How would you explain the standard deviation of an investment portfolio to my grandma?

How would you explain the standard deviation of an investment portfolio to my grandma?

This is not my content. It belongs to Franklin Parker. His incredible answer on Quora can be found here: https://www.quora.com/How-would-you-explain-the-standard-deviation-of-an-investment-portfolio-to-my-grandma/answer/Franklin-Parker-2?srid=tYFC

You are interviewing two pilots for the job of flying your private plane. You meet the first pilot and his name is George, he's handsome and a good talker:

So, you like George. He has good references and you find out that, over the course of his career, he has exactly hit the runway landing target on average. Cool, we like hitting the target.

Okay, next you meet the second pilot. His name is Mike:

Mike is very nice. He is well-mannered, carries excellent references, very professorial. Mike seems to fit the bill, but you find out that, unlike George, Mike has missed the runway landing target on average over his career. Not by much, mind you, just a few feet, but certainly a little.

Okay, great, EASY DECISION! George all the way. BUT,

Mike stops you on the way out and gets a passing glance at George's resume.

"Interviewing Georgie?"

"Umm...yes..." you stammer, not sure if you can reveal whomelse you are interviewing.

"I like him--I trained him you know. I wonder if he has figured out his landings? Those were always his toughest spot."

"Well, actually," you beam a little a your response, certain of your decision now, "landings seems to be his best feature! Turns out he hits the target exactly!"

"You mean on average? Well, to my knowledge, he has never actually hit the landing target! In fact, over the course of his career he has missed the target every time."

"Oh...uh....well, how is that possible?"

"He has just missed in such a way that it averages out perfectly! Just so you know, when I miss, I miss by only about 5% one way or the other--not enough to matter. Poor Georgie, he tends to miss by as much as 20% before or after!"

Mike walks away after you exchange pleasantries. You now get to decide which pilot gets the job.

And this is standard deviation. It measures by how much you miss the average. Clearly, with pilots, we want one with an extremely small standard deviation. We don't want them to miss by much--if at all! So, Mike is our clear choice. We can rely on him to consistently hit his average.

Quasar Chunawala

Quantitative Engineer at Goldman Sachs

7 年

So so cool! As an aside, Galton's board is a beautiful way to learn that a sum of i.i.d. rv's is Gaussian. :)

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