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Comment by Karellen | Hacker News Reader

> getting 10% average annual returns with 10% annual volatility is worst than getting 5% returns with 1% annual volatility.

Doesn't this depend on how long you're planning on investing for, and what your criteria for selling your investments are?

If you're planning on investing for at least 10 years, and you're willing to give yourself a 2-3 year window for selling your investments once they reach a threshhold you decide on ahead of time, isn't the 10%/10% investment better?

(e.g. if retirement is 20 years away, you might consider putting your funds in that sort of investment for 10 years, with a view to moving them to something less volatile in the 5 years after that, as soon as they cross a 10% annualised return threshhold during that window.)

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> isn't the 10%/10% investment better?

If you consider that "you don't know any better" and returns are normally distributed (i.e. you don't have some secret sauce nobody else knows about), then there is no dimension in which the 10/10 is better.

You can convince yourself intuitively by imagining how you would maximize each strategy. The amount of money you have is a factor of the risk you take, because if you want to do something risky you will not be able to borrow much, whereas if you want to do something safe you can easily borrow.

That is, you objective is to maximize your expected return, under the constraint of not breaking your risk limit.

Suppose you have a 10% annualized volatility risk tolerance. That's your budget.

If you invest it all in a 10% average return / 10% annual vol strategy, that's it.

Now if I propose you a 5% average return / 1% volatility strategy, you just have to go to the bank and borrow 10x your capital. You will have the same risk exposure (in dollar), but 5x the expected returns.

Until a black swan event bankrupts you because of the leverage you have taken on.

Is 10x borrowing even an option if we are talking retirement savings?

I don't know much about finance. I guess that at that point (you borrowed 10 times your net worth). This is no longer your investment, it's your lender's investment. They will adjust interest rate to match the riskiness of whatever you are doing, leaving you with net zero.

Borrowing money is not free.

> Is 10x borrowing even an option if we are talking retirement savings?

Of course it is, though not exactly by "borrowing money" in a "mortgage" sense. Margin trading is a way to take leverage, derivatives is another. The former is simpler but costly, the latter is cheaper and allows you much more than 10x leverage, though it requires some high school mathematical thinking.

What you're saying sounds right. But in practice, no one is going to lend me, a nobody, 5x my money. At least outside real estate, that's it's own crazy alternate reality.

5x leverage is nothing, most retail brokers will offer you much better future initial margins.

> you just have to go to the bank and borrow 10x your capital.

"just" is doing a lot of heavy lifting in that sentence.

> there is no dimension in which the 10/10 is better

It's clearly better in the expected return dimension. This strategy has 10% expected return, while the other strategy has 5%.

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