rstats – raisingBuffetts https://raisingbuffetts.com Mon, 18 Jan 2021 06:33:00 +0000 en-US hourly 1 https://wordpress.org/?v=6.5.5 https://raisingbuffetts.com/wp-content/uploads/2019/03/cropped-site-icon-2-32x32.jpg rstats – raisingBuffetts https://raisingbuffetts.com 32 32 To Rebalance Or Not? https://raisingbuffetts.com/to-rebalance-or-not/ Sat, 02 Nov 2019 01:39:17 +0000 https://raisingbuffetts.com/?p=1284 Continue reading "To Rebalance Or Not?"]]> Doveryai, no proveryai, a Russian proverb whose English translation Trust, But Verify made famous by the late President Ronald Reagan during negotiations with the Soviet Union has been a topic of debate ever since, not only in the realm of politics but also in many other aspects of wherever you think you might get tempted to use it. To help sort this out, Nan S. Russell in Psychology Today provides a context based usage approach that works just right.

When outcome is essential and matters more than relationship, use trust, but verify. When relationship matters more than any single outcome, don’t use it. 

So true that. But since there are no relationships to care for when it comes to being a good steward of our money, we should trust little and verify a lot. And that task becomes a lot easier with a bit of intuition and access to data.

So there is this thing called rebalancing and it means exactly as it sounds. Say we start with a 60/40 stock-bond portfolio and over time as the markets evolve, that allocation drifts to say 65/35. If the intent is to maintain a constant allocation, we’d sell the stock component of the portfolio, taking out the excess and buy into the bond portion to bring the allocation back to 60/40. That’s rebalancing.

And it sounds like a great idea. We sell something that has gone up and buy the other that has gone down – a classic buy low, sell high approach. So that’s great. But then I read something along the lines that rebalancing between stocks and bonds works but rebalancing within a category is not ideal or does not work as effectively.

Take stocks as a category for example. You’ll likely own some large company stocks, mid-size company stocks and some small ones. And then you’ll own developed market international stocks and emerging market stocks and so on. Not all of them will move in the same direction all the time. Some will zig while others zag. Or some will zig some while others will zig more and so on. So if you rebalance within a category, you would be theoretically doing the same thing that you ideally would want to do – buy low and sell high.

But now there’s this doubt and we need to get to the bottom of it to make sure all’s okay. So as we would do and as we should do, we test both approaches at once to validate that what we’ve done all along was not inferior to what we should have done.

So we go back to data and test whether an invest & forget approach works better than say rebalancing annually. Ideally we would and should rebalance as often as there is an opportunity to rebalance but let’s just assume we do it once each year. We’ll use data on annual returns for four asset classes to test the two approaches.

  • Large company U.S. stocks
  • Small company U.S. stocks
  • International stocks
  • U.S. bonds

We invest $100 in a portfolio comprised of these four asset classes at the start of the entire time period in varying proportions of 10% increments and assess whether rebalancing does what it is supposed to do. A snapshot of different portfolio combinations is shown below.

Each row is one portfolio and with 10% incremental allocation spread across four asset classes means 258 different portfolio combinations we get to try this on.

Starting with year 1, in year 2 in case of the rebalancing approach, we sell whatever has deviated to the upside from the original allocation and buy what has declined to bring the allocation back in line. For the invest & forget approach, we split and invest the original $100 into the allocation we started out with and let the money ride till the end of the period. The end of the period by the way is 2018 and the dataset contains 49 years of data starting in 1970. So we are comparing the ending values of each portfolio at the end of 2018 to test the rebalancing vs. invest & forget approach.

The first thing we should do to get a good feel is to look at how the ending values are distributed between the two options.

So clearly rebalancing works as is evident from a slight right shift of its distribution as compared to invest & forget. The spread is a bit wider though with rebalancing which is not desired but a bigger question is, are we comparing the same portfolios when comparing outcomes between the two? What we should ideally compare is the ending value of portfolio 1 in the invest & forget case with the ending value of portfolio 1 in the rebalanced case, the ending value of portfolio 2 in the invest & forget case with the ending value of portfolio 2 in the rebalanced case and so on.

