Thursday, April 13, 2017

Buy When There's Blood in the Streets? Market Timing with Volatility Triggers

An 18th century British nobleman, Baron Rothschild, was rumored to have made his fortune buying during the panic that followed the Battle of Waterloo against Napoleon. He is behind the often quoted saying "Buy when there's blood in the streets”, which he continued “even if the blood is your own." This post will share a framework that may identify regimes that benefit from buying when there's blood in the streets, as well as when the market is at the greatest risk of underperformance (potentially allowing investors to reduce risk before there is blood in the streets).


Market volatility has long been one of the most disruptive aspects to investing and investor behavior. Over the past few decades, U.S. investors have seen large portions of their equity wealth evaporate as market volatility spiked on multiple occasions.

January 31st, 1993* - December 31st, 2016

  • 4 Distinct S&P 500 drawdowns greater than 30%  
  • 15% realized monthly standard deviation of the S&P 500 (annualized) 
  • 5% to 29% range of one year rolling standard deviation of monthly S&P 500 return  
  • 20 average level of the VIX Index
  • 67 Month-ends where the VIX Index was > 30
  • 89.5 peak VIX value during 2008-2009 financial crisis
* The CBOE first started publishing the VIX Index in January 1993

Poor investor reaction to market volatility has contributed to the poor returns investors have captured. Analysis of Morningstar investor returns relative to the returns produced across US equity styles reveals the extent to which investors have undermined their own investment performance over time. Over the last decade the average investor realized returns that were as much as two percentage points lower each year than the relevant Morningstar category.

In the case of the Morningstar large-cap value category, investor behavior reduced compounded dollar returns by 40% over this ten year period relative to what the average fund within the category produced. If / when markets exhibit another period of heightened volatility – which at some point is bound to happen – and if investors continue to undermine their investment performance during these periods – which is likely to happen – a systematic approach that can reduce the impact of these swings in price and volatility may help investors stay on track.


We’ve all seen the caveat that “past performance is not indicative of future returns”. The same has been true regarding past levels of volatility (high or low) and future returns (i.e. the relationship between the VIX and forward returns is weak). On the other hand, past levels of market volatility has been correlated with future levels of market volatility (i.e. when volatility is high... it tends to stay high). Given returns have been similar irrespective of the VIX, while volatility has been lower when the VIX is low / higher when the VIX is high, risk-adjusted performance (return per unit of risk) has been higher when VIX (and volatility) has been low (the return numerator stays roughly the same, while the standard deviation denominator is higher in high volatility regimes).

To identify high / low volatility regimes, we can use the current level of the VIX (in the examples below, when the VIX is above or below the historical average of 20).
  • High Volatility Regime (VIX > 20): volatility is more likely to remain elevated
  • Low Volatility Regime (VIX < 20): volatility is more likely to remain low

But wait… there’s more.

The returns within high volatility regimes (those when the VIX ended the previous month above 20) can be broken down further, in this case split between periods when the VIX had declined or increased month-over-month. Since the VIX Index inception in 1993, during high volatility regimes when the VIX declined month-over-month (i.e. VIX was above 20, but the VIX was less than the previous month-end), returns have been materially higher than when the VIX was elevated and had increased, while the risk was also greatly reduced when the VIX had declined. In fact, the risk-adjusted returns when the VIX was elevated and declining closely match the high levels of those generated within low volatility regimes.


Given historical risk-adjusted returns have been much more favorable when the VIX ended the previous month below 20 or when the VIX was above 20 and declining, we can test the hypothetical performance of a model rebalancd monthly that has a risk-on allocation (stocks) when the VIX is low or declining and a risk-averse allocation (intermediate bonds) when the VIX is high and increasing.
  • Low volatility regime (VIX < 20 or declining): 100% S&P 500 Index
  • High volatility regime (VIX > 20 and increasing): 100% Bloomberg Barclays US Intermediate Treasury Index
The model’s results are promising. Not only have the returns been similar (in fact slightly higher) than a buy and hold allocation to the S&P 500, risk was greatly reduced resulting in materially higher risk-adjusted returns.


Although Baron Rothschild may have had the fortitude to buy when there was blood in the streets, the above framework reveals there may be other, potentially less stressful, ways to capture the opportunity. While this example is simplified – and of course hypothetical – a similar framework may help protect investors from undermining their own financial progress by reducing equity exposure before fear fully materializes and/or increasing equity exposure when fear is high and improving.

