Investing Math for Everyone


Math numerically expresses objective facts and reveals patterns. How can everyone evaluate the massive amount of numbers and invest with confidence? Markets go up and down daily, appearingly randomly. This leads some to see markets as a gamble or unreliable. We hope to show that everyone can focus on the time frame in order to take advantage of the investing’s simple math.

One of investing’s contradictions is that every investor will lose sometimes, in order to succeed over time. If you willingly accept that some losses, or said another way, price declines, are essential, then you can base your investing choices on historical evidence. While evidence is not a guarantee, it does affirm that your investing choices are rational and helps keep you from emotionally reacting by selling during price declines.  

Investing is of course a long term endeavor full of uncertainty, where the greater the potential for gain, the greater the risks that must be accepted. In dealing with uncertainty risk and valuation fluctuation, a logical response is to determine the mathematical best-worst case over a selected time frame to decide whether one can live with the outcomes. Investors desire wealth accumulation over time, so being willing and able to embrace emotional discomfort is a mindset that must be accepted. 

By investing broadly in a diversified, low cost manner, you can allow capital markets’ mathematical odds to be stacked in the investor’s favor across a predetermined time horizon. If the odds are stacked or ranked in your favor over time, the wins will ultimately outweigh the losses.  

The chart below shows that the longer your time horizon and commitment to holding onto stocks, the better your odds are to see your diversified stock portfolio have a positive result. 

Chart Source: Ben Carlson.

90 years of market data shows that by extending your time horizon, your odds of a positive result are on your side and even demonstrates that the compounding rates of return can be attractive. Even retirees often have a 20 to 30 year horizon to be invested, so the time horizon is still long term. To understand why a long-term perspective is important, consider the chart below.

The top line of the chart below shows the likelihood of earning a return of 20% or more per year for various asset classes over various time spans.  For example, Large Cap Value stocks earned 20% or more in 46% of the 91 years from 1927-2017.  But they earned 20% or more per year in only 23% of the 5-year rolling periods over that span (1927-31, 1928-32, …2013-2017).  Lower in the chart, they earned more than 10% in 76% of all 20-year periods (1927-46, 1928-47, …1998-2017) and more than 10% in all 30 year periods.  

Chart Source: Asset Dedication.
Visualizing U.S. Asset Class Returns Based on Time Horizons, Size, and Style. Retirement Management Journal, 2018.

Sometimes, what is wise does not appear very smart, especially in the short term. An advisor can help guide you through the ups and downs of markets and the emotions of being an investor. If you have questions about investing, please reach out to our team at Branning Wealth today.

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