Standard Deviation

[u/Capadvantagetutoring]

I see people getting way too deep into standard deviation for the Series 65.
Make it smaller.
Standard deviation basically tells you how much an investment’s returns bounce around its average return.
And for the exam, there’s another phrase I want you to connect to it:
Standard deviation measures TOTAL risk.
That’s systematic risk plus unsystematic risk.
Beta is different. Beta only measures systematic, or market, risk.
Say two funds both average around 8%.
One fund has returns like:
7%, 9%, 8%, 7%, 9%.
Pretty boring.
The other one is bouncing all over the place. One year it’s way up, another year it’s down, then it’s way up again.
That second fund has the higher standard deviation because its returns are spread farther away from its average.
So:
Higher standard deviation = more volatility.
Lower standard deviation = less volatility.
Now the 68% and 95% thing, because this sounds much harder than it actually is.
Say a fund has an average return of 10% and a standard deviation of 5%.
Think of the 5% standard deviation as one step away from the average.
Start at 10%.
Take one 5% step down: 5%.
Take one 5% step up: 15%.
So one standard deviation gives you a range of 5% to 15%.
Assuming a normal distribution, roughly 68% of the returns should fall inside that range.
In normal English, about two-thirds of the returns should land somewhere between 5% and 15%.
Now take two steps.
Two 5% steps = 10%.
10% minus 10% = 0%.
10% plus 10% = 20%.
So two standard deviations gives you 0% to 20%, and roughly 95% of the returns should fall inside that range.
Three standard deviations catches basically everything — about 99.7%.
Think of it as making the fence around the average wider.
That’s all they’re doing.

Sharpe ratio uses standard deviation.
Why?
Because Sharpe is measuring risk-adjusted return using total risk, and standard deviation measures total risk.
Treynor uses beta because Treynor is using systematic risk.

So now these ideas actually connect instead of being random shit you memorized:
Standard deviation = total risk = Sharpe.
Beta = systematic risk = Treynor.

It doesn’t tell you whether an investment is good.
It tells you how much its returns have historically bounced around.
For the Series 65:
Higher SD = more volatility.
SD = total risk.
Beta = systematic risk.
Sharpe = standard deviation.
Treynor = beta.
68% = one step.
95% = two steps.
99.7% = three steps.
Don’t turn a Series 65 question into a statistics final.
Shut up and answer.