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:

Monday, October 3, 2016

The Case for Put Writing in an Expensive Market

Pensions and Investments wrote about the interest pension plans have shown in put writing (seemingly one of the more misunderstood investment strategies out there) in a recent article Funds Go Exotic with Put-write Options to Stem Volatility. I thought the article did a nice job of outlining the case for the strategy as a risk reducing equity alternative. In this post I'll outline why current valuations among U.S. stocks may actually make the trade-off even more interesting (than normal) relative to an allocation to the S&P 500.

For a deeper dive into what put writing entails, including how they have the same economic exposure as covered calls... see past posts here and here.

But Shorting Naked Options Sounds Scary... How Can They Reduce Risk Relative to Stocks?

I regularly see articles / posts / tweets outlining the "complexity" and/or "danger" of put writing.

Example 1) The WSJ reported on the same topic In Scramble for Yield, Pension Funds Will Try Almost Anything:
Pension funds in Hawaii and South Carolina are plying an arcane options strategy called cash-secured put writing.
Example 2) AAII published an article Taking on Risk and Hoping the Strategy Doesn't Backfire where Charles Rotblut, the editor of the investment association, reveals the mistaken belief that covered calls provide a different exposure than put writing (click here for a chart showing they are identical):
If an investor holds a stock and writes call options (a strategy referred to as covered calls), the investor gives up potential upside if the option is called. Assuming the investor wrote the contracts with a strike price above what the stock cost to acquire, a profit is made, though a smaller profit than could have been made if the contract hadn’t been written.  
Conversely, all of the stock’s potential downside is taken on by the investor writing the put. Assuming the investor wrote the contracts with a strike price below what the stock cost to acquire, a profit can only be made if the premiums received and the proceeds from selling the stock exceed the loss incurred from being forced to buy the stock at a price below the put’s strike price
In reality... writing puts simply converts the upside potential of the stock market to a premium collected up front, while the downside (excluding the premium collected) remains the same. The result is a more consistent return stream (the premium collected cushions / offsets the downside when markets sell-off) while it has kept up with the S&P 500 since inception (despite the lower risk profile), given volatility is routinely overpriced by the market. In addition, puts tend to be priced more expensively than calls (in part) because they are less understood by investors, thus put writing has historically outperformed covered calls.

In other words, I largely agree with the P&I article that shifting equity exposure to put writing can reduce risk in any market environment:
The put-write strategy serves both as protection against downside risk and volatility but has the added bonus of providing income, said Frank Tirado, vice president of education, Options Industry Council, Chicago.

The Current Relative Opportunity for Put Writing Appears Greater than Normal

The current opportunity to shift a long position in the S&P 500 to put writing may be greater than normal given current extended valuations. The reasoning is as follows:
  • The opportunity cost of writing puts relative to owning stocks is the upside of the market (the upside is capped by what is collected as a premium when writing puts, but unlimited for stocks)
  • The upside of the market is greater when valuations are lower (and expected returns are higher) and lower when valuations are higher
  • With the S&P 500's cyclically adjusted P/E "CAPE" at 26.5, the market appears relatively expensive, thus upside potential / opportunity cost of stocks are very low vs history (another way of saying forward returns are likely lower than normal)
The data bears this out... going back to the CBOE PutWrite Index' 1986 inception, the S&P 500 has outperformed put writing when valuations were cheap and has underperformed put writing when valuations were expensive. In fact, while the S&P 500's forward return has varied by almost 8 points when the CAPE was below / above it's current 26.5 level, the forward seven year return of put writing has hardly varied when below / above this same 26.5 level.

Scatter plot of starting CAPE vs forward seven year CBOE PutWrite and S&P 500 returns.

Starting CAPE vs forward seven year CBOE PutWrite and S&P 500 returns.

Tuesday, September 13, 2016

Off Point: The Case for Home Loans

UPDATE: I had a nice discussion with Alex Rampell, partner at VC firm a16z, who provided me with a material detail that I missed that is both positive and negative. I greatly appreciate his time and while it does change the value proposition for homeowners, it remains unclear to me that the new benefit outweighs the new cost for most homeowners. That said, with the new information I can see where a homeowner with a sizable equity stake could value the flexibility it may provide and I do see where this could become a viable product a few iterations down the line.

