CASE STUDY UPDATE: Zoomd Technologies (ZOMD.V / ZMDTF)

April 20, 2025

I profiled Zoomd before, but the stock is significantly more undervalued today, so I decided to do this case study update.

Zoomd Technologies (ZOMD.V / ZMDTF) is an Israel-based digital advertising and monetization company that offers a mobile-first user acquisition platform powered by proprietary, patented technology. It provides advertisers with a unified dashboard connected to over 600 media sources and serves publishers as an onsite search engine. This unique position allows Zoomd to act as a one-stop shop for digital campaigns, helping advertisers target high-value users efficiently.

Zoomd’s platform sits atop the digital media ecosystem—integrated with social networks, device manufacturers, ad networks, and publishers—thus minimizing dependence on any single platform like Google or Facebook. With a strategic focus on high-growth sectors such as fintech, gaming, and e-commerce, Zoomd serves prominent clients like Sony Pictures, Crypto.com, and SHEIN, positioning itself as a scalable, privacy-proof solution in the evolving adtech landscape.

The market cap is $34.34 million while enterprise value is $28.67 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 2.48
    • P/E = 4.39
    • P/B = 1.97
    • P/CF = 4.47
    • P/S = 0.68

There are very low metrics of cheapness.

Insider ownership is 29.2%, which is very good.  ROE (return on equity) is 67.5%, which is excellent.  The Piotroski F_Score is good at 7.

Cash is $9.28 million while debt is $3.56 million.  And TL/TA is 38%, quite low.

Intrinsic value scenarios:

    • Low case: If there’s a bear market or a recession, the stock could decline temporarily. That would be a buying opportunity.
    • Mid case: The current P/E is 4.39 but should be at least 10. This translates into a share price of $0.80, which is over 125% higher than today’s stock price of $0.351.
    • High case: Arguably, the P/E should be 15.  This translates into a share price of $1.20, which is over 240% higher than today’s stock price of $0.351.

 

RISKS

    • Tariffs are weighing on the stock in the near term. But it’s likely that the U.S. and China will work out some sort of deal, at least in the medium term, which would lower tariffs significantly.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY: Total Telcom (TTZ.V / TTLTF)

April 13, 2025

Total Telcom Inc. (TTZ.V / TTLTF) is a Canadian microcap company providing remote asset management solutions through wireless technologies. With nearly 55% of its $3.37 million market cap in cash, no debt and solid profitability, the downside is limited. It has three main revenue streams—hardware sales, recurring communication services, and race-day equipment rentals—with total gross margins exceeding 60%. The recurring revenue business has reached break-even, and management expects further growth as new products are commercialized. The company’s real advantage lies in cost-effective, user-friendly integration of its technology, helping clients reduce manual labor, optimize operations, and manage assets remotely with low data usage and high reliability.

The business is capitalizing on emerging trends in satellite communications, environmental monitoring, and white-label partnerships. Management owns over 28% of the company and is aligned with shareholder interests through modest compensation and significant equity stakes. The company’s clean balance sheet and scalable business model position it well for future growth. With market demand rising for remote data solutions due to climate and infrastructure needs, and with satellite communication markets projected to quadruple by 2028, Total Telcom appears conservatively valued with limited downside and strong upside potential if growth accelerates through marketing and strategic partnerships.

The market cap is $3.37 million while enterprise value is $1.49 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 2.82
    • P/E = 15.58
    • P/B = 0.90
    • P/CF = 4.13
    • P/S = 2.35

Insider ownership is 28.8%, which is good.  ROE (return on equity) is 6.3%, which is low but should improve as the company’s earnings improve.  The Piotroski F_Score is decent at 6.

Cash is $3 million while debt is zero.  And TL/TA is 10.9%, exceptionally low.

Intrinsic value scenarios:

    • Low case: If there’s a bear market or a recession, the stock could decline temporarily. With 55% of the market cap in cash, no debt and solid profitability, the downside is limited.
    • Mid case: Net income could reach $500,000 in 2026 assuming $2.5 million in sales and a 20% net income margin. With a P/E of 15, the market cap would be $7.5 million.  This translates into a share price of $0.27, which is over 120% higher than today’s $0.12.
    • High case: With a P/E of 20, the market cap would be $10 million.  This translates into a share price of $0.36, which is almost 200% higher than today’s $0.12.

 

RISKS

    • Tariffs are weighing on the stock in the near term, but the company is looking to expand in places such as Canada, South America, Europe, and Australia. And as noted, with 55% of the market cap in cash, no debt and solid profitability, the downside is limited.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY: Canaf Investments (CAF.V / CAFZF)

April 6, 2025

Canaf Investments is a South African focused public company with four divisions:

Southern Coal – South Africa Southern Coal produces calcined anthracite, which is primarily sold as a substitute to coke in sintering processes.  Southern Coal supplies world leading steel and ferromanganese producers in South Africa.

Canaf Estate Holdings – South Africa Canaf Estate Holdings is a property investment company focused on acquiring, redeveloping and renting properties primarily within the suburbs of the old Johannesburg.

Canaf Agri – South Africa Canaf Agri is exploring investment opportunities in the agriculture sector in South Africa.

Canaf Capital – South Africa Canaf Capital is an investment company focused on providing capital for short-term financing to businesses and entrepreneurs in South Africa.

Of these four divisions, Sout Africa Southern Coal is by far the largest.

Canaf Investments is a tiny company engaged in boring businesses, thus the stock is completely overlooked by most investors.  But the stock is super cheap.

The market cap is $10.01 million while enterprise value is $3.16 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 1.11
    • P/E = 6.26
    • P/B = 1.52
    • P/CF = 2.37
    • P/S = 0.47

Canaf’s metrics of cheapness are exceptionally low.

Insider ownership is 17.6%, which is good.  ROE (return on equity) is 23.3%, which is excellent.

Cash is $8.5 million while debt is zero.  And TL/TA is 20.3%, low indeed.

Intrinsic value scenarios:

    • Low case: If there’s a bear market or a recession, the stock could decline temporarily. This would be a major buying opportunity.
    • Mid case: The current P/E is 6.26 but should be at least 12. That would mean the stock is worth $0.42, which is over 90% higher than today’s $0.22.
    • High case: Current EV/EBITDA is 1.11 but should be at least 7.  That would mean the stock is worth $0.59, which is 168% higher than today’s $0.22.

 

RISKS

    • As noted, if there’s a bear market or a recession, the stock could decline temporarily. This would be a major buying opportunity.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY UPDATE: Geodrill (GEO.TO / GEODF)

March 23, 2025

In July 2024, I talked about Geodrill (GEO.TO / GEODF).  But Geodrill’s situation has significantly improved since then, so I am going to update the investment thesis.

