A Better Robo Advisory

Building a Better Robo Advisor

The more we learned about the current crop of robo advisory firms, the more we realized we could do better. This brief blog post hits the high points of that thinking.

Not Just the Same Robo Advisory Technology

It appears that all major robo advisory companies use 50+ year-old MPT (modern portfolio theory). At Sigma1 we use so-called post-modern portfolio theory (PMPT) that is much more current. At the heart of PMPT is optimizing return versus semivariance. The details are not important to most people, but the takeaway is the PMPT, in theory, allows greater downside risk mitigation and does not penalize portfolios that have sharp upward jumps.

Robo advisors, we infer, must use some sort of Monte Carlo analysis to estimate “poor market condition” returns. We believe we have superior technology in this area too.

Finally, while most robo advisory firms offer tax loss harvesting, we believe we can 1) set up portfolios that do it better, 2) go beyond just tax loss harvesting to achieve greater portfolio tax efficiency.

Investment Tax Management Boosts Returns in Surprising Ways

Tax Deferral Illustrated

Figure 1. Tax Deferral benefits both parties.

A Common Tax Misconception

When asked to consider tax deferral investment strategies, many people instinctively conclude that tax deferral benefits the investor at the expense of the government. Such a belief is half-right. Tax deferral ultimately benefits both the investor and the government’s tax revenues. While there are exceptions involving inheritance, in most other cases both parties benefit. Figure 1 summarizes the relationship between higher after-tax returns and higher nominal net cash flows to the government.

The reason I lead with the government’s side of the tax equation is for tax policy wonks in Washington D.C. I suspect many of them already know this information, and this is simply another data point to add to their arsenal of tax facts. For the others, I hope this a wake-up call. The message:

When investors, investment advisors, and fund managers successfully defer long-term capital gains, investors and governments win in the long run.

The phrase “in the long run” is important. When taxes are deferred, the government’s share grows along with the investor’s. In the short term, taxes are reduced; in the long run taxes are increased. For the investor this long-run tax increase is more than offset by increased compounding of return.

Please note that all of these win/win outcomes occur under a assumption of fixed tax rates — which is 20% in this example. It is also worth noting that these outcomes occur for funds that are spent at any point in the investor’s lifetime. This analysis does not necessarily apply to taxable assets that are passed on via inheritance.

Critical observers may acknowledge the government tax “win” holds for nominal tax dollars, but wonder whether it still holds in inflation-adjusted terms. The answer is “yes” so long as the the investor’s (long-run) pre-tax returns exceed the (long run) rate of inflation. In other words so long as g > i (g is pre-tax return, i is inflation), the yellow line will be upward sloping; More effective tax-deferral strategies, with higher post-tax returns, will benefit both parties. As inflation increases the slope of the yellow line gets flatter, but it retains an upward slope so long as pre-tax return is greater than inflation.

Tax Advantages for Investors

Responsible investors face many challenges when trying to preserve and grow wealth. Among these challenges are taxes and inflation. I will start by addressing two important maxims in managing investment taxes:

  1. Avoid net realized short-term (ST) gains
  2. Defer net long-term gains as long as possible

It is okay to realize some ST gains, however it is important to offset those gains with capital losses. The simplest way of achieving this offset is to realize an equal or greater amount of ST capital losses within the same tax year. ST capital losses directly offset ST capital gains.

A workable, but more complex way of offsetting ST gains is with net LT capital losses.The term net is crucial here, as LT capital losses can only be used to offset ST capital gain once they have been first used to offset LT capital gains.  It is only LT capital losses in excess of LT capital gains that offset ST gains.

If the above explanation makes your head spin, you are not alone. Managing capital gains is really an exercise in linear programming. In order to make this tax exercise less (mentally) taxing, here are some simple concepts to help:

  • ST capital losses are better than LT capital losses
  • ST capital gains are worse than LT capital gains
  • When possible offset ST losses with ST gains

Because ST capital losses are better than LT, it often makes sense to see how long you have held assets that have larger paper (unrealized) losses. All things equal it is better to “harvest” the losses from the ST losers than from the LT losers.

