Constant rebalanced portfolio (CRP)

A constant rebalanced portfolio holds fixed proportions of wealth in each asset and rebalances back to them every period. With portfolio b on the simplex (bⱼ ≥ 0, Σbⱼ = 1) and daily price relatives xᵢ, wealth after n days is Sₙ(b) = ∏ᵢ bᵗxᵢ. Buy-and-hold is the opposite discipline: fixed share counts, drifting proportions.

It is the benchmark class Cover (1991) competes against, and the reason the universal-portfolio result is interesting rather than trivial — because the best CRP in hindsight is a much stronger opponent than the best stock.

Rebalancing is a source of return, not just risk control

The counterintuitive fact, and the one Cover's examples exist to demonstrate: a fixed mix of two assets can beat both of them. Over his 22-year sample, Iroquois Brands returned a factor of 8.92 and Kin Ark 4.13, while the 55/45 mix rebalanced daily returned 73.6. Commercial Metals returned 52.0 and Kin Ark 4.13; the 65/35 mix returned 144.0, so an investor "would not want any part of Kin Ark" and would be wrong by a factor of nearly three.

Rebalancing sells what rose and buys what fell, mechanically and without a view. The return it harvests comes from volatility and low correlation, not from prediction — which is why the effect disappears when the assets move together: IBM and Coca-Cola trade in lockstep in the same sample, and the best mix barely beats either.

This is mean-reversion's mechanism arriving from a different direction. The strategies on that page test for reversion and then bet on it; a CRP never tests anything and never forms a view, yet profits from the same oscillation. The two pages disagree about whether the bet needs to be justified in advance, and this one says nothing has to be forecast at all.

The catch, stated plainly

• Which mix? The gains above are for the mix that turned out best after seeing the outcome (S*ₙ = maxb Sₙ(b)). Picking b in advance is the actual problem, and it is what the universal-portfolio construction exists to answer.
• Costs. Daily rebalancing over ~5,600 trading days is a lot of trading, and Cover's analysis charges nothing for it.
• A CRP is not risk management. It is a fixed allocation rule. Nothing here sizes a position against drawdown or capital at risk — the corpus's standing gap on risk and portfolio construction is narrowed by this page, not closed.

Related

cover-universal-portfolios · universal-portfolio · mean-reversion · algorithmic-trading · market-regime-analysis · synthesis