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Tom Anichini tom@portfoliowizards.com Tom and his family live in San Diego County. He and his wife own Egg-Free Epicurean (peanut-free and tree nut-free, too), a specialty food brand his wife founded in 2009. Portfolio Wizards tom@portfoliowizards.com @TomAnichini LinkedIn/TomAnichini

Sep 302014

This application is interactive. Be patient as it loads.

Example: Unconstrained Maximum Sharpe Ratio portfolio
Notice the Contributions to Risk are proportionate to the Contributions to Returnmax-sharpe-portfolio

Example: Unconstrained Minimum Variance portfolio
Notice the Weights and Contributions to Risk are Equal

Example: Risk Parity portfolio
Contributions to Risk are equal


Asset ClassVolatilityExpected_Return
US Stocks20%8%
Int'l Stocks25%8%

Correlation matrix
US StocksInt'l StocksBondsREITsCommodities
US Stocks1.000.950.150.850.60
Int'l Stocks0.951.000.300.800.70

Weight: Asset Value divided by the greater of 1 and the sum of all Asset Values
Valuei / max(1, \Sigma Valuei )

Risk Contribution: Product of Asset’s Weight and its covariance with the Portfolio, scaled by the Portfolio’s variance
weighti\sigma i,Portfolio / \sigma 2Portfolio

Return Contribution: Product of Asset’s Weight and its Expected Return
weighti\mu i

Sharpe Ratio: Ratio of Expected Return to Volatility
\mu i / \sigma i

Note this is simply a “Return/Risk ratio,” which is not exactly the true definition of a Sharpe Ratio. However in the investment world vernacular the terms are interchangeable and for the purpose of this application their meanings are similar enough.

If you would like to know the precise definition of “Sharpe Ratio,” consult the source.

I created a slightly more elaborate version of this app in the Coursera course, Developing Data Products, the ninth of ten courses I took as part of the Johns Hopkins University Data Science certification.

 Posted by on September 30, 2014 Asset Allocation, Portfolio Risk 1 Response »
Sep 162014

Recently I have been playing with the R application, Shiny. Shiny offers a way to embed R applications on the web.

Here is a toy model I developed to illustrate the interaction between portfolio weights and contributions to portfolio risk. Access the app here: Visualize Portfolio Risk.

This is a slightly less elaborate version of my project in the Coursera course, Developing Data Products, the ninth of ten courses I took as part of the Johns Hopkins University Data Science certification.

 Posted by on September 16, 2014 Portfolio Risk No Responses »
Oct 172013

Ed. Originally written in 2011. Published in 2013

“Look ma, I have skill!”
An idea that would have been regarded as heresy in the 1990s has gained acceptance and respectability: the idea that investors are not rewarded for risk, systematic or otherwise.

Thanks to the long-term performance dominance of low volatility assets over the past few decades, producing an apparently informative backtest has become easy. Just make sure your ranking process favors lower volatility assets and your strategy has a nice tailwind.

Prior to the Fama/French litany it had been just as easy to find attractive backtest results by favoring Value and Small Caps. (And eventually, Momentum). That’s why regressing against Fama/French factors has become standard in any kind of investment anomaly or strategy analysis hoping to be taken seriously.

While Small Caps performed better than Large Caps in the long run, they have endured cycles of being out of favor for entire decades. Value and Growth have seen pronounced cycles too, and by construction the stocks favored by Momentum today might be quite different from the stocks favored by Momentum a year ago or a year from now.

Further, stocks can conceivably cross over categories. Small Caps can become Large Caps; Value can become Growth, and today’s Momentum stock might not be one in a year.

Stickiness of Low Volatility Means Low Volatility Strategies Enjoy Low Turnover
But when you rank stocks by volatility, you’re ranking stocks by something more permanent than Momentum, Capitalization, or Valuation. Stocks ranked today as Volatile are likely to have been ranked as Volatile a year ago, and probably will be in another year (if they’re still around).

The table below displays the rank correlation of the constituents of the SPY ETF as of July 29, 2011, sorted by trailing 1-year standard deviation of daily log returns, to their ranks the following year. The following year they’re sorted both by standard deviation and downside risk.

