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How to Calculate Risk and Reward

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In investing, it is widely accepted that without risk, there is no reward. By the same token, it doesn’t mean that one should take on excessive risk for a chance for little gain. The key to successful risk management, then, is the ability to calculate risk and reward; the right tool for this is the Capital Asset Pricing Model (CAPM). This article lays the groundwork for future articles where I will reference CAPM.

What is CAPM?

CAPM measures the risk and reward of an asset, relatively to the market. It answers the key question: is the risk that I’m taking worth it?

CAPM is expressed in the following equation:

Don’t let the symbols throw you off. This is just a fancy version of the high school algebra equation in the form y = q + bx, which says that y grows in a straight line as x grows, starting at point a and growing at a constant rate b.

Similarly, CAPM states that the expected return on your asset grows as you take on more risk (Beta, analogous to b), starting at the baseline, risk-free rate of return Rf, analogous to a. The risk-free/baseline rate of return is, in theory, the 10-year Treasury bond yield, but the S&P 500 is more practical as a baseline.

Beta (Bi) measures risk. This is a key term to hone in on, defined below:

Beta is first calculated as the covariance between the asset and the market (how much their prices move together), then divided by the variance (volatility) of the market (S&P 500).

In a nutshell, Beta tells us how sensitive the asset was to fluctuations in the market; it was unavoidable risk. Therefore, for any asset in our portfolio, we want Beta to be close to 0.

Another key component of CAPM is Alpha. I will spare you the equations, and you can get them at the wikipedia link provided below. Alpha measures the asset’s market-beating, risk-adjusted return; it tells us by how much the asset outperformed or underperformed the market after taking into account the risk (Beta) that we took. It is possible to beat the market nominally, but if Beta is too high (i.e. you took on took much risk by holding the asset), then Alpha becomes negative, meaning the asset underperformed the market on a risk-adjusted basis.

The bottom line: Alpha tells us if our risk was worth taking. For any asset in our portfolio, we want Alpha to be positive and as high as possible.

More detailed explanations on CAPM are here: https://en.wikipedia.org/wiki/Capital_asset_pricing_model

Shortcomings of CAPM

I referred to Beta and Alpha in the past tense because their calculations are based on prices from the past; we cannot predict the future with CAPM, but what model can? As such, we must treat Alpha and Beta as being one tool in our toolbox, rather than the end-all-be-all tool.

A more valid critique of CAPM is that it assumes Beta doesn’t change over time. I would agree that, as I’ve seen in my research, almost all assets have Beta that change over time. This makes sense because as a company matures, its risk profile changes. If it’s successful, its Beta falls as its Alpha rises over time. Furthermore, I don’t rely on Beta calculated by websites like Yahoo Finance, Google Finance, or any online brokerage website, because they give you one Beta calculated over 3 to 5 years. Instead, I calculate my own year-by-year Alpha and Beta to better reveal changes over time.

Give It A Try

I’ve set up an easy-to-use tool on a Google spreadsheet at the link below. Once you click on the link, the instructions can be found on top of the spreadsheet. Feel free to use it to do your own calculations.

https://docs.google.com/spreadsheets/d/15QPBwxS7Ij19X869jsMKPz1DLzCiBDs8veEwMuRE9zc/edit?usp=sharing

Conclusion

With the caveat that CAPM is imperfect and should complement other tools, you can use it to calculate risk and reward. By choosing investments that maximize Alpha and minimize Beta to zero, you can tip the risk-reward scale in your favor.

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