Two Really Big Things You Should Know About
The purpose of this article is to demonstrate two things that can significantly impact the results of your financial strategy, and of which you may not already be aware:
- Two equally sized investments with the same average rate of return can still result in two completely different ending value results at the end of a given period.
- You can wind up with more money, even with a lower average rate of return, by reducing volatility.
Much of the rest of this post dives deep into math demonstrations, but in case you don't have time or are distracted, I want you to remember the critical two points above.
If you take nothing else from this post, keep those two things in mind as you make decisions in the future.
Volatility is not just a psychological inconvenience that you can withstand by simply looking away or getting comfortable with it - it's a mathematical reality with real world implications.
Sequence of Returns
There's a concept called "Sequence of Returns" that we discuss quite a bit, most often because it can have a serious impact in the years around a person's retirement or financial independence age.
In short, it's roughly true that an investor with a very long-term time horizon can withstand volatility ("the ups and downs of the market") because, on average, equity returns have tended to be positive over long periods, even though they aren't over every time period in between.
This is much less true for people who plan to live off of their assets. Once you start pulling cash out of your asset base each year (most often in retirement, but it could be at any time of your life), the ups and downs matter more, and they run the risk of mattering permanently. This is because when the market is down and you pull out a fixed amount of money, then even when the market recovers fully, it can't recover fully for you. You already removed assets that would have appreciated during the recovery. This affects the outcome of every time period thereafter, and it's most damaging if it happens to you early in your withdrawal phase.
...But It Actually Matters for Other Reasons
In that explanation, I mentioned that it's "roughly true" that a long-term investor can afford some volatility. But why is that only roughly true?
If you're not withdrawing the money, then why does it matter which order the returns come in, as long as they average out?
It's because, mathematically, for any average rate of return, your result will be better with lower volatility.
One intuitive reason is that you need a higher return to compensate for a loss. If you invest $100,000, and you lose 50%, you will have $50,000. How much do you need to return to get back to $100,000? Do you just need to be up 50% to make up for the 50% loss? No - an increase from here of 50% only gets you back to $75,000. Obviously, you need to return a positive 100% to get from $50,000 to $100,000. Here, an average return of 0% (-50%, followed by +50%) gets you worse than an actual 0% return.
But even that's not the only situation in which it matters. Actually, even if you don't have any negative returns, you'll still be worse off having volatile returns.
Fun With Math
To demonstrate, here are some simple examples. To be clear, none of these are intended to reflect real investments. They are strictly imaginary and intended to demonstrate how the math works.
In each example, I've highlighted the last line to show what the ending value of a hypothetical initial $100k investment would have become giving the displayed rates of return each year:
Scenario 1 - Steady, Unchanging Returns (No Volatility)
In this case, you start with $100,000, and you experience an average 8% return simply by returning 8% every year. The returns don't deviate from 8%. At the end of the 10th year, in this example, you'd have over $215,000. This example shows what no volatility looks like; you achieve the average return by simply producing the exact average return period after period.
Scenario 2 - Introducing Volatility
In this case, the average return has not changed at all - half the time it's 0%, and half the time it's +16%, leading to an average of 8%. And in no (hypothetical) year have you lost any money. But still, after averaging 8%, simply by virtue of having each year's return differ from 8% along the way, you've wound up with less money in the end. This continues to hold true across examples - the higher that variation gets away from the average each year, the lower the overall growth over time, for any given average rate of return.
Scenario 3 - Even More Volatility
The only real difference here is that I've turned up the standard deviation to a level you might see more often in real life portfolios containing stocks/equities. All this shows is how much more noticeable the end-result difference may be by accepting a more volatile portfolio.
Scenario 4 - Using Diversification to Manage Volatility
In Scenario 4, things get a little more interesting. I've split our fictional assets into two made up investments, both of which produce 8% rate of return with 15% volatility, but the difference is they have up and down years in alternating years. There are some years throughout where we have more money than at the same point in Scenario 3 (because we've now avoided overall down years), but in the end, we have the same amount.
No magic has really occurred yet. Volatility is down, and average return is lower, leading to the same amount of money in the end.
Scenario 5 - The Magic of Rebalancing
Here is where all of the magic happens. In Scenario 4, you didn't have much to show for reducing volatility except for some years of better values in the middle - more or less what people think about when they think about volatility. But that leaves out something critical - in real life, you can rebalance. So what we did here is, every year when one investment was up and the other investment was down, we simply brought the portfolio back into its intended balance: 50% in each investment. We didn't time the market or pick stocks or know the future; all we did is bring the portfolio back to its original split.
When we did this, we returned the portfolio to 0% volatility, and do you recognize that final number? It's the same as if we had the mythical Scenario 1 imaginary investment that simply produces 8% every year without fail. But we didn't rely on the availability of that investment in reality, we reconstructed it from messier, much more volatile set of hypothetical investments. By combining low (or negative) correlation assets and rebalancing, in this example, even with the same returns and volatility in the underlying investments, the hypothetical result is $20k more, an increase of 20% more of the initial investment value.
Scenario 6 - Higher Returns, Less Money
Just for fun, I wanted to prove what I asserted at the top. I turned the average return up to 9% here and still wound up with less money, because of higher volatility (18%, not unlike many periods for the S&P 500). It is absolutely possible to achieve greater average rates of return and still wind up with less money in the end.
What To Do with This Information
The main point of the above is simply to value risk and volatility properly.
If there is a way to reduce your overall volatility and risk, it probably makes sense for you to do so, even if you've already made peace with taking risk in general.
Without drowning in additional math or spreadsheets, consider the following about correlation:
- If you can find assets that don't have a lot of correlation, then your overall volatility doesn't need to match that of the investments you choose.
- You might think that negative correlation isn't helpful, but it doesn't work out that way. It isn't that every time one is "up" the other will be "down" to offset. Two things can have positive expected average return and still have low or negative correlation.
What Does This Leave Out?
- It can admittedly be very difficult to find actual investments with high expected returns but low volatility. In fact, the future of returns and volatility are unknowable, so history tends to be the best proxy we have in trying to apply these theories to practice.
- It can also be very hard to find truly uncorrelated or negatively correlated investments that have appropriate risk and positive long-term expected returns. Same as above, it's also nearly impossible to know correlation in advance, but backward-looking exercises are common and tend to help inform the possibilities.
- Obviously, the exact returns and order of returns shown above were completely made up - we're not aware of an investment that produces any of those predictable patterns of returns, or any that are their exact mirrored opposite. But the math still works - if you change the simple pattern of returns but keep the level of volatility, you still get the same results.
- Finding, selecting, executing, and developing a system for rebalancing real investments constitute most of "the hard part." I hope you got a lot out of the analysis, but I strongly recommend you speak to a professional if you're interested in putting a financial strategy to work for yourself.
2025-7754189.1 Exp 03/27
Hypothetical examples are not intended to suggest a particular course of action or represent the performance of any particular financial product or security. Past performance is not a guarantee of future results. Indices are unmanaged and one cannot invest directly in an index. All investments contain risk and may lose value. Equities may decline in value due to both real and perceived general market, economic and industry conditions. Diversification and rebalancing do not guarantee profit or protect against market loss.