Simple Math Tips for Investing

Chris White Apr 19, 2022
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In this blog post, we aim to cover a few mental shortcuts for investing in stocks, and how these shortcuts can be used to our advantage. We might often look at our investment portfolios and have a general understanding of the percentage that we are down or up for the month or year, but these simple math tips will enable investors to plan out for the future and be prepared for any investment event. 


Declining Stock Prices – Understanding the Percentages

When stock prices decrease, the percentage amounts are much more different than when we refer to percentage increases. The theoretical lowest value that a stock can reach is $0, and so it is often hard for us to wrap our minds around the fact that a stock can decrease by 50%, three times. Intuitively, it makes more sense to us that a stock can decrease by 50% only twice, but in fact, a stock can decrease 50% on multiple occasions without even reaching $0.

Take for example the chart below. The stock first declines 50% from $2,200 to $1,100, and then a second decline of 50% from $1,100 to $550, and finally a third 50% decline from $550 to $275. This means that an investor's money would be halved on three separate occasions, for a total decline of 87.5%. 


Multiples Needed to Breakeven from Drawdowns

One of the most often misunderstood concepts in investing is the difference in percentages from a drawdown against an increase. For example, if a stock declines by 10%, a subsequent increase of 10% will not bring the investor back to breakeven, but rather an 11% increase in the price is required to break even. For example, a $10 stock declines by 10% to $9, a subsequent 10% rise from $9 brings the stock up to only $9.9. Below we have listed various drawdown percentages in increments of 10%, and the subsequent percentage increases needed to break even, along with their respective ‘multiples. For example, a 90% drawdown in the price of a $10 stock requires a 10X to bring the stock back up to $10. 


The Rule of 72 (and 144)

Compounding allows money to grow at an exponential rate, which is often a concept that we as humans have difficulty grasping. For example, $100 growing at 10% gets to $1,700 at the end of a 30-year period, but naturally, our brains couldn’t calculate this exponential amount. A good method to get around this is through the ‘Rule of 72’. The Rule of 72 states that the number of years it takes for invested money to double is 72 divided by the interest rate. For example, money growing at 10% annually will require 7 years to double (72 / 10 = ~7 years). The Rule of 72 can also be expanded to 144 – this would provide us with the time it takes to quadruple invested capital. For example, it would take 14.4 years to quadruple invested money growing at 10% annually (144 / 10 = 14.4 years). 


Lump-Sum vs. Cash Flows

Time is money, and money is time. One of the founding principles of investing is that cash upfront is almost always better than spread out over a period of time. To achieve the same ending amount, less money is required if it is provided in full upfront than spread out over time. To demonstrate this, we show below that $10,000 upfront grows to ~$25,000 in 12 years, growing at an annual rate of 8%. Conversely, an investor would require 12 payments of $1,225 ($14,700 total) earning 8% annually to have $25,000 by the end of 12 year period. Therefore, $10,000 upfront growing at 8% achieves the same ending goal as $14,700 spread out over 12 years.

$10,000 Upfront


12 Payments of $1,225



We hope that this quick overview on simple math tips for investing helps with developing mental shortcuts when considering portfolio values. We feel that these are all useful tips to know and can help investors with thinking ahead when planning out for retirement or other life goals. 


Research for Today, Invest for Tomorrow.

Chris Signature



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