**By Dr. Daniel Smith, WCI Columnist**

Many of you already use math in your professional practice. Anesthesiologists calculate volumes of anesthetic and their distributions. Pharmacists calculate renal clearances of drugs. Radiation oncologists calculate radiation doses, and so on. However, as sharp as your medical math may be, there are probably a few arithmetical nuances that, if you dig into, might help you squeeze a bit more return (and perhaps lower some risk!) from your portfolio.

In this article, I’m going to dig into three mathematical concepts and show you some pitfalls with each and how to avoid them!

**#1 Sequence of Returns Risk**

The first concept is called sequence of returns risk, which is essentially the risk that poor returns just before or during early retirement tank your portfolio’s value. Jim has written more about this in other posts.

Investing in Retirement Part 3

The Most Important Factor in Retirement Withdrawal Plans

This risk is most evident with a portfolio of volatile assets like stocks. Bonds and other fixed-income tend to weather bear markets and recessions in a more stalwart fashion. Let’s take a look at the fundamentals, how the math actually works, and how to mitigate it. If you’re in your 20s or 30s, either bookmark this page or read it for the benefit of your more elderly relatives.

Say you start with $500k in assets with 10 years before retirement and a contribution rate of $20K yearly. Your returns are -5%, -4%, -3%, -2%, -1%, 1%, 2%, 3%, 4%, 5% annually. Your final portfolio valuation would be $716,773.43. If you reverse the returns sequence so that the lower returns come last, you end instead with $678,761.30. That’s $38,012.13 difference; nearly 2 years' worth of contributions.

Without context, this doesn’t make a lot of sense. Why would reversing the sequence of returns make a difference? The answer is that with early low returns, you’re putting money into investments as they become cheaper! Later, as the returns increase, you reap the benefits of having purchased assets inexpensively. To the converse, if you buy (invest) while returns are higher, you’re putting money into a portfolio of expensive assets which drop in value more precipitously as the market sours. As you can imagine, the larger the annual contributions to the portfolio, the larger the disparity between the sequences becomes.

The math is even more telling when you start making withdrawals. You’ve decided to rest on the efforts of your life’s work and decide to draw down a comfortable $160,000/year from a 4 million dollar portfolio. You made this decision after reading a convincing article from your buddy about the “safe” 4% withdrawal rate. Fate, being what it is, has dealt you the returns previously illustrated, starting lowest returns first. At the end of just 5 years, your 4 million dollar nest egg has boiled and is now a paltry $2,687,027.40 despite withdrawing only $800,000 from it! At the end of the next 5 years (with the positive returns), your retirement is looking even less like steak and more like Alpo at $2,221,894.34, and you begin to reconsider donating plasma. While the bleeding has definitely slowed, it hasn’t stopped.

The magic 8 ball of life gives you a second chance, and you wind up with the good returns as a tailwind early in retirement. Though still not rosy, it’s less grim than what was previously played out. At the end of your tenth year playing senior-league bocce ball, your portfolio’s value is $2,525,991.35. For those playing at home, that’s a difference of $304,097.01.

The takeaway here is that low or negative returns in close proximity to retirement can put a strain on even a well-funded portfolio.

So, how does one mitigate this pitfall in retirement? Well, there are basically three ways:

- Push back your retirement age.
- Invest in fixed income assets that have a predictable income stream.
- Lower your withdrawals.

**Retiring Later**

The first choice, retiring later, is probably a fairly simple matter for most of the readers of this blog. I’m willing to bet you all have a fairly marketable set of professional skills which, even if practiced on a part-time basis, could generate a reasonable income. By pushing back retirement (or semi-retiring), you can likely face down the fiercest bear and perhaps even continue to invest, which is usually a good choice in a down market anyway. Bonus points for being able to defer required minimum distributions from your employer-sponsored retirement plan if you’re still working. This might also be a particularly good time to do some Roth conversions!

**Invest in Fixed Income**

Let’s examine the second option. If perhaps you’re burned out and want to finally make good on that promised trip to Barbados, you might be better suited by a bond or CD ladder. By changing a portion of your investments to those with predictable returns, you essentially mitigate the short-term market volatility that’s at the heart of this particular problem.

