Yesterday I sketched out a strategy which aimed to build a portfolio which aimed to reproduce the volatility dynamics found when choosing to hold stocks over longer or shorter periods of time.

The idealised view, if daily returns are independent of each other, is that volatility will increase according to the square root of time.

E.g. if we know each day's volatility is around 10%, holding for two days volatility will be `sqrt(2) * 10%`

, three days, `sqrt(3) * 10%`

and so on.

This is how we hope our new strategy's volatility grows as we throw more stocks into the portfolio,

For this, I took the DJIA constituents in a rather haphazard fashion and added them one by one into our strategy's portfolio, from DIS, WMT and V on up.

`MMM,AXP,AAPL,BA,CAT,CVX,CSCO,KO,DD,XOM,GE,GS,HD,INTC,IBM,JPM,JNJ,MCD,MRK,MSFT,NKE,PFE,PG,TRV,UTX,UNH,VZ,V,WMT,DIS`

It doesn't quite match the idealised line which assumes complete independence.

We *roughly* created independence by hedging out the market component, but of course I might hedge away market returns for both AAPL and INTC, and yet there will still be a dependence between them (any ideas for hedging away dependence further? - get in touch!).

Out of curiosity, I also graphed the Sharpes - surprisingly consistent - most portfolios report a Sharpe over 0.8.

Let's see how volatility increases in the equivalent equal weighted portfolios.

Surprisingly linear! Feel free to send me guesses about how the market weighted version looks.

While our strategy might be able to come closer to the 'ideal', beating the Equal Weighted portfolios is a piece of cake, which is the real benchmark.

How do the Sharpes compare?

Consistently lower risk adjusted performance.

Now, where's my afternoon slice of cake?

[When I first published this, I immediately thought I got something wrong with the vol charts - in fact I highly doubt I did - will write up my thinking tomorrow]