Geodrill is a leading drilling services provider focused on gold (90%+ of revenue) and other mineral exploration for major, intermediate, and junior mining companies across Africa and South America. Founded in 1998 by CEO Dave Harper—who still owns over 40% of the company—Geodrill has grown organically from one rig in 1998 to 102 rigs today, with operations in six countries—Cote d’Ivoire, Senegal, and Mali in West Africa; Egypt in North Africa; and Peru and Chile in South America.

The company is known for its quality and long-standing relationships with top-tier clients like Barrick, Newmont, and Kinross. It has successfully shifted its customer base toward senior miners (now ~90% vs. 70% previously) and more stable jurisdictions, securing multi-year contracts worth ~$200 million, providing visibility through 2027.

With gold prices now exceeding $3,000/oz, miners are reinvesting heavily, benefiting Geodrill’s growth prospects. Harper is seeking a sale at 5x EV/EBITDA, valuing the stock at $4.13—more than double its current price of $2.02.

Geodrill reinvested every penny of operating cash flow into expanding their fleet in the most recent year.

On the most recent earnings call, CEO Dave Harper pointed out that the company has been growing on average about 10% a year over the last 8 years.  Harper said of course the company would encounter challenges—there are always challenges—but that growth should be at least 10% a year going forward (if not more, given gold prices over $3,000 an ounce).

Harper said, “We’ve never been more bullish, never been more bullish, never been more bullish.”

Harper notes that the company drills in locations where gold is heavily mined, where it’s relatively easy to mine, but where other people don’t want to mine.

Harper pointed out the company is “really going to shine over the next four years. This will become a cash cow, mark my words.”

The market cap is $94.8 million while enterprise value is $86.7 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 2.69
    • P/E = 8.03
    • P/B = 0.79
    • P/CF = 4.52
    • P/S = 0.67

Geodrill’s metrics of cheapness are exceptionally low.

The company is planning to pay a dividend again—likely $0.01 per quarter this year and a larger dividend in 2026.

As noted, CEO and founder Dave Harper owns 40%+ of the shares.  ROE (return on equity) is 7.9%.  This is a bit low but will move higher because margins should continue to improve, given high gold prices.

Cash is $19.5 million while debt is $11.4 million.  TL/TA is 26%, which is excellent.

Intrinsic value scenarios:

    • Low case: If there’s a bear market or a recession, the stock could decline temporarily. This would be a major buying opportunity.
    • Mid case: As noted, Dave Harper owns 40%+ of the shares and is looking to sell at 5x EV/EBITDA. This would mean a stock price of $4.13 per share, which is over 100% higher than today’s $2.02.
    • High case: EBITDA could reach $50 million by 2027.  At an EV/EBITDA of 6x, the stock would have an intrinsic value of $6.04, about 200% higher than today’s $2.02.

 

RISKS

    • As noted, if there’s a bear market or a recession, the stock could decline temporarily. This would be a major buying opportunity.
    • Gold prices may fall.
    • There could be political instability in Africa or in Peru/Chile. This has rarely been an issue for the company in the past.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY: Pyxis Tankers (PXS)

March 2, 2025

Pyxis Tankers (PXS) is a disciplined, growth-oriented shipping company with a modern eco-fleet that positions it for long-term success. With a focus on mid-sized, eco-efficient vessels, strategic chartering, and a strong financial foundation, the company is well-positioned to capitalize on opportunities in the shipping industry.

(1) Pyxis Tankers operates a fleet designed for versatility, low operating costs, and fuel efficiency. The company currently owns:

    • Three medium-range (MR) product tankers
    • 2.2 dry bulk carriers

This modern, eco-efficient fleet allows Pyxis to remain competitive while ensuring resilience in demand-driven markets. With significant liquidity (“dry powder”) available, the company is actively evaluating the acquisition of up to two additional vessels, further expanding its growth potential.

(2) Pyxis has cultivated long-standing relationships with top-tier global customers, ensuring stability and operational efficiency.

As of January 24th, 2025, the company has secured:

    • 72% of available days for Q1 2025 booked for MR tankers at an average TCE rate of $24,750/day
    • 68% of available days for bulkers booked at an average estimated TCE rate of $15,400/day

With five vessels under short-term time charters and one on a spot voyage, Pyxis Tankers is well-positioned to benefit from rising charter rates, should the market continue to strengthen.

(3) One of Pyxis Tankers’ key advantages is its lean cost structure, which creates operating leverage as charter rates increase. The company maintains:

    • A primarily fixed cost structure, enabling improved earnings potential
    • Highly competitive daily operational costs per vessel, compared to U.S.-listed peers
    • A solid balance sheet with strong liquidity and modest leverage

This disciplined financial management allows Pyxis to remain resilient even in volatile market conditions while continuing to pursue strategic growth opportunities.

(4) The company is led by a highly experienced and incentivized management team, boasting over 100 years of combined expertise in the shipping and capital markets sectors. Key leadership highlights include:

    • Founder & CEO holds ~57% of shares, aligning his interests with shareholders
    • A well-respected Board of Directors, consisting of industry veterans with deep sector knowledge

This level of expertise and leadership stability ensures that Pyxis remains agile, strategic, and disciplined in navigating market cycles.

(5) Despite ongoing market uncertainty, Pyxis Tankers is well-positioned due to constructive demand fundamentals for both the product tanker and dry bulk sectors. Key valuation drivers include:

    • Solid global GDP growth supporting shipping demand
    • Limited vessel supply growth, creating favorable industry dynamics
    • A proven track record of navigating volatile shipping markets

With compelling valuation metrics and a strong financial foundation, Pyxis presents a high-value investment opportunity with significant upside potential.

Pyxis Tankers’ combination of a modern, efficient fleet, strong customer relationships, disciplined financial management, and experienced leadership makes it a standout player in the shipping sector. With continued strategic growth and a focus on operational efficiency, PXS is well-positioned for long-term success in the dynamic global shipping market.

PXS’s market cap is $37.9 million, while its enterprise value is $81.9 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 1.74
    • P/E = 1.27
    • P/B = 0.37
    • P/CF = 2.71
    • P/S = 0.81

ROE (return on equity) is 36.6%, which is excellent.  However, earnings may decline in the short term.

The Piotroski F_Score is 6, which is decent.

Insider ownership is outstanding at 57%.  Cash is $42.4 million while debt is $86.4 million.  TL/TA (total liabilities / total assets) is decent at 44.5%.

Intrinsic value scenarios:

    • Low case: If there’s a bear market and/or a recession, the stock could decline.  Also, the limited fleet size puts the company more at risk for any unforeseen maintenance or damages.
    • Mid case: Pyxis Tankers should have a P/CF of at least 5.  That would put the stock at $6.52, which is 85% higher than today’s $3.53.
    • High case: The company should trade at book value of $9.54.  That is 170% higher than today’s $3.53.