So that’s what we have done next and this is what we find when we do a portfolio by portfolio comparison of the ending values…

  • Out of 258 portfolios, each with a different asset allocation, the ending values of 243 portfolios that were annually rebalanced equaled or outperformed those of the invest & forget ones. So a 94% outperformance rate if the portfolios were rebalanced as compared to invest & forget.
  • 79 portfolios out of 258 that were annually rebalanced outperformed invest & forget ones by more than 10%.
  • And the ending values of three out of 258 portfolios outperformed invest & forget by more than 25%.

So rebalancing works or at least worked almost all the time. But what if the bond allocation was held constant at say 40%? The original thesis was that rebalancing is more effective between categories (stocks vs. bonds) versus within categories (within stocks or within bonds). So trying that out…

Apparently the same story here with the shift in distribution for the rebalanced case more to the right than for the invest & forget approach. Oh and by the way, because the bond allocation is held constant with only the remaining three asset classes in the stock category allowed to vary, only 60 portfolio combinations are possible.

A portfolio by portfolio comparison of the ending values yields the following results…

  • Out of 60 possible portfolios, each with a different asset allocation and a fixed bond allocation, the ending values of 59 portfolios that were annually rebalanced equaled or outperformed those of the invest & forget ones. So a 98% hit rate making the case even stronger for the rebalancing approach.
  • 25 portfolios out of 60 that were annually rebalanced outperformed invest & forget ones by more than 10%.
  • And one outperformed invest & forget by more than 25%.

So if you had to wager, rebalancing still wins.

What if you owned an all-stock portfolio? Would rebalancing still outperform invest & forget?

Appears to be a yes. And again as before, only 60 portfolio combinations are possible so a portfolio by portfolio comparison yields the following…

  • Out of 60 possible all-stock portfolios, the ending values with the rebalanced approach equaled or outperformed invest & forget each and every time. So a 100% hit rate in favor of rebalancing.
  • But none of them outperformed by more than 10% so not a big thumping vote for one over the other.

But what if the returns of the past do not repeat in the same sequence? Could the outcomes be different with a different sequence of returns?

To assess that, we sample returns for each asset class randomly and recreate the asset class returns dataset each time and compare the ending portfolio values between the two approaches. And just to make sure that we have at least attempted to try every which way to convincingly make one approach fail over the other, we do this 500 times. The results…

With portfolios constructed out of a combination of the four asset classes (large company U.S. stocks, small company U.S. stocks, international stocks and U.S. bonds)…

So a very strong vote in favor of rebalancing even with randomized returns sequences.

With a 40% constant allocation to U.S. bonds and the allocation to stocks allowed to vary…

Rebalancing wins here as well.

And for the stocks only portfolios (large company U.S. stocks, small company U.S. stocks & international stocks)…

So you’d be crazy to not rebalance your portfolios from time to time.

But here’s a thing. This whole thing is fundamentally based on the fact that mean reversion will always happen. That is, if an investment has deviated from its normal course either on the upside or the downside, it will always revert back to its mean course over the long term.

But what is long term? Ten years, twenty-five years, hundred years? We can only know this in hindsight maybe long after we are dead so that’s one thing to consider.

And what if an investment ceases to exist? Individual companies we know live and die all the time so to guard against that risk, we’d diversify into a sector. Could an entire sector vanish or never, ever revert back to its mean trajectory of growth? Of course.

What about countries? That’s easy, Japan.

The post-war rebuilding which eventually culminated into a real estate led economic boom of the 1980’s Japan was so big and went on for so long that just the fact that it all eventually came crashing down does not quite do enough justice to the sheer scale of that bubble. Edward Chancellor in his book, Devil Take The Hindmost chronicles the reasons for the boom and what led to its eventual implosion.

One of the key drivers for the boom…

Between 1956 and 1986, land prices increased 5,000 percent, while consumer prices merely doubled. During this period, in only one year (1974) did land prices decline. Acting on the belief that land prices would never fall again, Japanese banks provided loans against the collateral of land rather than cash flows.

Land prices will never fall again, wonder where we have heard that before? So the banks lent money just because the value of the land rose. And the more it rose, the more they lent, creating that self-fulfilling feedback loop of ever increasing prices, leveraged to the hilt. Things got so crazy that by 1989,

The grounds of the Imperial Palace in Tokyo were estimated to be worth more than the entire real estate value of California (or Canada, if you preferred).