Managing net ST capital gains can potentially save you a large amount of taxes, resulting in higher post-tax returns.

Tax Advantages for the Patient Investor

Deferring LT capital gains requires patience and discipline. Motivation can help reinforce patience. For motivation we go back to the example used to create Figure 1. The example starts today with $10,000 investment in a taxable account and a 30-year time horizon. The example assumes a starting cost basis of zero and an annual return of 8%.

This example was set up to help answer the question: “What is the impact of ‘tax events’ on after-tax returns?” To keep things as simple as possible a “tax event” is an event that triggers a long-term capital gains tax realization in a tax year. Also, in all cases, the investor liquidates the account at the start of year 31. (This year-31 sale is not counted in the tax event count.)

It turns out that it not just the number of tax events that matters — it is also the timing. To capture some of this timing-dependent behavior, I set up my spreadsheets to model two different timing modes. The first is called “stacked” and it simply stacks all tax events in back-to-back years. These second mode is called “spaced” because the tax events are spaced uniformly.  Thus 2 stacked tax events occur in years 1, 2, while 2 spaced tax events occur in years 10 and 20. The results are interesting:

Why tax deferral matters

Tax “event” impact on after-tax returns.

The most important thing to notice is that if an investor can completely avoid all “tax events” for 30 years the (compound) after-tax return is 7.2% per year, but if the investor triggers just one taxable event the after tax return is significantly reduced. A single “stacked” tax event in year 1 reduces after tax returns to 6.49% while a single “spaced” tax event in year 15 reduces returns to 6.67%. Thus for a single event the spaced tax event curve is higher, while for all other numbers of tax events (except 30 where they are identical) it is lower than the stacked-event curve.

The main take-away from this graph is that tax deferral discipline matters. The difference between 7.2% and 6.67% after-tax return, over thirty years is huge when framed in dollar terms. With zero (excess) tax events the after-tax result in year 31 is $80,501. With one excess tax event (with the least harmful timing!) that sum drops to $69,476.

In the worst case the future value drops to $51,444 with an annual compound after-tax return of only 5.61%.

Tax Complexity, Tax Modeling Complexity, and Other Factors

One of the challenges faced when bringing fresh perspectives to the tax-plus-investing dialog is in providing examples that paint the broad portfolio tax management themes in a concise way. The first challenge is that the tax code is constantly changing, so predicting future tax rates and tax rules is an imprecise game at best. The second challenge is that the tax code is so complex that any generalization will mostly likely have a counterexample buried somewhere in the tax code. The third complication is that baring significant future tax code changes and obscure tax code counterexamples, creating a one-size-fits-all model for investors results in large oversimplifications.

I believe that tax indifference is the wrong answer to the question of portfolio tax optimization. The right answer is more closely aligned with the maxim:

All models are wrong. Some are useful.

This common saying in statistics gets to the heart of the problem and the opportunity of investment tax management. It is better to build a model that gives deeper insight into opportunities that exist in reconciling prudent tax planning with prudent investment management, than to build no model at all.

The simple tax model used in this blog post makes some broad assumptions. Among these is that the long-term capital gains rate will be the same for 30 years and that the investor will occupy the same tax bracket for 30 years. The pre-tax return model is also very simple: 8% pre-tax return each and every year.

I argue that models as simple as this are still useful. They illustrate investment tax-management tax principles in a manner that is clear and draws the same conclusions as analysis using more complex tax modelling. (Complex models also have their place.)

I would like to highlight the oversimplification I think is most problematic from a tax perspective.  The model assumes all the returns (8% per year) are in the form of capital appreciation. A better “8%” model would be to assume a 2% dividend and 6% capital appreciation.  Dividends, even though receiving qualified-dividend tax treatment, would bring down the after-tax returns, especially on the left side of the curve.  I will likely remedy that oversimplification in a future blog post.