 

RISKS

There could be a bear market and/or a recession, during which shipping rates would likely fall leading to lower earnings and a lower stock price.

Limited fleet size puts the company more at risk for any unforeseen maintenance or damages.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY: Core Molding Technologies (CMT)

February 23, 2025

Core Molding is a manufacturer of injection molded plastics for a variety of products in different industries.  For example, dashboards, radio controls, bumpers, cup holders, truck stairs, snowmobile casings, decking, fencing, trash bins, and playground slides.

Roughly half of CMT’s revenue comes from trucking customers Navistar, Paccar, and Volvo where Core Molding manufactures bumpers, side panels, wind deflectors, and interior plastic components for these customers.  CMT has 5 large customers, each of which accounts for over 10% of their revenue.  But no single customer is over 20% of their revenue.

(h/t pcm983 of Value Investors Club.  See (you may have to register but it’s free): https://www.valueinvestorsclub.com/idea/CORE_MOLDING_TECHNOLOGIES/3525719676#description)

Core Molding runs its main facilities in Columbus, OH, and Matamoros, Mexico.  The company also has facilities in South Carolina, Minnesota, and Ontario.

CMT must maintain good relationships with its customers.  The large customers use just-in-time manufacturing.  Most orders come into CMT a few days before they are expected to be shipped or delivered to the client.  The finished product assemblers rely on many small- to mid-sized businesses to deliver goods quickly.  As a result, companies such as CMT tend to have their facilities close to the final product assembly factories.

In early 2018, CMT acquired Horizon Plastics but the acquisition was difficult to manage.  The CEO/Chairman who oversaw the acquisition left in late 2018 and the new CEO David Duvall took two years to fully integrate Horizon Plastics.

Management is highly transparent and approachable.  The CFO John Zimmer quickly replies to questions and is forthright about the company.  In its financial statements, CMT includes sales broken out by customer.

Core Moldings’s market cap is $118.8 million, while its enterprise value is $98.4 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 3.10
    • P/E = 7.62
    • P/B = 0.80
    • P/CF = 3.06
    • P/S = 0.37

These are low metrics of cheapness indeed.

ROE (return on equity) is 11%, which is OK.

The Piotroski F_Score is 6, which is decent.

Insider ownership is solid at 11%.  Cash is $42.6 million while debt is $24.3 million.  TL/TA (total liabilities / total assets) is excellent at 33%.

Intrinsic value scenarios:

    • Low case: If there’s a bear market and/or a recession, the stock could decline.  Or if there’s a slowdown in trucking, CMT’s revenue and earnings could decline.
    • Mid case: Core Molding should have a P/E of at least 15.  That would put the stock at $26.10, which is over 95% higher than today’s $13.26.
    • High case: The company should have an EV/EBITDA ratio of at least 8.  That would put the stock price of $30.62, which is 130% higher than today’s $13.26.

RISKS

There could be a bear market and/or a recession and the stock could decline.

There could be a slowdown in trucking, which is cyclical.  The company gets roughly 50% of its revenues from truck manufacturers.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY: FONAR Corporation (FONR)

February 16, 2025

Raymond Damadian is the founder of FONAR Corporation and he is one of the co-inventors of MRI technology.  The other co-inventor is Professor Paul Lauterber of Stony Brook University.  In the 1970s, they discovered how to use nuclear magnetic resonance technology—previously used in the chemistry lab to identify molecules—to form images of the internal tissues of the human body.  This was one of the great inventions in medicine.  Doctors rely heavily on the MRI exam to diagnose a wide variety of conditions, from brain and spine problems to organ problems to bone and ligament issues.

(h/t to anton613 of Value Investors Club.  See (you may have to register, but it’s free): https://www.valueinvestorsclub.com/idea/FONAR_CORP/5954105606)

Dr. Damadian also invented the FONAR Upright Multi Position MRI.  The Upright MRI produces images when a person is standing up or sitting (or anything in-between).  This means a more accurate diagnosis when examining things like the spine or the flow of cerebrospinal fluid—both of which appear differently when a person is standing up.  Also, a weight-bearing position is often the position in which a person experiences pain.

In 2011, Dr. Damadian used the FONAR Upright MRI to produce images of cerebrospinal fluid flow in eight MS patients.  The study demonstrated that leakage of cerebrospinal fluid may have caused brain lesions leading to MS.

There are many other conditions where the Upright MRI can provide a more accurate diagnosis, including abdominal prolapses, inguinal hernias, scoliosis, fallen cerebral tonsil disease, and Arnold-Chiari syndrome.

The MRI equipment business includes large manufacturers such as Hitachi, Siemens, General Electric, and Philips N.V.  It’s a highly competitive space.

The CEO of FONAR is Timothy Damadian, the founder’s son, who started working at the company in 1985 and worked his way up.  He became CEO in 2016.

FONAR was the first MRI company in the industry, introducing the world’s first commercial MRI in 1980.  FONAR’s business has two segments:

    • The medical equipment segment, which sells the Standup MRI.
    • The physician management and diagnostic services segment, which manages MRI scanners in New York and Florida. The bulk of the company’s revenues comes from this segment.  The company offers office space, repair and maintenance, medical record management, personnel management, IT services, management services, billing and collection, credentialism, compliance, and purchasing, among other things.

FONAR  introduced the Open MRI in 1980, the benefit being that the patient—who may be claustrophobic—does not have to be enclosed for the duration of the exam (30 to 60 minutes or longer).  Later on, the company invented the Upright MRI, which is even more useful.

Important Note: The demand for MRI scans continues to increase.

FONAR’s market cap is $104 million, while its enterprise value is $90.8 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 3.45
    • P/E = 11.61
    • P/B = 0.62
    • P/CF = 7.36
    • P/S = 1.03

Note:  The company is buying back stock, which is good because the stock appears materially undervalued with EV/EBITDA of 3.45 and P/B of 0.62.

ROE is 8.1%, which is low.

The Piotroski F_Score is 6, which is decent.

Insider ownership is low at 2.4%.  Cash is $54.3 million while debt is $41.2 million.  TL/TA (total liabilities / total assets) is excellent at 26.8%.

Intrinsic value scenarios:

    • Low case: If there’s a bear market and/or a recession, the stock could decline.  If the reimbursement rates from Medicare decline, that could cause the stock to fall.
    • Mid case: FONAR should have a P/B ratio of at least 1.0.  That would put the stock at $26.21, which is over 60% higher than today’s $16.25.
    • High case: The company should have an EV/EBITDA ratio of at least 8.  That would put the stock at $37.68, which is 130% higher than today’s $16.25.

