Time Diversification ... and what it means (maybe)

As I get older and older I seem to understand less and less.
Once upon a time I thought I understood what people meant when they referred to a
Rebalancing Bonus.
Now, I'm not so sure. The definition seems to have flourished, it's now part of the jargon ... and it now means different things to different people.
>Ain't that the truth! I remember when ...
I also thought I understood what people meant when they referred to Time Diversification.
>Yeah. I remember when ...
I thought, by "Time Diversification", one meant that :
"The risk of investing in volatile assets like stocks decreases as one's time horizon increases."
>Yeah. That's true. You wait long enough, you eventually make money in the market.
Well, that's not the understanding of some. Indeed, some people speak of the Fallacy of Time Diversification.
And that's confusing ... to me.
>But you're easily confused.
Consider the following:
Suppose a stock has a share price of $10.
The annual returns for this stock have
Mean = 8% and Standard Deviation = 25%.
Then, T years into the future, we'd expect a distribution of returns something like Figure 1.
Note that the "spread" in prices increases as T increases.
The "spread" is the uncertainty in stock price and is usually measured by the Standard Deviation.
We might then conlude that:
the Standard Deviation increases with Time 
 Figure 1

>Yeah, so?
So now let's actually define:
Risk = Standard Deviation 
>Don't tell me! Risk increases with time, right?
Yes, with that particular definition of risk.
However, let's define:
Sex Appeal = Standard Deviation 
>Don't tell me! Sex appeal increases with time, right?
Yes ... and at my age, that makes me feel warm all over
Okay, now let's take a more reasonable definition of risk:
Risk n The possibility of suffering harm or loss 
That's not my definition of risk. It's Webster's.
Now let's consider again our $10 stock and the probability that, after T years, the price is less than $10.
(That's a loss, eh?)
From the distributions of Figure 1 we can generate Figure 2.
After T = 2 years, the probability that the price is less than $10 is (about) 42%.
(See the red dot?)
After T = 10 years, the probability that the price is less than $10 is (about) 28%.
(See the magenta dot?)
 Figure 2

>Can I say it?
Be my guest.
Thank you.
>So you're still confused?
Always.
>So why do they call it "diversification"?
Your portfolio benefits from having lots of different assets. That's asset diversification.
Presumably it'll benefit from having lots of time. That's ...
>Yes. You're still confused.
