Andrew Ang of Columbia Business School has an important new paper out on SSRN. In it, he discusses mean variance optimization, the cornerstone of Modern Portfolio Theory. Unlike many other treatments in which portfolio construction through mean variance optimization is taken as gospel, Mr. Ang actually tests mean variance optimization against a wide variety of other diversification methods. This is the first article that I have seen that actually tries to put numbers to mean variance optimization. Here’s how he lays out his horserace:

I take four asset classes: U.S. government bonds (Barcap U.S. Treasury), U.S. corporate bonds (Barcap U.S. Credit), U.S. stocks (S&P 500), and international stocks (MSCI EAFE), and track performance of various portfolios from January 1978 to December 2011. The data are sampled monthly. The strategies implemented at time

tare estimated using data over the past five years,t-60tot. The first portfolios are formed at the end of January 1978 using data from January 1973 to January 1978. The portfolios are held for one month, and then new portfolios are formed at the end of the month. I use one-month T-bills as the risk-free rate. In constructing the portfolios, I restrict shorting down to -100% on each asset.

He tests a wide variety of diversification methods. As usual, simple is often better. Here’s his synopsis of the results:

Table 14 reports the results of the horserace. Mean-variance weights perform horribly. The strategy produces a Sharpe ratio of just 0.07 and it is trounced by all the other strategies. Holding market weights does much better, with a Sharpe ratio of 0.41. This completely passive strategy outperforms the Equal Risk Contributions and the Proportional to Sharpe Ratio portfolios (with Sharpe ratios of 0.32 and 0.45, respectively). Diversity Weights tilt the portfolio towards the asset classes with smaller market caps, and this produces better results than market weights. The simple Equal Weight strategy does very well with a Sharpe ratio of 0.54. What a contrast with this strategy versus the complex mean-variance portfolio (with a Sharpe ratio of 0.07)! The Equal Weight strategy also outperforms the market portfolio (with a Sharpe ratio of 0.41). De Miguel, Garlappi and Uppal (2009) find that the simple

1/Nrule outperforms a large number of other implementations of mean-variance portfolios, including portfolios constructed using robust Bayesian estimators, portfolio constraints, and optimal combinations of portfolios which I covered in Section 4.2. The1/Nportfolio also produces a higher Sharpe ratio than each individual asset class position.

That’s a lot to absorb. If we remove the academic flourishes, what he is saying is that **mean variance optimization is dreadful** and is easily outperformed by simply equal-weighting the asset classes. He references Table 14 of his paper, which I have reproduced below.

(click to enlarge to full size)

(He points out later in the text that although risk parity approaches generate a slightly higher Sharpe ratio than equal weighting, it is mostly due to bonds performing so well over the 1978-2011 time period, a period of sharply declining interest rates. Like most observers of markets, he would be surprised to see interest rates decline dramatically from here, and thus thinks that the higher Sharpe ratios may be unsustainable. Mr. Ang also mentions in the article that using a five-year estimation period isn’t ideal, but that using 20-year or 50-year data is no better.)

I find it ironic that although mean variance optimization is designed to maximize the Sharpe ratio—to generate the most return for the least volatility—in real life it generates the worst results. As Yogi Berra said, in theory, theory and practice are the same. In practice, they aren’t!

Mr. Ang also asks and answers the question about why mean variance optimization does so poorly.

The optimal mean-variance portfolio is a complex function of estimated means, volatilities, and correlations of asset returns. There are many parameters to estimate.

Optimized mean-variance portfolios can blow up when there are tiny errors in any of these inputs. In the horserace with four asset classes, there are just 14 parameters to estimate and even with such a low number mean-variance does badly. With 100 assets, there are 5,510 parameters to estimate. For 5,000 stocks (approximately the number listed in U.S. markets) the number of parameters to estimate is over 12,000. The potential for errors is enormous.

I put the fun part in bold. *Tiny* errors in estimating returns, volatilities, or correlations can cause huge problems. Attempting to estimate even 14 parameters ended in abject failure. We’ve written numerous pieces over the years about the futility of forecasting, yet this is exactly the process that Harry Markowitz, the father of Modern Portfolio Theory, would have you take!

Good luck with that.

To me, the implications are obvious. Diversification is always important, as it is a mathematical truism that combining *any* two assets that are not perfectly correlated will reduce volatility. But simple is almost always better. Mr. Ang draws the same conclusion. He writes:

Common to all these portfolio strategies is the fact that they are diversified. This is the message you should take from this chapter. Diversification works. Computing optimal portfolios using full mean-variance techniques is treacherous, but simple diversification strategies do very well.

The “simple is better” idea is not limited to asset class diversification. I think it also extends to diversification by investment strategy, like relative strength or value or low volatility. There’s an underlying logic to it—**simple is better, because simple is more robust**.

Some investors, it seems, are always chasing the holy grail or coming up with complicated theories that are designed to outperform the markets. In reality, you can probably dispense with all of the complex theory and use common sense. Staying the course with an intelligently diversified portfolio over the long term is probably the best way to reach your investing goals.