 

 RISKS

    • If there’s a bear market and/or a recession, the stock would probably decline.
    • If the reimbursement rates from Medicare decline, that could significantly lower earnings and thus the stock price.
    • Healthcare laws often change, and they could change in a way that adversely affects FONAR.
    • With its ownership of super-voting B and C shares, management controls the company without having a majority of the economic interest in the company.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY: Build-A-Bear Workshop (BBW)

February 9, 2025

Build-A-Bear Workship (BBW) runs a “make-your-own stuffed animal” business and also licenses its brand.  The company is transitioning to being primarily a brand monetization business that continues also to be a retailer.

(h/t HiddenInSight, Value Investors Club.  Please see the following (you may have to register but its free): https://www.valueinvestorsclub.com/idea/BUILD-A-BEAR_WORKSHOP_INC/3416620533)

BBW’s licensed store business entails BBW licensing its brand and store concepts to third parties (theme parks, hotels, etc).  This business is a franchise model: BBW has zero capital commitment or operating risk, but has the same profit per unit for BBW as running a store themselves.  This business is expanding quickly.  It’s already exceeded 130 units and could more than triple by 2028.  Licensing/Franchising is 7.5% of today’s revenues but ~36% of profits.

There’s plenty of space for U.S. growth, but the international opportunity is even larger.  Over half of new third-party stores will be opened internationally including new partners in Colombia and France.  It’s also noteworthy that international partners are established toy/kid retailers whereas U.S. partners tend to be hospitality-based operators.  As a result, international partners are typically multi-unit operators whereas some U.S. partners are single-unit operators.

There have been zero third-party closures in 21+ months even as other licensed/franchised retail establishments have been seeing significant closures.  Also, the ROI for partners often exceeds 100%.

There are several reasons investors have overlooked Build-A-Bear:

    • Investors who invested in BBW at the Covid lows have seen 2500%+ gains already, and they assume the story is over
    • Licensed/franchised sales add little to total revenue, and so its earnings potential is overlooked
    • Build-A-Bear investors lost significant money in 2007 and again in 2015, and so they don’t look at the stock anymore and therefore don’t see the transformation

Because BBW is becoming primarily a licensing company, its earnings quality should continue to improve.  Investors are likely to realize this eventually, causing the stock to move much higher.

Because the company produces roughly $50 million in free cash flow per year, it will continue to buy back more stock, recently announcing a new $100 million buyback program (20% of the market cap).

Build-A-Bear has trademarks that legally prevent competitors from using a similar “build your own stuffed animal” retail concept.  As for other toy/entertainment options, customers seem to like BBW for the unique experience of building one’s own bear.  Also, the company has continued to sell ~8 million bears per year for over 25 years despite the collapse of mall foot traffic.

By 2028: Third-party stores may exceed 400, producing a net income of $52 million.  Meanwhile, retail net income should hit $30 million.  So net income for 2028 should be at least $82 million.  EBITDA should hit $126.3 million.  Cash flow will be roughly $105 million.

The current market cap is $526.4 million while enterprise value is $595.8 million.

And here are the metrics of cheapness based on 2028 estimates (except for P/B, which is current):

    • EV/EBITDA = 4.72
    • P/E = 6.42
    • P/B = 4.09
    • P/CF = 5.01
    • P/S = 0.81

ROE is 42.9%, which is excellent.

The Piotroski F_Score is 6, which is decent.

Insider ownership is OK at 6.2%.  Cash is $25.2 million while debt is $102.1 million.  TL/TA (total liabilities / total assets) is reasonable at 55.0%.  The dividend yield is 2.1%.

Intrinsic value scenarios:

    • Low case: If there’s a bear market or a recession and/or if consumer spending declines and/or if there’s a decrease in mall traffic, earnings could drop and so could the stock.
    • Mid case: By 2028, Build-A-Bear should have a P/E of at least 15.  That would mean the stock is worth $88.36, which is over 130% higher than today’s $37.82.
    • High case: Arguably, by 2028, due to its capital-light licensing business, the company should have a P/E of 20.  That would mean the stock is worth $117.82, which is over 210% higher than today’s $37.82.

 

 RISKS

    • If there’s a bear market or a recession, the stock would probably decline.
    • A drop in consumer spending would cause earnings to drop.
    • Mall traffic continuing to decrease would hurt earnings.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

CASE STUDY UPDATE: InPlay Oil (IPO.TO / IPOOF)

February 2, 2025

Here is my investment thesis for InPlay Oil Corporation (ticker IPO in Canada and IPOOF in the U.S.), which is a Canadian oil and gas company based in Calgary, Alberta.

Their corporate strategy is as follows: “Disciplined light oil growth developing high rate of return assets to generate strong free adjusted funds flow with conservative leverage ratios while maximizing returns to shareholders.”

InPlay Oil has an excellent management team that has consistently delivered production and cash flow per share growth while reducing debt.  They have grown production at 15% a year the past 8 years and they have grown adjusted funds flow per share at 30% a year the past 8 years.  Furthermore, they have boosted reserves by 74% over the past 8 years.

Sustaining capital for 2025 is expected to be 25-30% less than 2024 because the company invested $20+ million in infrastructure the past 2 years.  The company also implemented strong hedge positions at favorable commodity prices to mitigate risk.

InPlay Oil is consistently more efficient (lower cost) than most of its peers in finding reserves and adding producing barrels.

The company also has a history of successful, highly accretive acquisitions.

The market cap is $105 million while enterprise value is $146.2 million.

Here are the metrics of cheapness:

    • EV/EBITDA = 2.94
    • P/E = 5.89
    • P/B = 0.51
    • P/CF = 1.70
    • P/S = 0.95

ROE is a bit low at 9.1%, but it’s improving.  The Piotroski F_Score is 7, which is good.

Insider ownership is 25.3%, which is excellent.  Debt is $40.4 million.  TL/TA (total liabilities to total assets) is 40%, which is solid.  The dividend yield is high at 10.1%.

Intrinsic value scenarios:

    • Low case: If there’s a bear market or a recession and/or if oil prices decline, the stock could decline.
    • Mid case: NAV based only on total proved reserves is $4.18 per share, which is 260% higher than the current stock price of $1.15 per share.
    • High case: P/CF is 1.70 but should be at least 8.00.  That would mean a stock price of $5.41, which is over 370% higher than today’s $1.15 per share.

 

RISKS

There could be a bear market or a recession and/or oil prices could decline.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.

The Signal and the Noise

January 19, 2025

I recently re-read Nate Silver’s book, The Signal and the Noise (The Penguin Press, 2012).

From a value investing point of view, it’s crucialto bear in mind that trying to forecast the stock market will typically cause you to make less money than you otherwise would. It’s far more reliable and profitable over the long term to stay focused on individual businesses without ever trying to predict the market or the economy.

Yet it’s worth reviewing Silver’s book because it discusses Bayes’ rule, which is essential for anyone trying to make predictions.

