You should never make a trade with negative expected return.
No!
You explain why in your post, but let me spell it out more explicitly. Diversification means that adding a negative expected return trade to a portfolio can INCREASE the return by adding a negatively returning, negatively correlated asset. Lets say we have two assets: “market” and “insurance”. Market returns 11%/year 9⁄10 years, down 50% the other year. Insurance returns −3^%/year 9⁄10 and up 22% the other year. Expected market returns are: 5%/2.6% (simple mean / compounded), insurance are: −0.5%/-.7% (mean / compounded). By your logic you should never buy the insurance, and yet if we have a portfolio which maintains a 15% allocation to our insurance asset our expected (compounded) returns increase.
Another way to reason about this is: there’s nothing special about zero nominal returns. So if you shouldn’t make a trade with negative expected return, you should be able to say the same thing about ~any return and by extension you should only put your $ in the highest returning asset… but that misses the whole value of diversification!
The only free lunch in finance is diversification.
(Emphasis mine) This is a strong claim, which I would dispute. Risk premiums (not in the sense you’ve used the word, but in the sense I understand it to mean) are an obvious example—some assets have a positive yield just for holding them, even after accounting for volatility… Leverage would be another example.
This is the principle behind index funds.
Kinda, sorta, maybe. It’s “a” principle behind them, but if diversification were the only concern, why would you want cap-weighted index funds? Why not equal-sector weight or equal-company weights or some other weights?
Being smart is cheap.
I can only assume you’ve never attempted to hire people to work for a quantitative hedge fund. If anything, this claim would undercut your main claim that QF is “so hard”. Unfortunately (or fortunately for your thesis) being smart is really expensive.
Small nitpicks:
No!
You explain why in your post, but let me spell it out more explicitly. Diversification means that adding a negative expected return trade to a portfolio can INCREASE the return by adding a negatively returning, negatively correlated asset. Lets say we have two assets: “market” and “insurance”. Market returns 11%/year 9⁄10 years, down 50% the other year. Insurance returns −3^%/year 9⁄10 and up 22% the other year. Expected market returns are: 5%/2.6% (simple mean / compounded), insurance are: −0.5%/-.7% (mean / compounded). By your logic you should never buy the insurance, and yet if we have a portfolio which maintains a 15% allocation to our insurance asset our expected (compounded) returns increase.
Here is a concrete real-world example: (60⁄40 + tail hedge).
Another way to reason about this is: there’s nothing special about zero nominal returns. So if you shouldn’t make a trade with negative expected return, you should be able to say the same thing about ~any return and by extension you should only put your $ in the highest returning asset… but that misses the whole value of diversification!
(Emphasis mine) This is a strong claim, which I would dispute. Risk premiums (not in the sense you’ve used the word, but in the sense I understand it to mean) are an obvious example—some assets have a positive yield just for holding them, even after accounting for volatility… Leverage would be another example.
Kinda, sorta, maybe. It’s “a” principle behind them, but if diversification were the only concern, why would you want cap-weighted index funds? Why not equal-sector weight or equal-company weights or some other weights?
I can only assume you’ve never attempted to hire people to work for a quantitative hedge fund. If anything, this claim would undercut your main claim that QF is “so hard”. Unfortunately (or fortunately for your thesis) being smart is really expensive.