Chicago Quantum Analysis of 1,755 Dividend Paying US Common Stocks (Jan 4, 2021 market close)

On January 4, 2021, after a down day in the US equity markets, I decided to do a ‘big run’ of our quantum algorithm against all US common stocks in four major exchanges. This included 3,569 stocks across NASDAQ (Q&G), NYSE and NYSEAmerican.

I was going to trade on this ‘in-house’ run but in a YouTube AMA this morning I disclosed the picks instead with a commitment to not take a position in any stocks listed for at least 24 hours. The Chicago Quantum Net Score (CQNS), which maximizes expected return (based on the Capital Asset Pricing Model), and minimizes variance during the measurement period. This is a proprietary reformulation of the Sharpe Ratio concept to run on a quantum computer.

So, the CQNS portfolio consists of four, evenly weighted US listed stocks (25% invested in each), $DHI, $KELYB, $SLGN, and $WIT. However, it took us a while to get there, and this article will tell the story. There was at least one surprise (NYSE lists and sells retail bonds…who knew?).

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Performance of the portfolio over the past year: DHI, KELYB, SLGN & WIT

What do I see when I view this chart? I view four stocks that move in different directions on most days, but overall they went up as a team (equally weighted positions to start). In this case, the portfolio was up about 40% last year. We want to find zigs and zags between the stocks and we do.

I left the ‘dividend validation’ selection on. This selection would now only analyze stocks that pass data validation and that paid a dividend during that period. This left us with 1,755 stocks to analyze.

We recognize this has been a very strong US equities market, and our model provided a market return index of 17.26%, and a riskfree rate of return of 1%. All 1,755 stocks together provide a portfolio with a Sharpe Ratio of 7.28, based on an expected return of 25.27%, and a standard deviation of daily returns of 3.47%. From this, you should understand that BETA is > 1 when compared to the SPY (S&P 500 ETF) we use to calculate stock BETAs. Had we only included S&P 500 stocks, BETA would be 1.0, and expected returns would be 16.08%. The NASDAQ and Russell 2000 both outperformed the S&P 500 this past year.

In Phase 1, we run a series of classical analyses to select 119 stocks in an ‘allstar’ portfolio. In Phase 2, we take those 119 stocks and analyze them for the absolute best portfolios, using classical solvers and the D-Wave Systems Advantage 1.1 quantum annealing computer.

Our solvers for this run include Monte Carlo, Genetic Algorithm, Simulated Annealer, Particle Swarm Optimization, Simulated Bifurcator, TABU (multi-start), D-Wave Simulated Annealer, and the D-Wave Quantum Annealer.

Three charts created by our custom coded simulated bifurcator.
Three charts created by our custom coded simulated bifurcator.

In last night’s run, our simulated bifurcator could not find the best 150 stock portfolio. However, from the looks of these three charts, it might have been able to if we let it run longer (than the ~500 iterations in this run). Time was running short, and it was approaching 10pm. We did have good success in Phase 2, where our SBM selected an attractive 12-stock portfolio.

Lately we have invested in making our solvers work more quickly and efficiently. In many cases, these can be considered independent optimizers which together give us their best portfolios (based on the CQNS minimum score). When we see convergence between the solvers, it gives us greater confidence. Sometimes, we run solvers repeatedly, and more deeply, to force that convergence. We did that last night (e.g., we ran 2M Monte Carlo samples per portfolio size at the end to ‘give it time’ to find the best portfolio).

So, what happened is we picked three stocks and one was a bond. Ugh, we spent hours finding that the best combination of stocks was two risky stocks and a bond. $TVC and $TVE are the Tennessee Valley Authority PARRS. They are ‘putable’ $25 retail bonds where the interest rate can be reset at will by the TVA, and the retail investor can return the bond for $25 at any time. So, the price does not move very much, and it is based on interest rate swings and resets by the TVA. You can see the 5-day price action below, and see that it can trade like a stock. BTW, the rate reset down to ~2.2%, which cost each $25 bond about $0.75 in value.