Investment Tax Management Summary

  1. Tax deferral does not hurt government revenues; it helps in the long run.
  2. Realized net short-term capital gains can crater post-tax investment returns and should be avoided.
  3. Deferral of (net) long-term capital gains can dramatically improve after-tax returns.
  4. Tax deferral strategies require serious investment discipline to achieve maximum benefit.
  5. Even simple tax modelling is far better than no tax modelling at all.  Simple tax models can be useful and powerful. Nonetheless, investment tax models can and should be improved over time.

How to Write a Mean-Variance Optimizer (Part III)… In R

Parts 1 and 2 left a trail of breadcrumbs to follow.  Now I provide a full-color map, a GPS, and local guide.  In other words the complete solution in the R statistical language.

Recall that the fast way to compute portfolio variance is:

The companion equation is rp = wTrtn, where rtn is a column vector of expected returns (or historic returns) for each asset.  The first goal is to find find w0 and wn. w0 minimizes variance regardless of return, while wn maximizes return regardless of variance.  The goal is to then create the set of vectors {w0,w1,…wn} that minimizes variance for a given level of expected return.

I just discovered that someone already wrote an excellent post that shows exactly how to write an MVO optimizer completely in R. Very convenient!  Enjoy…

http://economistatlarge.com/portfolio-theory/r-optimized-portfolio

Surpassing the Frontier?

Suppose you have the tools to compute the mean-return efficient frontier to arbitrary (and sufficient) precision — given a set of total-return time-series data of asset/securities.  What would you do with such potential?

I propose that the optimal solution is to “breach the frontier.”  Current portfolios provide a historic reference. Provided reference/starting point portfolios have all (so far) provided sufficient room for meaningful and sufficient further optimization, as gauged by, say, improved Sortino ratios.

Often, when the client proposes portfolio additions, some of these additions allow the optimizer to push beyond the original efficient frontier (EF), and provide improved Sortino ratios. Successful companies contact  ∑1 in order to see how each of their portfolios:

1) Land on a risk-versus-reward (expected-return) plot
2) Compare to one or more benchmarks, e.g. the S&P500 over the same time period
3) Compare to an EF comprised of assets in the baseline portfolio

Our company is not satisfied to provide marginal or incremental improvement. Our current goal is provide our client  with more resilient portfolio solutions. Clients provide the raw materials: a list of vetted assets and expected returns.  ∑1 software then provides near-optimal mix of asset allocations that serve a variety of goals:

1) Improved projected risk-adjusted returns (based on semi-variance optimization)
2) Identification of under-performing assets (in the context of the “optimal” portfolio)
3) Identification of potential portfolio-enhancing assets and their asset weightings

We are obsessed with meaningful optimization. We wish to find the semi-variance (semi-deviation) efficient frontier and then breach it by including client-selected auxiliary assets. Our “mission” is  as simple as that — Better, more resilient portfolios

Approaching the Frontier

Disclosure: The purpose of this post is to show how I, personally, use the HALO Portfolio Optimizer software to manage my personal portfolio. It is not investment advice! I use my personal opinions about which assets to select and expected one-year returns into the optimizer configuration.  The optimizer then provides an efficient frontier (EF) based on historic total-return data and my personal expected-return estimates.

I use other software (User Tuner) to approach the EF, while limiting the number and size of trades (minimizing churn and trading costs).  Getting exactly to the EF would require trading (buying or selling) every asset in my portfolio — which would cost approximately $159 in trading costs for 18 trades. Factoring in bid/ask spreads the cost would be even higher.  However, by being frugal about trades, I was able to limit the number of trades to 6 while getting much closer to the EF.

Past performance is no guarantee of future performance, nor is past volatility necessarily indicative of future volatility.  Nonetheless, I am making the personal decision to use past volatility information to possibly increase the empirical diversification of my retirement portfolio with the goal of increasing risk-adjusted return.  Time will tell whether this approach was successful or not.

In my last post I blogged about reallocating my entire retirement portfolio closer to the MVO efficient frontier computed by the HALO Portfolio Optimizer.  The zoomed in plot tells the story to date:

5_7_2014_realloc

The “objective space” plot is zoomed in and only shows a small portion of the efficient frontier. As you can see the black X is closer to the efficient frontier than the blue diamond, but naturally the dimensions are not the same. Using a risk-free rate of 0.5% the predicted Sharpe ratio has improved from 0.68 to 0.75 – a marked increase of about 10.3%.  [If you crunch the numbers yourself, don’t forget to annualize σ.]

