Diversification is a negative price lunch | Hacker News Reader

Diversification is a negative price lunch

outcastbeta.com

16 pointssebg9 comments

The author has a feew things wrong. First of all, growth due to compounding is geometric, not exponential. He has the two used interchangeably when they are vastly different over any reasonable timeframe.

Second, compounding isn't magic. Invest $1,000 at 5% annual ror over 25 years, and your final amount is -$3400. To actually grow exponentially as the author wants, an investor has to contribute additional principal on a periodic basis. Now, when you combine those two ideas, the question becomes: With my extra $200, should I buy more of the same stock or some of new stock? That's where diversification fits into an investor's strategy, and as copious amounts of data show, increased diversification has a higher annual ror compared to fixed asset investing. In fact, the ultimate diversification strategy is to buy a small piece of the total market aka index funds, and the historic annualized ror shows how effective this strategy is.

What's your definition of exponential?

If I invest $1,000 at 5% annual return, I expect to have 1000 * (1.05)^n after n years. That fits my definition of exponential - time is an exponent in the formula.

It's really not a matter of interpretation. Geometric and exponential growth are well defined mathematical concepts.

Geometric functions can have exponents. This does not imply the function is exponential. These are very different things.

https://en.m.wikipedia.org/wiki/Exponential_growth

The page you cite gives the formula for exponential growth as:

  {\displaystyle x_{t}=x_{0}(1+r)^{t}}

Um, right, let me translate that into something that can display here:

  x(t) = x(0) * (1+r)^t

Well, if you look at the formula I gave for compound interest:

x(t) is the value at time t,

x(0) is the value at time 0, namely $1000,

(1+r) is 1.05,

and t = n, the number of years.

So, from your own cited article, how is that not exponential?

Or were you agreeing with me, and disagreeing with glitchc?

My quibble was about geometrics vs exponential, but beyond the mathematical distinction of discreteness, they are equivalent, so I stand corrected on that front.

Is that a good thing or a bad thing?

Short term it’s good, you get better annual returns; long term it’s bad ( it doesn’t compound as much), according to their arguments.

It's a good thing basically it means that diversification removes risk and makes you money.

I've written a (simpler) article on the subject, which can serve as an introduction to this topic: https://alicegg.tech/2023/03/09/shannon-demon

i would like to suggest not to use the collective first-person voice (especially in the first sentence), as it can trigger pushback in some readers

Reply on news.ycombinator.com