Thursday, July 27, 2017

When Big Numbers Attack: Corporate Defined Benefit Plans are Not the Problem

I started my career working closely with corporate pension plans, thus when I saw the following article in my twitter feed causing alarm I thought there might be an interest in some context and a reality check into the supposed corporate pension crisis. Note that state and local pensions are a completely different story.

Let's go to Bloomberg's article titled 'S&P 500’s Biggest Pension Plans Face $382 Billion Funding Gap':
People who rely on their company pension plans to fund their retirement may be in for a shock: Of the 200 biggest defined-benefit plans in the S&P 500 based on assets, 186 aren’t fully funded. Simply put, they don’t have enough money to fund current and future retirees.The situation worsened for more than half of these funds from fiscal 2015 to 2016. A big part of the reason is the poor returns they got from their assets in the superlow interest-rate environment that followed the financial crisis. It’s left a hole of $382 billion for the top 200 plans. 
The reality is corporate pension plan participants are completely fine and the article simply regurgitates a straw man argument that has cost employees the security that a defined benefit "DB" pension provides.


I'm going to oversimplify things a bit, but at a high level corporate pensions have assets (straight forward - they are what they are) and liabilities which are the benefits that participants have earned and are owed. These liabilities are a bit more complex because even if you know roughly what is owed in the future, you don't know exactly what those liabilities will cost in today's dollars. 

The way a corporate pension backs into this value is through a discount rate. The end result is liabilities are worth less today than in the future given the present value of a dollar today is worth more than in the future. An example... assuming liabilities for a plan are $100 / year for 25 years discounted at 4.3% (more on that later), they are worth $1614 (less than $100 x 25 = $2500) as seen below.

Cash Flows Discounted Back to a Present Value at a 4.3% Discount Rate Each Year

Total value of 25 years of $100 / year discounted back at 4.3%


$382 billion!!!! 

That number seems big, but notice there is no mention of the relative scale of that. According to P&I as of 9/30/16:
Among the 200 largest retirement plans, assets totaled $6.79 trillion as of Sept. 30, up 6.2% from the year earlier. Of this, $4.83 trillion belonged to DB plans (up 5.5%) and $1.96 trillion to DC plans (up 8%).
So that big $382 billion number was ~8% of total plan assets as of 9/30/16 (global stocks have also happened to go up ~17% since that time so the funded status has likely improved quite a bit since). 


Corporate pensions are required to discount liabilities at a rate roughly equal to a corporate bond of similar duration as their pension liabilities. The rationale being that's the rough rate a debtor would require, but also because when a plan is fully funded (i.e. 100% assets to cover future liabilities at this discount rate) the plan could simply invest the proceeds in long corporate bonds and call it a day (it's more complex than that, but close enough for this post - it also happens to be the basis of liability driven investing "LDI" and why pensions own a lot of long bonds). The discount rate is extraordinarily low right now given where market rates and spreads are and can be thought of how much it would cost a corporation to fund their underfunded status. So a big part of the reason some plans are underfunded hasn't been due to their asset performance in the "superlow interest-rate environment that followed the financial crisis" per Bloomberg, but rather because their liabilities have increased in present value terms due to the superlow interest-rate they are discounted by.

Looking at Intel's latest annual report (the poster child in the article as they are the most underfunded plan in % terms), we see they used a 4.3% discount rate at year-end. 

This rate has huge implications for the liability calculation. Assuming a move up in rates to just 5%, we can see that the present value of liabilities in the previous examples goes down more than 6%. In reality, assuming pensions have a duration of ~20 years, a ~40 bp higher rate as of 9/30/16 would have pushed the underfunded status of pensions to $0 without a change in asset valuations.


Back to Bloomberg:
Last month, the 70,000 participants in the United Parcel Service Inc. pension plan learned they won’t earn increased benefits if they work after 2022. Late last year DuPont Co. announced it would stop making payments into its pension plan for 13,000 active employees, and Yum! Brands Inc. offered some former employees a lump-sum buyout to offload some of its pension liabilities. General Electric Co. has a major problem. The company ended its defined benefit plan for new hires in 2012, but its primary plan, covering about 467,000 people, is one of the largest in the U.S. And at $31 billion, GE’s pension shortfall is the biggest in the S&P 500.
Now the reality of what this means...
  • UPS / DuPont: these moves have nothing to do with past pension liabilities or risk to participants. That has to do with corporations de-risking their balance sheets by moving future benefits from defined benefit (they have the obligation to pay an amount) to defined contribution (a one off payment into a 401k). Benefits that have already been earned are not changed.
  • Yum! Brands: this is an option for employees to leave their plans at the current present value of their liabilities. Options have positive values for option holders, so this is a good thing.
  • GE: $31 billion is certainly GE's problem, but it is not their employees issue unless the company goes bankrupt, cannot make the payment in bankruptcy, and the participant is above the threshold guaranteed by the PGBC (a government agency that backstops corporate pensions for a fee - and is required). None of this likely matters as GE has an equity cushion for participants of $222 billion (i.e. their market cap) and if GE wanted, they could simply add $31 billion in debt to fund their plan and make this optical issue go away (something they may be forced to do down the line in increments given rules)
As for Intel (the poster child as the least funded pension), they have unfunded obligation of $2 billion or less than one quarter of earnings.

Monday, July 24, 2017

The Case for the Harmonic Mean P/E Calculation

The most recent "analysis" seemingly spreading like wildfire across the perma-bear community was performed by Horizon Kinetics in their most recent quarterly commentary. Their claim is that the price-to-earnings of the Nasdaq (or any index really) is much higher than reported because we are being fed a manipulated harmonic mean rather than arithmetic mean for the price to earnings ratio (don't worry, I'll explain the difference). While the piece also claims excluding non-earners from the calculation is wrong (something I also don't agree with), I'll ignore that portion for now* as it is more nuanced, a separate argument in their piece, and because their specific argument for the arithmetic mean is so clearly wrong.


