# Do hedge fund trading desks use portfolio optimization?

I tend to think that hedge funds that actively trade (and most of the ones I have seen trade very actively), don't use optimization methods like MVO or Black-Litterman.

Not only do they need to come up with E(R) and risk levels for their thousands of positions, but because their portfolio turns over so often, the outputs are pretty much meaningless the next day. Am I correct in this assumption?

IF so, who uses optimization methodologies? Mutual funds? Pension Funds?

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## 3 Answers

I work on Quant hedge fund. My answer is: YES and NO:) Advanced optimization techniques are popular in academia but less useful on the street.

Specifically, the answer really depends on which type of strategies you are trading.

• For equities long-short portfolios, some level of optimization is needed, partly because they need to trade on large sizes on hundreds of stocks.

• Statistical arbitrage guys tend to have market-neutral positions, and they need optimization to achieve beta or dollar neutrality.

• For futures trading shops, the scope of optimization is rather small. Since contract value of futures is usually large and contract size is integer number only, you don't usually need to use sophisticated optimization technique to decide whether you want to trade 8 lots or 10 lots. In this case, maybe integer programing is more relevant.

• For fundamental guys, their position sizing is quite discretionary, and optimization is not usually required.

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Portfolio optimization techniques are used quite a bit by hedge funds. I think you misunderstand how portfolio optimization operates in the context of an active trading strategy. Your question suggests a view of portfolio optimization as a tool to adjust portfolio weights arrived at by a separate, active strategy. Under that approach, you are correct, the weights would no longer be optimal if the active strategies are allowed to turn positions over without any re-optimization of weights.

However, there is nothing stopping funds from optimizing their portfolio daily and even intra-day. Also rather than thinking of the trading strategy and portfolio optimizer as distinct systems, consider these as a single, integrated system. The "trading strategies" are really just E(R) (in your symbology). If the view on a stock changes then E(R) changes and the portfolio can be re-optimized to reflect this change. This way, the portfolio optimization is the source of the trade rather than something tacked on afterwards. The more often E(R) change significantly, the more "active" the strategy is.

There is a substantial literature describing portfolio optimization techniques intended for active management. This paper is a nice place to start. The distinguishing characteristic of these approaches is that they account for transaction costs. Absent costs, it is adequate to just compute optimal weights whenever an input changes using standard techniques. Accounting for costs requires us to model how the weights are changing in time, which standard techniques do not address. I also suggest you take a look at the optimal execution literature, as there is much overlap.

Although many funds do use portfolio optimization with active strategies, there are various reasons why some funds choose not to. Some lack the specialized expertise to formulate and solve the relevant problems quickly and reliably. Many funds reason that finding accurate return forecasts is more important than portfolio risks and so focus their resources on the former. It can also be difficult to get portfolio managers and traders to accept a single optimized solution as they often prefer to have control over their own positions. Lastly and perhaps most importantly, portfolio optimization has a definite stigma attached to it by the practitioner community. I believe the oft committed mistake is in thinking of portfolio optimization as a "turn the crank" procedure rather than as certain general ideas that usually need to be carefully applied to the specific problem domain.

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My experience in statistical arbitrage desks (primarily equities) and CTAs is somehow different than @Simon's. From my perspective, I have used and seen plenty of portfolio optimization tools. However, I have most often operated in a layered architecture.

A layered architecture is an architecture where independent automated traders are stacked, each and everyone independent from the others. For example, if the desk would only trade stock pairs, in such architecture you would have $n$ automated pair strategies on $n$ different pairs. Every strategy aims for market neutrality, according to the definition of market neutrality most appropriate for the strategy implemented within the trader.

On top of the automated traders there's the porfolio management software which:

1. allocates capital between the traders exploiting a portfolio optimization algorithm; Therefore, the input of the optimization problem is not the expected distribution of each single asset returns but the expected distribution of the returns of each trading strategy
2. consolidates orders, netting off positions: a buy order of 10 SPX from trader A, and a sell order of 5 from trader B will trigger a buy order of 5 at porfolio level;
3. manages risks, enforces compliance, etc

In terms of literature, the most popular portfolio optimization book I have seen on desks is Attilio Meucci's "Risk and Asset Allocation" (Springer, 2009)

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