While a 10.3% Sharpe ratio expected improvement is very significant, there is obviously room for compelling additional improvement. An expected Sharpe ratio of just north of 0.8 is attainable.

The primary reason the portfolio has not  yet moved even closer to the efficient frontier is due to 18.6% of the retirement portfolio being tied up in red tape as a result of my recent voluntary severance or “buy-out” from Intel Corporation. [ Kudos to Intel for offering voluntary severance to all of my local coworkers and me.  It is a much more compassionate method of workforce reduction than layoffs!  I consider the package offered to me reasonably generous, and I gladly took the opportunity to depart and begin working full time building my start up.]

Time to Get Technical

I won’t finish without mentioning a few important technical details. The points in the objective space (of monthly σ on the horizontal and expected annual return on the vertical) can be viewed as dependent variables of the (largely) independent variables of asset weights. Such points include the blue diamond, the black X, and all the red triangles on the efficient frontier. I often call the (largely) independent domain of asset allocation weights the “search space”, and the weightings in the search space that result in points on the efficient frontier the “solution space.”

One way to measure the progress from the blue diamond to the X is via improvement in the Sharpe ratio, which implicitly factors in the CAL, or the CML for the tangent CAL.  As “X” approaches the red line visually it also approaches the efficient frontier quantitatively and empirically.  However, X can make significant progress towards the efficient frontier, say point EF#9 specifically, with little or no “progress” in the portfolio weights from the blue diamond to the black X.

“Progress” in the objective space is reasonably straight forward — just use Sharpe ratios, for instance. However measuring “progress” in the asset allocation (weight) space is perhaps less clear. Generally, I prefer the use of the L1-norms of differences of the asset-weight vectors Wo (corresponding to original portfolio weight; e.i. the blue diamond), Wx, and Wef_n. The distance of from the blue diamond  in search space to the red triangle #9 is denoted as |Wef_9 – Wo|1 while the distance from X in the search space is |Wef_9Wx|1.  Interestingly, the respective values are 0.572 and 0.664.  Wis, by this measure, actually further from Wef_9 in search space, but closer in objective space!

I sometimes refer to these as the “Hamming distances” (even though “Hamming distance” is typically applied to differences in binary codes or character inequality counts of two strings of characters.) It is simply easier to say the “Hamming distance from Wx to Wef_9” than the “ell-one norm of the difference of Wx and Wef_9.”

I have been working on an utility temporarily called “user tuner” that makes navigating in both the search space and the objective space quicker, easier and more productive. More details to follow in a future post.

Why Not Semi-Variance Optimization?

Frequent readers will know that I believe that mean semi-variance optimization (MSVO or SVO) is superior to vanilla MVO. So why am I starting with MVO? Three reasons:

  • To many, MVO is less scary because it is somewhat familiar. So I’m starting with the familiar “basics.”
  • I wanted to talk about Sharpe ratios first, because again they are more familiar than, say, Sortino ratios.
  • I wanted to use “User Tuner”, and I originally coded it for MVO (though that is easily remedied).

However, asymptotically refining allocation of my entire portfolio to get extremely close to the MVO efficient frontier is only phase 1.  It is highly likely I will compute the SVO efficient frontier next and use a slightly modified “User Tuner” to approach the mean semi-variance efficient frontier… Likely in the next month or two, once my 18.6% of assets are freed up.

Inverted Risk/Return Curves

Over 50 years of academic financial thinking is based on a kind of financial gravity:  the notion that for a relatively diverse investment portfolio, higher risk translates into higher return given a sufficiently long time horizon.  Stated simply: “Risk equals reward.”  Stated less tersely, “Return for an optimized portfolio is proportional to portfolio risk.”