Let's start with a case study Horizon Kinetics provides outlining how they believe the P/E for an equal weighted three stock portfolio (with an investment of $1 million to each) should be calculated.

One business earns $100,000 per year, so it has a price‐to‐earnings ratio of 10x; the second earns $50,000, for a P/E ratio of 20, and the third earns only $20,000 and so has a P/E of 50. This last one is probably situated on a high‐ growth street corner. Averaging the three P/E ratios of 10, 20 and 50 means that the average P/E of the 3‐ company portfolio is 26.7x. So far, so good.
Not a good start...

The 3-company portfolio clearly does not have a P/E of 26.7x when you take a step back and think about what you as an investor own in aggregate. The companies in the case study earn $100,000 (10% yield on $1 million) + $50,000 (5% yield on $1 million) + $20,000 (2% yield on $1 million) = $170,000, which is a 5.7% yield on $3 million total investment. A $3 million total investment divided by $170,000 of earnings = (1/ 5.7% yield) = a P/E of 17.65x, which is 66% LOWER than their calculation.

The easy way to view the correct harmonic mean calculation is to think about what you own in terms of earnings yield (getting to an average earnings yield and then backing into the P/E is the harmonic mean calculation). In this example:
  • Company A: 10x P/E = 10% earnings yield (1/10)
  • Company B: 20x P/E = 5% earnings yield (1/20)
  • Company C: 50x P/E = 2% earnings yield (1/50)
(10% + 5% + 2%) = average yield of 5.67%. 1/5.67% = the correct 17.65x aggregate P/E.

Visualizing this makes it clearer. The left-hand chart shows the earnings yield for each company, while the right hand chart shows the contribution from each company in total (the earnings of each company divided by the whole $3 million investment - then stacked). We'll revisit the right hand chart to show how an extreme multiple can overly influence the arithmetic mean of the P/Es when we review their second case study.


Horizon Kinetic's next case study is worse because the error in the result is so obvious as it includes a company with an extreme high P/E ratio.
Observe the following hypothetical equal‐weighted 4‐stock portfolio consisting of a range of low, somewhat high and egregiously high‐valuations, ranging from 10x to 300x. A simple average results in a portfolio P/E of 90x.
  • Company A: 10x P/E or 10% yield
  • Company B: 20x P/E or 5% yield
  • Company C: 30x P/E or 3.3% yield
  • Company D: 300x P/E or 0.33% yield
An average P/E of (10x + 20x + 30x + 300x) / 4 = 90x implies an earnings yield of just over 1% (1/90). Compare this to the average earnings yield of 10% + 5% + 3.3% + 0.33% = 4.67% average, which gets you to a correct aggregate portfolio P/E of 21.4x (1 / 4.67%).

Visualizing this case study again shows their error more clearly. On the right hand side we can see that the earnings contribution of a 25% weight to the first three stocks alone yields more than 4.5% (10% x 25% + 5% x 25% + 3.3% + 25% = 4.575%), so by their rationale the earnings of company D contributes -3% to the overall portfolio (i.e. something akin to company D losing $140,000 on their $1,000,000 investment instead of having small, but positive earnings).

And of course, their ridiculous conclusion.
That completes the strange journey of transforming a fairly understandable, if alarming, P/E of 90x into the more comforting Harmonic Mean P/E ratio of only 21.5x.
And the even more bearish takeaway of an investment in the Nasdaq 100.
No active manager would be permitted to manage a concentrated, high‐P/E portfolio for an institutional client.

* you are paying a price to own the lack of historical earnings (which is a case for including these companies), but the fact is these non-earners have often been the fastest growing companies in the Nasdaq, thus including their negative historical earnings ignores their future potential (a case for excluding these companies from the valuations calculation)

Tuesday, July 18, 2017

EconomVIX...A Summary of Past VIX Posts

RCM Alternatives has a great piece (HT Tadas) outlining what the VIX is, the market for VIX related products, and how to think about volatility as an asset class. It also happens to contain my new favorite quote for anyone thinking about trading volatility:

Still, if you cannot see the VIX futures curve in your head, burning $100 bills is probably more profitable than trading them.
I'll piggyback on the RCM piece given the interest in volatility trading strategies (due to the remarkable run of some of the short VIX ETPs) and link to old posts that I've previously done on the subject that I thought might be helpful.

What Exactly Does the VIX Tell Us?

How a Low VIX Can Remain an Expensive Hedge

A Framework for a Short VIX Allocation

Breaking Down Volatility of the VIX

Utilizing the Money Sucking $UVXY to Improve Risk Adjusted Returns

Using the VIX Futures Term Structure to Reduce Equity Exposure

Adding a VIX Signal to Momentum

The Case for a Steady Volatility-State Managed Portfolio

Thursday, May 25, 2017

Yes. Demographics and Economic Growth Matter for Equity Returns

Quick note... for those not already listening, my buddy Patrick O’Shaughnessy has one of the (if not the) best investing podcasts out there with his podcast Invest Like the Best. Each week he sits down with some of the best capital allocators, investment thinkers, etc... in the world and really allows his guests to share deep insights. I highly recommend it to anyone reading this who isn't already doing so.