Year-endCorrelation of this year's Standard Deviation with
Next year's
Correlation of this year's Standard Deviation with
Next year's Downside Risk


Notice two things: first, today’s volatile stocks tend to be next year’s; second, whether you rank by standard deviation or by downside risk doesn’t seem to make much difference.

While this data set is survivorship-biased, even in data sets that aren’t subject to survivorship bias this pattern remains. Which means if you want to manage a Low Volatility portfolio, chances are it won’t have to have high turnover.

Lake Woebegone Backtests
We’ve now endured a few decades when systematic risk has mostly been punished, which is one reason why you’re seeing so many “low volatility” and “minimum volatility” strategies appearing. All these back-tested results are above average! Whether the return to systematic risk turns out to have been a myth remains an open question to many, but when you’re exploring new investment products and strategies, keep in mind that we’ve just lived through an era when almost any strategy with lower risk than cap weighted indices will have outperformed those indices. Look for low volatility bias. Is low volatility an explicit part of the author’s strategy, or was it an unintended consequence that happened to be in favor?

Given the dominance of the superior performance of Low Volatility over the past several decades, superior backtest results you see today are likely to have another feature in addition to exposure to the Fama/French factors: a Low Volatility tilt.

Not that there’s anything wrong with Low Volatility – just make sure that whenever you’re evaluating the performance of a manager, an ETF, or a vendor, you’re aware of how much of a Low Vol effect there is in the data.

 Posted by on October 17, 2013 Benchmarks, Portfolio Risk No Responses »
Oct 102012

Update, Nov. 7 2012: Evidently the interviewer was Bob Litterman, renowned in several areas of quantitative finance, especially for the Black-Litterman model.

The first several times I heard of or read about risk parity I was puzzled. The media, it seemed, had distilled descriptions of risk parity into some variation on “a leveraged bond portfolio” or “portfolio in which the bonds are leveraged until they have the same volatility as equities.” The first time I grasped what risk parity really is was when I read Chris Levell’s piece for NEPC.

It was clear that risk parity was something broader than as described by the media: it was simply a portfolio in which the assets’ contributions to variance were equal. Notice the lack of any mention of the words “bonds” or “leverage” in that definition.

Somehow the attention the investment media pays to risk parity focuses on examples of multi-asset class portfolios that use leverage. In Qian’s earliest writing on risk parity, he described one possible implementation as simply an alternative to a bond portfolio, one with better diversification than a bond-only portfolio.

Bottom line: you can find examples of risk parity portfolios with no bonds and with no leverage, and yet when people talk about risk parity they almost always refer to them as leveraged bond portfolios. The Risk Parity Tower of Babel (RPTB) endures.

RPTB Comes to Chicago
Eugene-Fame-or-Don-Rickles?I was glad to see that Eugene Fama had agreed to appear at the CFA Institute annual meeting in Chicago this past spring. Fama is always interesting, opinionated, and he does not speak in public often enough. Former students know he is often quite funny, sometimes hilarious. At times taking a class from him seemed like taking a class from Don Rickles.

In class Fama spent considerable time discussing empirical papers. Whenever he wanted to fast-forward the discussion he would just ask, “OK, what’s the punch line?”

Fama delivers the punch line
Listen to this interview of Fama at this year’s CFA conference in Chicago.

Even if you’re not a CFA Institute member you may listen to the session in iTunes, and I encourage you to do so.

While it is interesting throughout, the session becomes comical at the 41st minute. Here is my attempt at a transcription:

Interviewer: “What do you think of the risk parity asset allocation strategy?”

Fama: “Never heard of it.”

Fama: “What is it…”

Interviewer: “OK…” (laughter) “uh…”

Fama: “…in my terms?”

Interviewer: “I think it’s the idea that you, uh, find a bunch of different asset classes…”

Fama: “mm-hmm”

Interviewer: “…and then use leverage to get them all to the same volatility. Equal risk across different asset classes…”

Fama: “OK.”

Interviewer: “and, uh, Bridgewater has done this very successfully for a long time.”

Fama: “OK. Stupid!”

(Loud laughter)

Interviewer: “OK.”

Fama: “If you think about your portfolio problem, you never start with a proposition like that. What you’re thinking about if you’re a mean-variance investor is, how do I form these things to minimize variance? That would not tell you to lever them up all in the same way.”