As I assimilated the CAPM doctrine in grad school, part of my brain rejected some CAPM concepts even as it embraced others.  I remember seeing a graph of asset diversification that showed that randomly selected portfolios exhibited better risk/reward profiles up to 30 assets, at which point further improvement was minuscule and only asymptotically approached an “optimal” risk/reward asymptote.  That resonated.

Conversely, strict CAPM thinking implied that a well-diversified portfolio of high-beta stocks will outperform a marketed-weighted portfolio of stocks over the long-term, albeit in a zero-alpha fashion.  That concept met with cognitive dissonance.

Now, dear reader, as a reward for staying with this post this far, I will reward you with some hard-won insights.  After much risk/reward curve fitting on compute-intensive analyses, I found that the best-fit expected-return metric for assets was proportional to the square root of beta.  In my analyses I defined an asset’s beta as 36-month, monthly returns relative to the benchmark index.  Mostly, for US assets, my benchmark “index” was VTI total-return data.

Little did I know, at the time, that a brilliant financial maverick had been doing the heavy academic lifting around similar financial ideas.  His name is Bob Haugen. I only learned of the work of this kindred spirit upon his passing.

My academic number crunching on data since 1980 suggested a positive, but decreasing incremental total return vs. increasing volatility (or for increasing beta).  Bob Haugen suggested a negative incremental total return for high-volatility assets above an inflection-point of volatility.

Mr. Haugen’s lifetime of  published research dwarfs my to-date analyses. There is some consolation in the fact that I followed the data to conclusions that had more in common with Mr. Haugen’s than with the Academic Consensus.

An objective analysis of the investment approach of three investing greats will show that they have more in common with Mr. Haugen than Mr. E.M. Hypothesis (aka Mr. Efficient Markets, [Hypothesis] , not to be confused with “Mr. Market”).  Those great investors are 1) Benjamin Graham, 2) Warren Buffet, 3) Peter Lynch.

CAPM suggests that, with either optimal “risk-free”or leveraged investments a capital asset line exists — tantamount to a linear risk-reward relationship. This line is set according to an unique tangent point to the efficient frontier curve of expected volatility to expected return.

My research at Sigma1 suggests a modified curve with a tangent point portfolio comprised, generally, of a greater proportion of low volatility assets than CAPM would indicate.  In other words, my back-testing at Sigma1 Financial suggests that a different mix, favoring lower-volatility assets is optimal.  The Sigma1 CAL (capital allocation line) is different and based on a different asset mix.  Nonetheless, the slope (first derivative) of the Sigma1 efficient frontier is always upward sloping.

Mr. Haugen’s research indicates that, in theory, the efficient frontier curve past a critical point begins sloping downward with as portfolio volatility increases. (Arguably the curve past the critical point ceases to be “efficient”, but from a parametric point it can be calculated for academic or theoretical purposes.)  An inverted risk/return curve can exist, just as an inverted Treasury yield curve can exist.

Academia routinely deletes the dominated bottom of the the parabola-like portion of the the complete “efficient frontier” curve (resembling a parabola of the form x = A + B*y^2) for allocation of two assets (commonly stocks (e.g. SPY) and bonds (e.g. AGG)).

Maybe a more thorough explanation is called for.   In the two-asset model the complete “parabola” is a parametric equation where x = Vol(t*A, (1-t)*B) and y = ER( t*A, (1-t)*B.  [Vol == Volatility or standard-deviation, ER = Expected Return)].   The bottom part of the “parabola” is excluded because it has no potential utility to any rational investor.  In the multi-weight model, x=minVol (W), y=maxER(W), and W is subject to the condition that the sum of weights in vector W = 1.  In the multi-weight, multi-asset model the underside is automatically excluded.  However there is no guarantee that there is no point where dy/dx is negative.  In fact, Bob Haugen’s research suggests that negative slopes (dy/dx) are possible, even likely, for many collections of assets.

Time prevents me from following this financial rabbit hole to its end.  However I will point out the increasing popularity and short-run success of low-volatility ETFs such as SPLV, USMV, and EEMV.  I am invested in them, and so far am pleased with their high returns AND lower volatilities.

