---
title: "MPT (Markowitz)"
description: "MPT (Markowitz) applies Markowitz's mean-variance framework: for a given level of risk, hold the mix of instruments with the highest expected return."
canonical_url: "https://fincanva.com/glossary/mpt-markowitz"
last_updated: "2026-10-06"
md_url: "https://fincanva.com/glossary/mpt-markowitz.md"
---

# MPT (Markowitz)

MPT (Markowitz) is the [allocation method](/glossary/allocation-and-allocation-method) built on Harry Markowitz's mean-variance Modern Portfolio Theory: for any level of risk you are willing to carry there is a mix with the highest expected return, and for any return one with the lowest risk. Because instruments do not move in lockstep, a mix can be less volatile than the instruments inside it.

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

## How does Fincanva handle it?

The method picker labels it **"MPT (Markowitz)"** and describes it as "Modern portfolio theory: optimize on a risk/return objective". It is offered inside a single [strategy](/glossary/strategy) and inside a [Combined](/glossary/strategy-in-a-combined), and has one optional variant, **Resampled**.

- **MPT is included from the Advanced plan**, at the strategy level and inside a [Combined](/glossary/combined) alike; Free and Starter do not offer it. See [what each plan includes](/docs/account-security/what-each-plan-includes).
- On a plan that does not include **Weight limits**, turning them on is refused with the [plan level](/glossary/plan-level) that includes them named, while MPT keeps running.
- **Resampled starts at Ultimate**: on Advanced, turning it on is refused and the app names the plan that includes it. See [what each plan includes](/docs/account-security/what-each-plan-includes).
- **Optimization target** defaults to **Optimal**; **Resampled** is off by default.
- Its constraints — **Position direction** (strategy level only, starting at **Long/short**), **Weight limits** (off; **Min weight** 0 and **Max weight** 0.5 when on) and **Force diversification** (off) — are set as [Limit MPT's weights](/docs/strategies/limit-mpt-s-weights) describes.
- The [calculation window](/glossary/calculation-window) (**In-sample**, 12 months by default) supplies the risk and return inputs, and the **Covariance matrix** choice decides how volatilities and correlations are estimated from it; a newly chosen MPT starts on Ledoit-Wolf · constant correlation — see [covariance matrix](/glossary/covariance-matrix).
- Weights are recomputed at every [rebalance](/glossary/rebalance), so an MPT weighting moves over the life of a [backtest](/glossary/backtest).

**Weight limits**

Included from Ultimate upwards. See [what each plan includes](/docs/account-security/what-each-plan-includes).

## What is the efficient frontier?

The efficient frontier is the set of portfolios not beaten on both counts at once: none can raise expected return without raising risk, or lower risk without lowering expected return. Every other combination sits below it. For two instruments the expected return is the weighted average of the two, but the volatility is not:

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

where:

- the two weights, adding to 1
- each instrument's expected return
- each instrument's volatility, squared
- the correlation between the two instruments' returns

The correlation term is what makes the frontier curve: the lower the correlation, the more the mix's [volatility](/glossary/volatility) falls below the weighted average of the two volatilities.

## Which optimization target can you choose?

The **Optimization target** control picks the point on the frontier the method aims at: "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](/glossary/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 |

### How is Black-Litterman related to MPT?

**[Black-Litterman](/glossary/black-litterman) is an allocation method built on MPT**, listed in the picker as a method of its own. It runs the same optimisation with every MPT setting and changes one input: the expected returns, replaced by a steadier estimate tilted toward momentum. So it offers **Optimal** and **Max return** but not **Min volatility**, which does not use them. Moving between the two in the picker keeps every MPT setting.

## What does the Resampled option do?

**Resampled** repeats the optimisation on many resampled versions of the window's history and holds the average of the weights: "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:

- the average set of weights actually held
- the Number of samples
- the weights the optimisation returns on sample b

A lucky stretch that made one [instrument](/glossary/instrument) look best favours it in only some 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 count filled in — at the default: "Very slow to compute: every rebalance repeats the optimization 100 times."
- The averaged weights are no longer a single point on the textbook efficient frontier.

## What does it look like in practice?

Instrument A has an expected return of 6% and volatility of 10%; B has 10% and 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 pair of numbers is one point on the frontier. The low correlation bought a lot: 10.9% volatility, only 0.9 points more than A alone, for 1.6 points more expected return. Sliding from 100% A to 100% B traces the whole curve; the frontier is its upper edge.

### What is the expected return based on?

The expected returns and volatilities are estimates read off the historical calculation window — not forecasts. Two backtests over different windows can produce different "optimal" weights from the same instruments, because the inputs changed. Picking the window whose weights looked best is [overfitting](/glossary/overfitting), and searching many windows for it is [data snooping](/glossary/data-snooping-bias).

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

Fincanva is for education and illustration only. It is not personalised financial advice, and past or simulated results do not predict future ones. [Read the Terms Addendum](https://fincanva.com/terms/addendum#section-3)