And the post-crash recovery didn’t quite materialize or hasn’t yet materialized due to structural reasons that are unique to Japan, though there are signs that things might be finally on the mend. But then they have a long way to go.

Back to the rebalancing or not rebalancing question at hand, so if a portfolio design is done not considering the fact that there might not ever be a mean reversion, we are doomed.

And I might have insinuated before that I am strongly in one camp or the other but I am not completely sold on either. So I employ a mix of both. And that’s because I don’t know the future. No one knows the future but try one must with as much supporting research and evidence. And a bit of intuition.

Thank you for reading and persevering through.

Until later.

Cover image credit – Matthew T Rader, Pexels

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Take Mean-Variance Optimization With A Boatload Of Salt… https://raisingbuffetts.com/take-mean-variance-optimization-with-a-boatload-of-salt/ Sat, 28 Sep 2019 01:01:58 +0000 https://raisingbuffetts.com/?p=1147 Continue reading "Take Mean-Variance Optimization With A Boatload Of Salt…"]]> In a 1952 paper published in the Journal of Finance titled Portfolio Selection, Harry Markowitz laid out a framework that literally transformed the landscape around how portfolio management should be done. Later dubbed the Modern Portfolio Theory or MPT, that seminal paper would go on to eventually earn him the Nobel Prize in Economics about four decades later. And you might have come across a bit of this if you are doing anything remotely tangential to institutional money management. Or at least you should have. Heck, even if you are not a professional money manager, it’s not all bad to at least be aware of what this is all about. Who knows, you might be better at this than the so-called professionals.

So what’s the paper about? Designing diversified portfolios through the use of uncorrelated asset classes as a way to invest optimally with a goal to earn the highest rate of return for a given level of risk. Yes, it’s a mouthful but this simple yet intuitive approach to portfolio management didn’t exist until 1952. At least no one attempted to formalize it and present it in a way he did.

And the ‘right’ amount of diversification is all about correlation or to be more precise, uncorrelation between different investments in a portfolio. Owning stakes in 10 different technology companies is not diversification. Or spreading your bets between say a portfolio that invests in the Dow vs. the S&P 500 index is not diversification. How do we know? Because again, correlation but before we jump into that, a bit about the different types of investments or asset classes you could consider to design your portfolio.

So we know an investment. Buying that stock in the hope that it appreciates in value while it pays dividends (or not) is an investment. Buying that bond that pays interest until it matures is an investment. Or that piece of real estate that provides rental income is an investment. But what’s an asset class? I got my hands on returns data published in the Feb 2019 issue of the Financial Planning magazine by the Steele Mutual Fund Expert for 7 major asset classes going back to 1970. We’ll use this and probably some other data series to do whatever we need to do here.

Those asset classes are Large U.S. Equity, Small U.S. Equity, Non U.S. Equity, Bonds, Cash, REITs and Commodities.

Large U.S. Equity comprises of all large publicly traded companies in these United States. What constitutes large could be different based on the organization assembling that asset class but in general, it means all companies with market capitalization of $10 billion or more. Then there’s an asset class that owns small companies. There’s one that owns non-U.S. companies, there’s one that owns bonds, real estate etc.

Real estate here is not the home you own. Owning that is akin to owning a single company stock or a bond. Real estate here is the entire real estate sector represented by REITs or Real Estate Investment Trusts. What’s a REIT? It’s a publicly traded entity that owns or finances income producing real estate spanning a variety of sectors. For example, that mall you just visited, that could be owned by a REIT. Or that apartment complex where you rent your home? That’s more than likely owned by a REIT. So is that office park or that hospital etc. So a REIT might specialize in one type of real estate but REITs as an asset class gives you broad exposure to every type of real estate. That’s diversification but diversification within a segment of an economy.

And commodities is exactly what it means, owning commodities like gold, silver, copper, oil, wheat, corn etc. You don’t own them physically but you own a stake in a collection of them and someone holds and keeps them safe for you. Yes, you have questions and I’ve got to explain more but for now, just assume that you bought a collection of stuff and held it till 2018 (the last year for which we have data for).

But why not do all this portfolio optimization with individual stocks? Or say bonds? The math is the same so it is doable but what we have here is 49 years of data. And we know a lot can change in 49 years. How much? Take the Dow Jones Industrial Average (DJIA) index for example and compare its constituents in 1970 to the present day constituents.

