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# Expect More Return For Your Portfolio's Risk

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## Summary

• You can optimize stock portfolios by analyzing covariance and expected returns.
• We see three ways to evaluate portfolio risks and returns.
• A challenge is computing all available combinations of portfolios.

The markets are very confusing.  Recently, we have seen significant money flows coming into the market, then stopping, include Federal Reserve Bank financial asset purchases and international money flows.  Federal Reserve announces extensive new measures to support the economy and https://bit.ly/2ZzcaEX

We believe investors can reduce portfolio risk (defined as W.t * E * W) and maximize portfolio returns (defined as W * R) by looking at all possible portfolios out of a set of highly liquid US equities. W is the weighted vector of assets, E is the stock covariance matrix over the past year, and R is your estimate of each stock's expected annual return.

Sounds easy, right?  Just compute the covariance for your universe of stocks, figure out a valid return estimate, and run through all the combinations.  It isn't that easy after all.  Here are three ways to look at this:

1.  Sharpe Ratio which uses Modern Portfolio Theory / Markowitz https://en.wikipedia.org/wiki/Harry_Markowitz, and would suggest R is calculated by taking the BETA of each stock (covariance of each stock with the market, divided by the market variance), and multiplying it by the return for that stock (minus the risk free rate), then add back the risk free rate.  This has been working for decades.  We use it too.

2.  Chicago Quantum Ratio which simplifies the returns portion of the ratio.  This eliminates the need to estimate a market return and a risk free rate, and just use the covariance of each stock with the market.  We call this the market momentum.

3.  Chicago Quantum Net Score which takes an entirely different approach to balancing risk and return for portfolios.  It subtracts a measure of annual expected return for each portfolio from a measure of risk of that portfolio.  We can either look for the lowest overall answers, or the answers closest to zero.

By using these measures, you can evaluate any set of stocks and look for those that intrinsically move together in the right way to minimize expected variance in portfolio returns.

As an example, you might intuitively look at International Paper (IP) and International Business Machines (IBM) and think that as long as the economy is growing, people need more computers and pencil and paper.  However, if you look at 40 stocks that you might like to hold, the covariance will tell you over the recent past if they moved together or not.  Did they cancel out each others movements but still rise?

During turbulent markets, these measurements also need to change.  As we developed these measures in 2020, we have had to incorporate the dramatic movements up and down.  Moving forward, our metrics change in up or down markets.

For small groups of stocks it is easy to iterate through all combinations of equities.  The number of portfolios is 2^n - 1.  We can do 16 and up to 24 assets very quickly.  It takes hours to run 28 stocks, which are 268M portfolios to be analyze.  For 40 stocks, or 1.1T portfolios, this would take far longer than the markets allow.

So, we find shortcuts and approximations through the use of random sampling, genetic algorithms, and quantum annealing computers.  These help us build portfolios on the Efficient Frontier.  We also use simulated annealers and a simulated bifurcator in our next stage of research.

Our startup, Chicago Quantum, https://www.chicagoquantum.com, has figured out a way to do this efficiently using classical computers (e.g., laptops and workstations) and using a quantum annealing computer by D-Wave Systems.  We have published two articles to arXiv, with a third on the way.

Thank you for reading.  The author does not have any position in any of the stocks mentioned in this article, nor does he/she intend to start a position in the next 72 hours.

Analyst's Disclosure: I am/we are long SPY.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

We are not active traders and do not plan to modify any positions in the next 30 days.

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