What did I miss?

I missed that Point does in fact share in the downside with the homeowner if the home price falls below Point's "risk-adjusted value" (and the loss has not eaten away all of the homeowners equity). Point places a risk-adjusted value on each home at the time they take a stake (i.e. if the home has a market value of $1,000,000, it sounds like they'll typically strike a risk-adjusted value at some price below that). Once the home declines below that risk-adjusted price, Point shares in the loss at their ownership stake (i.e. if they took a 10% equity stake in the home, they share in 10% of the losses below that risk-adjusted value).

I would note that the risk-adjusted value is also an incremental cost to the homeowner that I initially missed. If a $1,000,000 home has a Point risk-adjusted price of $900,000 and is sold the very next day at $1,000,000, then it sounds like Point is entitled to a 20% cut of the $100,000 "gain" even though the market didn't move.

Where I personally can see this eventually being a viable product is for an individual that bought low (likely a long time ago), is now sitting on a house worth a LOT of money, and is liquidity constrained (i.e. cannot afford the monthly interest payments associated with a HELOC). Retirees planning to move in the next ten years (Point requires they are paid out of their equity stake within ten years) would be one demographic falling into this camp, as would technology folk who have been buying up property all over San Francisco when we hit our next tech recession (please please please happen sooner than later).

My dialogue with Alex also made it pretty clear to me that the longer term goal of Point is to build a platform where all these details would more dynamically sort themselves out. For now, the initial analysis below does understate the downside (i.e. the amount captured by Point is actually higher given the risk-adjusted price), but also understates the upside (i.e. the homeowner can benefit by more than the interest savings if prices move lower). For those with a high LTV (loan-to-value), thus lower equity cushion, I believe the initial analysis remains a good enough proxy for the payout structure as the benefit of the put received (i.e. the loss Point offsets in a market decline) is only there until the total equity is wiped out (banks get paid back first).


I am pretty sure there will be a ton of other posts tomorrow about Point (a "home equity partner") given the huge response to Marc Andreessen's tweet (if not... check out the responses here - UPDATE: the great Matt Levine has a take here). As a result, I'll skip whether or not the fractional home equity investor is really just a predatory lender, how they will / won't disrupt the mortgage industry, or whether it marks the VC top. Instead I'll focus on the investment case against swapping out of a traditional mortgage loan and "selling" Point a fraction of your home equity. I make a lot of assumptions in the below, but if anything looks off, please let me know. TLDR: don't do it.

Swapping from a Loan: A Homeowner's Perspective

The real benefit of fractional equity for homeowners will be for those that cannot afford the initial 20% down payment and cannot borrow from family. Unfortunately, Point will not solve this issue as:

To be eligible for Point, you’ll need to retain at least 20% of the equity in your home after Point's investment.
As a result, this is a pretty straight forward swap for a homeowner that is otherwise reliant on borrowing. The homeowner is simply swapping out the cost of interest payments for the opportunity cost of the housing appreciation associated with whatever equity stake is sold should markets rise.

In the below analysis, I assume a $1,000,000 home where an investor swaps out 10% ($100,000) from a ten year interest only loan and instead "sells" that 10% stake to Point.

Assuming a 3% interest only loan for ten years and a 33% tax rate for interest deduction benefits, we get a 2% / year after-tax savings (3% x [1 - 0.33%] = 2%) for the homeowner due to the reduced notional loan. This comes out to $2000 of savings per year or $20,000 over a ten year period. In return, the homeowners gives up 200% of the upside on the stake sold and is charged 3% up front. Unfortunately, the homeowner doesn't appear to receive any incremental benefit should markets fall as the homeowner takes first loss on the minimum 20% equity stake homeowners are required to retain. Andreessen's VC firm a16z outlines:
Point gets paid back after the bank, but before the homeowner,
Given Point gets paid back before the homeowner, this capital structure provides a huge benefit to Point at the expense of the homeowner (i.e. heads Point wins, tails the homeowner loses). There could be examples where Point also takes a hit, but the homeowner appears to have already been wiped out an amount equal to Point's stake at that point.