Only 4 companies that existed in 1970 still remain in the Dow. What happened to the rest? Some got acquired or merged with other companies but most flamed out. And yet the DJIA continued to march on higher from around 800 points in 1970 to 26,000 points today. And that’s not factoring in any dividends. So if you’d done this math in 1970 with the companies of that time and built a portfolio around them, your situation is likely not looking that hot now. And building statistics-based portfolio models requires that the asset class does not vanish which it does in many cases when you build a portfolio around just individual stocks and bonds.

Okay, so we have returns data on these seven asset classes. How can we get a sense of how they have performed over these many decades? We start with the distributions. What do they look like? Are they narrow or wide? Is there any bimodality in the data? All this with this one plot below.

Stacking the plots makes comparisons easy and here’s what we can conclude…

  • That faint line in the middle of each plot is the median. Half the returns are below that line and half above. From what I see, small U.S. equity seems to have the highest median returns followed by real estate and then large U.S. equity. I say median returns for large U.S. equity and real estate are almost identical. Median returns for commodities and non-U.S. equity are comparable which are then followed by bonds and then cash. So we should know which one would have generated the most amount of wealth, right? Small U.S. equity for now but we’ll see.
  • As long as the returns are randomly distributed, you’d want more of them to be on the right of the 0% line than to the left which happens to be the case with each asset class above.
  • Cash and bonds have lower spreads (risk) and lower median returns than other asset classes. That’s expected if you believe that there should exist a risk premium as you take on more volatility with your investments.
  • The spread (standard deviation to be more precise) for commodities appears to be the widest but quite a big chunk of the returns happens to be on the left of the zero line when compared to other asset classes. That has implications and we’ll see.

So what made the most amount of money?

Real estate or REITs to be more precise and by a wide margin. And look at the difference in value between that and say small U.S. equity. Almost a double in REITs vs. small U.S. equity even though the median return for small U.S. equity is in fact higher than that for REITs. So why this apparent discrepancy?

You would have sensed it by looking at the spreads but variance or the volatility in returns is what makes that big of a difference. Not that REITs didn’t have years where the returns were negative but they were not as many as small U.S. equity. And look at commodities. You would have made more money being an investor in supposedly safe bonds than in commodities even though there were more years with higher returns in commodities than they were for bonds.

Before we move on, a bit about the median and the mean (average). Median is the half way point when you sort a data series in ascending or descending order. Say you have a data series with 5 data points; 3, 2, 5, 9, 7. The sorted series then is 2, 3, 5, 7, 9. The median hence is the number 5. We know the average or the mean and that is (3 + 2 + 5 + 9 + 7) / 5 = 5.2. Had to get this out of the way because up until now, we have been making statements using the median values but we need to come back to the mean because that is what this is all about.

The summary then for the average or mean returns and volatility for the 7 asset classes under consideration is as shown below.

REITs actually earned just a hair bit higher annual returns on average than small U.S. equities but with 3% lower standard deviation. And an investment in commodities sucked even after earning 9.5% returns on average and thank the volatility number associated with that asset class for that.

So just returns are not enough. Risk adjusted returns is what counts. A 50% drop in the value of your portfolio does not take a 50% return back to break-even. You need a 100% return to get back to what you started out with. So minimizing that drop in the first place means that it would be a lot less harder to come back to where you were in case your portfolio experiences bouts of volatility. Which it will from time to time.

But even investing in the ‘best’ of asset classes did not come without its own issues. Compare for example bonds to large U.S. equities and REITs.

Bonds of course didn’t make you as much money but they allowed you to sleep like a baby as is evident from the drops in value above from time to time for large U.S. equity and REITs as compared to bonds. Another way to calculate the frequency of heart burns you’d have to endure is to compare drawdowns between the three asset classes.

So quite a few times, you experienced gut-wrenching drops in the value of your portfolio in REITs and in large U.S. equity even though in the end, you came out way ahead. And there’s no guarantee of anything. That 50% drop could have turned into a 60% or a 70% drop. That’s the price you paid to make all that money by persevering and hanging on through that for dear life. And that’s if you did but not many do.

