1/
Get a cup of coffee.
In this thread, I'll help you understand the Volatility Tax.
Whether you're a fundamentals-driven, buy-and-hold investor or an esoteric derivatives trader, this thread will help you hone your craft -- by sharpening your probabilistic reasoning skills.
Get a cup of coffee.
In this thread, I'll help you understand the Volatility Tax.
Whether you're a fundamentals-driven, buy-and-hold investor or an esoteric derivatives trader, this thread will help you hone your craft -- by sharpening your probabilistic reasoning skills.
2/
Imagine we have 2 stocks: A and B.
A is the ultimate steady compounder. Each year, the stock rises 15% -- like clockwork.
B is much more volatile. Some years, it RISES 50%. Other years, it FALLS 20%. The odds are 50/50 each year -- like a series of independent coin flips.
Imagine we have 2 stocks: A and B.
A is the ultimate steady compounder. Each year, the stock rises 15% -- like clockwork.
B is much more volatile. Some years, it RISES 50%. Other years, it FALLS 20%. The odds are 50/50 each year -- like a series of independent coin flips.
3/
Notice that, in any particular year, the *average* (or *expected*) return of B is the SAME as that of A.
That's because, in any year, the *average* of the 2 possible 50/50 outcomes for B (+50% and -20%) is (50 - 20)/2 = +15% -- the SAME as A's steady return.
Notice that, in any particular year, the *average* (or *expected*) return of B is the SAME as that of A.
That's because, in any year, the *average* of the 2 possible 50/50 outcomes for B (+50% and -20%) is (50 - 20)/2 = +15% -- the SAME as A's steady return.
4/
The difference between A and B lies NOT in their *average* return per year, but in the SPREAD of outcomes around this average.
For A, this spread is *zero*. Each year, we get the same +15%.
But for B, the spread is *35%*. Because +50%/-20% is simply 15% +/- 35%.
The difference between A and B lies NOT in their *average* return per year, but in the SPREAD of outcomes around this average.
For A, this spread is *zero*. Each year, we get the same +15%.
But for B, the spread is *35%*. Because +50%/-20% is simply 15% +/- 35%.
5/
So, if we're planning to simply buy and hold one of these stocks for a long time (say, 20 years), we should be pretty much indifferent between A and B, right?
After all, they both have the exact same expected return in every single year.
But that's NOT how volatility works.
So, if we're planning to simply buy and hold one of these stocks for a long time (say, 20 years), we should be pretty much indifferent between A and B, right?
After all, they both have the exact same expected return in every single year.
But that's NOT how volatility works.
6/
To see why, let's do a *probabilistic* analysis.
Suppose both A and B are at $100/share today.
Analyzing A is simple. The stock just rises 15% each year. So, after 20 years, it will be at ~$1,636.65/share.
And if we buy and hold A for these 20 years, our CAGR will be 15%.
To see why, let's do a *probabilistic* analysis.
Suppose both A and B are at $100/share today.
Analyzing A is simple. The stock just rises 15% each year. So, after 20 years, it will be at ~$1,636.65/share.
And if we buy and hold A for these 20 years, our CAGR will be 15%.
7/
Analyzing B is a little more complicated -- because there are many possible outcomes.
So, let's take this 1 year at a time.
After 1 year of holding B, there are 2 possible outcomes. We could either be UP 50% or DOWN 20%.
Analyzing B is a little more complicated -- because there are many possible outcomes.
So, let's take this 1 year at a time.
After 1 year of holding B, there are 2 possible outcomes. We could either be UP 50% or DOWN 20%.
8/
That leaves us with an *expected* stock price of $115 in a year -- the same as what A's stock price will be at that time.
And after 1 year, our expected CAGR from B will be +15% -- also the same as A's CAGR.
So far, no surprises.
That leaves us with an *expected* stock price of $115 in a year -- the same as what A's stock price will be at that time.
And after 1 year, our expected CAGR from B will be +15% -- also the same as A's CAGR.
So far, no surprises.
9/
What happens when we take this 1 more year forward -- that is, 2 years of buying and holding B?
Now, there are 3 possible outcomes. They're NOT all equally likely.
The *expected* stock price of B after 2 years is $132.25 -- again the SAME as A's stock price after 2 years.
What happens when we take this 1 more year forward -- that is, 2 years of buying and holding B?
Now, there are 3 possible outcomes. They're NOT all equally likely.
The *expected* stock price of B after 2 years is $132.25 -- again the SAME as A's stock price after 2 years.
10/
But here's the interesting thing:
Even though A and B have the SAME expected *stock price*, B's expected 2-year *CAGR* is LOWER than A's.