Most of us, even many scientists, do a poor job when it comes to making predictions and when it comes to updating our beliefs. To understand why we make these errors so often, it helps to recall that we have two different mental systems:

System 1: Operates automatically and quickly; makes instinctual decisions based on heuristics.

System 2: Allocates attention (which has a limited budget) to the effortful mental activities that demand it, including logic, statistics, and complex computations.

Usually we rely on System 1 to make predictions. Most of the time, these predictions are accurate because they deal with areas of life with very high predictability, like the fact that there is gravity.

But when we encounter complex phenomena where only the careful use of proper statistical thinking can help us make good decisions, System 1 nearly always makes mistakes. In these situations, we have to slow down and consciously activate our System 2.

Once we’ve learned to activate System 2 when it is required, there are two separate steps we need to learn:

  • First, we must train ourselves to make good predictions on the basis of all available evidence.
  • Second, we must train ourselves to test our predictions and to update our hypotheses on the basis of new information. This is where Bayes’ rule comes in.

Here is an outline for this blog:

  • Ignore Macro Forecasting; Focus on Individual Businesses
  • Scientific Progress
  • Out of Sample Events
  • Foxes vs. Hedgehogs
  • Thinking Very Big and Very Small
  • Chaos Theory
  • Earthquakes
  • Economic Forecasting
  • Bayes’ Rule
  • The Problem of False Positives
  • Conclusion

Note: Bayes’ rule is in the running as the most important formula in artificial intelligence. Although a market-beating AI value investor may be 10-20 years away, it’s interesting to follow some of the developments.

 

IGNORE MACRO FORECASTING; FOCUS ON INDIVIDUAL BUSINESSES

No one has ever been able to predict the stock market with any sort of reliability. Ben Graham, the father of value investing, had about a 200 IQ. Buffett calls Graham “the smartest man I ever knew.” Here is what Graham said about market forecasting:

… if I have noticed anything over these 60 years on Wall Street, it is that people do not succeed in forecasting what’s going to happen to the stock market.

If you’re a value investor buying individual businesses when their stocks are cheap, then macroeconomic variables generally aren’t relevant. Furthermore, most investors and businesspeople that pay attention to political and economic forecasts end up worse off as a result. Here are a few good quotes from Buffett on forecasting:

Market forecasters will fill your ear but never fill your wallet.

We will continue to ignore political and economic forecasts, which are an expensive distraction for many investors and businessmen.

Charlie and I never have an opinion on the market because it wouldn’t be any good and it might interfere with the opinions we have that are good.

If we find a company we like, the level of the market will not really impact our decisions. We will decide company by company. We spend essentially no time thinking about macroeconomic factors. In other words, if somebody handed us a prediction by the most revered intellectual on the subject, with figures for unemployment or interest rates or whatever it might be for the next two years, we would not pay any attention to it. We simply try to focus on businesses that we think we understand and where we like the price and management.

The great economist John Maynard Keynes developed a similar investment philosophy to that held by Buffett and Munger. Though Keynes was a true genius, he failed twice trying to invest based on macro predictions. Finally, he realized that a concentrated value investment approach was far more effective.

Keynes did very well over decades as a focused value investor. His best advice:

  • Buy shares when they are cheap in relation to probable intrinsic value;
  • Ignore macro and market predictions, and stay focused on a few individual businesses that you understand and whose management you believe in;
  • Hold those businesses for many years as long as the investment theses are intact;
  • Try to have negatively correlated investments (for example, the stock of a gold miner, says Keynes).

 

SCIENTIFIC PROGRESS

One of Silver’s chief points in the book is that we have more data than ever before, but the signal is often overwhelmed by the noise. Says Silver:

Data-driven predictions can succeed – and they can fail. It is when we deny our role in the process that the odds of failure rise. Before we demand more of our data, we need to demand more of ourselves.

When it comes to demanding more of ourselves, what Philip Tetlock and Barbara Mellers are doing with The Good Judgment Project is very worthwhile: http://www.goodjudgment.com/

Silver points out that if the underlying incidence of true hypotheses is low, then it’s quite likely we will have many false positives. John Ioannidis has already shown this – with respect to medical research – in his 2005 paper, ‘Why Most Published Research Findings Are False.’ Silver spoke with Ioannidis, who said:

I’m not saying that we haven’t made any progress. Taking into account that there are a couple of million papers, it would be a shame if there wasn’t. But there are obviously not a couple of million discoveries. Most are not really contributing much to generating knowledge.

 

OUT OF SAMPLE EVENTS

There were many failures of prediction related to the 2008 financial crisis. Silver observes that there is a common thread to these failures:

  • The confidence that homeowners had about housing prices may have stemmed from the fact that there had not been a substantial decline in U.S. housing prices in the recent past. However, there had never before been such a widespread increase in U.S. housing prices like the one that preceded the collapse.
  • The confidence that the banks had in Moody’s and S&P’s ability to rate mortgage-backed securities may have been based on the fact that the agencies had generally performed competently in rating other types of financial assets. However, the ratings agencies had never before rated securities as novel and complex as credit default options.
  • The confidence that economists had in the ability of the financial system to withstand a housing crisis may have arisen because housing price fluctuations had generally not had large effects on the financial system in the past. However, the financial system had probably never been so highly leveraged, and it had certainly never made so many side bets on housing before.
  • The confidence that policy makers had in the ability of the economy to recuperate quickly from the financial crisis may have come from their experience of recent recessions, most of which had been associated with rapid, ‘V-shaped’ recoveries. However, those recessions had not been associated with financial crisis, and financial crises are different.

Silver explains that these events were out of sample, which was a major reason for the failed forecasts. The problem is that few forecasters ever want to look for examples and evidence outside of what their models have already considered:

We will be forced to acknowledge that we know less about the world than we thought we did. Our personal and professional incentives almost always discourage us from doing this.

We forget – or we willfully ignore – that our models are simplifications of the world. We figure that if we make a mistake, it will be at the margin.

In complex systems, however, mistakes are not measured in degrees but in whole orders of magnitude…

One of the pervasive risks that we face in the information age… is that even if the amount of knowledge in the world is increasing, the gap between what we know and what we think we know may be widening. This syndrome is often associated with very precise-seeming predictions that are not at all accurate.

 

FOXES VS. HEDGEHOGS

Silver tabulates Philip Tetlock’s descriptions of foxes versus hedgehogs. (Tetlock is the author of Expert Political Judgment: How Good Is It? How Can We Know? and also Superforecasting: The Art and Science of Prediction.)

