- Portfolio Optimization
- >
- Identify common stock portfolios from entire US stock exchanges (quantum & classical, up to 3,600 stocks)

## Identify common stock portfolios from entire US stock exchanges (quantum & classical, up to 3,600 stocks)

**SKU:**

**What you do:**

You select the US common stock exchanges for us to analyze (one, several or all). You may have other choices and comment boxes to complete during checkout.

Once you place your order, please email us (or text) your information:

- Your name
- Your email address(es)
- Your phone (optional, in case we need to reach you)
- Any special requests

Please email these to jeffrey@quantum-usaci.com and research@quantum-usaci.com, or text to 1.312.515.7333 (US, Verizon Wireless)

Your payment confirmation comes from the payment processor.

**What we do:**

We run our analysis and select the best portfolio(s) according to our quantum algorithm. We return you a .PDF report via email (or another way you prefer). We return it within 24 hours...possibly much faster.

The report will list any unique results from data validation and the best portfolio(s) we find. If our solvers do not converge on one 'best' portfolio, we provide you the portfolios they do find. We will always provide you the best portfolio chosen by the quantum annealing computer (D-Wave Systems Advantage 1.1 or 2000Q). We provide you any insights from the run (e.g., was it easy to find a 'best' portfolio, did certain solvers do better).

Phase 1: We analyze all the stocks in the exchange that pass data validation to find the best 'N' stocks in a portfolio, typically between 60 & 130 stocks. We provide you this large, efficient & diversified portfolio of 'allstars.'

Phase 2: We analyze that 'allstar' portfolio of N stocks (typically 60 to 130 stocks) to find the absolute best portfolio with the lowest CQNS score. We use the quantum annealing computer by D-Wave Systems in this phase.

We wait until the trading day is over, but can use today's intraday price data if you ask.

If you provide non-US listed stocks, we will include if the data is available via Yahoo Finance.

**What you should expect from the results:**

This algorithm is looking at the past 252 trading days and giving you the portfolio that had the desired characteristics (lower risk and higher return) in the past. We believe these portfolios may behave in the same way moving forward, for as long as 10% of the time, or 25 trading days.

We view this as a buy and hold strategy for up to 25 days, but have seen the effects last as long as 35 days. We have seen offsetting stocks in these portfolios where some rise while the others fall, but overall the portfolio rises. In a few cases, one 'high flyer' carries the portfolio. Why does this happen? If the BETA values selected are higher than market average, then the stocks may move more than the market. If the risk is lower for those stocks, and the BETA is higher, then we may see investors attracted to those stocks in the short-term.

**The value proposition:**

You can figure out how to compare risk and return and gather the price data. You could do this classically with pencil and paper, or with a spreadsheet, or use intuitive guesswork. We started out this way before developing our CQNS model.

We believe this would take a long time to learn and master, mistakes are hard to discover, and the data can be tricky to download and validate. Also, this is computationally hard. There are many portfolios to check. For example, if you provide 64 stocks, we search for the lowest score from within 2^64 or 1.8446744e+19, or 1,844,674,400,000,000,000 potential portfolios.

Finally, this service runs the algorithm on a quantum annealing computer by D-Wave Systems Inc., which requires specialized knowledge and expertise that we have.

**Explanations:**

What is the Chicago Quantum Net Score? The Chicago Quantum Net Score is a proprietary quantum algorithm that scores each equally weighted portfolio.

It has 2 parts that are subtracted from each other:

- expected return of the portfolio (based on the BETA of the stocks and the average market return for the measurement period, usually ~ 252 trading days)
- expected risk (or variance) of the portfolio (based on the variance of that portfolio for the measurement period)

To make the model work correctly, we set the CQNS value for no stocks and all the stocks at approximately zero. We search for the lowest CQNS value. Based on the stocks you provide, the balance between risk and reward is set and the model seeks the most return with the least risk. This is also called an efficient portfolio, because you cannot get more expected return for the same amount of risk.

What is your platform of classical solvers that you will use?

The following classical solvers are included in this service:

Quantum Annealer

Monte Carlo

Simulated Annealing

Genetic Algorithm

Simulated Bifurcator

Particle Swarm Optimization

TABU (Multi-Start)

We use a quantum computer to run our quantum algorithm in this service.