"Real GDP Growth Doesn't Matter for Equity Returns" is Wrong 

Patrick's guest this week was David Salem, the founding president and CIO for The Investment Fund for Foundations. The discussion was great as always, but I would like to focus on one small aspect related to where in the world he currently finds value. He specifically makes the case for Asia ex-Japan ex-China for a number of reasons I agree with (value and alignment of management with shareholders), but he seemingly gets one aspect (which he views as a negative) wrong based on his view of what historical analysis reveals. The point of this post is to outline this flaw with supporting data because it's a common theory and one that can seemingly be dismissed when the data itself is viewed. It also happens to makes his case for an allocation to Asia ex-Japan ex-China even stronger.

First to David (bold mine):
We also have some money allocated under present conditions to I’ll call it Asia ex-Japan ex-China. Here’s where a careful study of long-term capital market history will tell you, and my favorite source of this is of course is Elroy Dimson, Paul Marsh, and Mike Staunton’s book Triumph of the Optimist and all the sequels to it, will tell you that high growth economies that are flattered by relatively high growth rates of the GDP level and by favorable demography tend to generate surprisingly, perhaps to many people, sub-par returns. So. You’re a value guy, I’m a value guy. We get that. 
So, why would we be chasing return for long-term capital in Asia ex-Japan and even ex-China, and it’s because I’d say almost notwithstanding the favorable demographics and the relatively favorable debt profile the prices, the current prices at which interest can be acquired in well managed businesses where the managements have a sufficient, not perfect, but sufficient alignment of interest with outside shareholders, they tend to be family controlled and family dominated.
To summarize… he has found value in Asia ex-Japan ex-China DESPITE its favorable growth and demographics. To be blunt… this appears to be a common mistake and one that is likely flat out wrong. Here are other heavy hitters quoting Dimon, Marsh, and Staunton making the same case.

The Financial Times, Rising GDP not always a boon for equities (bold mine):
Analysis by Elroy Dimson, Paul Marsh and Mike Staunton of the London Business School of 19 major countries between 1900 and 2011 shows that the correlation between the compound real rate of return on equities and the compound growth rate of real per capita GDP is minus 0.39. Investors would have been best off investing in the most sluggish economies.  
Similar analysis of 15 major emerging markets between 1988 and 2011 produces a remarkably similar negative correlation of minus 0.41. To be fair, some other combinations produce correlations nearer to zero. 
But, to the chagrin of emerging market bulls, whichever way the data are interrogated, a meaningful positive correlation between GDP growth and equity returns remains elusive.

The Economist, A Puzzling Discrepancy:
The annual report on markets by Elroy Dimson, Paul Marsh, and Mike Staunton of the London Business School (produced in association with Credit Suisse) is always good value and this year's effort is no exception. The main theme is related to emerging markets and will be the focus of this week's column. But one oddity emerged in the course of the report that is quite difficult to explain and is worth exploring in more detail. 
An oft-quoted argument for investing in emerging markets is their superior economic growth. But the professors have pointed out in the past that economic growth and equity returns are not correlated at all. 
This Economist article was in reference to the 2014 Credit Suisse Yearbook (which contains all the pertinent data) and is fortunately still available online. Let's take a look. The data for the following charts were all pulled from Table 1 in the pdf (reproduced below for any of you nerds that wants easy access).

Decomposition of Real GDP Growth and Economic Returns (1900-2013)

Real GDP Population Growth Per Capita Real GDP Real Return on Equities
Canada 3.63% 1.65% 1.95% 5.75%
Australia 3.35% 1.61% 1.71% 7.37%
USA 3.29% 1.27% 1.99% 6.45%
South Africa 3.20% 2.08% 1.10% 7.39%
New Zealand 2.89% 1.53% 1.34% 6.01%
Mean 3.27% 1.63% 1.62% 6.59%
Ireland 2.83% 0.05% 2.77% 4.09%
Portugal 2.70% 0.61% 2.08% 3.66%
Sweden 2.70% 0.54% 2.15% 5.77%
Spain 2.66% 0.82% 1.82% 3.62%
Switzerland 2.16% 0.80% 1.36% 4.41%
Mean 2.61% 0.56% 2.04% 4.31%
Japan 3.68% 0.94% 2.71% 4.11%
Norway 3.19% 0.70% 2.47% 4.26%
Finland 3.04% 0.63% 2.39% 5.31%
Netherlands 2.83% 1.06% 1.75% 4.95%
Italy 2.71% 0.53% 2.17% 1.91%
Denmark 2.49% 0.70% 1.78% 5.21%
France 2.30% 0.43% 1.87% 3.17%
Belgium 2.25% 0.43% 1.81% 2.63%
Austria 2.21% 0.31% 1.89% 0.67%
Germany 2.03% 0.37% 1.66% 3.23%
UK 1.84% 0.39% 1.45% 5.33%
Source: Dimson, Marsh, and Staunton

The Issue: Per Capita GDP is the Wrong Measure

The first chart is a reproduction of the chart from the yearbook that is commonly shared to make the case that real GDP and real equity returns have a limited or negative relationship. Even Dimson, Marsh and Staunton state investors do not capture economic growth (bold mine) based on the downward slope and r-square of 0.10.
The horizontal axis measures the growth in per capita real GDP, while the vertical axis displays the annualized real return, including reinvested dividends, from each equity market over the entire period since 1900. In the cross section of countries, it appears that equity investors do not capture benefits as a result of economic advancement, as measured by per capita real GDP.

Let's think about the apples to oranges issue here. Per capita GDP is the level of GDP per person, whereas equity growth is the equity returns in aggregate. This would be like wondering why you can't lose weight after eating a full pizza every night because it only has 300 calories per slice. What matters isn't the calories per slice, its what is the calorie level (economic output) in aggregate for the full pie.