$TVC bond price action over the past 5 days (ranging from about 25.25 to about $25.40 per bond / share)
$TVC bond price action over the past 5 days (ranging from about 25.25 to about $25.40 per bond / share)

Well, we cannot recommend two stocks and a bond! So, had to remove the $TVC and run Phase 2 again. The challenge was that the initial 119 stocks might have been influenced by the inclusion of $TVC, so we also added 31 incremental stocks that were selected in the 2nd and 3rd best portfolios. We were up to 150 stocks heading back into Phase 2.

We had a significant trade-off to make with this choice of 150 stocks. The D-Wave Advantage 1.1 can embed a maximum of ~160 fully-embedded vertices, or cliques (clique = stock). However, we have only ever successfully run 138 stocks on the D-Wave. By selecting 150 top stocks, we believe we had a better chance of selecting a great portfolio (from 150 ‘allstars’ instead of only 118), but we gave up the chance of running this one quantum.

Our Particle Swarm Optimizer (PSO) solver is also a new addition. In this run of 150 stocks, it picked a three-stock portfolio which selected two of the finalists, and added a third, new stock. It received a slightly worse CQNS score. FYI, we use Pyswarm in python to power our PSO.

Findings from our second Phase 2 run (150 stocks). We had concurrence and convergence across our solvers to the same three-stock portfolio, which had the best CQNS rating. Our Bespoke simulated annealer picked a four-stock solution with a slightly worse rating (it added a 4th stock), and we chose that portfolio for publication. There are still choices to make in selecting portfolios for our clients, or general population readers.

So, how did this portfolio perform on its first day? Pretty well.

A few notes:

We do not have a position in any of the stocks mentioned in this article, nor do we intend to initiate a position in the next 24 hours.

We like exchange-listed stocks (vs. OTC) because of the added liquidity, visibility and compliance protection they provide. BTW: this does not mean they will pay a dividend next year.

We add $KELYA to our tracking as $KELYB is thinly traded compared to $KELYA. Experienced investors would most likely want to hold $KELYA due to greater liquidity and price transparency through trading volume.

Data downloaded: January 4, 2021, overnight after market close.

Validation: Dividends paid in the measurement period (252 prior trading days). Positive BETA, and adjusted close prices > 0, and continuously traded for the 252 trading days.

Exchanges: NYSE, NASDAQ Global Select Markets (Q) (SM), NASDAQ Global Markets (G) (SM), NYSEAmerican

No income funds, no preferreds, no bonds (we hope), common stocks.

We are not brokers. We are not investment advisors. We are not registered with FINRA. This is not investment advice. Please do your own due diligence and research before investing. Investments in equities can and do lose money. Please be careful and only invest what you can afford to lose.

These stocks are part of a portfolio (a buy and hold portfolio) that has the lowest Chicago Quantum Net Score. For more info, please read our research here:

Stock 1: D.R. Horton, Inc, $DHI

Consumer Cyclical — they make and sell houses

Stock 2: Kelly Services, Inc. $KELYB

Workforce and employment solutions

Stock 3: Silgan Holdings Inc. $SLGN, 13,200 employees

Manufacture and sell rigid consumer packaging & (industrial and chemical applications): Metal, closures, plastics (tin cans)

Stock 4: Wipro Limited $WIT

Indian-based information services provider with 185K employees

The effects of the CQNS can be expected to last 10% of the trading days that went into the analysis: Analysis: 252 trading days. Effect: 25 trading days (we have seen up to 35 days).

For more information about this relatively complex topic, please visit our website at WWW.CHICAGOQUANTUM.COM or contact me directly.

+1.312.515.7333 (cell)

Thank you for your interest.

Written by

Jeffrey Cohen, President of US Advanced Computing Infrastructure, Inc., & founder of Chicago Quantum (SM). We use quantum algorithms & our quantum platform

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