Minimum MAD

Also seen as: mean absolute deviation optimisation, MAD

What is the mean absolute deviation?

The mean absolute deviation is the average distance between each day's portfolio return and the portfolio's average return over the window:

where: $T$ is the number of days in the calculation window, $r_{p,t}$ is the portfolio's return on day $t$, and $\bar{r}_p$ is its average daily return. In words: how far, on a typical day, the portfolio lands from where it usually lands — counting a day twice as far away as twice as bad, not four times as bad.

When does Minimum MAD differ from minimising variance?

When returns have outliers. If returns were normally distributed, minimising MAD and minimising variance would lead to the same weights; the two part ways when some days are far more extreme than the rest. So a large gap between Minimum MAD's weights and the Min volatility weights of MPT on the same instruments is itself a sign that their history has fat tails.

What Minimum MAD does not offer is an efficient-frontier picture or a target to choose: it has one objective and no settings.

How does Fincanva handle it?

• Minimum MAD is offered at both levels: across the instruments of a strategy, and across the strategies of a Combined.
• It has no settings of its own. It reads the calculation window (In-sample, 12 months by default) and works on the daily returns themselves, so it does not read the Risk estimation choice.
• The picker marks it "slow to compute": each rebalance solves an optimisation over every day of the window.

Which plan includes Minimum MAD?

It depends on your plan, at each level where the method is offered.

Inside a strategy

Included from Ultimate upwards. See what each plan includes.

Inside a Combined

Included from Ultimate upwards. See what each plan includes.

What does it look like in practice?

A window holds 250 days on which an instrument moves 1% away from its average, and one day on which a data glitch or a one-off event puts it 20% away.

• In variance, each ordinary day adds 0.01² = 0.0001 and the one extreme day adds 0.20² = 0.04 — as much as 400 ordinary days. That single day outweighs the rest of the window put together.
• In MAD, each ordinary day adds 0.01 and the extreme day adds 0.20 — as much as 20 ordinary days. It counts, but it does not decide.

An optimiser minimising variance would reorganise the whole portfolio around that one day; Minimum MAD treats it as one bad day among many.