How Hedgehogs Think

  • Specialized: Often have spent the bulk of their careers on one or two great problems. May view the opinions of ‘outsiders’ skeptically.
  • Stalwart: Stick to the same ‘all-in’ approach – new data is used to refine the original model.
  • Stubborn: Mistakes are blamed on bad luck or idiosyncratic circumstances – a good model had a bad day.
  • Order-seeking: Expect that the world will be found to abide by relatively simple governing relationships once the signal is identified through the noise.
  • Confident: Rarely hedge their predictions and are reluctant to change them.
  • Ideological: Expect that solutions to many day-to-day problems are manifestations of some grander theory or struggle.

How Foxes Think

  • Multidisciplinary: Incorporate ideas from different disciplines and regardless of their origin on the political spectrum.
  • Adaptable: Find a new approach – or pursue multiple approaches at the same time – if they aren’t sure the original one is working.
  • Self-critical: Sometimes willing (if rarely happy) to acknowledge mistakes in their predictions and accept the blame for them.
  • Tolerant of complexity: See the universe as complicated, perhaps to the point of many fundamental problems being irresolvable or inherently unpredictable.
  • Cautious: Express their predictions in probabilistic terms and qualify their opinions.
  • Empirical: Rely more on observation than theory.

Foxes are better forecasters than hedgehogs. But hedgehogs – because of their big, bold predictions – are much more likely to be interviewed on television.

Silver describes three broad principles that he relies on in the FiveThirtyEight forecasting model:

Principle 1: Thinking Probabilistically

Each forecast comes with a range of possible outcomes. The distribution of possible outcomes is an honest expression of the uncertainty that exists in the real world. What typifies a good forecaster is that the range of possible outcomes is itself supported by the later results of the forecasts. In other words, if you examine all the times when a good forecaster said there was a 90 percent chance of an event happening, those predicted events should have happened about 90 percent of the time.

Foxes very often give a range of possible outcomes, while hedgehogs rarely do.

Principle 2: Update Your Forecasts

When good forecasters get new information that changes the probabilities associated with their prediction, they update their prediction accordingly. A fox has no trouble changing her mind if that’s what the new evidence suggests.

Unfortunately, some people think changing one’s mind on the basis of new evidence is a sign of weakness. But if the forecaster is simply incorporating new information as well as possible, that’s a sign of strength, not weakness. Silver quotes John Maynard Keynes:

When the facts change, I change my mind. What do you do, sir?

Principle 3: Look for Consensus

Very often the consensus estimate is better than most (and sometimes all) individual forecasts:

Quite a lot of evidence suggests that aggregate or group forecasts are more accurate than individual ones, often somewhere between 15 and 20 percent more accurate depending on the discipline.

A common experiment is to present a group of at least thirty people with a jar of pennies, and then ask each person in the group to guess how many pennies are in the jar. In nearly every case, the average guess of the group is more accurate than every individual guess.

Stock prices can be thought of in this way. But there are exceptions occasionally.

The lesson for the fox – in addition to recognizing when the aggregate is likely the best estimate – is to attempt to implement a process of aggregation within your own mind. Try to incorporate as many different types of information and points of view as possible in the process of developing a prediction.f

 

THINKING VERY BIG AND VERY SMALL

Sometimes innovation is very incremental, while other times it involves a big jump forward:

Good innovators think very big and they think very small. New ideas are sometimes found in the most granular details of a problem where few others bother to look. And they are sometimes found when you are doing your most abstract and philosophical thinking, considering why the world is the way that it is and whether there might be an alternative to the dominant paradigm. Rarely can they be found in the temperate latitudes between these two spaces, where we spend 99 percent of our lives. The categorizations and approximations we make in the normal course of our lives are usually good enough to get by, but sometimes we let information that might give us a competitive advantage slip through the cracks.

Most great forecasters constantly innovate and improve.

 

CHAOS THEORY

Silver explains how chaos theory applies to systems in which two properties hold:

  • The systems are dynamic, meaning that the behavior of the system at one point in time influences its behavior in the future;
  • And they are nonlinear, meaning they abide by exponential rather than additive relationships.

Trying to predict the weather is trying to predict a chaotic system:

The problem begins when there are inaccuracies in our data… Imagine that we’re supposed to be taking the sum of 5 and 5, but we keyed in the second number wrong. Instead of adding 5 and 5, we add 5 and 6. That will give us an answer of 11 when what we really want is 10. We’ll be wrong, but not by much: addition, as a linear operation, is pretty forgiving. Exponential operations, however, extract a lot more punishment when there are inaccuracies in our data. If instead of taking 5 to the 5th power – which should be 3,215 – we instead take 5 to the 6th power, we wind up with an answer of 15,625. That’s way off: we’ve missed our target by 500 percent.

This inaccuracy quickly gets worse if the process is dynamic, meaning that our outputs at one stage of the process become our inputs in the next. For instance, say that we’re supposed to take five to the fifth, and then take whatever result we get and apply it to the fifth power again. If we’d made the error described above, and substituted a 6 for the second 5, our results will now be off by a factor of more than 3,000. Our small, seemingly trivial mistake keeps getting larger and larger.

The weather is the epitome of a dynamic system, and the equations that govern the movement of atmospheric gases and fluids are nonlinear – mostly differential equations. Chaos theory therefore most definitely applies to weather forecasting, making the forecasts highly vulnerable to inaccuracies in our data.

Sometimes these inaccuracies arise as the result of human error. The more fundamental issue is that we can only observe our surroundings with a certain degree of precision. No thermometer is perfect, and if it’s off in even the third or the fourth decimal place, this can have a profound impact on the forecast.

Silver notes that perhaps the most impressive improvements have been in hurricane forecasting. Twenty-five years ago, the National Hurricane Center missed by an average of 350 miles when it forecasted a hurricane’s landfall three days in advance. Today the average miss is only about one hundred miles. (Forecasters have not gotten much better at forecasting hurricane intensity, however, since the forces that govern intensity occur at a much smaller scale.)

 

EARTHQUAKES

Seismologists have specific definitions for prediction and forecast:

  • A prediction is a definitive and specific statement about when and where an earthquake will strike: a major earthquake will hit Kyoto, Japan, on June 28.
  • Whereas a forecast is a probabilistic statement, usually over a longer time scale: there is a 60 percent chance of an earthquake in Southern California over the next thirty years. (149)

The United States Geological Survey (USGS) holds that earthquakes cannot be predicted, but they can be forecasted. Silver includes the following table in his book:

FIGURE 5-2. FREQUENCY OF A MAJOR (>= MAGNITUDE 6.75) EARTHQUAKE WITHIN A 50-MILE RADIUS

Anchorage 1 per 30 years
San Francisco 1 per 35 years
Los Angeles 1 per 40 years
Seattle 1 per 150 years
Sacramento 1 per 180 years
San Diego 1 per 190 years
Salt Lake City 1 per 200 years
Portland, OR 1 per 500 years
Charleston, SC 1 per 600 years
Las Vegas 1 per 1,200 years
Memphis 1 per 2,500 years
Phoenix 1 per 7,500 years
New York 1 per 12,000 years
Boston 1 per 15,000 years
Philadelphia 1 per 17,000 years
St. Louis 1 per 23,000 years
Atlanta 1 per 30,000 years
Denver 1 per 40,000 years
Washington, DC 1 per 55,000 years
Chicago 1 per 75,000 years
Houston 1 per 100,000 years
Dallas 1 per 130,000 years
Miami 1 per 140,000 years

 

According to the Gutenberg-Richter law, for every increase of one point in magnitude, an earthquake is ten times less frequent. Thus, given information on past earthquakes and their magnitudes in a given area, it’s straightforward to predict the frequency of more powerful earthquakes in the same area.

