periodically if the percentages drifted from your target. However, you would have suffered many drawdowns, sometimes extreme, lasting months or years. A week ago, I gave some examples as part of a series that started with my June 3 post for current U.S. markets, What Now: Sell, Rebalance, or Rotate? 

This week's posts will introduce rotation as an an altenative to rebalancing. Today's examples are for U.S. stock and bond markets dating back to 1919. Four investment strategies are applied to this 100-year period:

• 100% in the S&P 500, with dividends reinvested.
• 100% in 10-year Treasury bonds with interest reinvested.
• 60% in the S&P 500 and 40% in 10-year Treasuries. At the end of each month, either reinvest the income in its source or, if the percentage in stocks has drifted to 55% or 65%, then rebalance stocks and bonds to their respective targets.
• Either 100% in the S&P 500 or 100% in 10-year Treasuries, according to their recent performance, checked at the end of each month.

Comparing the strategies over the 100-year period from April 1919 to March 2019, 60-40 rebalancing and 100-or-0 rotation were virtually identical in one key way: over the long term, their equity exposures were virtually the same, 60.9% for rebalancing and 60.6% for rotation. In both cases, the portfolio tended to drift more toward stocks than toward bonds. For rebalancing, the long-term exposure to stocks was therefore slightly above the target of 60%. For rotation, the similar outcome over the full 100 years is an interesting coincidence. However, over shorter 25-year intervals, the stock-exposure of 100-or-0 rotation was variable.

Between 1944 and 1969 (depicted above), 100-or-0 rotation was 69% in stocks, on average. That happened because during these years, stocks strongly outperformed bonds. (See this earlier post for some possible reasons.) Then, continuously holding 100% in the S&P 500 would have been the best strategy; rotation often avoided bonds and thus out-performed rebalancing; and Treasuries were exceptionally weak, actually falling behind the inflation rate.

The next 25 years told a different story, as illustrated below. A sharp recession in the mid-1970's, followed by high inflation and high interest rates, then by prolonged rate cuts, combined overall to make the total return of bonds competitive with stock-returns. The strategy of 100-or-0 rotation responded in kind, allocating even-handedly, with an average stock-exposure of 53%. For the full 25 years, rotation beat all the other strategies, not by putting all its eggs in one basket, or by juggling two baskets at all times, but by opting periodically for the basket that better suited the changing financial environment.

The four 25-year periods since 1919 exhibited a variety of environments, including the two described above; the bull market of the 1920's and Great Depression of the 1930's; and the dot-com bubble, Great Recession, and recent bull market of the 21st century. Across it all, if given 25 years, a strategy of 100-or-0 Rotation ...

• Beat 60-40 Rebalancing, every time
• Beat 100% invested in the S&P 500, three of four times
• Beat 100% placed in 10-year Treasuries, every time
• Beat inflation handily, for every 25-year period

In forthcoming posts, I'll continue this introduction to rotation as an investment strategy, examining questions like these:

• Using both raw returns and risk-adjusted metrics, how did rotation fare across 25-year periods and across countries?
• What about drawdowns, as in "flash-crashes" and major recessions? Did rotation handle them better than rebalancing?
• Is 100-or-0 the best way to do rotation, at all times and for all investors? Or would less drastic exchanges be better, depending on circumstances?

Finally, regarding how, exactly, to implement a rotation strategy, I will get there in due course. The main idea is pretty simple: check monthly and pick the better of two investments, stocks or bonds. I'll save the specifics until more of the details and nuances have been explained.

Suppose from 1944 to 1969, you held and rebalanced a portfolio matching the S&P 500 index and 10-year U.S. Treasury bonds. Would that have been the optimal investment strategy for those 25 years? This post answers the question, using data similar to posts earlier this week on recent 25-year periods for the Nikkei 225 in Japan and the Dax 30 in Germany. It's all part of a series that follows up my June 3 post about current U.S. markets, What Now: Sell, Rebalance, or Rotate? 

Comparing this chart to the previous ones for Japan and Germany, one difference stands out. Stocks were indisputably the superior investment. The worst drawdown in the total return of the S&P 500 from April 1944 through March 1969 was -22.3%. In the usual parlance, that's merely a "correction," not a "crash." In the worst single month, had you held all your money in stocks, your loss on paper would have been -14.4%. Those drawdowns, admittedly not small enough to match Treasury bonds, were far less painful than the maximums exceeding -65% and the monthly values around -25% for stock-portfolios in Japan and Germany from 1994 to 2019.

Remarkably, the cumulative real return of an all-stocks portfolio in the U.S., from 1944 to 1969, was 10.4% per year. After inflation! Incredible. The real buying power of your dollars would have grown 11-fold in 25 years. Of course, you had to be there. You had to be alive  then with money to invest. And you had to be smart enough or lucky enough to place all your chips on stocks, at a time when the world war was not yet over, the G.I. Bill not yet conceived, the baby-boom not begun, interstate highways unknown, air-travel restricted to the wealthy, and rationing of necessities the norm. Maybe you would have foreseen that there was nowhere to go but up.

