Portfolio mix: six assets, one covariance

An asset that swings a lot pays for it in compound growth. If it falls 50% and then rises 50%, it ends at 75%, not where it started. Over time the median path grows by roughly average return minus half the variance (volatility squared ÷ 2). At 30% volatility that drag is 4.5 points a year.

Hold two assets that do not move together and rebalance them now and then: their ups and downs partly cancel, so the mix swings less than either one, while the average return stays the same. Less swing means less drag, so the mix compounds faster than each of its parts. This is sometimes called Shannon's demon, after Claude Shannon, who showed it with two coin-flip assets. The trick only works while the assets stay unrelated. As the correlation rises toward 1, the benefit disappears.

Weekly total returns in EUR (dollar assets converted at the ECB rate), measured over the same weeks for all six: . The window starts when bitcoin's euro price starts.

The simulation does not take a covariance matrix as input. It draws weeks from the record, in blocks of about 8 weeks, and reads all six assets from the same drawn week. So if a week had stocks −10%, bitcoin −25% and gold +2%, a simulated week has all three together. Correlation, fat tails and crashes that bunch up come straight from the data: the simulated correlations match the measured ones to within . Each asset's past average return is removed first and our assumed expected value is put back, so the past decade's winners get no head start. Mixes are rebalanced to their weights once a year. Pre-tax, no costs.

The correlation and volatility above are measured and fairly stable. The expected returns are guesses, and the optimiser trusts them completely: it piles into whichever asset looks a little better and drops one that looks a little worse. Below, the same simulated weeks with different views. The "capped" column keeps any asset at or below and bitcoin at or below .

The real record with yearly rebalancing. This is hindsight: semis and bitcoin had an extraordinary decade, and we already know they survived. It is here to show how much the rebalanced mixes kept, not as a guide to the next five years.

Set the weights and, if you disagree with ours, the expected value of each asset. The browser reruns the same method on 2,000 paths: the same weeks, the same block draw, the same pinning of the average. "Find best Sharpe" searches all 3,003 mixes in 10% steps under your views.