B has an expected 2-year CAGR of only +12.27%, against A's 15%.
That's the Volatility Tax. HIGHER volatility leads to LOWER CAGR.
But here's the interesting thing:
Even though A and B have the SAME expected *stock price*, B's expected 2-year *CAGR* is LOWER than A's.
B has an expected 2-year CAGR of only +12.27%, against A's 15%.
That's the Volatility Tax. HIGHER volatility leads to LOWER CAGR.
11/
The pattern continues beyond 2 years as well.
For example, when we look 3 years out, B's expected CAGR falls further to ~11.36% -- while A's holds steady at 15%.
And yet, both stocks continue to have the same expected *price* -- $152.09 per share.
The pattern continues beyond 2 years as well.
For example, when we look 3 years out, B's expected CAGR falls further to ~11.36% -- while A's holds steady at 15%.
And yet, both stocks continue to have the same expected *price* -- $152.09 per share.
12/
No matter how far into the future we go, both A and B will continue to have the SAME expected stock price -- growing at 15% per year.
But while A's expected CAGR will remain at 15%, B's will keep falling -- until it eventually converges to ~9.54%.
No matter how far into the future we go, both A and B will continue to have the SAME expected stock price -- growing at 15% per year.
But while A's expected CAGR will remain at 15%, B's will keep falling -- until it eventually converges to ~9.54%.
13/
For example, B's 20-year expected CAGR is only ~9.82%.
Why? Where exactly did the remaining 15% - 9.82% = ~5.18% of CAGR go?
Well, that ~5.18% is LOST because of B's *volatility* from year to year. That's the Volatility Tax.
For example, B's 20-year expected CAGR is only ~9.82%.
Why? Where exactly did the remaining 15% - 9.82% = ~5.18% of CAGR go?
Well, that ~5.18% is LOST because of B's *volatility* from year to year. That's the Volatility Tax.
14/
This all seems a bit counter-intuitive.
How can 2 stocks have the SAME expected price, but *different* expected CAGRs?
It's because of *non-linearity*. CAGR is a *non-linear* -- in fact, *concave* -- function of stock price.
This all seems a bit counter-intuitive.
How can 2 stocks have the SAME expected price, but *different* expected CAGRs?
It's because of *non-linearity*. CAGR is a *non-linear* -- in fact, *concave* -- function of stock price.
15/
And concave functions like CAGR tend NOT to be swayed too much by extreme values of their inputs.
So, even though B's stock price 20 years hence can be as high as ~$332.53K/share, such extremes impact the *stock price* expectation FAR more than the *CAGR* expectation.
And concave functions like CAGR tend NOT to be swayed too much by extreme values of their inputs.
So, even though B's stock price 20 years hence can be as high as ~$332.53K/share, such extremes impact the *stock price* expectation FAR more than the *CAGR* expectation.
16/
It's a bit like what happens when Warren Buffett walks into a McDonald's containing, say, 20 other customers.
The *average* net worth of that McDonald's customers goes up by billions of dollars.
But the *median*/*most likely* net worth barely budges.
It's a bit like what happens when Warren Buffett walks into a McDonald's containing, say, 20 other customers.
The *average* net worth of that McDonald's customers goes up by billions of dollars.
But the *median*/*most likely* net worth barely budges.
17/
In the same way, when the SPREAD around an average annual return is high, extreme stock price outcomes become MORE likely.
But the *compounding* of such bets year after year actually drives *down* expected long-run CAGRs.
That's Volatility Tax.
In the same way, when the SPREAD around an average annual return is high, extreme stock price outcomes become MORE likely.
But the *compounding* of such bets year after year actually drives *down* expected long-run CAGRs.
That's Volatility Tax.
18/
In other words, IF two assets have similar *average* annual returns, but one of them is more volatile than the other, then, over time, in a "buy and hold" setting, the LESS volatile asset usually has a very good chance of beating the more volatile asset.
In other words, IF two assets have similar *average* annual returns, but one of them is more volatile than the other, then, over time, in a "buy and hold" setting, the LESS volatile asset usually has a very good chance of beating the more volatile asset.
19/
This seems to suggest that volatility creates its own kind of risk.
But many fundamentals-driven investors believe that volatility and risk have nothing to do with each other.
So, how do we square this circle?
This seems to suggest that volatility creates its own kind of risk.
But many fundamentals-driven investors believe that volatility and risk have nothing to do with each other.
So, how do we square this circle?
20/
Usually, the logic espoused by such investors is that market prices are tied to -- and will sooner or later reflect -- fundamentals like assets, earnings, cash flows, etc.
