The way someone talks tells me more about nationality than anything else.
If you have an American accent but claim to be Irish, I pause.
I pause because the meaning of being Irish is different across the pond. Something is lost in translation.
Claiming to be Australian with a Chinese accent gives me pause again! But it's the other way around this time.
That's a testament to certain places which have a way of making you feel at home wherever you come from.
Doesn't matter how you talk or what you look like in New York City; know the basics and you'll be treated as a local.
Duality is about viewing the something from different angles and learning more about it.
Let's compare returns over time to individual stock returns.
Firstly build a market neutral portfolio.
Every position is hedged by the S&P 500, so that on average a movement in Ford for example is canceled out by a movement in the S&P 500. A crude way of leaving Ford specific returns behind.
Moreover, we'll weight every position inversely by volatility. So if Ford has 1% volatility we buy $100; 2% only $50. Every holding will have a volatility of $1.
I incrementally (and pseudo-randomly) added stocks to the portfolio initially containing Ford.
A marginal increase in volatility slows as more stocks are included in the portfolio.
A large break occurs when SBUX is added to the portfolio. Instead of an expected small increase of overall volatility, it's inclusion reduces the portfolio volatility.
Usually that's a positive, but for our purposes a little unexpected. Obviously there's a nice diversifying relationship between SBUX and the previous five portfolio holdings which isn't covered by overall market events (i.e. the S&P 500 hedge).
Our market neutral inverse vol weighted portfolio more or less matches expectations. I threw the 11 positions together off the cuff and the R2 is ~80% compared to the expected curve.
Repeated random generation of larger portfolios will give more robust results.
The expected curve is of course the square root of the number of holdings.
We just created a portfolio of stocks whose returns are pretty independent of each other. Without trying too hard.
And, as we incrementally add positions our volatility drops - just as we'd expect daily volatility to drop (on average!) as our holding period increases from 1 day to 11 days.
I.e. the factor drops by the square root of time or number of positions.
Period and number of holdings are now interchangeable.
Connecting the Dots
We travelled from portfolio construction to mimicking simple short term volatility dynamics.
Could we mimic more complicated dynamics?
Create a portfolio which as it gets larger mimics being invested for a longer period?!
Or even better, could we start the other way around, with a timing strategy (e.g. momentum) and end up mimicking a stocking picking strategy (e.g. growth)?
Mimicking in either direction will probably leave your strategy with a strong accent - but you will certainly learn something new.