Yesterday I wrote up a post, and immediately after, was sure I got something wrong.
This is the offending chart.
Volatility increases linearly as we add more positions to the equally weighted portfolio. What I failed to mention is that each position was weighted by 100% of the portfolio. So two positions meant the portfolio was leveraged 2x and so on.
Well, not necessarily.
What was I trying to do again? Compare volatility of a portfolio of stocks with an idealised portfolio's volatility over time, right?
The longer we hold a portfolio, the larger volatility becomes, but the increase decreases at the rate of a square root of time.
Whereas with a portfolio of stocks, the opposite usually happens. As we add stocks the volatility decreases due to diversification.
Two well known characteristics, both pointing in opposite directions.
A small conundrum!
In fact, we just need to think a little more about what we are doing.
We are likening stock picking to holding periods.
Each holding period we invest 100% of our portfolio in assets, which means each stock 'pick' should be worth 100% of our asset's value.
Modelling 1, 2 or 3 periods is the same as a portfolio's value of 100%, 200% or 300% of our actual current net value.
How about we go the other way? Each period's investment is deleveraged.
I.e. if we are modelling a portfolio over 30 periods, we invest 1/30th of our portfolio each period; which is analogous to equal weighting a portfolio of 30 stocks.
How does our volatility 'growth' look now?
As expected; when we add more stock picks to our portfolios our volatility drops.
The equal weighted portfolio hits a floor of 70%, i.e. 30% of the volatility of just owning one stock is diversified away. But our Stock Pick / Timing duality strategy keeps dropping as we add more stocks.
Each stock we add to our equal weighted portfolio is largely made up of 'beta', i.e. more or less the same as any other.
Whereas, with our duality strategy each stock had its beta hedged away, every time we add a new stock to our portfolio we are adding something new and idiosyncratic.
Think about it like this. Usual portfolio building is like creating an evil army of clones or androids which is always susceptible to one point of failure.
This duality strategy builds portfolios which become a team of whacky troubled heroes which happen to work great together.
No single point of failure.