Let’s say you take $500,000 of your portfolio and purchase five high-quality bonds (or bond funds), each with a principal value of $100,000 and maturing in 1, 3, 5, 7, and 9 years. Over the course of those 9 years, you’ll receive the coupon payments for each of those respective bonds and their principal at the end of their respective maturities.

If you’re not wild about purchasing individual bonds and would like to diversify somewhat within that asset class, consider a bond fund with an average maturity that meets your needs. Keep in mind that bond funds can carry bonds of varying investment grades, underlying investment bases (mortgages, treasuries, corporates, municipals, etc.), and somewhat varying maturities. These all somewhat alter the risk composition of the fund.

Since this is supposed to be the safe part of your portfolio, don’t mess around with any fund containing concentrated risks or many if any junk grade bonds. Jim recommends Treasuries or TIPS, which are the safest (with TIPS rising and falling somewhat with inflation), but remember that CDs and their accrued interest are also FDIC insured up to $250,000 per depositor per bank.

Remember that bonds bear interest rate risk and that the rise in interest rates can lower the bond’s market value unless held to maturity. Similarly, inflation will diminish the purchasing power of your dollars, which is the scourge of fixed income. Hedge against this with your existing stock and real estate allocation or by purchasing TIPS.

For Single Premium Immediate Annuities (SPIAs), understand that you’re paying for a fixed rate of income but are completely giving up your principal. Also, you are dependent upon that company’s solvency to fund your retirement. Variations on annuities—for example, where your heir can receive a lump sum at death—usually have a lower rate of return (after all, they’re hoping to make money on you). The devil is in the details with these products.

**Lower Your Withdrawal Rate**

Let’s say you’re disappointed by dismal yields on bonds and can’t abide the idea of working another day, then the last option may be for you. Simply lowering your withdrawal rate can vastly extend the projected longevity of your retirement portfolio. Going back to our $4 million portfolio, let’s say you decide that a fixed 2.5% withdrawal rate doesn’t sound so bad. Even assuming a miserly 2% annualized return on your portfolio (maybe your spouse went to all 20-year treasuries while you were watching Yankees vs Mets), your 2.5% withdrawal rate will extend your portfolio to a Methuselahn 81 years. However, at a 4% withdrawal rate, your portfolio will last around 35 years, which isn’t necessarily a bad thing, provided you’re willing to expire on schedule to avoid penury.

**#2 Arithmetic Return vs Annualized (Geometric) Return**

With the lion’s share of this article devoted to the more practical sequence of returns, I’d like to pull back the curtain just a bit on the more esoteric concept of how returns are actually calculated. Let’s perform a thought experiment.

What is the return of a $100,000 portfolio with the returns we so thoroughly investigated above (-5%, -4%…4%, 5%)? Did you think it was $100,000? Actually, it’s $99,451.02. (By the way, it doesn’t matter in what order those returns are placed, i.e. the commutative principle of multiplication means the total return will be the same regardless.) How can that be, you ask, that the total return of a portfolio whose yearly returns average 0% are actually lower than the starting amount? You’re seeing the difference in arithmetic and geometric returns!

Arithmetic returns are those which are simply an average of the yearly returns of a portfolio. Let’s say for simplicity’s sake that your portfolio returned -50% in the first year and +50% in the second year. Your arithmetic return is 0%, but you still have a negative geometric return over the first two years. How is that? Well, if you start with $100 and lose 50%, you have $50 after the first year. If you then earn a positive return of 50%, you’ve gained $25 (50% of $50) for a total return over the two years of -25%; annualized, that number is -13.4%. That annualized return is also known as the geometric return or compounded annual return. Annualized return is the return you’d have to earn each year for an investment to grow (or shrink) from its starting value to its ending value, assuming no cash flow into or out of the investment. The algebra is devastatingly boring (no offense, quants); it’s much easier to use a financial calculator.

The most important point regarding the difference between the two kinds of returns is one of marketing.

Funds love to market (and magazines publish) arithmetic returns. Don’t be misled by the promise of princely returns only to later find them viridescent and warty. Remember, annualized returns are always lower than arithmetic unless the yearly, periodic returns are exactly the same every year.