As far as specific predictions are concerned, however, weather forecasters are much further along than seismologists. Weather forecasters have been able to develop a good theoretical understanding of the earth’s atmosphere because they can observe a great deal of it. Seismologists, on the other hand, are trying to predict the results of events that mostly occur fifteen kilometers below the earth’s surface. So it’s far more difficult for seismologists to develop a model of what is actually happening.

Overfitting: The Most Important Scientific Problem You’ve Never Heard Of

Mistaking noise for a signal is overfitting. If the model fits past observations too loosely, it is underfitting. If the model fits past observations too closely, it is overfitting. Overfitting is a much more common error than underfitting, as Silver describes:

This seems like an easy mistake to avoid, and it would be if only we were omniscient and always knew about the underlying structure of the data. In almost all real-world applications, however, we have to work by induction, inferring the structure from the available evidence. You are most likely to overfit a model when the data is limited and noisy and when your understanding of the fundamental relationships is poor; both circumstances apply in earthquake forecasting.

…Overfitting represents a double whammy: it makes our model look better on paper but perform worse in the real world. Because of the latter trait, an overfit model eventually will get its comeuppance if and when it is used to make real predictions. Because of the former, it may look superficially more impressive until then, claiming to make very accurate and newsworthy predictions and to represent an advance over previously applied techniques. This may make it easier to get the model published in an academic journal or to sell to a client, crowding out more honest models from the marketplace. But if the model is fitting noise, it has the potential to hurt science.

… To be clear, these mistakes are usually honest ones. To borrow the title of another book, they play into our tendency to be fooled by randomness.

 

ECONOMIC FORECASTING

Economists have a poor track record of predicting recessions. But many of them may not have good incentives to improve.

Silver examined, from 1993 to 2010, economic forecasts of GDP as stated by economists in the Survey of Professional Forecasters. The Survey is unique in that it asks economists to give a range of outcomes and associated probabilities. If economists’ forecasts were as accurate as they thought, then from 1993 to 2010, only 2 forecasts out of 18 would fall outside their prediction intervals. But in fact, actual GDP fell outside the prediction intervals 6 times out of 18.

If you examine how economic forecasts have actually performed, writes Silver, then a 90 percent prediction interval spans about 6.4 points of GDP:

When you hear on the news that GDP will grow by 2.5 percent next year, that means it could quite easily grow at a spectacular rate of 5.7 percent instead. Or it could fall by 0.7 percent – a fairly serious recession. Economists haven’t been able to do any better than that, and there isn’t much evidence that their forecasts are improving.

Silver met with the economist Jan Hatzius, who has been somewhat more accurate in his forecasts (in 2007, he warned about the 2008 crisis). Silver quotes Hatzius:

Nobody has a clue. It’s hugely difficult to forecast the business cycle. Understanding an organism as complex as the economy is very hard.

Silver liststhree fundamental challenges economists face, according to Hatzius:

  • First, it is very hard to determine cause and effect from economic statistics alone.
  • Second, the economy is always changing, so explanations of economic behavior that hold in one business cycle may not apply to future ones.
  • Third, as bad as their forecasts have been, the data that economists have to work with isn’t much good either.

Some data providers track four million statistics on the U.S. economy. But there have only been eleven recessions since the end of World War II. Silver:

If you have a statistical model that seeks to explain eleven outputs but has to choose from among four million inputs to do so, many of the relationships it identifies are going to be spurious. (This is another classic case of overfitting – mistaking noise for a signal…)

For example, the winner of the Super Bowl correctly ‘predicted’ the direction of the stock market in 28 out of 31 years (from 1967 thru 1997). A test of statistical significance would have said that there was only a 1 in 4,700,000 possibility that the relationship was due to chance alone, says Silver.

…of the millions of statistical indicators in the world, a few will have happened to correlate especially well with stock prices or GDP or the unemployment rate. If not the winner of the Super Bowl, it might be chicken production in Uganda. But the relationship is merely coincidental.

Economic variables that are leading indicators in one economic cycle are often lagging indicators in the next economic cycle.

An Economic Uncertainty Principle

Feedback loops between economic forecasts and economic policy can be particularly problematic for economic forecasters. If the economy looks like it’s at risk of going into recession, then the government and the Federal Reserve will take steps to lessen that risk, perhaps even averting a recession that otherwise would have occurred.

Not only do you have to forecast both the economy and policy responses. But even when you examine past economic data, you have to take into account government policy decisions in place at the time, notes Silver. This issue was first highlighted by economist Robert Lucas in 1976. Silver continues:

Thus, it may not be enough to know what current policy makers will do; you also need to know what fiscal and monetary policy looked like during the Nixon administration. A related doctrine known as Goodhart’s law, after the London School of Economics professor who proposed it, holds that once policy makers begin to target a particular variable, it may begin to lose its value as an economic indicator….

At its logical extreme, this is a bit like the observer effect (often mistaken for a related concept, the Heisenberg uncertainty principle): once we begin to measure something, its behavior starts to change. Most statistical models are built on the notion that there are independent variables and dependent variables, inputs and outputs, and they can be kept pretty much separate from one another. When it comes to the economy, they are all lumped together in one hot mess.

An Ever-Changing Economy

An even more fundamental problem is that the American and global economies are always evolving. Even if you correctly grasp the relationships between different economic variables in the past, those relationships can change over the course of time.

Perhaps you correctly account for the fact that the U.S. economy now is dominated more by the service sector. But how do you account for the fact that major central banks have printed trillions of dollars? How do you account for interest rates near zero (or even negative)?

The U.S. stock market seems high based on history. But if rates stay relatively low for the next 5-10, the U.S. stock market could gradually move higher from here. U.S. stocks may even turn out, in retrospect, to be cheap today if there has been a structural shift to lower interest rates.