What is BETA? BETA in our model is the movement of a stock relative to a market index. We offer two choices, either $SPY, an ETF that tracks the S&P 500 or $QQQ, an ETF that tracks the NASDAQ 100.

What is a portfolio's Expected Return? A portfolio's Expected Return in our model is the average BETA value of the portfolio's stocks multiplied by the annual Market Return.

What is the annual Market Return? This is the average of three US stock market indices, subject to floor and ceiling values to remove anomalies. We set a floor because investors do have a minimum expectation of stock market returns. We set a ceiling because investors do not expect a great year to repeat in exactly the same way the next year.

What is a portfolio's variance? The variance of a portfolio is the amount of variability of the price change of that portfolio's stock price over the measurement period. People usually think of a 'bell shaped curve' in a random sample, with the highest point being the typical return, and the variance is how wide the bell is. Most investors prefer higher returns with lower variance (so they don't have many 'bad days').

What is an equally weighted portfolio? This is a portfolio where each stock starts with the same value invested. So, a $1.00 portfolio with 2 stocks would have $0.50 invested in each.

How do you validate the data? We validate your data by checking the adjusted close prices (as provided by Yahoo Finance) are available for every day, and the prices are positive. We check for stocks with a positive BETA (because who wants a stock that goes down when the market goes up)? We omit stocks with BETA > 4.0, as that usually indicates an anomaly.

Why is the CQNS a quantum algorithm? The traditional way of finding efficient portfolios, or those portfolios that are expected to deliver a maximum return for a given level of risk, is to use the Sharpe Ratio. This divides expected return (%) by the standard deviation of the returns (%). This ratio is simple, as we divide two percentages to get a real number (say 5.10). A quantum annealing computer cannot perform multiplication or division, so we need to reformulate the Sharpe Ratio into something that works similarly. Our formulation works on quantum annealing computers, and therefore is a quantum algorithm.

What are these solver types that we use? The best way is to point you to Wikipedia, after we give you a few 'plain English' words of explanation of each.

Quantum Annealer - Uses quantum energy level (think of atoms jumping around trying to find their 'groove'). When we start, atoms are still and are loaded with data. As the atoms heat up, they jump around and seek out the lowest energy level where they can settle in, which equates to the lowest CQNS score. As the system cools, the atoms become more still and only look in their immediate area. Finally, we stop and read the atoms (or qubits), calculate the CQNS scores and whether the portfolio found was valid, and we keep the valid portfolios.

Monte Carlo - roll the dice, purely random chance

Simulated Annealing - based on temperature. When it is hot, we search more widely. As it gets colder we focus our search.

Genetic Algorithm - based on taking the best parts of each portfolio and creating new portfolios. Should always move us to better solutions. Add in mutations to capture 'nearby' portfolios.

Simulated Bifurcator - we simulate a pressure chamber. We form portfolios by having individual stocks migrate to be either in or out of the portfolios. We push the stocks in, and pull them out, and the pressure is the amount of impact applied from the matrix of data we created. We are looking for convergence as the pressure increases.

Particle Swarm Optimization - we have a set of particles that are each starting out in different parts of the portfolio search space (the 2^64 search space). Each one finds the best answer per turn, and the group of particles has momentum attracting all particles towards the center of gravity of the best answers. Over time, the particles settle into their best local solutions, and the center of gravity also moves to the best local solution found.

TABU (Multi-Start) - This one seems to operate mostly randomly with the best answers found collected and stored in memory for the next iteration. We generally do not find better answers than we find in a Monte Carlo run.

**Disclosure**

We think investors need to do their own due diligence on the companies and ensure they understand the risks associated with investing. Our model does not look at the fundamental value of companies. It looks only at the adjusted closing prices and the patterns and covariance between stocks held in that data.

Note: The algorithm and methods used are in a state of research and development, and are subject to frequent change and development. These are subject to modification, tuning and testing. Do not rely on this service for your investment decisions. This is not investment advice. We are not investment advisors.

Thank you for your order and your business.