**#3 Volatility**

I think volatility may be the most underappreciated finance word in the American investor’s lexicon, and it has far more implications than the day-to-day swings of the market. Volatility is difficult to appreciate until you know its derivation but is most commonly defined as standard deviation. Math aside, standard deviation relies on three things:

- Number of periods you’re evaluating
- Mean of those periods’ returns
- Difference between the periodic return (yearly return, monthly return, daily return, etc.) and the mean of the returns

As the number of periods increases, volatility diminishes. As the periodic returns stray further from their mean, the volatility increases. If you think in algebra (perish the thought), look up the formula for “standard deviation of a sample” and plug in some numbers yourself to see how it works.

Why is this even important? Put simply, volatility is understanding to what degree returns may differ from their average. If your time horizon for investing is 30 years, then broad market returns over months or even years are just volatility. Spoiler alert, just about every bit of data that crosses the financial news is just volatility. Remember, while historical returns aren’t perfect, they’re likely one of the best estimates retail investors have of future returns. If a stock zooms to the sky in a short period of time, it’s statistically much more likely to crash right back down to earth than to maintain its lofty perch.

Another detriment of high volatility is that it can reduce returns; this is known as volatility drag. More volatile assets, like emerging markets stocks, tend to underperform less volatile securities with the same arithmetic return. This is, in reality, the difference between geometric returns and arithmetic returns made manifest. How does this help you? When it comes to selecting assets for your portfolio, if two assets have similar arithmetic returns and long-term risk profiles, picking the less volatile asset puts money into your pocket. For bonus points, it’s also part of the reason that leveraged stock funds tend to underperform their forecasted returns.

The last thing I’d like to point out about volatility is its psychological effect on investors. The same folks who put money into the market while it’s going up are also typically the same investors who pull money out near the bottom. The crash and rapid rebound in spring of 2020 was probably a bellwether regarding what kind of investor you are. If you looked that nasty drop in the eye and bought another hundred shares of VT, you’re likely the kind of person whom volatility doesn’t bother. The other end of the spectrum is populated by those who responded to last spring’s stock drubbing with a fast exit to cash and a bottle of Mylanta. If your portfolio’s volatility causes you to sell low just to sleep at night, your portfolio is likely too volatile or too risky.

In short, volatility is like a region’s weather: variable day to day but consistent when viewed over the long term. The ugly side of volatility is the slow attrition of your returns when compared to similar but less volatile assets. Last, volatility is like a rollercoaster; if you can’t tolerate the ups and downs, don’t get on that particular ride. Full disclosure, I have motion sickness, and you’ll find me planted firmly next to the funnel cake stand.

**In Search of the Conclusion**

In summary, hedge your sequence of returns risk with safe fixed income, beware the gleam of the top fund manager’s shiny returns (he statistically won’t be there next year anyway), and treat volatility like static on the radio—tune it out the best you can and ignore the rest until the reception gets better.

*What do you think? Do you think of investing in terms of mathematics? Why or why not? Comment below!*

Invest in stocks with qualified dividends directly. Bond funds can sell early or buy inappropriate. Don’t sell your dividend stocks unless management fails. Thanks

Hey Alex, that’s a great point about dividend stocks. Their price also tends to be less volatile than non-dividend yielding stocks, which is helpful in weathering brief market downturns. I would however be concerned with two issues: first, dividend stocks still correlate too closely with the broad market (r of close to 0.9) which runs the risk of principal loss; second, dividends are paid out of earnings or cash reserves and run the risk of loss of the former and depletion of the latter in long bears or depressions. You can ladder your own TIPs, treasuries, or a mix without concern for fund mismanagement if you want to avoid that pitfall.

Serve more of this, please.

Superb post.

It’s always a good idea to become more intelligent when it comes to investing. Any knowledge with practical applications can be used as leverage. It’s not wise to just pour money into investments you don’t know much about yet people have won the money game by simply investing in basic mutual funds over decades. Although they won it doesn’t mean a person should settle for just this only.

Great article. Let us not forget Options. Very low risk strategies can be employed that can guarantee a very good return from the market trading Options.

There are no “very good” guaranteed returns. If you can’t see the risk yet, keep looking! It’s there somewhere.