Furthermore, as Silver points out, you never know the next paradigm shift that will occur. Will the future economy, or the future stock market, be less volatile or more? What if breakthroughs in technology create a much wealthier economy where the need for many forms of human labor is significantly curtailed? Is that the most likely way that debt levels can be reduced and interest rates can move higher? Or will central banks inflate away most of the current debt by printing even more money and/or by keeping rates very low for many more years? No one really knows.

Economic Data is Very Noisy

Most economic data series are subject to revision. Average GDP could be revised up to very high GDP or revised down to a recession. Silver:

So we should have some sympathy for economic forecasters. It’s hard enough to know where the economy is going. But it’s much, much harder if you don’t know where it is to begin with.

 

BAYES’ RULE

Eliezer Yudkowsky of the Machine Intelligence Research Institute provides an excellent intuitive explanation of Bayes’s rule: http://www.yudkowsky.net/rational/bayes

Yudkowsky begins by discussing a situation that doctors often encounter:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

Most doctors estimate the probability between 70% and 80%, which is wildly incorrect.

In order to arrive at the correct answer, Yudkowsky asks us to think of the question as follows. We know that 1% of women at age forty who participate in routine screening have breast cancer. So consider 10,000 women who participate in routine screening:

  • Group 1: 100 women with breast cancer.
  • Group 2: 9,900 women without breast cancer.

After the mammography, the women can be divided into four groups:

  • Group A: 80 women with breast cancer, and a positivemammography.
  • Group B: 20 women with breast cancer, and a negativemammography.
  • Group C: 950 women without breast cancer, and a positivemammography.
  • Group D: 8,950 women without breast cancer, and a negativemammography.

So the question again: If a woman out of this group of 10,000 women has a positive mammography, what is the probability that she actually has breast cancer?

The total number of women who had positive mammographies is 80 + 950 = 1,030. Of that total, 80 women had positive mammographies AND have breast cancer. In looking at the total number of positive mammographies (1,030), we know that 80 of them actually have breast cancer.

So if a woman out of the 10,000 has a positive mammography, the chances that she actually has breast cancer = 80/1030 or 0.07767 or 7.8%.

That’s the intuitive explanation. Now let’s look at Bayes’Rule:

P(A|B) = [P(B|A)P(A)] /P(B)

Let’s apply Bayes’ Rule to the same question above:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

P(A|B) = the probability that the woman has breast cancer (A), given a positive mammography (B)

Here is what we know:

P(B|A) = 80% – the probability of a positive mammography (B), given that the woman has breast cancer (A)

P(A) = 1% – the probability that a woman out of the 10,000 screened actually has breast cancer

P(B) = (80+950) / 10,000 = 10.3% – the probability that a woman out of the 10,000 screened has a positive mammography

Bayes’ Rule again:

P(A|B) = [P(B|A)P(A)] /P(B)

P(A|B) = [0.80*0.01] / 0.103 = 0.008 / 0.103 = 0.07767 or 7.8%

Derivation of Bayes’ Rule:

Bayesians consider conditional probabilities as more basic than joint probabilities. You can define P(A|B) without reference to the joint probability P(A,B). To see this, first start with the conditional probability formula:

P(A|B) P(B) = P(A,B)

but by symmetry youget:

P(B|A) P(A) = P(A,B)

It follows that:

P(A|B) = [P(B|A)P(A)] /P(B)

which is Bayes’ Rule.

 

THE PROBLEM OF FALSE POSITIVES

In the case of the age forty women who had a positive mammogram, we saw that only about 7.8% actually had cancer. So there were many false positives. Out of 10,000 age forty women tested, 950 tested positive but did not have cancer.

Silver explains how, in the Era of Big Data, if you look at published scientific results, there are likely to be many false positives. Assume that 100 out of 1,000 hypotheses are actually true. Further assume that 80% of true scientific hypotheses are correctly deemed to be true, while 90% of false hypotheses are correctly rejected. So now we have four groups:

  • True positives: 80 of 100 hypotheses that are true are correctly deemed true
  • False negatives: 20 of 100 hypotheses that are true are incorrectly deemed false
  • False positives: 90 of 900 hypotheses that are false are incorrectly deemed true
  • True negatives: 810 of 900 hypotheses that are false are correctly deemed false

So you can see, under these assumptions, that we’ll have 80 true hypotheses correctly identified as true, but 90 false hypotheses incorrectly identified as true. Silver comments:

…as we know from Bayes’ theorem, when the underlying incidence of something in a population is low (breast cancer in young women; truth in a sea of data), false positives can dominate the results if we are not careful.

 

CONCLUSION

Most of us, including scientists, are not very good at making probability estimates about future events. But there are two pieces of good news, writes Silver:

  • First, our estimates are just a starting point. Bayes’ theorem will allow us to improve our estimates every time we get new information.
  • Second, with practice – and trial and error – we can get much better at making probability estimates in the first place. For instance, see: http://www.goodjudgment.com/

Silver explains the importance of testing our ideas:

Bayes’ theorem encourages us to be disciplined about how we weigh new information. If our ideas are worthwhile, we ought to be willing to test them by establishing falsifiable hypotheses and subjecting them to a prediction. Most of the time, we do not appreciate how noisy the data is, and so our bias is to place too much weight on the newest data point…

But we can have the opposite bias when we become too personally or professionally invested in a problem, failing to change our minds when the facts do. If an expert is one of Tetlock’s hedgehogs, he may be too proud to change his forecast when the data is incongruous with his theory of the world.

The more often you are willing to test your ideas, the sooner you can begin to avoid these problems and learn from your mistakes… It’s more often with small, incremental, and sometimes even accidental steps that we make progress.

 

BOOLE MICROCAP FUND

An equal weighted group of micro caps generally far outperforms an equal weighted (or cap-weighted) group of larger stocks over time. See the historical chart here: https://boolefund.com/best-performers-microcap-stocks/

This outperformance increases significantly by focusing on cheap micro caps. Performance can be further boosted by isolating cheap microcap companies that show improving fundamentals. We rank microcap stocks based on these and similar criteria.

There are roughly 10-20 positions in the portfolio. The size of each position is determined by its rank. Typically the largest position is 15-20% (at cost), while the average position is 8-10% (at cost). Positions are held for 3 to 5 years unless a stock approachesintrinsic value sooner or an error has been discovered.

The mission of the Boole Fund is to outperform the S&P 500 Index by at least 5% per year (net of fees) over 5-year periods. We also aim to outpace the Russell Microcap Index by at least 2% per year (net). The Boole Fund has low fees.

 

If you are interested in finding out more, please e-mail me or leave a comment.

My e-mail: [email protected]

 

 

 

Disclosures: Past performance is not a guarantee or a reliable indicator of future results. All investments contain risk and may lose value. This material is distributed for informational purposes only. Forecasts, estimates, and certain information contained herein should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed.No part of this article may be reproduced in any form, or referred to in any other publication, without express written permission of Boole Capital, LLC.