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NOTE: The part about W is oversimplified for flow of reading.  The bulkier explanation is y is stepped from y = ER(W) for minVol(W) to max expected-return of all the assets (Wmax_ER_asset = 1, y = max_ER_asset_return), and each x = minVol(W) s.t. y = ER(W) and sum_of_weights(W) = 1.   Clear as mud, right?  That’s why I wrote it the other way first.

 

Capital Allocation

Let’s start with the idea that CAPM (Capital Asset Pricing Model) is incomplete.   Let me prove it in a  few sentences.  Everyone knows that, for investors, “risk-free” rates are always less than borrowing (margin) rates.  Thus the concept of CAL (the capital asset line) is incomplete.  If I had a sketch-pad I’d supply a drawing showing that there are really three parts of the “CAL” curve…

  1. The traditional CAL that extends from Rf to the tangent intercept with the efficient-frontier curve.
  2. CAC (capital-asset curve)
  3. CAML (capital-asset margin line, pronounced “camel”)

Why?  Because the CAML has it’s own tangent point based on the borrower’s marginal rate.  Because the efficient frontier is monotonically-increasing the CAL and CAML points will be separated by a section of the EF curve I call the CAC.

All of this is so obvious, it almost goes without saying.  It is strange, then, that I haven’t seen it pointed out in graduate finance textbooks, or online.  [If you know of a reference, please comment on this post!]  In reality, the CAL only works for an unleveraged portfolio.

CAPM is Incomplete; Warren Buffett Shows How

Higher risk, higher return, right?  Maybe not… at least on a risk-adjusted basis.  Empirical data suggests that high-beta stock and portfolios do not receive commensurate return.  Quite to the contrary, low-beta stocks and portfolios have received greater returns than CAPM predicts.   In other words, low-beta portfolios (value portfolios in many cases) have had higher historical alphas.  Add leverage, and folks like Warren Buffett have produced high long-term returns.

Black Swans and Grey Swans

On the fringe of modern-portfolio theory (MPT) and post-modern portfolio theory (PMPT), live black swans.   Black swans are essentially the most potent of unknown unknowns, also known as “fat tails”.

At the heart of PMPT is what I call “grey swans.”  This is also called “breakdown of covariance estimates” or, in some contexts, financial contagion.  Grey-swan events are much more common, and somewhat more predictable… That is if one is NOT fixated on variance.

Variance is close, semivariance is closer.  I put forth the idea that PMPT overstates its own potential.  Black swans exists, are underestimated, and essentially impossible to predict.  “Grey swans” are, however, within the realm of PMPT.   They can be measured in retrospect and anticipated in part.

Assets are Incorrectly Priced

CAPM showed a better way to price assets and allocate capital.  The principles of semivariance, commingled with CAPM form a better model for asset valuation.  Simply replacing variance with semivariance changes fifty years of stagnant theory.

Mean-return variance is positively correlated with semivariance (mean semi-variance of asset return), but the correlation is far less than 1.   Further, mean variance is most correlated when it matters most; when asset prices drop.  The primary function of diversification and of hedging is to efficiently reduce variance.  Investors and pragmatists note that this principle matters more when assets crash together — when declines are correlated.

The first step in breaking this mold of contagion is examining what matter more: semivariance.   Simply put, investors care much less about compressed upward variance than they do about compressed downward variance.   They care more about semivariance.  And, eventually, they vote with their remaining assets.

A factor in retaining and growing an AUM base is content clients.  The old rules say that the correct answer the a key Wall Street interview question is win big or lose all (of the client’s money).  The new rules say that clients demand a value-add from their adviser/broker/hybrid.  This value add can be supplied, in part, via using the best parts of PMPT.  Namely semivariance.

That is the the end result of the of the success of semivariance.  The invisible hand of Sigma1, and other forward-looking investment companies, is to guide investors to invest money in the way that best meets their needs.  The eventual result is more efficient allocation of capital.  In the beginning these investors win.  In the end, both investors and the economy wins.  This win/win situation is the end goal of Sigma1.