Black-Litterman

Also seen as: Black-Litterman model, BL, Bayesian mean-variance, momentum views

The method picker lists it as "Black-Litterman", right after MPT (Markowitz), and describes it as "Markowitz with corrected expected returns: a stable equilibrium tilted by momentum views". It is an allocation method offered both inside a single strategy and inside a Combined.

How does Black-Litterman correct the expected returns?

Black-Litterman blends two estimates of each instrument's expected return — an equilibrium, which is stable, and a set of views — weighting each by how much it is trusted. In its textbook form the blended ("posterior") expected returns are:

where: $\Pi$ is the vector of equilibrium returns, $Q$ the returns the views expect, $P$ says which instruments each view is about, $\Omega$ is the uncertainty of the views, $\Sigma$ is the covariance matrix of the instruments and $\tau$ scales the uncertainty of the equilibrium. In words: the result is a weighted average of the equilibrium and the views, where the more certain a source is, the more it pulls the estimate toward itself. The optimiser then works on $\mu_{BL}$ exactly as MPT works on the historical averages.

The app describes the method's momentum views as "Starts from a stable equilibrium and tilts it toward the instruments with momentum. The views are computed for you: you don't enter any forecast." The equilibrium it starts from is built from the instruments' risk, not from their market capitalisation.

Which optimization targets can Black-Litterman aim at?

Black-Litterman offers two of MPT's three targets: Optimal (the default) and Max return. The app describes them as "Optimal = best risk-adjusted return. Max return = highest expected return regardless of risk."

Min volatility is not offered, because the lowest-risk portfolio is chosen from the covariance matrix alone and does not use expected returns — the one input Black-Litterman changes. On Min volatility it would make (almost) no difference, so the target stays with MPT (Markowitz).

What are the momentum views, and which settings control them?

The views are each instrument's recent momentum measured against the others, recomputed at every rebalance from the data available on that date, so a backtest never uses information from after the date it is simulating. The Momentum views section of the method has two settings:

• Momentum months — how far back momentum is measured; from 1 to 24, 12 by default.
• View confidence — "Higher = momentum weighs more against the equilibrium." From 0.1 to 10, 1 by default.

Momentum can reverse sharply, and a Black-Litterman tilt reverses with it: a higher view confidence makes the weights follow recent winners more closely, for better and for worse.

How does Fincanva handle it?

• Black-Litterman is included wherever MPT is: it has no plan level of its own, so any plan that includes MPT (Markowitz) includes it, at the strategy level and inside a Combined alike. See what each plan includes.
• Optimization target defaults to Optimal; Max return is the other choice.
• Momentum months defaults to 12 and View confidence to 1.
• Every other setting is MPT's own and behaves as described on Modern Portfolio Theory: position direction (strategy level only), weight limits, force diversification, the Covariance matrix choice and the Resampled option, with the plan levels stated there. With Resampled on, the Black-Litterman estimate is computed once and every resample reuses it.
• Moving between MPT (Markowitz) and Black-Litterman keeps your settings. Choosing Black-Litterman on an MPT strategy keeps every MPT setting and moves a Min volatility target to Optimal; choosing MPT (Markowitz) again keeps them too and drops the momentum views.
• A strategy saved before Black-Litterman became its own method keeps running exactly as saved. If it had the Black-Litterman switch on with the Min volatility target, it is now shown as MPT (Markowitz), because that combination uses (almost) no expected returns; the first time you edit its MPT settings, it is saved without the switch.
• The calculation window (In-sample) supplies the risk and momentum inputs, and weights are recomputed at every rebalance, so a Black-Litterman weighting moves over the life of a backtest.

What does it look like in practice?

Take one instrument whose equilibrium return is 6% and whose momentum view says 12%. In the textbook blend, if the equilibrium and the view are trusted equally, the expected return used is halfway between them: (6% + 12%) / 2 = 9%. If the view is trusted twice as much as the equilibrium, it counts twice: (6% + 2 × 12%) / 3 = 10%.

Plain MPT would have used the historical average of the window directly — which, after a strong run, can be far above either number and pile the portfolio into that one instrument. Black-Litterman's estimate moves toward momentum only as far as its confidence allows, which is why its weights change more gradually. The numbers here illustrate the textbook blend; they are not the exact figures Fincanva computes for a given confidence setting.

Choosing the momentum months or the view confidence that made a past backtest look best is overfitting, and searching many combinations for that best one is data snooping.