Or maybe the habits of rationing food and buying war-bonds would have inclined you toward the perceived safety of Treasuries. What a mistake that would have been! Over the next 25 years, your real returns would have gone negative. Treasury bonds, in that period, were anything but safe. Cumulatively, they suffered a -16% loss in buying power, as their -0.7% real rate of return compounded. No single month announced this loss. The worst one was merely -2.4%. Japan's and Germany's more recent government bonds had monthly drawdowns twice that amount, but they also had more numerous months of positive, inflation-adjusted returns that generated real gains in the long run.

​The quarter-century from 1944 to 1969 was, coincidentally, when the Bretton Woods Agreement governed global currencies. It made the dollar dominant, governing world markets, for better or worse, by the force of U.S. ownership of the majority of the world's gold. Interest rates in the U.S. were capped for many years early in that period, for fear of post-war deflation, when the reality was an inflationary spike in prices. Then, when interest rates were belatedly allowed to rise, they did so slowly but inexorably for the rest of the period, causing bond prices to fall, also slowly and inexorably. Perhaps misguided monetary governance like this will never happen again. Or maybe not this pattern in particular, but another one crafted in a future time of uncertainty, with similar unforeseen and unhappy consequences. We won't know until, if, and after it may happen.

In the final analysis, the U.S. experience from 1944 to 1969 conveys the same lesson as did the German and Japanese results for 1994-2019. Had a post-war investor in the U.S. opted for the compromise of investing half in stocks and half in Treasuries, rebalancing them monthly to 50-50, if needed, when they drifted to 45-55, then the outcome after 25 years would have been quite satisfactory. In round numbers, the maximum drawdown would have been a tolerable -10%; the worst month, only -8%; and the annualized real return, a handsome 5%.

Summing up the three cases, we have one (Japan, recently) where going all-in on bonds was best; another (the U.S., a half-century earlier) where that would have been a disaster; and two where stocks were best, once by a small amount (Germany, recently) and once by a huge margin (the post-war U.S. again). A rebalancing strategy was never best nor worst, yet all three times it beat inflation. The rub, however, is that rebalancing only partly managed the problem of severe drawdowns.

Next week, posts in this series will continue with a fresh look at a different strategy, rotation, to examine whether it can succeed when rebalancing comes up short.

Yesterday's post examined rebalancing as a strategy for investing in Japanese stocks and government bonds over the last 25 years. Today's post applies the same analysis to the German DAX 30 index, German government bonds, and German inflation rates, all evaluated in Euros, for the same period from April 1994 through March 2019. It's part of a series that follows up my June 3 post about current U.S. markets, What Now: Sell, Rebalance, or Rotate? 

At first glance, the chart for Germany seems much like Japan's. Drawdowns were big, compared to real returns. Rebalancing, while it did not eliminate every period of distress, had some benefits as a compromise between investing wholly in stocks or in bonds.

On close inspection, however, German markets during this period, although similar in many respects to those in Japan, were also different in at least one important way.

​Yes, the maximum drawdown of -68% for a portfolio invested 100% in the DAX 30 was a debacle nearly identical to Japan's -66%. And, yes, the peak drawdown for government bonds was much easier to endure, hitting about -10% in both countries. And in both cases, a rebalanced portfolio split the difference. The biggest drawdown was about -31% for an investor who went half in stocks and half in government bonds, in the local currency, while rebalancing to 50-50 whenever the end-of-month allocation shifted to stocks shifted past 45% or 55%.

The worst-performing months were also virtually identical in the two countries. Both had worst-month drawdowns around -25% for their all-stocks portfolios, -4% for government bonds, and -10% for 50-50 rebalanced portfolios.

What's interesting, however, is how the two countries differed on real returns, the cumulative annualized gains after adjusting for local inflation. In Japan, the rebalanced portfolio matched the performance of government bonds, which fared better than stocks. In Germany, stocks and bonds switched postions. The DAX 30 provided the better eventual outcome. And rebalancing? It went with the winner, matching German stocks this time.

Had you been a newbie investor in Germany or Japan in 1994, could you have known with any certainty whether to bet on stocks or on bonds for the next quarter century? Of course not. But if you hedged your bet by rebalancing equally across the two classes of investments, your end-result would have been as good as placing the lucky bet.

That's a powerful argument in favor of rebalancing as a strategy. But wait! Is the benefit limited to recent examples like these two, where mature markets in developed countries were all beset by asset bubbles, the Great Recession, and the financial engineering of central banks?  To expand the analysis, the next post will examine yet another example, the U.S. S&P 500 from 1944 to 1969, when the economic and financial setting was decidedly different.

This post is the first of several examining the basis of my June 3 post, What Now: Sell, Rebalance, or Rotate? Today, the topic is whether rebalancing a portfolio of stocks and bonds was an effective strategy in the past 25 years for investors in Japanese markets. In the days ahead, I'll present similar data for Germany and the U.S., and for a strategy of rotation rather than rebalancing.