Real GDP Accounts for THE Most Important Piece... Population Growth

Now let's take a look at an apples to apples comparison... the total real economic output produced (real GDP) vs the total real equity return over the same period. We now see a scatter plot that moves up and to the right (vs down to the right). I would note that this exact chart is produced ON THE SAME PAGE as the above chart in their 2014 yearbook, but has seemingly been ignored.

Despite the stronger relationship between real GDP and real equity returns, there is an even stronger relationship out there... population growth (i.e. the piece REMOVED from the per capita GDP calculation). I have not found this specific chart produced anywhere else in their yearbooks, but at a 0.56 r-square it is clearly the strongest relationship of the three (despite the lowest r-square result most often quoted), thus explains when you remove it why you get a non-existent relationship.

Summary: The Case for Asia ex-Japan ex-China is even Stronger

To bring this full circle, David Salem outlined that he has found value in Asia ex-Japan ex-China DESPITE its favorable growth and demographics. Instead, there is a case to be made that the allocation may make sense ONLY due to the favorable growth and demographics (it certainly does not appear to be a reason not to own this region). Combined with the attractive valuations in these markets, especially relative to the developed world, there is a very strong case to be made for diversifying to emerging / high growth countries.

Monday, March 20, 2017

Capturing Mean Reversion Via Momentum

Ben from A Wealth of Common Sense recently posted an update of his "favorite chart", which stacks the calendar year performance of a variety of asset classes.

As Ben points out:
There’s little rhyme or reason for how these things play out from year-to-year so it provides a good reminder for investors to understand that any single year’s performance in the markets is fairly meaningless.
While the year to year performance is rather random, this post will weigh the benefit of mean reversion (allocating to risk assets that have underperformed and stack low on the quilt) vs momentum (allocating to risk assets that have worked well and rank high on the quilt).

Asset Class Performance Over Longer Time Frames

The chart below shows the same asset classes that Ben highlighted, but rather than rank the asset classes by calendar year performance, it ranks them by rolling five year returns as of the end of February for each year (I picked end of February simply because that was the last data point).

There is a lot of interesting information here. One of the more interesting aspects is how mean reversion AND momentum can be seen over various time frames. Asset classes appear to be mean-reverting over longer periods (note the strong relative performance of US equities at the beginning of the 2000's, the poor relative performance through the mid to late 2000's, and the strong relative performance we are currently experiencing - while EM and international stocks were the opposite) and asset classes that have done well continue to do well (momentum) over shorter periods (note that if something did well the previous five years, it tended to stick around in the years to follow).

Allocating by Mean Reversion and Momentum

Using the February 1997 data as a starting point, we can look at the performance over several different time frames to determine whether mean reversion or momentum makes more sense. In this example I narrowed the universe down to equity-like holdings (US - small, mid, large-, International, EM, and REITs) as I personally don't necessarily believe commodities, cash, or even bonds should always be long-term strategic investment holdings (a conversation for another day).

Five year allocation: In this example, an allocation to the worst two performing asset classes over the last 5 years (mean reversion) and the best two performing asset classes (momentum) are held for the next five years. There is a HUGE caveat in this analysis as since 1997 there have been only 3 periods of rebalancing (so take the exact results with a grain of salt, though this has been verified in past research performed by Meb Faber).

Mean Reversion Momentum
2002-2007 21.10% 10.81%
2007-2012 1.80% 2.30%
2012-2017 8.67% 6.80%
Geometric Return 10.24% 6.58%

One year allocation: The reason I didn't bother to build out the five year allocation analysis further (to remove the issue outlined above) is that it doesn't really matter once you see the shorter-term results. In this example, we allocated to the bottom two / top two performing asset classes from the previous five years, but held on for the following 12-months (more data points than above, but we'll have a lot more below).

Mean Reversion Momentum
2003 -15.3% -19.9%
2004 64.5% 50.9%
2005 13.3% 21.0%
2006 13.9% 21.3%
2007 16.9% 23.5%
2008 -8.1% 4.4%
2009 -43.0% -53.0%
2010 76.9% 73.7%
2011 30.8% 26.2%
2012 -1.1% 1.4%
2013 15.2% 7.8%
2014 7.0% 18.7%
2015 2.9% 17.1%
2016 -19.0% -7.8%
2017 23.1% 22.0%
Geometric Return 8.0% 9.7%

Monthly allocation: In this case we allocated to the bottom two / top two performing asset classes from the previous five years, but held on for the following one month (performance is shown for the 12-months ending February of each year).

Mean Reversion Momentum
2003 -15.2% -14.7%
2004 48.7% 57.4%
2005 13.2% 12.3%
2006 13.9% 34.9%
2007 14.1% 23.9%
2008 -8.2% 5.4%
2009 -42.1% -56.1%
2010 78.8% 73.1%
2011 35.5% 24.4%
2012 -1.2% 1.6%
2013 17.4% 5.7%
2014 4.4% 24.3%
2015 3.0% 13.8%
2016 -18.9% -9.8%
2017 23.2% 23.6%
Geometric Return 7.5% 10.1%

Mean Reversion Captured via Momentum

Asset classes mean revert over longer periods, but this analysis provides a good starting point for the hypothesis that it can can be captured more effectively through momentum than by allocating to a down-an-out area of the market. The chart below shows that the best performing asset class was emerging markets for an extended period roughly 5 years after being the worst ranked asset class in 2002, REITs in 2012 were the best after being the worst ranked asset class during the financial crisis, and US stocks more recently were the best after ranking poorly for much of the period following the financial crisis.

For an investor the takeaway is good news... rather having to allocate to an underperforming asset class over the past x years, simply wait for that underperforming / cheap asset class to start performing well. While you may miss the exact turn, you may be able to capture the longer run success when the asset class starts working without having to deal with the pain that created the opportunity. 