Chicago Booth comedy
One of Fama’s best known students is Cliff Asness, co-founder of AQR and one of the world’s best known hedge fund managers. Asness is also one of the most vocal proponents of risk parity. I assume Fama and Asness are on pretty good terms since in 2004 Asness endowed $1 million to Chicago Booth for classroom in Fama’s name. Fama asking “what it it?” shows that when he and Asness communicate, they’re not talking shop!

Reconciling “stupid” with non-stupid practitioners
Fama is correct: A mean-variance investor would never leverage bonds as the interviewer described.

At the same time, Cliff Asness is not stupid, and neither is risk parity. Nor are Ray Dalio, Wai Lee, Bob Prince, or Ed Qian, to name a few of its better known practitioners.

I will attempt to explain why risk parity is not stupid, and reconcile the explanation with Fama’s take. It’s really quite simple:

Risk Parity investors are not mean-variance investors!

As Fama elaborated on his answer he qualified his interpretation as that of a mean-variance investor. But a risk parity investor is not a classic mean-variance investor!

The difference between a mean-variance investor and a risk parity investor
A mean-variance investor’s objective is to maximize return relative to risk, consistent with his utility for return versus risk. A risk parity investor’s objective is to maximize a specific type of diversification, that being contribution to portfolio variance. By ignoring expected return in his objective function, an risk parity investor is implicitly skeptical or agnostic about modeling expected returns. No “mean” -> no “mean-variance”.

The interviewer’s description was due to the Risk Parity Tower of Babel. I would have preferred the interviewer to have said “risk parity is an allocation method in which the assets’ contributions to portfolio variance are equal. By the way, Cliff Asness is one of its loudest evangelists.”

Sep 262012

Many of this site’s visitors are interested in learning about risk parity, especially how to obtain risk parity weights using Excel. The PortfolioWizards Risk Parity Excel workbook is easily the most popular download on the site.

Recently a hedge fund manager contacted me who had been playing with the risk parity workbook. He asked whether it is possible to have a risk parity portfolio with short positions. The short answer is: sometimes.

To test this idea I used the 5-asset risk parity workbook and altered its configuration. I wanted to allow one asset’s weight to be negative; this required I remove the constraint Weight>=0 and add a constraint that the weight be less than zero for the asset I wished to sell short. I was able to obtain risk parity portfolios with Commodities sold short, with REITs sold short, and with Bonds sold short. However I was unable to find risk parity allocations with either US Stocks or International Stocks sold short.

In order to obtain the respective results with short positions in either of Commodities, REITs, or Bonds, Solver did not find the weights without help. I had to play with the starting weights (especially for Bonds), giving Solver a hint.

NB: The out put from this workbook reflects its inputs, which I made up. Do not mistake them for forecasts or predictions. The numbers are intended as placeholders for your own assumptions. Do not rely on the numbers provided.

5-asset Risk Parity portfolio, Short Commodities


5-asset Risk Parity portfolio, Short REITs


5-asset Risk Parity portfolio, Short Bonds
The “short bond” portfolio is long 100% risk assets and short nearly 300% bonds. Interestingly its allocation resembles a poor man’s 2x inverse of E-Trac’s risk-off ETN, OFF, short nearly 3x capital in Bonds and long everything else.

This does not prove risk parity solutions are always possible, never mind advisable
It really depends on your assumptions about your assets’ covariances. I populated the risk parity workbooks with fictitious data, including a correlation coefficient between US and International stocks of 0.95, which is really more of a “stress environment” correlation coefficient than a typical one. With a lower correlation coefficient between them, the possibility for a risk parity portfolio grows.

Caveat Venditor!
While this is a fun diversion, keep in mind that the distribution of returns for an asset sold short is quite different from that of an asset held long. A covariance alone is probably insufficient to capture the risk of a short position. A long position’s worst possible return is -100%; a short position’s is unlimited. It’s easy for inexperienced investors to dismiss that difference, but from a risk management perspective that difference is critical. Further, the dynamics of managing a portfolio with short positions feel backward. “Good” trades result in smaller and smaller positions, which means if you wish to adhere to your risk budget you have to sell short more and more. “Bad” trades grow position sizes, requiring you to buy (gulp) something that has risen in price in order to trim your position.

May 122012


For several years I managed quantitative equity portfolios at Freeman Investment Management. The firm had been a pioneer in creating low volatility strategies, both long-only and long-short.