I respectfully disagree

Thank you for the interesting article. I wonder, though, if the standard deviation should be divided by an investment’s return in order to make a fair comparison among investments. This normalized std deviation is simply the coefficient of variation (CV). By comparing the CV’s of various investment options, one may be able to get a more accurate assessment of risk/reward. For example, one can be misled into thinking a bond is a safe investment if its std deviation is ‘only’ 3%; however, if the expected return is only 1%, then the CV has a very high (risky) value of 3%/1% = 3. I realize that the CV cannot be applied to investments with zero or negative returns; nevertheless, I think it is a better measure of riskiness than the std deviation. I’d appreciate your insights. Perhaps we should be looking at the Sharpe Ratio, rather than std dev, since the Sharpe Ratio is more closely aligned with CV?

Dr. G, thanks for your comments. Your questions are the natural next step in the conversation about the mathematics of financial analysis. The coefficient of variation is constructed from the mean and the standard deviation and is, as you wrote, a way to sort investments by risk. I think CV’s utility is best realized when selecting among securities of like type, i.e. among corporate bond funds or syndicated real estate debt funds. The rationale is this: I am generally aiming for a certain return from each class of security and want to select between offerings of each security type to minimize risk within that type of security. I would employ CV after my general asset allocation to stocks, bonds, real estate, etc. Comparing among security types with CV or Sharpe allows me to focus on market risk. There are other considerations outside of just market risk that don’t lend themselves well to mathematical analysis. I’ll give an example, corporate bonds (investment grade) are first in line to claim against the remaining value in a company in the event of bankruptcy. If an investment grade corporate yields 5%, and a large company stock also is expected to yield 5% (via discounted cash flows or whatever method you prefer), then I’ll have to take into account that legal difference between the two types of securities. Ostensibly, I’m being compensated financially (in the form of higher return) for that difference in legal treatment between securities, but I would prefer to just be able to compare like to like and not base an investment decision on the murky waters of the legal system or bankruptcy proceedings more than necessary. Similarly, different securities have potentially different tax treatments: debt vs equity real estate, oil/gas ventures, dividend vs non-dividend stocks, etc. There are also currency risks in comparing foreign vs domestic securities that things like CV (or Sharpe) can’t quantify because of geopolitical changes. While we love to think of the market as efficient, it’s not perfectly so, nor predictable. In summary, I think you get a more accurate (if perhaps similarly precise) use of CV among security types or subtypes, and it is absolutely more useful than simple SD for comparing securities.

The sharpe measure is predicated upon similar underpinnings as CV, except you’re subtracting out the “risk-free” treasury rate and then dividing by SD. To be brief, my thoughts mirror those as for CV, except I think Sharpe is a bit more precise.

One more example to play devil’s advocate. Let’s say you can get a 3% return with a 30 year treasury and a 9% return with a junk bond (let’s assume the junk bond’s maturity is 30 years as well). Let’s also assume the treasury has a third the CV the junk bond does. In order to obtain the ostensible yield of the junk bond, you’re forced to triple leverage the treasury in order to obtain the same level of yield (or buy 3x as much). CV and Sharpe work at minimizing risk of value loss per unit yield but that’s only part of the picture.

Splendid questions by the way.

Daniel – Thank you for your informative and illustrative reply. I do have a few follow-up comments and questions.

1) Some authors equate the terms risk, volatility, and uncertainty. This ambiguity has been confusing to me. My eyes were opened, however, when I read Howard Marks comments “The difference between volatility and risk” (https://www.sr-sv.com/the-difference-between-volatility-and-risk/). His in-depth comments “Risk Revisted Again” are also a worthwhile read (https://www.oaktreecapital.com/docs/default-source/memos/2015-06-08-risk-revisited-again.pdf).

2) If you look at the first link above, there is a plot of risk vs. return in which the spread of the std deviation is drawn for four hypothetical investments. I’ll call the left-most one ‘bonds’ and the right-most one ‘stocks. As expected, the spread is the smallest for ‘bonds’. The intent of my initial question has to do with the returns that are one 1 std deviation below the mean. For brevity, I’ll call that the minimum return. As drawn, the diagram shows that the minimum return is highest for bonds and lower (actually negative) for stocks. However, it is not hard to imagine a case where the return of bonds is so low, that the minimum return for bonds is lower than for stocks. This was the intent of my initial question – can bond yields become so low that it is less risky to put money in cash and/or stocks. This seems counter intuitive and hence my confusion on how to assess the riskiness of fixed income investments that are not held to maturity or, in the case of bond funds, not held to the duration.