If you cannot handle this extent of volatility, you add bonds and cash because as you can see, there’s hardly any volatility associated with either of them. You didn’t make a killing but as stated before, you slept well. But there’s a caveat especially with bonds which we’ll get to later.

So how big of a slice should bonds and cash occupy your portfolio? Or better yet, how can you create a portfolio that lets you choose the amount of heart burn you are willing to endure? And what’s the ideal portfolio mix that gets you the best return with the least amount of risk? We use mean-variance optimization (or as Fredo would say, “I’m smart.”) to attempt to answer such questions.

Say you mix and match different investments in varying proportions and you get portfolios with risk-return scenarios like below.

Risk here of course means volatility (standard deviation). One of those portfolios is marked in red and the other in green. Both delivered the same return but with starkly different risk levels. And of course you’d pick the lower risk portfolio for the same given return.

Or how about the two portfolios below in red and green?

You’d not pick a portfolio that’s red over say green. Why would you.

Or say you are 22, just out of college and in your first job trying to decide what investments to populate your 401(k) with. You could and should decide to go all out on the risk-return spectrum by choosing a portfolio shown in green on the far right below. You don’t quite yet have as much financial capital to worry about volatility but you sure do have plenty of human capital ahead of you that you’d slowly and eventually convert to financial capital. And because you are adding to your savings with each paycheck, a bit of volatility might actually help than hurt as you get more opportunities to accumulate assets at depressed prices.

Or you could be in retirement where you have pretty much exhausted your human capital and are sitting on a boatload of financial capital that you would slowly extract to live on. You’d rather then own the portfolio in green shown on the lower left.

You would have sort of noticed a theoretical upper bound across the risk spectrum in terms of the returns you can expect from combining investments in varying proportions as shown below.

That’s what’s called the Efficient Frontier. Portfolios on that frontier are considered optimal, offering the highest expected return for a given risk. Portfolios that lie below that frontier are considered sub-optimal and do not generally compensate for the portfolio risk you bear.

So now that we’ve got that straight, we’ll use the data we have on those asset classes and assign them weights in 10% increment and create portfolios (7,658 of them in total) to see which ones lie where on this risk-return spectrum.

We’ll pick 5 different portfolios to dig a bit deeper into their contents and to extract any insights if any.

Portfolio_7658 is the highest risk portfolio that’s allocated to and you guessed that right, 100% into commodities. And it’s not an optimal portfolio because it’s nowhere close to the Efficient Frontier.

Portfolio_920 is the lowest risk one that owns 10% bonds and 90% cash. No surprise there.

Portfolio_2823 delivered the highest average return and it’s comprised entirely of REITs. Again, expected as we saw before.

Portfolio_4575 lies on the Efficient Frontier with 10% volatility. It’s allocated to 20% large U.S. equity, 30% to bonds, 40% to REITs and 10% to commodities. A bit decent but not ideal and will explain why (I am not done yet 🙂 ).

Portfolio_4755 lies on the Efficient Frontier as well but with 15% volatility. It’s allocated to 20% large U.S. equity, 70% to REITs and 10% to commodities. Again not ideal.

So now you start to see issues with formulaic approach to portfolio construction. Some don’t make sense, some are too heavy into a few asset classes and some are overly lop-sided. But just for the fun of it, we’ll see what each of these portfolios did if you’d picked one of them at the start of the period and rebalanced annually to the same allocation you started out with.

As expected, Portfolio_2823 did the best as it was entirely comprised of REITs. Portfolio_4755 did about the same and was more diversified. I would have picked that over Portfolio_2823 any day though that still was REITs heavy.

But the entire premise of all this is that it relies on historical data. You can do all the math you want but we know that thing we hear everywhere we look. And that is, past performance is not a predictor of future results. How would you have known to pick only REITs when you created that portfolio 50 years ago? That’s your entire adult life. You’ve got this one shot to get from point A to point B so taking that chance requires a level of obliviousness that borders on well, obliviousness. Or even if you did pick it ‘right’, what are the chances that you hung on through all the ups and downs that a heavily concentrated portfolio would have exposed you to.

Plus what happened in the past is unlikely to be repeated again, at least not in the same way and that’s all due to what interest rates have done over these last many decades. Take bonds for example.