[…] On the downside of mean-variance optimization. (Systematic Relative Strength) […]

[…] durable portfolios. We’re just never going to get to some kind of optimal portfolio. Mean variance optimization, in fact, turns out to be one of the worst methods in real life. We’ll have to make do with durable portfolio construction. It may be messy, but a […]

[…] Orthodox thinking will keep you out of trouble. In the investment industry, if you build a client’s portfolio in rigid conformance with Modern Portfolio Theory, your firm will back you and it is unlikely that you will ever be successfully sued, regardless of how horribly things turn out for the client. And make no mistake—building portfolios based on mean variance optimization doesn’t have a very good track record. […]

[…] Modern Portfolio Theory Implodes: Mean Variance Optimization Bites the Dust An older post well worth a read, especially when tempted to add another layer of complexity to your method. You know you want to. […]

[…] play a supporting role. All of these factors are moving targets, none more so than returns. Mean variance optimization, in practice, is a complete bust because obviously no one can reliably and consistently predict […]

“In recent weeks, I really wanted to keep the other aspects of the magazine intact

This immense explosion of outrage and horror around this episode wouldn

programs like “Law and Order” and legal commentators on cable TV news shows shape public opinion by depicting defense lawyers as arrogant and greedy.Looking at the Senate, Three Republicans joined seven Democrats in the majority.With the playoffs well out of reach The chances were there during an encouraging second half. (Obama cut his request for new spending from $200 billion to $80 billion, they say. Free”Lean on Me” A six-week nutritional and exercise program for ages 9-15 Meets Tuesdays and Thursdays through Oct 17 5:30-6:30 pm Patuxent Health Center 230 W Dares Beach Rd, 410-535-8233.

I like it when individuals gget together and share views.

Greaqt blog, keep it up!

my blog post yahoo web hosting help (bigcontact.com)

Hello everybody, here every one is sharing these knowledge, therefore it’s

good to read this weblog, and I used to visit this web site every day.

Remarkable! Its in fact awesome post, I have got much

clear idea on the topic of from this paragraph.

My weeb page – cremation pricing

Attractive component of content. I simply stumboed upon your webssite and in adcession capitall tto

say that I acquuire actually enjoyed account your blog

posts. Anyway I will bbe subscribing in yur aygment and even I fulfillment yoou

get admission to constawntly rapidly.

Alsso vijsit my site … sacramento cremation

I do not even understand how I finished up right here, however

I assumed this publish used to be great. I don’t recognize

who you are but definitely you are going to a famous blogger for those who are

not already. Cheers!

excellent put up, very informative. I’m wondering why the opposite

specialists of this sector do not notice this. You must proceed your

writing. I’m confident, you’ve a great readers’ base already!

of course like your web site however you need to check

the spelling on several of your posts. A number of them are rife with spelling issues and I to find it

very troublesome to tell the reality then again I’ll certainly

come again again.

I do not even know the way I finished up right here, but I thought this post used to be great.

I don’t understand who you’re but definitely you are going to a well-known blogger

if you are not already. Cheers!

Thanks designed for sharing such a pleasant opinion, paragraph

is nice, thats why i have read it completely

Mr Andrew Ang, garbage in garbage out. You confuse a methodology using a black and white construct. I have had remarkable results with MVO. However, it takes work. There are many factors/inputs/constraints plus the universe of instruments. Try exploding out the universe to give the model a greater ability to differentiate. This is an art and science. Academics perhaps would do a better job if they were managing real money and their jobs were at stake. It appears that Mr Ang started with the hypothesis that MVO is useless and then proceeded to find and example and data to prove his hypothesis. Mr Ang you are no Nobel prize winner and I would applaud your conclusions if you offered a superior alternative.

To conclude:

To conclude our webinar, Markowitz provided two excellent quotes. The

first relates to the art of mean–variance optimization: “In the right hands,

mean–variance analysis is as flexible as a set of oil colors in the hands of

Picasso, Van Gogh, or Rembrandt, and in the wrong hands, it’s just paint by

numbers and you don’t know what you’re going to get.” Finally, with regard to

investing in general and dealing with all of the unknown variables, he shared

advice he was given by a professor when he was young: “Don’t ask, ‘What do

I know?’ Ask, ‘How should I act?’”

* * * *

However, the world’s leading digital lifestyle brand product wins recently launched series of ultra-thin 0.7mm iPhone5 phone protective shell, which is the world’s leading mobile phone shell with NGT technology, which addresses the phone too thick shell bad experience, letting the phone shell more toughness, not easily deformed, seemingly played better protection gap thickness is only 0.1mm, but the story is far behind not so simple.

Appreciation to my father who told me concerning this weblog, this website is in fact awesome.

cbd oil 1oz (30ml) with 100mg CBDModern Portfolio Theory Implodes: Mean Variance Optimization Bites the Dust • Systematic Relative Strength • Dorsey Wright Money Management Systematic Relative Strength

I am impressed with this web site, really I am a big fan.

Yoս coulɗ ɑlso receive money fοr Һaving fun іf you prefer to play

games օn tһе Web ᴡithin yoᥙr time!

You wil fіnd Web siges tһɑt may pay tɦeir customers tо plasy games, гead

е-mails, ɑnd join online survey sections.

Great goods from you, man. I have understand your stuff

previous to and you are just too excellent.

I really like what you have acquired here, really like what you are stating

and the way in which you say it. You make it enjoyable and you still care for

to keep it sensible. I cant wait to read far more from you.

This is actually a terrific site.

Hindi Motion pictures – Get information on the newest Hindi Motion pictures, New Hindi Movie Releases, Bollywood Motion pictures releasing this week and upcoming Hindi Films on Bollywood Hungama, India’s premier bollywood

portal.