3) I’d like to note that the distribution of returns for the S+P 500 is not normally distributed in the critical low-return (left side) tail. As a result, any risk estimates that use a normal-distribution assumption will significantly underestimate the risk of loss. This is clearly illustrated by Ton Yiu (https://towardsdatascience.com/are-stock-returns-normally-distributed-e0388d71267e).

Sorry for the long post but, being retired, I have a special interest in understanding the risk profile of my investments and have always found the concepts a bit confusing and opaque. Thanks again!

One of the better ways to think about it are that volatility is the risk of temporary loss and real risk is the risk of permanent loss. Bernstein uses the terms shallow risk (volatility) and deep risks (inflation, deflation, confiscation, and devastation).

Thank you very much, WCI, for the reference to Bernstein and his thoughts about risk. I began reading his comments on risk and the Efficient Frontier after your post and it has really helped me sort things out. In particular, I found this comment particularly enlightening,… “Throughout the world in the twentieth century, fixed income investors have suffered permanent losses in inflationary storms which equity investors were able to avoid……. the absence of leverage and with sufficient liquidity, retirement savings are not wiped out by too high of standard deviation, but rather by real-world events.” BTW, I happened to come across a plot of the Efficient Frontier for each decade starting in 1950. Yowser! It is amazing how different each curve is depending on the decade. It really is a moving target, unfortunately, over one’s life span.

Yes, the efficient frontier is an interesting theoretical concept, but it’s almost practically useless. You can only know it retrospectively. And if you knew what was going to happen, you wouldn’t diversify anyway. You’d just invest it all in what was going to do the best.

Hey Dr. G- I will have to agree with Jim that volatility is really a temporary loss which can be mitigated by just having some cash in your retirement of a year or even 2 years. Risk gone!

But if you were just planning on having bonds as ballast in retirement and no cash because you are trying to eek out more return, then now volatility goes from a temporary loss risk to a now permanent, real risk given you might have to sell bonds when they are really down and lock in a permanent loss. then yes certain bonds can really tank and be worse than even stocks. For example, I asked a question below about using long term treasuries because risk parity folks would argue they should be the best ballast to equities given lowest correlation to equities compared to other bonds, but the problem is LTT’s can tank worse then equities given the huge interest rate risk. In a high interest rate environment, the “minimum return” that you described for LTT’s would be lower than stocks if not held until maturity.

Sounds like though you have immense financial knowledge and I bet you’ve constructed a reasonably simple portfolio and draw down strategy to meet your goals!

Hey Dr. G, some good thoughts and questions here. A few comments and maybe a bit of an answer to your questions, though more of a perspective.

Regarding the first link, I’d like to take that first graph with a grain of salt. What you’re seeing is risk/return on the x and y-axes respectively. What you’re not seeing is time on a z-axis. Take for example a cross sectional sample questionnaire of a population regarding two variables: percentage of the population who work at a formaldehyde plant and percentage of the population who develop skin cancer. While you may see a correlation between workers at the plant and skin cancer, you can’t suggest risk because it’s an observational study at one point in time. Similarly, if you track those two groups of people backward in time in that (ostensibly stable) population, you can calculate an “odds ratio” but cannot calculate a “relative risk.” This is a closer suggestion of likelihood but still cannot be truly called relative risk as the study is retrospective. If you start the study and then follow those longitudinally, then you could make the calculation for relative risk. All that to say, the graph given in the first link is similar to the cross-sectional questionnaire of a sample population. It makes no allowance for time and as such more resembles a volatility graph than a graph of risk. We can’t know future outcomes, but we can backtest portfolios of different kinds of equities. This equates to something more like an odds ratio, but it’s better than the result from the cross-sectional study we were given before. In “Stocks for the Long Run” by Jeremy Siegel, he pointed out that stocks outperformed bonds in only 61% of years after 1802, but that they bested bonds in 80% of ten-year periods and in 100% of 30-year periods. Note that I read this statistic in one of Bill Bernstein’s book (The 4 Pillars of Investing) and just shamelessly lifted that quote from his website on the same book.

http://www.efficientfrontier.com/t4poi/Ch1.htm

Regarding your comments about risk and bonds and the question thereupon predicated, “risk” is just the possibility that your money’s not there when you need it: stock market losses, inflation, confiscation/nationalization, nuclear winter, etc. like Jim mentioned. Given the most likely scenario is inflationary risk, I’d say that there’s indeed a return at which reliance upon bond income for the preponderance of your retirement cash flow. The hedge should be some reasonable allocation of equity and TIPS. How much do you need? Calculate “real” dollars of living expenses per year and calculate what you’d have to put into an annuity, CD/Bond ladder, TIPS, and what you’d get from social security (probably the least secure of all these except the annuity given the shortfall in funding). Purchase that amount of fixed income and hold to maturity.

