Expected Values: Valuing Risk/Reward

Incorporating A Statistics Mindset in Investing

I’ve had the urge to write recently, put some pen to paper to get out some creative investing juices. I haven’t had many stocks to write about that I’ve been personally investing in and I do try my best not to spam your email box with any of my plethora of sub-par ideas. If I gave my subscribers around 5-6 actionable ideas a year, I’d be happy.

However, that leaves me with tons of time to just stare at my Subscriber count and wishing I had something to write about! So today, I wanted to simply put some pen to paper diagnosing my mindset on Risk/Reward and how I innately process adding to existing positions, opening new positions, and position sizing.

My approach is neither fully art or fully quantitatively calculated. However, combining a conceptual approach with underlying quantitative reasoning seems to have worked out well for me thus far.

“You don’t need to be a rocket scientist. Investing is not a game where the guy with the 160 IQ beats the guy with 130 IQ.” - Warren Buffett

A Simple Equation

Every investor utilizes this mindset to some degree, whether they know it or not. Properly utilizing the mindset is another concept entirely. In statistics though, it’s called an Expected Value.

Expected Value = E ( X ) = μ = ∑ x P ( x )

This looks like a 160 IQ guy concept. It’s not. It’s simply saying, it’s the summed probability of every outcome. In investors case, this is the risk/reward concept.

Let’s layout a simple example:

• You hypothetically found NVDA in the mid-2010s. You maybe thought to yourself… “[Insert Your Name Here], I think this could do 20x over the next 10 years… or I’m wrong and it goes to nothing.” Let’s say… you thought it was a 50/50 chance between these two outcomes.

• The Expected Value equation would give the following:

  • Probability of 10x = .50

  • Probability of 0x = .50

  • Expected Value or E(X) = (.50)*(10x) + (.50)*(0x) = 5x. Simple!

  • A 5x expected value would return a 19.6% compounded annual growth rate and you took into account your conceptual idea of what the risk/reward profile was. This is an oversimplified concept, but it’s worth diagnosing further! Big wins can make higher risk profiles worth considering.

The Great’s Methodology Deconstructed

The equation and mindset above is great in theory but how do we translate this into actionable ideas going forward. To simply rely on theory alone though is like trying to navigate a treasure map without a compass – you might have a plan, but good luck finding the X without direction.

Investors always use this methodology to match their style:

Warren Buffett: Being described as a mathematical prodigy and learning under Graham, Buffett optimized the risk area of the formula for shorter duration timelines in his early career.

Early days Net/Nets: These were lower risk opportunities, due to the companies trading under book value. However, they rerated and had lower reward profiles. An example yearly return breakdown might look conceptually like:

• 5% chance it goes to 0

• 10% chance it goes 20% lower

• 10% chance it stays level

• 25% chance it goes up 25%

• 25% chance it goes up 50%

• 25% chance it goes up 100%

• Expected Value = (.05)(0x) + (.10)(.80x) + (.10)(1x) + (.25)(1.25x) + (.25)(1.5x) + (.25)(2x) = 1.3675% (~ 37% annual return profile expected)

Now, this is an example of the best to do a rerate style. He found high probability opportunities with low downside. Another interesting example is David Gardner, the founder of The Motley Fool, who famously picked Amazon in 1997 and has held through to a 100 Bagger status. He has coined a buy and hold strategy across a number of opportunities that he expects can all be big winners!

***With a group of 100 holdings… if only 2 of your holdings 100x over 20 years and the rest go to 0, your expected return across the entire portfolio is still 7.2%. If 5 of them 100x, your returns skyrocket to 17.5% annualized across your entire portfolio.

Find Your Style

All of this goes back to the idea that each investor, even the pros, need to find the style that works for them.

I try to be unique with my style. I still run a concentrated portfolio but I love conceptualizing the risk/reward between holdings. An example a year ago on February 3th, 2023 was when I sold POOL 0.00%↑ and purchased Auto Partner APR 0.00%↑ with the proceeds.

• Pool Corp:

  • With my napkin math return calculator, I found that I was expecting a 10-12% return breakdown over the long term. However, being a large cap in the US in a market I knew well, the risk was very low. The company traded at an 18 PE and would put up 8-10% revenue growth going forward, return good amounts of capital to shareholders and do well. Low risk, slightly market beating returns.

• Auto Partner:

  • With my napkin math return calculator on my blog post, I found that I was expecting a near 20% CAGR. The company was trading at an 11 PE, was putting up topline growth in the 20-25% range, had pulled forward margins but not tapped out, and a high quality management team.

This decision worked out for me this past year.

What’s funny is that if I was expected a difference of a 20% vs 10% compounded annual results over 10 years, Auto Partner had the ability to be a significantly more risky investment with the same return expectations. However, I did the work on the company and found the risk profile was also much lower than investors were underwriting. A company of that quality trading at an 11x PE was a lucky find.

Moving Forward

What’s interesting about this approach is that it improves an investors portfolio incrementally. With each new position, the risk and reward profile needs to be compared against the current holdings and the reward needs to be high enough to make up for a lack of knowledge of risk within an industry, make up for Capital Gains tax if you have to sell, or any other factors.

When I sold Pool Corp, I liked the trade up in portfolio quality and return expectations. Now, new positions are being compared against Auto Partner which is trading at a 15 PE, is putting up mid-20s growth rates, has scale-based economics incorporated, and is extremely shareholder friendly.

If I find a new position with a better Expected Return or similar returns and lower risk, I’ll probably purchase some. This approach has naturally led me to concentration with long term compounders with high returns on capital/assets, enjoying some form of competitive advantage. However, I also have 2-3 special rerates in my portfolio where the short-term Reward side of the equation was enticing for the amount of risk I was undertaking.

Once these short-term holds no longer make sense and the reward has played out, I will sell them. Each investor can find their own style. However, each investors also has the obligation to understand the Expected Value of what their style yields and make sure they have the temperament, discipline, and capital on hand to support their style of play.

Hope you enjoyed this short article! Have a great Saturday.