Why Mean-Variance Optimization Is Difficult to Apply Reliably

# Does mean-variance portfolio optimization provide a real edge to those who use it?


# Does mean-variance portfolio optimization provide a real edge to those who use it?












Mean-variance optimization (MVO) is a 50+ year concept, and perhaps the first seminal idea of quantitative finance. Still, as far as I know, less than 25% of AUM in the US is quantitatively managed. While a small minority of fundamental managers use MVO, that is counterbalanced by statistical arbitrage and HF strategies that often use optimization but not MVO, so the percentage of AUM not allocated using Markowitz' invention is surely not less than 70%. My questions:

- if MVO is such a great idea, why after all this time, so few people use it?

- if MVO was such a bad idea, how come companies like Axioma, Northfield and Barra still make money off it?

- is there there a rationale for the current mixed equilibrium of users and non-users?

A few caveats on what I just said: i) perhaps the first and most important idea in finance is that of state-contingent assets, which is Arrow's; ii) I am focused on the buy side. I believe that optimization is widely used for hedging on the sell side.

## Answer by Patrick Burns (score 11, accepted)

https://quant.stackexchange.com/a/362

Hey, it's early days yet. After all it is still called MODERN portfolio theory.

I think there are two main issues and they are both really cultural:

1) specifying alphas 2) wild results

Alphas

I agree with Gappy that alphas are the key thing you need to have effectiveness (unless you are doing minimum variance). Having a vector of expected returns is quite a natural thing for quant managers. But it is something foreign to fundamental managers. They have to map their views into a number for each asseet in the universe. That is not necessarily an easy task, and probably would seem like busywork.

I've proposed an optimization that minimizes distance to an ideal target portfolio (subject to constraints). But I haven't exactly been overrun with fundamental managers clamoring for it.

Wild answers

If you take a textbook optimization at its word, you're likely to do some pretty strange things. That has given optimization quite a bad reputation in many quarters. The solution is quite simple: either impose a turnover constraint or increase trading costs to account for the uncertainty of the expected returns (and, less so, the variance matrix). Using trading costs is the better approach but getting the trading costs right is a project in itself.

## Answer by glyphard (score 4)

https://quant.stackexchange.com/a/337

- The biggest problem with mean-variance optimization is that the sensitivity of the estimated covariance matrix. Mean variance optimization assumes that one "knows" the covariance of each asset with every other asset, or that the covariance matrix is constant. Without this assumption the MVO framework is not tractable.

- Axioma and others do a lot more than just MVO.

- None of the approaches are foolproof. An approach that is easy to calculate (MVO), usually has some unpalatable consequences. Things that are difficult to calculate usually provide a false sense of security when it comes to robustness.

Wilmott is a good source to consult for the balance between easy and complex.

## Answer by Hans Radtke (score 4)

https://quant.stackexchange.com/a/365

In addition to the points above, I'd say that asset managers also have to bear two things in mind that limit their ability to "properly" optimise their portfolios:

1) general restrictions on asset allocation (regulatory, contractual, common-sense) 2) transaction cost

In my experience, asset managers do use a variety of optimisation techniques occasionally (rather than constantly) and in order to inform their decisions (rather than trading on them 1:1). Quite often, they would also get their brokers to run an optimisation after whatever technique is currently in fashion and to suggest appropriate trades on the back of that. They will then think about it - which is, after all, what active managers are being paid for - and do what they think is sensible.

Hans

## Answer by MichaelJ (score 1)

https://quant.stackexchange.com/a/12840

- Most money is not quantitatively managed, as you point out. If those managers don't use any quantitative methods in their process then it doesn't really matter if MVO is a 50+ or 500+ year old concept. Also, since there are many subtleties to proper application of these techniques to a particular strategy, it is unlikely that a manager would use them if she didn't understand them thoroughly. Among quant managers, the techniques are quite common although they are certainly not universally applied.

- You seem to be thinking about this in a bit of a black and white way. A lot of people use these methods so there is a market for software implementations. The universe of potential MVO users includes prop shops, banks, hedge funds, fund of funds, mutual funds, and individuals. This is a diverse set of market participants. There are users and non-users of MVO in all of these groups.

- The basic issue is that MVO can often lead to (provably) worse performance when estimates of returns are too far from realized values. The percentage of money managers that produce numerical return predictions as part of their process is really quite small. Many self-proclaimed quant funds trade mechanical buy-sell rules tuned via back-testing and do not use any explicit models for forecasting. In this context, return predictions are slapped on after-the-fact so that MVO can be attempted. This can create systematic errors in the forecasts that completely undermine the optimization. Proper application of the techniques needs to combine good models of forward returns, sensible constraints, adequate accounting for and modeling of transaction costs, and accurate forecasts of volatilities and correlations. Messing up any of these components can ruin the system. Few managers have the expertise to apply the methods successfully.

## Answer by NBF (score 0)

https://quant.stackexchange.com/a/63795

I agree. Any old covariance matrix works pretty much. This is why we have risk parity and hierarchical risk parity which are basically restrictions on covariance (diagonal or block diagonal) which on the surface seem pretty extreme but really are meh. The main reason for their success is the restrictions on alphas which are notorious hard to estimate and estimate consistently.

Axioma does sell indices. And it sells super cool robust versions of MVO. But the bog standard ones are the primary drivers. In spite of their issues MVO is used by a great number of quant equities or quantamental equities funds. Barra is everyone’s risk model of choice.

## Answer by elbarto (score 0)

https://quant.stackexchange.com/a/63812

In quite a seminal paper, the authors actually show most of the time, naive diversification ($1/N$) outperforms all kinds of fancy optimization strategies.