What it means
Traditional portfolio theory treats risk as volatility, meaning how widely returns swing around the average. That counts a surprise gain as just as risky as a surprise loss, which is not how most people feel about their money.
PMPT fixes this by only counting returns that fall short of a chosen target. The target is called the minimum acceptable return, or MAR.
It might be zero, the rate of inflation, or the 6% a pension scheme needs to meet its promises. Returns above the MAR are not penalised at all, and returns below it are measured as shortfalls.
The main risk measure in PMPT is downside deviation, which is a form of standard deviation (a standard measure of spread) calculated using only the shortfalls. The most common performance measure built on it is the Sortino ratio, which divides the excess return over the MAR by the downside deviation.
A higher Sortino ratio means more return per unit of bad-outcome risk. Managers use PMPT when returns are lopsided, for example with options strategies, hedge funds or any portfolio where big losses are more likely than big gains.
In those cases ordinary volatility can make a risky strategy look safe. Downside-focused measures show the tail more honestly.
The approach has limits. The answer depends heavily on the MAR chosen, and downside deviation needs plenty of data to estimate well.
It is best used alongside, not instead of, simpler measures. A practical way to start is to write down the investor's real goal before looking at any statistics.
If the goal is to avoid losing capital, the MAR is zero, and if it is to keep pace with rising prices, the MAR is the inflation rate. Once that number is fixed, the same historical returns can be re-ranked to show which strategies actually serve the goal.
In practice
Real-world examples.
Example
A family office compares two funds with the same overall volatility. One loses money in sharp bursts, while the other has mostly smooth results with occasional large gains. PMPT shows the first fund has a much higher downside deviation and ranks it lower. The office then caps its allocation to the first fund and tops up the steadier one.
Example
A pension scheme needs a 5% return to stay fully funded. Its trustees set 5% as the MAR and judge managers on the Sortino ratio relative to it. A manager who beats the market but often misses 5% scores poorly. Over several years this keeps the scheme focused on meeting its promises rather than on beating an index that may not matter to its members.
Example
A retiree drawing income from a portfolio sets a MAR equal to the inflation rate. The adviser then selects investments that rarely fail to keep up with prices, even if that means giving up some upside. The adviser reviews the figure each year, since both inflation and the retiree's needs change.
Formula
Calculation
Sortino ratio = (portfolio return - MAR) / downside deviation
Suppose a portfolio returned an average of 9% a year, the investor's MAR is 4%, and the downside deviation is 5%.
Excess return = 9% - 4% = 5%, which is the reward above the bar the investor set.
Sortino ratio = 5% / 5% = 1.0.
A second portfolio returned 7% with a downside deviation of 2%. Its excess return is 7% - 4% = 3%, so its Sortino ratio is 3% / 2% = 1.5. Although the first portfolio earned more, the second delivered more return for each unit of downside risk.Case study
Seen in the real world.
Brightwater Capital is a fictional investment firm choosing between two strategies for a client who cannot tolerate losses. Strategy A has a standard deviation of 12%, and Strategy B has 10%, so a traditional comparison favours B. The illustrative twist is that B's losses are concentrated in a few severe months, so its smooth average hides a nasty tail that the client would feel acutely.
The firm sets a MAR of 3% and calculates downside deviations of 4% for A and 7% for B. Strategy A's Sortino ratio comes out higher, and the firm recommends it.
The client's committee later reviews the analysis and understands why a lower headline volatility did not mean lower risk. The firm adds the MAR and Sortino ratio to its standard reports and agrees to revisit the MAR with the client every year, so the analysis stays tied to real goals rather than to a number set once and forgotten.
Watch out
Common mistakes.
- Choosing a MAR without thinking about it. A MAR of zero and a MAR of 8% give very different answers for the same portfolio.
- Assuming PMPT replaces modern portfolio theory. It refines how risk is measured, but still relies on diversification and expected returns.
- Using too little data. Downside deviation depends on a handful of poor periods, so a short history gives an unreliable figure and can make a risky strategy look safe.
Questions
People also ask.
What does PMPT stand for?
Post-Modern Portfolio Theory, a downside-risk extension of the portfolio theory that treats all volatility as risk.
How is the Sortino ratio different from the Sharpe ratio?
The Sharpe ratio divides by total volatility, while the Sortino ratio divides only by downside deviation. This means upside surprises do not reduce the score.
Who should use PMPT?
Anyone with a clear return target or liability to meet, such as pension schemes, endowments and income investors.
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