Regarding the long left tail (skewness) of equity returns (a good read here is the Black Swan by Taleb and The Investor’s Manifesto by Bernstein), you’re absolutely correct in the short term. In the long term, compounding positively skews (long right tail) the returns of higher returning assets (chapter 6 of The Portable Financial Analyst by Kritzman), so it all comes back to time horizon of investing (overall lowering volatility) and how long you can stick to a reasonable asset allocation and hunker down.

Using expected returns makes the result entirely dependant on the value chosen. This is not too challenging for bonds at the short end. Across the range of terms, bond yields are good predictors of returns, with inflation the unknown.

For stocks, returns vary so widely that an approach based on expected returns could yield wonderful or terrible COV, depending on whether one predicted a 30% increase, a 50% drop, or somewhere in between.

Afan, hopefully people aren’t using tools like COV for short-term modeling of stocks. The single best predictor of short term stock returns is the arithmetic mean of past returns, however, if one wanted to do such a thing. I would hope one would use COV or Sharpe as tools for a security class over the course of a decade or more, which is still fairly short term.

dominating article dude! the hardcore math is awesome- got to break out the my AP stat book from high school! and also I did have to google some of those words you used as well- Methuselahn- really- awesome:)

Danny what do you think about the risk parity folks who say the best way to balance out equities in your portfolio is long term treasuries because of they have the lowest correlation to stocks? Does this mathematically make sense? And does that low correlation between these 2 asset classes hold in all types of market environments? Is there another statistical measure that would disprove this risk parity claim, may CoV or Sharpe ratios like mentioned above?

Hey Rikki, thanks for the comment; hope you got something useful out of it! My best knowledge of risk parity is admittedly limited. What I understand about risk parity is the use of options/leverage to boost returns on otherwise less-risky securities like treasuries. The thought is that you not only get the lower correlation to equities with something like treasuries but that you can get better returns both out of the security being levered individually and from the portfolio as a whole with total lower risk. Basically, it’s a leverage/option strategy on risk-adjusted return. The “parity” part of risk parity means that the total risk is equal among asset classes in a portfolio by design. Risk parity portfolios did well during ’08-’09 as the flight to safety from equities and real estate simultaneously led to huge returns in treasuries.

A few thoughts on that principle in general. The first is that, outside of leverage/options use, risk parity portfolios fall *within* the Markowitz “efficient frontier.” It is so by design and necessitates (in order to obtain equity-like yields) the use of leverage in order to bolster returns. Second, leverage is a fickle financial mistress. Long-term capital management and Lehman Brothers, one a hedge fund full of Nobel laureates and the second one of the oldest and largest investment banks in the country, folded despite exceedingly well-intentioned theories behind why their use of leverage was safe. Third, the best time to lever treasuries would be when yields aren’t this low. 30 year treasuries are still yielding less than 2%, and best estimates of inflation year over year as of writing are over 5%. Triple-levering treasuries after fees incurred for active management and options premiums would probably still lose money in today’s environment. Fourth, leverage of even safe assets can still lose big. The phenomenon known as stagflation would be devastating to the 60/40 of equity/levered treasury portfolio. Fifth, leveraged ETFs are pretty tax-inefficient and given that most 401k providers and administrators don’t want to (ironically) offer risky, leveraged investment options means you’d have to hold them in a taxable brokerage account or a checkbook IRA. The brokerage account taxability makes that investment strategy even less profitable. Sixth, and this is a bit glib but back-tested doesn’t mean future proofed.

TL:DR I’d be very cautious of risk parity solutions. Research shows in general that lower volatility portfolios do tend to outperform the market over the long run. Maybe a factor tilt would be a better long-term play than using options? Also, as an aside, leveraged funds experience “decay” in their returns due to increased volatility. Though this is less of an issue with treasuries, it still dampens returns.