We know the deal with bonds. As interest rates go down, bond prices go up. And up they have with the relentless bull market in bonds since the early eighties when interest rates were double digits to where they are now. Can the bond bull market continue? Not a chance and hence building portfolios based on historical returns data on bonds will of course not turn out great.

That interest rate tailwind is there for stocks as well.

Why? Say you need to make a capital investment to increase production of whatever stuff you are in the business of making. So you go to a bank for a loan for say a duration of 10 years. The prevailing interest rate at the time is say 10%. Now you make those interest payments on time for the first year and record whatever profits your business generated which of course is net of interest expense. But say the rate declined to 8%. What would you do as a steward of that business? You’d run to the bank to refinance at the now lower rate. You suddenly don’t have as much interest expense and hence your net profit rises. And so does the value of your business or the stock price, all else remaining constant.

And it’s even truer with real estate than with stocks.

Real estate is packaged commodities. It just sits there. It does provide a service and that is shelter but beyond that, not much. It’s not going to create a cure for cancer or reinvent the way how we live or travel or communicate. It’s also an extremely interest rate sensitive asset and likely more so. We see evidence of that with the obvious negative correlation above between rates and an investment in REITs. Can the REIT out-performance continue? Very unlikely.

But it’s not that you completely ignore this theory. You use a bit of it and a bit of your understanding of history, business and the economy and create a portfolio that is just right for you. I’ve shared some of my thoughts on how to go about doing that here and will do more from time to time. But in the end, you are the one who will have to persevere and endure all the ups and downs associated with your choices in the coming decades. Because as Morgan Housel quotes,

Something stupid you can stick with will probably outperform something smart that you’ll burn out on.

So your ability to stick with what you own in your portfolio provided you have justifiable (to you for sure) and quantifiable reasons to own what you own is what will ultimately count.

So long and long.

Until later.

Cover image credit – Quang Nguyen Vinh, Pexels

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The Other Big Risk… https://raisingbuffetts.com/the-other-big-risk/ Sun, 10 Mar 2019 02:57:40 +0000 https://raisingbuffetts.com/?p=117 Continue reading "The Other Big Risk…"]]> Volatility is one risk we cannot escape from when deploying our savings into the capital markets. And that’s a risk we have learned to accept because barring the stupid us and our behavior, the probability of messing up our finances with a decently diversified portfolio over a long-term is virtually nil.

So that’s that but the other big risk of course is the probability of outliving our savings. And volatility is one reason we tune our portfolios depending upon when, how much and for how long we are going to draw income from our savings.

But what could really throw a monkey-wrench into all our planning is the pattern associated with that volatility. Are the ups and downs of our portfolios random or is there an inherent pattern to how those returns transpire? Peter L. Bernstein in his book ‘Against The Gods: The Remarkable Story of Risk‘ hints at caution against over-reliance on historical data for just this reason.

So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician’s trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. Even though many economic and financial variables fall into distributions that approximate a bell curve, the picture is never perfect. It is in those outliers and imperfections that the wildness lurks.

That is that even if you were able to extract the key statistical measures from past data, you don’t want to just go on and use them to predict what future returns will amount to. That’s because without taking into consideration the current market environment and those outlier events, you could be way off from what you planned.

And the sequence of how those portfolio returns come about during retirement could be one of those outlier events that determines whether you depart with millions left behind or your money departs way before you depart. The technical term for this and as implied is the sequence of returns risk. That’s one more risk we need to plan for and to understand its implication, we’ll walk through just what could go wrong even when we have done everything right.

So even though an over-reliance on past data could lead us astray with our plans, we still need some basic metrics to anticipate what future returns could look like. So we do just that and use historical performance data for both stocks and bonds in some combination of each in a given portfolio to simulate those outlier scenarios. We first fit a simulated distribution (in yellow) of returns for stocks over a distribution of the actual past returns (in pink) as shown below to see if a bell-shaped distribution of returns assumption holds.

It does to some extent for this one sample so we go with this assumption and extract the mean (average) and the volatility (standard deviation) associated with that distribution as a baseline to help predict future returns. The average historical return for stocks by the way is the black, dashed line which shows that stocks on average have returned around 10% annually during this entire time-frame.

We do the same for bonds and extract the relevant parameters to help us with predicting future returns. The average actual historical return for bonds is shown by the black, dashed line below.