The chart above summarizes total returns for three portfolios invested in Japanese markets from April 1994 through March 2019.  All the underlying data for prices, interest, total returns, and inflation are in local currency (Yen).

During this period, a prescient investor would have simply bought 10-year government bonds and held them. No stocks, no rebalancing, no worry! Why so?

At one point, government bonds were 10.5% below their previous peak for the period, as indicated by the bar for 25-year drawdown in the chart. Looking at your portfolio and seeing an unrealized loss over 10% could be troublesome. But you would have seen much worse with an all-stocks portfolio (-66.4%). A portfolio invested 50-50 in Japanese 10-year government bonds and the Nikkei 225, rebalanced monthly if it drifted to 45-55, would have mitigated the drawdown, yet remained alarming (-31.3%). In short, bonds had the least-bad losses.

Those drawdowns were not instantaneous. They evolved over several months. Could you have seen them coming, and perhaps taken some action? One way of doing so would be to monitor your portfolio every month, and assess the drawdown since the previous month. Had you done so, your worst monthly outcomes would have been -4.6% for bonds, -23.8% for stocks, and -10.7% for rebalancing. Losses of this magnitude can occur in a single day, as they did in the U.S. in 1929 and 1987. So the maximum drawdown in any month is credible as an estimate of the risk that is unavoidable for a portfolio. If you consider a potential unavoidable loss of 10% to be tolerable, then, at least for the case of recent history in Japan, rebalancing might be, for you, a strategy worth considering.

Potential drawdowns would be the only criterion that mattered if you were concerned exclusively about risks, not about benefits. Realistically, you likely have a personal preference to accept some temporary risk, provided that you get some eventual reward. Maybe you will tolerate a transient drawdown of X% if, in the long run, you stand to gain Y%.

With long-run returns, one concern (in fact, a hidden but pernicious risk) is that they may cover a period with high inflation. If your long-run return is 10% but inflation is 8%, your buying power, or real return, is just 2%. Thus, the risk-benefit calculation requires, in this data, comparing drawdowns with real (inflation-adjusted) returns.

Happily, in Japan for the last 25 years, inflation was nearly zero. In some years, the opposite occurred, with deflationary declines in prices that occasionally made bonds the indisputable investment of choice. As shown in the chart, rebalancing captured some of these benefits, matching an all-bonds portfolio over the full 25-year period; both portfolios generated real returns near +2%. Stocks, if you held them all that time, would have eventually pulled your results into the black, but only barely (+0.3% after adjusting for inflation).

In hindsight, had you been there, years ago, deciding how to invest in Japan for the next quarter-century, would you have gone all-in on government bonds? If not, and you instead opted for the compromise method of rebalancing, you would have done equally well in the end, and measurably better than by putting all your money on stocks. Along the way, however, you would have had to weather some nasty storms. In subsequent posts, I'll examine whether Germany and the U.S. were similar and whether, in all three countries, rotation would have proven superior.

On June 1, a new method I've been analyzing recommended rotating out of stocks and into bonds, in both tax-sheltered and taxable accounts, except for low-volatility stocks. The method was developed from 100 years of historical data for US stocks, treasury bonds, and inflation; 25 years of data for international stocks, bonds, and inflation; and 25 years of indexes for minimum volatility stocks worldwide. Here's a chart that illustrates how the method would have performed since 1919 in the US. 

One line in the chart shows a portfolio invested fully and continuously in a fund that tracks the S&P 500, with dividends reinvested. Another line shows full and continuous investment in a simulated fund of 10-year US Treasuries, with interest reinvested. For comparison, another line shows a simulated fund invested 60% in the S&P 500 and 40% in 10-year Treasuries, rebalanced monthly if the percentages drift to 65-35 or 55-45. The best results, however, are for a simulated fund using one version of the new method. It is invested either 90% in the S&P 500 and 10% in 10-year Treasuries, or vice versa, using a simple decision-point at the end of each month. It requires no more effort than monthly rebalancing, but generates smaller drawdowns and bigger returns.

I'll call the new method "rotation" to distinguish it from rebalancing. In brief, rotation ...

• Does not try to pinpoint the top or bottom. In fact, it is ordinarily a bit late.
• Does not prevent drawdowns. But it greatly reduces them, by design.
• Can easily be calibrated to limit tax consequences. Monthly churn is not necessary.
• Can align with personal tolerance for risk. A 90-10 split is not the only option; others, in fact, are ordinarily better.
• Has been robust, historically, across periods of high or low inflation, trending or choppy markets, and growing, stagnant, or recessionary economies in developed countries.
• Offers guidance about when and for whom the method is advisable. Sometimes, for some individuals, rebalancing may be better.

In the weeks ahead, I'll show more examples of rotation at work in various markets, with real and simulated investment funds. And, on July 1, I'll start posting monthly results using the method, allowing you to track it in real time.

For many months, my pro bono work for non-profits has limited the time I've been able to invest in this site. To repair neglected and outdated material, I will be making several changes in November and December. Some rarely used pages will be removed. Pages visited more often will be updated, if needed. Please add a comment to this post, if you have feedback or suggestions.