In addition to managing low volatility portfolios, at Freeman we had been advocating using volatility indices instead of style indices, both as performance benchmarks and as explanatory variables in style analysis. We had created and maintained our own analogs to the Russell style indices in which we divided the Russell 1000 and 2000 universes into Low Volatility and High Volatility halves, reconstituting on the same schedule as Russell. The table below offers a performance summary.

Return measureFreeman 1000
Low Volatility
Freeman 1000
High Volatility
Freeman 2000
Low Volatility
Freeman 2000
High Volatility
Arithmetic mean11.93%11.96%14.62%12.31%
Geometric mean11.64%10.45%14.32%9.55%
Std. Deviation13.13%19.68%15.04%24.77%
Annualized monthly return statistics, 1979 – January 2010. Excludes IPOs. Source: Freeman Investment Management

As unimpressive as these results are for High Volatility stocks, keep in mind these are well diversified cohorts containing several hundred stocks. The results are even worse for the High Volatility stocks if you slice the universes into volatility deciles.

Given these results, why would a rational investor hold High Volatility stocks?
We used to ask clients, consultants, and prospects that question all the time. It was rhetorical, but I believe I now know the answer.

In September 2011 I wrote a post about modeling expected returns. In that post I wrote about the method described by Jacquier, Kane, and Marcus for obtaining an unbiased estimate of return over a forecast horizon of length H, given observations from a sample period of length T.

It surprises many to learn that the unbiased estimation formula is a weighted average of the Arithmetic mean and the Geometric mean of the sample return data, and that the weights depend on the ratio of the length of the future horizon, H, to the length of the sample period, T:

Expected log return over H periods =

(1-  \frac{H}{T} )   \hat{ \mu_A}  +   \frac{H}{T}  \hat{ \mu_G}

where   \hat{ \mu_A} and  \hat{ \mu_G}  represent the respective logs of the arithmetic and geometric means of the sample period.

So what does this have to do with rational investors holding volatile assets?
This formula implies that, given a long enough forecast horizon H, all assets with positive volatility have an unbiased expected return that is negative. Not just High Volatility assets, ALL assets. The Arithmetic Mean is always greater than the Geometric Mean, so if you keep extending the forecast horizon H, eventually the unbiased forecast return becomes negative.

When you rebalance a diversified portfolio, you are engaging in volatility capture. So long as you rebalance regularly, as a rational investor you should hold volatile assets in your portfolio; how much depends on your rebalancing and holding period horizons.

Dec 272011

With as much fun as I’ve been having consulting and blogging for PortfolioWizards, I have decided to accept an offer to join GuidedChoice, a robo-advisor located in San Diego.


GuidedChoice has an accomplished team of professionals including Sherrie Grabot, Harry Markowitz, Ming Yee Wang, and Ganlin Xu. They have worked together for over a decade. I look forward to joining the team and contributing to the firm’s future.

Thank you to all my clients, friends, and supporters.

PS: Just don’t turn off that RSS feed.

 Posted by on December 27, 2011 GuidedChoice 1 Response »
Dec 222011

Dynamic Trading Rules: Change the Time Window and a Different Picture Emerges
Further examining a 200-day Moving Average (200MA) strategy for mitigating downside risk, I was recently examining how the picture changes when you alter the time window for assessing these strategies.

Below is a scatterplot of a dynamically managed strategy using 200MA (vertical axis) versus Buy & Hold (horizontal axis). It excludes assumptions about transaction costs, slippage, and interest on cash.

200MA-comparison-trading-daysOne day price returns, S&P 500 Stock Index, October 19, 1950 – December 16, 2011
Source: PortfolioWizards, Yahoo! Finance
Past performance does not predict future performance


The plot above doesn’t tell you much, because you basically see a diagonal line when the 200MA is invested and a horizontal line when it’s not.

Group these trading days into proper calendar months, and the picture shifts a bit.

200MA-comparison-calendar-monthsOne month price returns, S&P 500 Stock Index, November, 1950 – November, 2011
Source: PortfolioWizards, Yahoo! Finance
Past performance does not predict future performance


Now we’re starting to see something vaguely resembling the payoff diagram of an at-the-money call option, but not quite. The one thing that’s clear: this scatterplot has an unequivocal lack of observations in the upper left quadrant, meaning if there’s a return advantage at all it DOESN’T come from positive returns while the market is down; it would have to come from compounding zero or small negative returns when the market is down a lot more.