Before I get arrested for committing more statistical crimes, if you were to retire today, expecting anything more than 3% in annual returns from a Treasury bond portfolio is outright lunacy. And hence even if the average return for bonds in the past was 5%, we’ll use a static 3% for the bond component of our portfolios during retirement. And while we are at it, we’ll also apply a 30% haircut to the average predicted return for stocks during retirement while preserving the same volatility estimate as in the past.

Why do that? For bonds, it’s clear. Just look at where interest rates are today.

What we can reasonably expect out in the future is either rates remaining the same or rising.

And we know what a rising rate environment does to the price of bonds and hence the 3% total return assumption for the bond component of our portfolios.

Paying interest on bonds (issuing debt to finance operations) is a cost to businesses and a rising rate environment means that the cost to service that debt will rise as well. That implies a decline in profitability for businesses that rely on debt financing and that along with where the stock market valuations are today means a 30% haircut on future stock market returns assumption is quite reasonable.

Using these corrected return estimates and past volatility measures, we predict what future stock market returns could look like.

That intermittently random pattern of returns is what we could typically expect though this is just one sample. But what if the sequence of stock market returns of the future follow this pattern?

Or this?

Shown below is what a $1.25 million portfolio invested in a 60/40 stock/bond mix that is re-balanced annually grows to during 35 years in retirement for the three patterns of stock market returns described above. Remember that the bond component is assumed to yield a static 3% during this entire time-frame.

Why start out with a $1.25 million portfolio? That’s because this number assumes a $50,000 inflation-adjusted income draw for each year in retirement and the so-called 4% rule for withdrawal rate at the start gets us to a portfolio size of $1.25 million.

So regardless of the sequence of returns, the final value of the portfolio is the same. And that’s because we are not drawing income from this portfolio yet and hence is left to compound for all those years in retirement.

But this is what happens if we were to draw a 4% annual inflation-adjusted income stream off of the starting portfolio balance.

If the stock markets crater first like what would have happened to us if we were unlucky enough to retire say in 2007 or any other prior stock market peaks, we could run out of money very quickly. And that’s with doing everything right. It’s just that we were dealt a bad hand of the returns distribution.

So what do we do? We save more where instead of relying on say drawing 4% from our portfolios, we get by on drawing 3%. Or even 2%. Why? Say instead of a $1.25 million portfolio to start with, if we had saved up double that amount (ouch), that same $50,000 in income need is a 2% inflation-adjusted withdrawal rate. And that could be had from the dividends and interest payments alone without the need to touch principal. Heck, if that is our income need on a $2.5 million portfolio, we can skip owning bonds in entirety and just live on stock dividends in perpetuity and still have plenty left (if that is our goal).

If doubling of savings is not a possibility, another option as highlighted by Dr. Wade Pfau, Professor of Retirement Income Planning at The American College of Financial Services in this piece is to use a rising glidepath approach to stock allocation while simultaneously reducing the bond component of our portfolios in retirement. That’s counter to what traditional asset allocation models recommend but what this strategy entails is starting out with a very low allocation to stocks right when we retire and gradually increasing that to say 100% stocks towards the later stages of our life in retirement. That’s not likely to completely eliminate the risk of running out of money but will greatly improve the odds of being able to sustain our lifestyles during the entirety of our retirement, so the paper says.

Here’s an example of what happens with the three portfolio return scenarios when we start out with a 10% allocation to stocks and incrementally increase that to 100% stocks through retirement.

So now, instead of running out of money in say year 10 for the worst-case sequence of returns pattern, we were able to extend our income drawing time-frame by double the number of years.

But this apparent safety does not come free as seen by the ending portfolio values for the other two scenarios.

So that was a lot of number crunching and pretty plotting but in an environment where future capital market returns are expected to be low, saving more buys us that ticket to not becoming a victim to an outlier event. Because to quote from that same book by Peter L. Bernstein again,

The essence of risk management lies in maximizing the areas where we have some control over the outcome while minimizing the areas where we have absolutely no control over the outcome and the linkage between effect and cause is hidden from us.

So market returns will be whatever they will be but we know this one thing that still remains in our control and that is how much we save. And of course, the sooner we start, the more time we have for the money to compound and the easier the going gets.

Thank you for reading.

Until later.

Cover image credit – Artem Bali, Pexels

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