Thursday, February 23, 2017

The Potential Return-Free Risk of Bonds

I've read too many posts / articles that outline why a rise in rates is good for long-term bond investors (as that would allow reinvestment at higher rates). While this can be true depending on the duration of bonds owned and/or for nominal returns over an extended period of time, it is certainly not true over shorter periods of time and absolutely not true for an investor in most real return scenarios... even over very long periods of time.


I'll take a step back and go to an interesting question posed by George Pearkes the other day (abbreviations removed for clarity):

Anyone care to estimate how big losses would be if you rolled 10 year US Treasuries at constant maturity for next 10 years w/ 25 bps of rate rise per quarter?
My response (completely translated from Twitter speak for clarity) was:
  • A 25 bp move per quarter is roughly a 2% loss per move given the current duration of around 8 years (0.25% x 8 = 2%).
  • So an investment would lose money each quarter until the yield (currently 2.4%) is greater than 8% (8% / 4 quarters in a year = 2%, which would offset the loss from the rate hike). 
  • Given an 8% yield would happen during year 6 (6 years x 4 quarters x 0.25% = 6% hike + current 2.4% = 8.4% at the end of year 6).
  • Year 6 is around midway of the 10 year horizon, so total return would be close to 0% cumulative over the ten years.
This was pretty close to being correct. The chart on the right shows the path of rates assuming a 0.25% rise per quarter, while the chart on the left shows the cumulative return for an investor (slightly above 0% over this period).

In the above example, a 0.25% rise per quarter (1% per year) is pretty extreme, but even a smaller 50 bp / year rise would result in lower returns (~10%) than no move (1.024^10-1 = ~27%).


Another problem for investors is that a rise in nominal rates does not occur in isolation. A rise is typically a function of a credit concern (much more likely with corporate / muni debt than treasuries), supply / demand imbalance, or inflation. For this exercise, I'll focus on the impact of inflation.

Nominal rates moved relatively closely with inflation from the late 1980's until the global financial crisis as investors demanded a real rate (nominal rate less inflation) of ~2% over that period (the recent period of QE pushed them much lower). It's the 1970's that highlights the real risk of inflation in a rising rate scenario; inflation overshot expectations, which created an environment in which inflation pushed real rates into negative territory (bond investors lost from rising rates and negative real carry).

Back to the scenarios... taking the same 0.25% rise in rates per quarter (1% / year) shown above and applying two alternative inflation paths, the left hand chart below shows the return profile if real returns were a constant 5% (i.e. inflation was consistently 5% below nominal treasury yields - in itself very optimistic for investors), while the right hand chart shows the return profile if real returns were a constant 2% (i.e. 3% higher inflation on the right hand side than left). In either scenario, the returns are decimated (not surprisingly... when inflation is higher, they are decimated more).

If you think the nominal return paths are too pessimistic (likely), let's take a look at a few scenarios that seem like pretty realistic possibilities based on market expectations for both rates and inflation. On the left hand chart we show a 20 bp rise per year with 1.5% real yields (settling at ~4.5% yields with 3% inflation) and on the right hand chart we show a 15 bp rise per year scenario with 0.5% real yields (settling at ~4% yields with 3.5% inflation). In each of these scenarios there are cumulative losses over ten years in real terms.

My takeaway... if you think rates are poised to rise in the future... think twice about owning them. While the risk-free return of cash is hard to accept at current levels, that return may end up being more attractive than the return-free risk of bonds if rates do rise.

Monday, January 9, 2017

The Asymmetry of Reaching for Yield at Low Spreads

Bloomberg Gadfly's Lisa Abramowicz (follow her on twitter here) outlined in a recent piece The Credit Boom that Just Won't Die the insatiable demand for investment grade credit.

Last month, bankers and investors told Bloomberg's Claire Boston that they expected U.S. investment-grade bond sales to finally slow after six consecutive years of unprecedented issuance. But the exact opposite seems to be happening, at least if the first few days of 2017 are any guide. The debt sales are accelerating, with the biggest volumes of issuance ever for the first week of January, according to data compiled by Bloomberg.
Lisa followed up this morning with a tweet outlining similar demand within high yield pushing the spread to treasuries to 3.83%, the lowest level since September 2014. That 3.83% option adjusted spread is the excess yield a high yield investor demands above a treasury bond of similar duration. Note that I did not say to be paid above a treasury bond of similar duration. The reason is historically high yield bonds have (on average) returned ~3.5% less than their yield going back 30 years due to credit events (the chart below is from a previous post The Case Against High Yield).

As a result, with a current option adjusted spread of 3.83%, if high yield bonds returned what they have returned relative to their spread ON AVERAGE since 1986, high yield bond investors should only expect a forward return that matches that of a treasury bond with similar duration (with a whole lot more risk).

But things can get worse

The next chart compares the option adjusted spread "OAS" of the Barclays High Yield Index relative to the forward excess performance vs treasury bonds of a similar duration since 1995. Note that yield to worst data goes back to the mid 1980's, whereas OAS only goes back to the mid 1990's hence the different time frame than the example above. The chart clearly shows the strong relationship between the two, but note that the upside potential of high yield is much more symmetrical at higher OAS levels, whereas there is more downside when starting OAS is at lower levels. This is driven largely by where in the credit cycle we are when OAS is low (often near the end) vs when OAS is high (often near the beginning).

In fact, we can see in the chart above that when we were at similar levels of OAS as we currently sit, high yield has never provided excess returns to treasuries more than its starting OAS. In fact, the chart below breaks out each of these ~80 starting periods when OAS was less than 4% and we can see that not only did high yield bonds underperform their starting OAS in every instance, the likelihood of underperforming treasuries has been much more prevalent (and with a higher degree of underperformance) than the likelihood of outperforming treasuries (the red line shows that on average high yield bonds underperformed treasuries by 2% at similar levels).

