Exploring Risk Models

As I continue to explore patterns in beta-client data, I clearly see one common difference.  For globally-diversified, and asset-diversified ETF- and mutual-fund-based portfolios 36-month, monthly modified-semivariance and variance based portfolios tend to converge to produce similar results.   This is in sharp contrast to stock-based portfolios, where variance (MVO) and semivariance (PMPT) portfolios display a significant trade-off between Sharpe and Sortino ratios.

My preliminary conclusion, based on poring through individual optimized-portfolios, is that variance and semivariance are closely correlated for portfolios based on sufficiently-diversified ETFs.  On the other hand, the difference between variance-optimized, semivariance-optimized, and hybrid (blend of variance- and covariance-optimized) portfolio is significantly different if individual stocks and bonds are analyzed.  [Sufficiently-diversified in this context does not mean diversified per se.  It only means relative diversification within a given ETF or set or ETFs/ETNs/Mutual Funds.)

These preliminary findings suggest that semivariance and variance based optimizations are highly correlated for certain asset classes (and expected returns) while differing for other asset classes (and expected returns).  Stock-pickers are more likely to see benefits from semivariance-based optimization than are those who select from relatively-diverse ETFs.

These preliminary findings are causing a shift in the approach taken by Sigma1.  Since, so far, Sigma1 beta partners are primarily interested in constructing portfolios based primarily or exclusively around ETFs, ETNs, and mutual funds, our company is focusing more on Sharpe ratios (because they are quicker to optimize for than Sortino ratios).

Because Sigma1 HAL0 portfolio-optimization is tuned to optimize for 3 objectives this presents an interesting question:  “Your investment company wishes to optimize portfolios based on 1) expected return, 2) minimal variance, and 3)  <RISK MEASURE 3>?”

Sigma1 is posing questions:  What is your third criterion?  What is your other risk measure?   Answer these questions, and Sigma1 HAL0 software will optimize your portfolio accordingly; showing the trade-offs between Sharpe ratios and your other chosen risk metric.

Sigma1’s 3-objective-optimization is causing a few financial-industry players to ask the question of established optimization engines, “Can you do that?”  Sigma1 Software can.  Can your current portfolio-optimization software do the same?

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.



A Choice: Perfectly Wrong or Imperfectly Right?

In many situations good quick action beats slow brilliant action.   This is especially true when the “best” answer arrives too late.  The perfect pass is irrelevant after the QB is sacked, just as the perfect diagnosis is useless after the patient is dead.  Lets call this principle the temporal dominance threshold, or beat the buzzer.

Now imagine taking a multiple-choice test such as the SAT or GMAT.   Let’s say you got every question right, but somehow managed to skip question 7.   In the line for question #7 you put the answer to question #8, etc.   When you answer the last question, #50, you finally realize your mistake when you see one empty space left on the answer sheet… just as the proctor announces “Time’s up!”   Even thought you’ve answered every question right (except for question #7), you fail dramatically.   I’ll call this principle query displacement, or right answer/wrong question.

The first scenario is similar to the problems of high-frequency trading (HFT).  Good trades executed swiftly are much better than “great” trades executed (or not executed!) after the market has already moved.   The second scenario is somewhat analogous to the problems of asset allocation and portfolio theory.  For example, if a poor or “incomplete” set of assets is supplied to any portfolio optimizer, results will be mediocre at best.  Just one example of right answer (portfolio optimization), wrong question (how to turn lead into gold).

I propose that the degree of fluctuation, or variance (or mean-return variance) is another partially-wrong question.  Perhaps incomplete is a better term.  Either way, not quite the right question.

Particularly if your portfolio is leveraged, what matters is portfolio semivariance.  If you believe that “markets can remain irrational longer than you can remain solvent”, leverage is involved.  Leverage via margin, or leverage via derivatives matters not.  Leverage is leverage.  At market close, “basic” 4X leverage means complete liquidation at a underlying loss of only 25%.  Downside matters.

Supposing a long-only position with leverage, modified semivariance is of key importance.  Modified, in my notation, means using zero rather than μ.  For one reason, solvency does not care about μ, mean return over an interval greater than insolvency.

The question at hand is what is the best predictor of future semivariance — past variance or past semivariance?  These papers make the case for semivariance:  “Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility” and “Mean-Semivariance Optimization: A Heuristic Approach“.

At the extreme, semivariance is most important factor for solvency… far more important than basic variance.  In terms of client risk-tolerance, actual semi-variance is arguably more important than variance — especially when financial utility is factored in.

Now, finally, to the crux of the issue.   It is far better to predict future semivariance than to predict future variance.  If it turns out that past (modified) semivariance is more predictive of future semivariance than is past variance, then I’d favor a near-optimal optimization of expected return versus semivariance than an perfectly-optimal expected return versus variance asset allocation.

It turns out that respectively optimizing semivariance is computationally many orders of magnitude more difficult that optimizing for variance.  It also turns out that Sigma1’s HAL0 software provides a near-optimal solution to the right question: least semivariance for a given expected return.

At the end of the day, at market close, I favor near-perfect semivariance optimization over “perfect” variance optimization.  Period.  Can your software do that?  Sigma1 financial software, code-named HAL0, can.  And that is just the beginning of what it can do.  HALo answers the right questions, with near-perfect precision.  And more precisely each day.







Wall Street Interview

Years ago, a successful friend of mine was telling me stories about his early Wall Street interviews with a big-name investing house.   One stood out to me.   The question:

If you had to invest $1,000,000 for a client, and your had only two choices, which would you choose?   (A) “Invest” the whole $1,000,000 on red or black at the roulette wheel.  (B) “Invest” on red or black $1000 at a time, one thousand times.

My friend said he knew the right answer, to that question and most of the others.  I believe he was offered this particular job, but declined it in lieu of better offers elsewhere.  Anyhow, he asked what my answer would be.

I said (B).  If single zero roulette, the client can expect to lose on 1/37 (about 2.7%);  if double zero, 2/38 or about 5.3%.   My friend said, sorry, wrong answer.  If you lose money for a high-net-worth client, even 2.7%, they are likely to be disappointed and take their business elsewhere.  If you double their money, a roughly 50/50 proposition, you will have an ecstatic client who will stick their $2,000,000 with you for years.  If you lose their whole $1,000,000 they will be disappointed and walk away, but “them’s the breaks.”

This story resonates with me to this day.  This is an absurd question from a financial standpoint, but it is a powerful question on ethics.  The business rationale behind answer (A) is valid.  However, I chose to work for a company where the correct answer is (B).