Regarding the Pearson (correlation) coefficient, it should hold in most market environments *over the long run.*

I would backtest risk-parity solutions over thirty year periods against simple 60/40 splits of a total stock equity equivalent and 20 year treasuries with annual rebalancing of the latter, net of inflation-adjusted fees/premiums/taxes for both portfolios, as the determinant of success. I don’t have the tools to compute such a feat, but maybe WCI could convince someone like Rick Ferri to do it (Rick, if you do this, publish it in the CFA Journal). I imagine you’ll find some periods where risk parity performed well and some where it performed poorly, though I’d be willing to place some money on more the latter than the former. CoV and Sharpe would generally support the more complex risk parity portfolio as it’s designed on a *risk-weighted* basis, to answer your question specifically.

thanks man, seem your knowledge of risk parity is not so limited. yeah, I don’t think I would subscribe to the risk parity folks love of levered funds nor obsession with gold, but the long term treasury thing I found interesting. I was just going to go 60/40 in retirement and use just an intermediate government bond fund, but was intrigued that a long term gov’t bond fund might actually be less risky. Although not levered, I would think a long term treasury fund would have gotten hammered along with stocks during the stagflation bear market of 73/74′. Unfortunately, using portfolio visualizer or portfoliocharts to try and model a portfolio with long term treasuries is not possible as these type of funds don’t go back that far.

by the way, given the title of the post I guest your a poison fan? My first name is spelled the same as the drummer- we are the only 2 dudes in the whole world that spell our name Rikki!

I agree with your points for sure, except I would still be leery of interest rate/inflation risk with long term govt bonds. I see rising government debt as a big incentive to devalue the currency, and the massive $$ printing we are doing (senate just passed 1 trillion infrastructure bill) lends to that fear. 60/40 is very reasonable in retirement provided the 40% will cash flow your needs adequately. For me, I’d do TIPS over treasuries or fixed rate instruments. Haha you called me on the Poison reference. Good stuff!

would you think though that you might not need TIPS as equities are already a good hedge against inflation if you are doing a 60/40 portfolio? And the only time I can think of where equities might not hedge inflation would again be in the 73/74′ bear market where equities tanked in the setting of high inflation, but if you have treasuries those would have gone up and you could draw down those, right? I am just trying to construct my future 60/40 portfolio to be as simple as possible yet a portfolio that will react dynamically and can hedge against different market conditions, whether it’s inflation/deflation in the setting of a bear market.

TIPS and equities hedge inflation in different ways so I think it’s easy to justify the presence of both in a portfolio.

Agree with Jim. Consider that equity markets don’t always “behave” the way they’re purported to behave. You may have an inflationary environment with low equity returns and flat or negative capital appreciation in those same equities. You’d be glad for TIPS indexed to inflation. (basically the stagflation you mentioned)

Thanks for an Interesting article, Dan! I saved it for when I want to take some time to read carefully and learn from it.

A spreadsheet model or two would, or will make it easier for me to read, understand the math and learn from it.

Appreciate your good contribution!

–Fred Huffman

Fred, I had some more technical details and examples in the original version. It was getting a bit ponderous for a blog post, however. I’ll see if I can post a link to some examples and math in a few days!

Great information, thank you!

Great article, thank you for posting. I look forward to seeing more like this!

Thanks, Rikki, for your comments about bonds and risk parity. I have to read up on risk parity since that is a new concept for me. I found Daniel’s comments in that regard to be really instructive. It is really nice that his responses to comments are so comprehensive. Yes, I have a very, very simple portfolio. BTW, the ‘Dr’ in my name refers to a doctorate in engineering and not an MD.

Great article on relevant metrics that every investor should understand.

Great explanation on volatility.

Volatility is such a dangerous thing because people that are not afraid of losing money will be too optimistic and think “wow, this can only go up!” – and they almost always lose a lot of money over time.

I think in efficient frontier theory, an investment that has the same expected return as another is superior if their standard deviation of returns (volatility) is less. It seems that the upside from volatility never compensates for the downside.

Glad you liked it. Agreed, volatility really only benefits speculators!

nahh man I love volatility! It allowed me to buy stock cheap last year when they were on sale 🙂 but yes I agree with you if you don’t know your true risk tolerance volatility then is very dangerous and has torpedoed many investors in the past.