What if we freed ourselves from examining calendar-based time windows? What if we just looked at “round-turns,” where a “round-turn” is measured over a full cycle of being fully invested and fully uninvested, regardless of how long or short those cycles might be?

When we do this, the picture clarifies.

200MA-comparison-buyhold-round-turnsRound-turn price returns, S&P 500 Stock Index, October 19, 1950 – December 16, 2011
Source: PortfolioWizards, Yahoo! Finance
Past performance does not predict future performance


This picture is remarkably similar to that of an at-the-money call option. It would appear that the way an effective volatility management strategy depending on 200MA works is it allows you to participate in protracted positive runs and limits your participation in protracted negative runs.

What are the risks?


  • transaction costs might be considerable
  • round-turns could be as short as two trading days or as long as several calendar years
  • total returns would be different, as these plots ignore the positive returns due to dividend income
  • this strategy is vulnerable to price jumps in both directions – it offers no protection for abrupt price drops in tame market environments, and won’t participate in rebounds after protracted market declines
  • this discussion is silent on how to implement this information in your asset allocation process, or whether you even should do it at all

Dec 212011

This year I’ve written a few times about using the 200-day Moving Average (200MA) as a market timing indicator.

Evolved Perspective on the 200-Day Moving Average
Since my last posts my appreciation for and complaints about 200MA have evolved. I previously wrote that if enough speculators begin blindly following the 200MA it could lead to market instability, reminiscent of portfolio insurance becoming so popular by October 1987. I since have realized there is a huge difference between following a 200MA trading rule and employing portfolio insurance: the portfolio insurance strategy calls for you to keep selling as the market falls while the 200MA rule calls for you to sell only once. That simple difference, I think, makes the 200MA potentially far less destabilizing than portfolio insurance.

Forget About Timing Returns; Focus on Timing Volatility
I’m more of a sigma guy than an alpha guy. Get the risk control right, I figure, and the returns should take care of themselves. Hence I much prefer to assess 200MA in terms of separating periods of higher and lower volatility than in terms of separating periods of higher and lower returns.

In that respect it seems to do an excellent job.

Below is a comparison of cumulative returns to SPY since inception in January 1993 between a Buy&Hold strategy and a zero trading cost, zero slippage 200MA strategy, where you hold SPY only on days following when the prior day’s close exceeded its 200MA (and otherwise earn zero on uninvested cash). Bottom line: depending on the endpoint, you get 70% to 130% of the Buy&Hold return while being invested only 2/3 of the time, for essentially 2/3 of the volatility.

Source: PortfolioWizards, Yahoo! Finance
Past performance does not predict future performance.

Watch Out: Spreadsheets Don’t Know When You Forgot to Offset Your Inputs
I cannot emphasize enough that any apparent return advantage or disadvantage seems to depend entirely on your beginning and ending points. End the analyis in February 2009 and 200MA seems like a can’t miss strategy; end it in February 2000 and you’re fired.

But cumulative returns aside, I have to admit its ability to sit out protracted periods of high volatility and drawdown is fairly convincing.

All that said, beware of making a rookie mistake. The earliest price available on Yahoo! Finance for SPY was January 29 1993, making November 11, 1993 the first trading date available with a 200-day average. This means the earliest you could have realistically executed a 200MA strategy would have been November 12, 1993, employing the 200MA threshold as of November 11, 1993. A rookie mistake would be to anchor the decision criterion for November 12 on the November 12 200MA, which of course you could not have known. While you might think a single day look-ahead bias might taint the results negligibly, the actual bias is, as Will Farrell would say, ginormous.

Assuming perfect foresight of whether the day’s closing price would be above or below the 200MA – an offset of only one row in your decision criterion – would have resulted in a simulation looking like this:

Source: PortfolioWizards, Yahoo! Finance
This illustration depicts a strategy result assuming perfect foresight, which is not and would not have been possible.

So, if you’re going to manage portfolio composition according to 200MA indications of higher and lower volatility, be my guest. Just make sure if you simulate a result too good to be true, it probably is.

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