For the past 60 years, digital computers (DCs) have become indispensable tools of modern society. Algorithms are so pervasive that we use them every day barely noticing. Algorithms perform most of commercial flights’ operations, choose our commuting route for avoiding traffic, find the websites that match a searched term… Our smartphones are more powerful than the systems used by NASA to put a man on the moon. Why would we need a new computing paradigm, when the current one seems to satisfy our every need?

No matter how fast and powerful DCs may become, some problems are simply intractable. Finance has a good lot of them. A few examples:

- Dynamic portfolio optimization: Computing an optimal trajectory for a portfolio under realistic assumptions is a NP-Complete problem. See an example here: http://ssrn.com/abstract=2649376
- Clustering: Clustering algorithms often rely on heuristics. It would be desirable to replace some of these heuristics with a brute force search over an unfathomably large number of combinations. Good clustering methods have applications on risk management and regression analysis. See an example here: http://ssrn.com/abstract=2708678
- Scenario analysis: Often investors would like to evaluate the distribution of outcomes under an extremely large number of scenarios, generated at random. Current approaches, like copulas, are too unrealistic/restrictive.
- Option pricing: Some complex derivatives are path-dependent. Evaluating a large number of paths can be computationally expensive.

There is no hope for solving these problems in polynomial time, much less ever finding a closed-form analytical solution. Quantum Computing (QC) offers the promise of being able to solve these problems in a matter of days, rather than in years.

Suppose that you are a large asset manager. Every time you rebalance your portfolio, your investors lose a fortune, as a consequence of transaction costs and price impact (slippage). In an environment where most funds struggle to make single digit returns, losing 3% on rebalancing costs is a death sentence by a thousand cuts. A QC could find a portfolio that is globally optimal over multiple investment horizons, hence significantly reducing the need for rebalances and their associated losses. QCs’ advantage is not that they can compute such portfolio faster than DCs. DCs simply cannot solve this problem for us. A second advantage is, by reducing the need for rebalancing, large asset managers will starve the high frequency algorithms that prey on them. So rather than trying to legislate against high frequency algorithms (a task that, 6 years after the flash crash, has led to nothing), maybe we should just let them go bankrupt.

This is merely one example of how QCs could solve several major challenges faced by finance professionals. In a few years, QC applications will disrupt finance just as much as the DCs transformed our business decades ago. And like with every disruptions, there will be winners and losers. It is important for professionals to become acquainted with some basic features of QCs, so that they don’t get left behind.

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MichalMay 11, 2016With all due respect, Marcos, an assumption, on which a causation cit.: “most funds struggle to make single digit returns, losing 3% on rebalancing costs” stands, sounds rather wild, while there is certainly a big distinction between the motivations — those applicable for funds are by far other than expectations of those, who have put their funds into Assets-Under-Management investment pool.

Please, do you have any quantitative data support or any public source(s) citation(s) for such opinion?

Thank you for your kind answer on this subject, in advance & looking forward to fresh Q4Q news.

Marcos Lopez de PradoMay 11, 2016Hi Michal, thanks for your comment.

Let me give you an example. Corporate bonds constitute a very popular asset class among institutional investors. U.S. investment grade corporate bonds have an average bid-ask spread of over 1.5%. U.S. high yield corporate bonds have a wider bid-ask spread, of several percentage points. Other asset classes, like real estate or private equity, have even larger bid-ask spreads. And that’s just for trading the first $1!

Large asset managers experience transaction costs much greater than the bid-ask spread, because of the market impact from large transactions no only widens the bid-ask spread, but it also displaces the mid-price.

SarvagyaApril 11, 2019This post makes a bold assumption that quantum computing can be a paradigm shift in financial modeling, risk management and/ or portfolio optimization. While I am a big proponent of quantum computing, I haven’t seen any serious paper that does try to tackle fundamental challenges in financial modeling. You did list two references one of which aims at using quantum annealing approach to solving multi-step portfolio optimization. But why focus on quantum adiabatic model (and convert it into a QUBO) when we can also employ gate model? Developing quantum optimization algorithms that (approximately) solves the problem…

mayukh mukhopadhyayJuly 3, 2019Dr. Marcos,

Visionary article. Would love to have an Appendix or a supplement chapter in the next reprint of your equally phenomenal book, AIFML, on Quantum Finance.