So, IF these fundamentals are growing steadily, why should we worry about volatility?
For example:
Usually, the logic espoused by such investors is that market prices are tied to -- and will sooner or later reflect -- fundamentals like assets, earnings, cash flows, etc.
So, IF these fundamentals are growing steadily, why should we worry about volatility?
For example:
21/
Then, there's this wonderful insight from Charlie Munger, suggesting that the return an investor gets from buying and holding a company will approximately equal the return the company itself is able to earn on its capital -- regardless of volatility:
Then, there's this wonderful insight from Charlie Munger, suggesting that the return an investor gets from buying and holding a company will approximately equal the return the company itself is able to earn on its capital -- regardless of volatility:
22/
Does this mean volatility doesn't matter?
That the Volatility Tax doesn't exist?
To answer this, we have to examine the assumptions behind these seemingly opposite conclusions.
Does this mean volatility doesn't matter?
That the Volatility Tax doesn't exist?
To answer this, we have to examine the assumptions behind these seemingly opposite conclusions.
23/
Yes, it's true:
IF market prices in the long run are ultimately tied to "fundamentals" (earnings, cash flows, etc.), and IF a company is able to *steadily* compound these fundamentals, then the Volatility Tax does NOT apply.
Yes, it's true:
IF market prices in the long run are ultimately tied to "fundamentals" (earnings, cash flows, etc.), and IF a company is able to *steadily* compound these fundamentals, then the Volatility Tax does NOT apply.
24/
Under these assumptions, a company that can grow fundamentals steadily at 15% forever CANNOT have a stock that behaves like a series of 15% +/- 35% independent coin flips.
The two models are just not compatible with one another.
Under these assumptions, a company that can grow fundamentals steadily at 15% forever CANNOT have a stock that behaves like a series of 15% +/- 35% independent coin flips.
The two models are just not compatible with one another.
25/
However, the words "steadily" and "forever" are doing a LOT of work here.
Very few companies (if any) can compound fundamentals at the exact same rate year after year.
More often than not, there's *volatility* in these *fundamentals* themselves.
However, the words "steadily" and "forever" are doing a LOT of work here.
Very few companies (if any) can compound fundamentals at the exact same rate year after year.
More often than not, there's *volatility* in these *fundamentals* themselves.
26/
For example, a company may grow cash flows at 15% per year *on average*.
But if that 15% growth in fundamentals is actually more like 15% +/- 10% each year, then the long run compounding of capital at the company WILL suffer the Volatility Tax.
For example, a company may grow cash flows at 15% per year *on average*.
But if that 15% growth in fundamentals is actually more like 15% +/- 10% each year, then the long run compounding of capital at the company WILL suffer the Volatility Tax.
27/
Of course, for many companies, the volatility of their business fundamentals may be much smaller than the volatility of the market price of their stock.
In such cases, the drag on returns due to the Volatility Tax may be small. But it's unlikely to be *zero*.
Of course, for many companies, the volatility of their business fundamentals may be much smaller than the volatility of the market price of their stock.
In such cases, the drag on returns due to the Volatility Tax may be small. But it's unlikely to be *zero*.
28/
To learn more about volatility, I recommend reading @KrisAbdelmessih and @bennpeifert.
For example, this article by Kris illuminates several connections between the Volatility Tax, lognormal distributions, and the Black-Scholes formula.
moontowermeta.com/solving-a-comp…
To learn more about volatility, I recommend reading @KrisAbdelmessih and @bennpeifert.
For example, this article by Kris illuminates several connections between the Volatility Tax, lognormal distributions, and the Black-Scholes formula.
moontowermeta.com/solving-a-comp…
29/
Please join Kris and me tomorrow (Sun, Jan 9) at 1pm ET, for a new Money Concepts episode on all things volatility.
Kris has been thinking deep thoughts on volatility and risk for many years. Here's a wonderful chance to pepper him with questions!
callin.com/link/NIyleDLMeS
Please join Kris and me tomorrow (Sun, Jan 9) at 1pm ET, for a new Money Concepts episode on all things volatility.
Kris has been thinking deep thoughts on volatility and risk for many years. Here's a wonderful chance to pepper him with questions!
callin.com/link/NIyleDLMeS
30/
If you're still with me, thank you very much!
Volatility is almost the defining feature of all kinds of asset values and market prices. I hope this thread helped you appreciate some of the finer points around it.
Have a great weekend!
/End
If you're still with me, thank you very much!
Volatility is almost the defining feature of all kinds of asset values and market prices. I hope this thread helped you appreciate some of the finer points around it.
Have a great weekend!
/End
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