Modern Portfolio Theory

Also seen as: MPT (Markowitz), MPT, mean-variance optimisation

The method picker labels it "MPT (Markowitz)" and describes it as "Modern portfolio theory: optimize on a risk/return objective". It is one of the six allocation methods offered inside a Combined and one of the eleven offered inside a single strategy.

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."

Target	Aims at
Optimal (default)	the best return per unit of risk — the Sharpe-ratio sense of "best"
Min volatility	the lowest-risk point on the frontier
Max return	the highest expected return, with no regard for the risk that comes with it

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.

Control	Effect
Position direction (strategy level only)	"Long-only requires every weight ≥ 0. Long + Short allows negative weights (short positions)." At the Combined level MPT is positive-only by construction, so this control does not appear there.
Weight limits	"Constrain each instrument's weight to a range" — turning it on reveals Min weight and Max weight, which every instrument's weight must then respect.
Diversification	"Force diversification" spreads weights more evenly across instruments instead of letting the optimisation concentrate them in a few. On a small set of instruments it can leave nothing that satisfies every constraint at once.

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.

Defaults in Fincanva

• 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.
• 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.

Worked example

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, and a backtest is not a prediction. See Is this financial advice?.