So if you are looking at the low yields of treasury bonds and searching for an alternative or believe that the spread of high yield may help cushion performance from any further rise in treasury rates, I would tread very carefully.

Thursday, December 22, 2016

Using Absolute Momentum to Positively Skew Calendar Year Returns

There are instances where I "borrow" an idea from someone (actually... most of my posts were at a minimum inspired by someone else). In this case, I am stealing the initial concept from Ryan Detrick who posted the following chart of annual U.S. stock returns going back ~200 years as there is a lot of interesting information in his chart. As Ryan pointed out in a supporting post most returns were between 0% and 10%, but returns varied pretty broadly during recessions:

Yes, more recessionary years saw negative returns more often than not, but surprisingly there have been some strong equity returns during years that had an official recession take place. Obviously most of these big gains took place as the recession was ending; still, this is eye-opening and reinforces not focusing too much on just fundamentals, but also incorporating valuations and technicals.

I recreated his chart below using Ibbotson data going back to 1927 (the data goes back to 1926, but you'll see shortly why I selected 1927) and to highlight his point on recessions, I added yellow cells to show final years of a multi-calendar year recession to clearly show the strong performance available for investors that owned stocks after the stock market was already crushed during the initial stages of the recession. Note there are some differences in which years we show as being recessionary. I am not sure of Ryan's source, but I just went to Wikipedia.

Avoiding the Downturn and Capturing the Upturn

So is it possible to avoid much of the drawdown at the start of a recession and capture the rebound? 

Fortunately, it might just be. 

The below recreates the above table, but with one slight twist. Instead of a buy and hold allocation to U.S. stocks, the below utilizes the following allocation rules:
At each month-end, if the total return index is greater than the 10-month moving average of the total return index stay in stocks... otherwise buy U.S. treasuries.
The 10-month moving average calculation pushed the first calendar year of the strategy to 1927, hence the 1927 start in both charts.

Remarkably, while this simple model did reduce some of the strongest calendar years, it resulted in no calendar year return of less than -25% and "converted" most of the tough recession years to much more manageable down years. As remarkable, this simple momentum model was able to capture most of the rebound years (i.e. the yellow cells showing the last year of a multi-year recession), as well as the strong performance of the two positive returning recessions (1945 and 1980).

Tuesday, December 13, 2016

Betting on Perfection

To earn a decent return going forward, how reliant on multiple expansion are buy and hold investors in the S&P 500? Let's take a look at one measure.

The first chart plots forward 10-year returns for the S&P 500 at various starting 5 point "CAPE" valuation buckets (i.e. less than 10x P/E all the way through above 30x) against the change in the starting P/E relative to the P/E in ten years (i.e. whether the P/E multiple expanded or contracted) going back to Ibbotson data inception in 1926. The chart shows the strong relationship between forward performance and the change in the multiple, as well as the impact of the starting valuation (the cheaper the starting valuation, the higher the returns and the more likely the index will exhibit multiple expansion, whereas the more expensive the starting valuation, the lower the returns and the more likely the index will exhibit multiple contraction).

The next chart plots the same information, but uses forward real returns (i.e. adjusted for inflation). It is interesting to see the tight convergence of returns during periods of P/E multiple contraction irrespective of starting valuation, indicating that some of the decent nominal returns during contractionary periods in the first chart at lower starting valuations occurred during inflationary environments (mainly the 1970's).

So where do we currently sit... at the current 28.3x CAPE, decent forward returns will require the multiple remaining elevated (or becoming more elevated) as no change would equate to a roughly ~4% real return in the model. While no change is certainly a possibility, the below chart shows the CAPE has declined in all previous 67 ten year periods since 1926 when the CAPE was greater than 28x, with an average and median decline of around 40% (which would take us right back to the historical average of ~18x), which at the current valuation models out to a roughly 0% real return over 10 years.

None of this is a sure thing, especially over the short-run. Despite being expensive three years ago, the S&P 500 has returned 10% annualized since. It just happened to have benefited from moving from the 15th percentile of most expensive CAPE to the 6th most expensive. While it absolutely can get more expensive from here, that's simply not the long-term buy and hold bet I would want to make when there are cheaper opportunities available outside and within the U.S..

Monday, December 12, 2016

A Dynamic Approach to Factor Allocation

ETF Trends (hat tip Josh) showed the following "quilt" of large cap factor calendar year returns in the post Low Volatility is Not a Buy and Hold Strategy.

Author John Lunt's takeaway (bold mine):
It is reasonable to conclude that low volatility is not a buy and hold strategy. This is not because it is unlikely to outperform over the long term, but rather because few investors are likely to survive multiple years of underperformance. Recent months have witnessed money flowing out of the low volatility and minimum volatility ETFs. Is this money flowing into different factor ETFs, or is it moving back to the market cap-weighted ETFs? Rather than abandoning factors during their periods of underperformance, investors may want to consider the opportunities that exist in factor blending and in factor rotation.
I agree completely and in this post I'll outline one potential framework to allocate to factors that diversifies across a few approaches and across time. Update: following my publishing of this post I received a comment that a lot of the work in the below was built out in further detail in a white paper by Ronald Balvers and Yangru Wu titled Momentum and Mean Reversion Across National Equity Markets. I recommend anyone interested in the framework to take a deeper look there.


