Types of Randomness

By Schultz Collins Investment Counsel on May 19, 2023

Types of Randomness: Investing in the Stock Market 

This article presents different Types of Randomness and illustrates what it’s like to invest in the stock market. Without going into statistical jargon, we’ll go over four hypothetical sequences of return and the type of investors they would appeal to. By the end of the article, you’ll have a better understanding of randomness and why you could want some of your assets invested in stock markets. 

Figure 1 illustrates the first hypothetical sequence of return. The sequence is the pink line on the chart, the horizontal axis represents time, and the vertical axis is the value of the investment at different points in time. The line is straight, so the series has no randomness, and therefore the value of the investment is known throughout time. Since the value is predetermined, the sequence provides risk-free returns.  

There are no truly risk-free investments, but certificates of deposit are often considered a proxy for this type of return progression. This return series would appeal to investors who want known, positive, constant returns. However, we haven’t considered factors like fees, taxes, and inflation. Furthermore, the expected return from this sequence builds wealth at a pace that may be too slow for many investors. A pattern of return with no randomness looks appealing initially, but there’s a high cost for avoiding randomness.   

Figure 1 

The chart reflects hypothetical returns and are for illustrative purposes only. 

The second hypothetical sequence we’ll look at is illustrated in Figure 2 and introduces us to random returns. The chart shows the value of the asset going up, sometimes sharply, and going down, sometimes precipitously, through time. The value changes without any discernable pattern. Furthermore, the series gravitates around the zero value.  

This type of randomness is known as a White Noise sequence, and the random noise coming from a nonexistent radio station is often used as an example. Since the sequence jumps up and down around the zero value, it doesn’t build wealth at all. No one would invest in an asset that produced such a progression of return. 

Figure 2 

The chart reflects hypothetical returns and are for illustrative purposes only. 

The third hypothetical sequence we’ll look at is illustrates another type of randomness, and it is depicted in Figure 3. This randomness is called a Random Walk sequence, and the way a drunk person walks home from a bar is often used as an example. The drunkard will eventually get home, but the path taken will deviate from the most direct route. 

Likewise, the chart goes up and down, but will eventually get back to its starting point of zero. Unlike a White Noise series however, a Random Walk sequence will have cycles of upward and downward trends. These cycles may appear predictable, but they are completely random. Furthermore, the cycles can last for very, very long periods of time, so the value can be way up or way down. The Random Walk sequence appeals to gamblers who love risk and think they can predict when the line will go up or down.  

Figure 3 

The chart reflects hypothetical returns and are for illustrative purposes only. 

Figure 4 shows the final hypothetical sequence we’ll look at, and it combines aspects of the three series we already examined. Like the Random Walk, this sequence has cycles that may appear predictable, but, in fact, are not. Like the White Noise series, this sequence can move sharply when looking at very, very short periods of time. And like the Risk-free Return series, this sequence has a long-term positive trend.  

However, this sequence has a much higher long-term trend, and that’s why someone would want to invest in this return sequence over the Risk-free Return series. The higher long-term trend is called the Risk Premium, and is the theoretical reward given to investors for exposing their assets to this type of randomness. Diversified portfolios invested in stock markets also exhibit Risk Premiums. So, if you are comfortable with this type of randomness, you may want some of your portfolio invested in diversified stocks.  

Everyone is different though. If you are having a hard time accessing your own comfort level with different types of randomness, or just want a deeper understanding of them, we can help.  

Figure 4 

The chart reflects hypothetical returns and are for illustrative purposes only. 

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Disclaimer: Schultz Collins is a group comprised of investment professionals registered with Hightower Advisors, LLC, an SEC registered investment adviser. Some investment professionals may also be registered with Hightower Securities, LLC, member FINRA and SIPC. Advisory services are offered through Hightower Advisors, LLC. Securities are offered through Hightower Securities, LLC.  

This is not an offer to buy or sell securities. No investment process is free of risk, and there is no guarantee that the investment process or the investment opportunities referenced herein will be profitable. Past performance is neither indicative nor a guarantee of future results. The investment opportunities referenced herein may not be suitable for all investors.  

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This document was created for informational purposes only; the opinions expressed herein are solely those of the author(s) and do not represent those of Hightower Advisors, LLC, or any of its affiliates.