Payout Diagram

The below payout diagram assumes an investor doesn't pay back the loan for the max 10 years (the longest period of time before Point is owed their investment back) and that the increase in home value comes solely from market appreciation (i.e. no upgrades paid for by the homeowner). The dotted line represents the starting house price and we can see that the homeowner is better off if the price does not move or if the price declines, as they pocket the $20,000 they would have otherwise paid in after-tax interest. In return, the homeowners break even if the market rises a bit more than 1% a year, given the interest savings and 3-4% up front cost, a rate that is forecast to be less than the rate of inflation.

Unfortunately it gets worse if the homeowner remodels (one of the benefits of owning a home). Per point:
Many homeowners use Point funds to pay for remodeling costs. You can remodel your home but there are limits on adding additional debt to the home to pay for remodeling. Please also note that Point will share in any increase in property value due to remodeling changes you might make.
Let's be clear... if a homeowner sells a $100,000 stake in order to invest in a new kitchen, increasing the value of the home by $100,000, Point captures 20% of that $100,000. Note that $20,000 ($100,000 x 20%) equals the entire benefit of avoiding the interest payments for the full ten years, meaning there is no longer any net upside of choosing Point vs a loan at time = 0. The dotted line represents the new starting point assuming the $100,000 was used to upgrade the home (note the green line cross at ~$0).

As for the cost at inception, these payoff diagrams are classic naked call payoffs and the interest savings can be viewed as the premium collected for selling those calls (i.e. the $20,000). Assuming these calls expire in 10 years, we can try to value them using the Black-Scholes formula. Using the assumed inputs:
  • Notional: $200,000 (200% upside of $100,000)
  • Strike: $1,000,000
  • Current (Remodeled Home) Spot: $1,100,000 
  • Risk free rate (assumed 2%)
  • Volatility (the annual volatility from 2006-2016 for the Case Shiller index was 9%)
We get a value of roughly $60,000. Assuming any home price movement will be on top of 2% / year inflation, these calls move up to a rough value of $100,000. All for $20,000 in saving.

Keep the loan.

Tuesday, September 6, 2016

How a Low VIX Can Remain an Expensive Hedge

One of my favorite Twitter follows @LadyFOHF shared the below scatter chart from Morgan Stanley that attempted to map areas of the global market that were both cheap (valuation ranks at the lower end of its 10-year history) and defensive (a low or negative correlation to global equities).

One of the few trades listed as having both characteristics was the VIX Index. Let's take a look.

The VIX is Not Investable

The chart below shows the percentile rank of the VIX index over the ten year time frame outlined in the Morgan Stanley chart. The VIX Index was indeed near it's all time low, ranking in the lowest 6th percentile of its ten year history at Friday's close (9/2/16) when the VIX closed at 11.98. 

But an investor cannot invest in the VIX Index. Rather an investor can buy or sell the consensus view of where the VIX will be, most easily through VIX futures or ETPs (for more details on the VIX term structure, take a look at a past post here).

VIX Futures have Diverged

The below looks at the rank of historical 2nd month VIX futures contract prices (i.e. where consensus views the VIX as being when the 2nd closest VIX future contract matures - which currently makes up the largest holding of VIX ETPs) and we see a different picture. As of Friday's close, the second month contract was "only" in the 30th percentile in terms of price at a value of 16.375, more than 35% higher than the VIX Index itself.

VIX Futures Rank Divergence vs Future Returns

This 20%+ gap in rank of the VIX Index and the 2nd month VIX futures contract is pretty extreme, indicating investors believe (and are pricing in) a higher VIX in the future that is more "normal" to history; a very different view than the exuberance the current level of the VIX implies.

Going back to the initial question of whether the VIX is cheap... the below chart takes the historical gap (from the green chart above) and projects out forward daily performance (annualized) of the S&P 500® VIX Short-Term Futures Index (the index benchmarked within the VXX ETP) of various scenarios. Similar gaps show that VIX prices were at extremely expensive levels (not cheap levels) and it actually presented a buying opportunity for the S&P 500 (11.9% returns when the gap was positive). 

To summarize... while an investor should hardly ever be long VIX futures as they rarely provide a positive return, it is the the term structure of the VIX (i.e. VIX futures relative to the current level of the VIX), rather than the level of the VIX itself, that is likely to be a better signal of whether VIX futures are rich or cheap.