MPT (Markowitz)

Also seen as: Modern Portfolio Theory, mean-variance optimisation, Markowitz optimisation

The method picker labels it "MPT (Markowitz)" and describes it as "Modern portfolio theory: optimize on a risk/return objective". It is an allocation method offered both inside a single strategy and inside a Combined, and it has one optional variant, Resampled, that changes how its inputs are treated. Black-Litterman is built on MPT and appears in the picker as a method of its own.

What is the efficient frontier?

The efficient frontier is the set of portfolios that are not beaten on both counts at once — for each of them, you cannot raise expected return without also raising risk, and you cannot lower risk without also lowering expected return. Every other combination sits below the frontier and is dominated by one on it.

For a two-instrument portfolio, the expected return is the weighted average of the two expected returns, but the volatility is not:

$$E(R_p) = w_A E(R_A) + w_B E(R_B)$$ $$\sigma_p = \sqrt{w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \rho_{AB} \sigma_A \sigma_B}$$

where: $w_A$ and $w_B$ are the two weights (adding to 1), $E(R)$ is an expected return, $\sigma$ is a volatility, and $\rho_{AB}$ is the correlation between the two instruments' returns. The correlation term is what makes the frontier curve: the lower $\rho_{AB}$ is, the more the mix's volatility falls below the weighted average of the two individual volatilities.

Which optimization target can you choose?

The Optimization target control picks which point on the frontier the method aims at. The app describes the three options exactly like this: "Optimal = best risk-adjusted return. Min volatility = lowest portfolio risk. Max return = highest expected return regardless of risk."

What do the MPT constraint toggles do?

Three controls narrow which portfolios the optimisation is allowed to pick from. They change the answer by changing the admissible set — a tighter constraint can only move the result away from the unconstrained frontier point, or make the problem impossible to satisfy at all.

The weight-limit bounds themselves depend on the level and the direction: inside a Combined the weights run from 0 to 1; inside a single strategy set to Long-only they also run from 0 to 1, and set to Long/short they run from −1 to 1.

The weight limits have to be mutually satisfiable. A minimum weight that, multiplied by the number of instruments, comes to more than 100% cannot be met by any portfolio — and when that happens today, no weights are produced and the app shows no error message.

What does the Resampled option do?

Resampled repeats the optimisation on many resampled versions of the window's history and averages the weights they produce. The app describes it as "Michaud's method: repeats the optimization on many samples of the history and averages the results", with the effect "Steadier weights, less sensitive to noise."

$$\bar{w} = \frac{1}{B} \sum_{b=1}^{B} w^{(b)}$$

where: $B$ is the Number of samples, $w^{(b)}$ is the set of weights the optimisation returns on sample $b$, and $\bar{w}$ is the average that is actually held. In words: a lucky stretch that made one instrument look best in the observed history favours it in only some of the samples, so the average holds it at a moderate weight rather than piling onto it.

• Number of samples runs from 10 to 1,000 and starts at 100.
• It is very slow to compute, and the app says so with the sample count filled in — at the default: "Very slow to compute: every rebalance repeats the optimization 100 times."
• The price is that the averaged weights are no longer a single point on the textbook efficient frontier.

How is Black-Litterman related to MPT?

Black-Litterman is an allocation method built on MPT, listed in the method picker as a method of its own rather than as an option inside MPT. It runs the same optimisation with every MPT setting on this page, and changes one input: the expected returns, which it replaces with a steadier estimate tilted toward momentum. Because only the expected returns change, it offers the Optimal and Max return targets and not Min volatility, which does not use them. Moving between MPT (Markowitz) and Black-Litterman in the picker keeps every MPT setting.

How does Fincanva handle it?

• MPT is included from the Advanced plan, at the strategy level and inside a Combined alike; Free and Starter do not offer it in either place. See what each plan includes.
• Its weight limits start one plan level higher, at Ultimate. On Advanced the method runs, but turning Weight limits on is refused with the plan level that includes it named; Ultimate and Professional allow it. See what each plan includes.
• The Resampled option starts at Ultimate, a step above the method: on Advanced, turning Resampled on is refused and the app names the plan that includes it, while MPT keeps running. Ultimate and Professional allow it. See what each plan includes.
• Optimization target defaults to Optimal.
• Weight limits are off by default; when you turn them on, Min weight starts at 0 and Max weight at 0.5 (50%).
• Force diversification is off by default.
• At the strategy level Position direction starts at Long/short, so shorting is allowed until you switch it to Long-only; at the Combined level MPT has no direction control and is positive-only.
• The calculation window (In-sample) supplies the risk and return inputs, and defaults to 12 months.
• The Covariance matrix choice decides how volatilities and correlations are estimated from that window; a newly chosen MPT starts on Ledoit-Wolf · constant correlation — see covariance matrix.
• Resampled is off by default.
• Weights are recomputed at every rebalance from the window ending at that date, so an MPT weighting moves over the life of a backtest rather than staying fixed.

What does it look like in practice?

Instrument A has an expected return of 6% and volatility of 10%; instrument B has an expected return of 10% and volatility of 20%; their correlation is 0.2. Hold them 60% / 40%:

• Expected return: (0.6 × 6%) + (0.4 × 10%) = 7.6%.
• Volatility: √(0.6²×0.10² + 0.4²×0.20² + 2×0.6×0.4×0.2×0.10×0.20) = √0.01192 = 10.9%.

That single pair of numbers is one point on the frontier. Note what the low correlation bought: the mix carries 10.9% volatility, only 0.9 percentage points more than holding the calmer instrument A alone, while its expected return is 1.6 percentage points higher. Sliding the weights from 100% A to 100% B traces out the whole curve, and the frontier is the upper edge of it.

What is the expected return based on?

The expected returns and volatilities that MPT works from are estimates read off the historical calculation window — they are not forecasts. A mean-variance result is therefore only as stable as those estimates: two backtests over different windows can produce different "optimal" weights from the same instruments, because the inputs themselves changed. Picking the window whose weights looked best is overfitting, and searching across many windows for that best answer is data snooping.

Fincanva describes how this method works; it does not recommend it or any target within it.