For simplicity, I used the same indices outlined in the ETF Trends post with the exception of the below two tweaks:
  1. I added a small cap index (S&P 600 Smallcap Index)
  2. I swapped out the S&P 500 Dividend Aristocrat Index for the MSCI USA High Dividend Yield Index; the issue with the S&P 500 Dividend Aristocrat Index for this analysis is that it has a size tilt (it's equal weighted) and a momentum / quality tilt (it holds companies that have increased dividends every year for the last 25 consecutive years built in as well). Neither are a bad thing at all, just not the pure dividend exposure I want for this analysis.
  3. I went back another five years (which does bring up an important boom / bust regime for the analysis)
Similar to what was outlined in the ETF Trend piece, certain factors had more favorable long-term returns over 15 and 20 years (small cap, low volatility, momentum, and high dividend), while high beta and value (of all things) weighed on performance (note that the Russell 1000 Value Index outperformed the S&P 500 Value Index used in the analysis by 100 bps, which shows that getting the factor right may not be enough if you get the implementation part wrong - but I'll save that for another day). 

The below shows the updated factor quilt. Note the quality index only went back 15 years, hence the blank 1996-2000 data.


Intermediate Time Frames: Momentum is the Winner

Momentum tends to work better over shorter periods of look back periods (6, 9, 12 months). The chart below shows momentum and mean reversion using 12-month  returns for the indices and one can see that momentum outperformed over the longer time frame. That said, note that almost all of the outperformance came in the first 10 years as a relative momentum strategy was able to cruise through the bubble.

Longer Time Frames: Mean Reversion is the Winner

Mean reversion on the other hand tends to work better over longer look back periods, in part because valuations tend to matter more over longer time frames (while sentiment is a shorter term signal). We can see that momentum continued to outperform the index over this twenty year period, but not nearly to the extent it had using a shorter signal.

Combining Signals

Given momentum works better over shorter periods and mean reversion works better over longer periods, we can combine the two to diversify allocations by the momentum factor and by time. The result is a portfolio with similar returns, but much more consistent tracking to the S&P 500 (tracking error goes from 9.5% for mean reversion and 8.3% for momentum, to 5.8% for the combination).

Taking it one step further, the below adds cash as an allowable asset class for momentum (i.e. an allocation can only occur if the twelve month return outpaced cash), turning momentum into a more absolute return oriented strategy (mean reversion continues to exclude cash as an asset class).

There are still shorter periods of time in which the blend will underperform, but the blended strategy (with the ability to go to cash) has provided consistent outperformance over three year periods (85%  of the time over the last twenty years). In addition, the relative performance has tended to have a linear relationship with starting valuation (i.e. it tends to outperform going forward when stocks appear relatively expensive) in part because of the ability to move to cash in the case of momentum and in the likelihood of allocating to a less frothy segment of the U.S. stock universe in the case of mean reversion. Something to keep in mind given the current cyclically adjusted P/E "CAPE" has crossed 27x.


Certain factors have shown the ability to outperform over longer periods of time, but can and do underperform over shorter periods. These periods can be challenging for investors that cannot remain disciplined. As a result, a strategy that consistently follows a set of diversified rules to allocate across factors may help reduce behavioral issues of holding onto a strategy that differs from the S&P 500. Given the historical performance of this sort of strategy tends to do relatively better when market valuations are expensive, it may be an interesting approach to allocate across factors going forward.

Wednesday, November 30, 2016

Predicting Forward 60/40 Returns

In a recent post, Long-Term Bonds Behave More Like Stocks Than You Might ThinkLawrence via Fortune Financial fame outlined:

It shouldn't be surprising that long-term Treasurys exhibit almost the same degree of volatility as equities. After all, as we discussed in A Better Way to Think of Cash, Bonds, and Stocks, stocks are essentially high-duration instruments, or perpetuities. The further out on the duration scale you go with bonds, the more likely they will behave like equities, even if they are of the highest quality.
The longer duration means that forward long-term nominal returns of long bonds are much more predictable than those of intermediate-bonds (after all, you are locking in a nominal return over that longer time frame). Similarly, stock valuations tend to be much more predictive over longer time frames than shorter time frames, which are driven more by sentiment.

Following Lawrence's lead (and given that few investors invest in long bonds or invest only in stocks or bonds in isolation), I thought it might be of interest to see if we can "calculate" the historical duration of a U.S. 60/40 portfolio and then use this information to try to predict where we are headed. The goal of this is not to scare investors (it may / will), but rather to show that simply investing in a U.S. only balanced portfolio may not cut it going forward.


Using S&P 500 and Barclays U.S. Treasury data going back to 1973 and Ibbotson data going back pre-1973 to 1926 (as far back as that data goes), I attempted to solve for the best fitting relationship of forward returns relative to the starting yield of a 60/40 portfolio over various time frames. My methodology for starting yield was as follows:
  • Stock Yield: I first calculated the Cyclically Adjusted P/E "CAPE" for each time frame using a backward looking time frame equal to that used in the calculation of the forward return analysis (for example... the standard CAPE formula smooths after inflation earnings over a 10 year time frame - for the 5 year time frame in my analysis, I created a 5 year CAPE - for the 20 year time frame, I created a 20 year CAPE), then I turned the CAPE into a yield by taking 1 / CAPE (i.e. a CAPE of 20 = a yield of 1/20 or 5%)
  • Bond Yield: U.S. 10 Year Treasury Rate
  • 60/40 Yield: Simply 60% the Stock Yield + 40% the Bond Yield
The below chart shows the fit between starting yield and forward returns over times frames from five to twenty years, with the tightest fit being a time frame of 14 years.

The chart below shows how the analysis looked for a sampling of these times frames.


The full equation for the tightest fit of starting yield and forward nominal returns for a 60/40 portfolio over a 14 year time frame was as follows:
Forward Annualized Returns = 1.246 x Starting Yield + 0.0118
We can see in the following chart that this ex-post calculated formula did a great job at predicting future returns given starting yield. Forward returns were +/- 1.5% of actual annualized returns in 2/3 of all time frames and 80% of all time periods since 1950.

My main takeaway is how amazing the fit has been without any knowledge (ex-ante) of a wide range of inflationary and economic environments. Over any given 14 year window the main driver of performance was the nominal yield of the 60/40 portfolio, while the inflationary / economic environment seemingly only impacted things on the margin (something to keep in mind for those that think a huge economic rebound will solve current valuation issues).

In addition, one can see that excluding the very high starting yields of the 1970's / early 1980's (driven by cheap stocks and high interest rates following a period of very high inflation), the nominal starting yield of a 60/40 portfolio was relatively consistent hovering above / below 6-7% in most instances. Unfortunately, the current period appears to be an outlier to the low-end given high multiples for stocks and low yields for bonds, resulting in a starting yield at a 90+ year low.


The below chart takes all of the nominal yields / returns in the chart above, but reduces the starting yield and forward returns by the forward 14 year inflation rate (a figure that was known only after the fact). To project future real returns, I show two paths... one assuming 2% inflation and one assuming 4% inflation.

You can infer that realized real returns will be worse if inflation moves higher and I have a hard time imagining inflation moving lower in the years to come (I very well may be wrong, but I don't know how our system would handle disinflation given the high levels of nominal debt that would be difficult to pay back without inflation). The result are likely forward real returns for a 60/40 portfolio in the 0-2% range pre-tax with more downside in my view than upside (post-tax - you can take off another 1-2%).


Perhaps a separate post for another day, but some initial thoughts:
  • Diversify equity exposure to cheaper markets abroad
  • Rethink the value proposition of active management in inefficient markets
  • Look for an alternative anchor to bonds, such as managed futures
  • Look outside traditional stocks and bonds with regards to asset classes
  • Diversify by time, not only asset classes (i.e. momentum)
  • Be very tax aware (put more money in your retirement accounts)
  • Save more

Wednesday, October 26, 2016

A Framework for a Short VIX Allocation

It has historically paid to be a seller of volatility for at least two reasons...

1) Volatility is typically overpriced relative to realized volatility

The chart on the left shows the VIX index (predicted volatility) relative to the forward realized volatility of the S&P 500, while the chart on the right shows the variance between the two (anything > 0 means the VIX index was higher than the realized volatility)

2) VIX futures typically price the cost of longer dated contracts higher
The chart below shows the steepness of the VIX futures term structure. Anything below 100 means the value of the CBOE 1-Month Volatility Index (VIX) is less than the CBOE 3-Month Volatility Index (VXV). This is typically the case to compensate the seller for uncertainty, which benefits a short VIX position (all else equal).

Creating a Model

Given these historical structural advantages of a VIX short, I thought it would be of interest to share how one might make an allocation within a portfolio to capture these benefits while maintaining characteristics of a long stock position. The below analysis goes back roughly to the inception of VIX futures and carves out a portion of a stock allocation for a short VIX position via the S&P 500 VIX Short-term Futures Inverse Index (the index for ETPs XIV and SVXY). An investor can simply carve out a percentage of their allocation (call it 10% or 20%) and call it a day, but a risk weighting scheme has historically added about 1% to returns per year, while reducing risk, and it provides a framework for how one might add additional asset classes to the mix (also shown below).

The Equal Risk Weight Methodology Used Below is as Follows:
Weight next month exposure to the S&P 500 and S&P 500 VIX Short-term Futures Inverse Index by risk weighting based on historical 6-month standard deviation (using month-end data) and rebalance monthly.

Model Version 1.0 (Stock / VIX Short, Equal Risk-Weighted)

Example Weights

Note that this framework resulted in higher modeled performance with better risk-adjusted returns (higher sharpe ratio), though it did come with higher risk in the form of higher standard deviation and higher drawdown.

Model Version 2.0 (Stock / Dynamic VIX Short, Equal Risk-Weighted)

Instead of a static short to VIX futures, version 2.0 allocates to the short VIX position only when the term structure favors a short on a daily basis (i.e. when the previous close was in contango - see chart above or here for more about investing based on the term structure - the weight remains determined by the previous month-end). The modeled results are improved (higher return, higher risk-adjusted return, and lower drawdown), but overall risk in terms of standard deviation remains higher as well.

Model Version 2.1 (Version 2.0, but Scaled Down): 

This iteration takes the rules from version 2.0 and waters down the weight of both stocks and bonds with cash to match risk profile of the S&P 500 (note - this is absolutely data mined or I wouldn't have known a ~70% weight to the results from version 2.0 and 30% to t-bills would have resulted in the 14.3% standard deviation of the S&P 500). The modeled portfolio is improved in just about every manner and has an additional 30% of the portfolio now sitting in cash that is available for an alternative allocation. Note a 37.5% weight gets to the same 7.6% return and results in a standard deviation of almost 1/2 that of the S&P 500 and drawdowns of only 1/3 that of the S&P 500. 

Model Version 1.1 (Add Bonds to Version 1.0): 

This iteration takes the rules from version 1.0 (a static VIX short, even if the VIX term structure is in backwardation), but throws long bonds in the mix. This is more akin to traditional risk parity, so I included the performance of a stock / bond risk parity iteration in the performance chart below as well (i.e. an allocation excluding the VIX short). 

Example Weights

The result is an improved sharpe ratio, largely due to the negative correlation of bonds with stocks over this time frame, and more "bang for your buck" that even a small unlevered allocation to a high volatility VIX short provides (more was written on that feature here). Please note this has been the golden age of risk parity, thus this level of performance is unlikely to continue.

See also: