Mean Reversion Threshold: Technical Whitepaper

1. Abstract

This paper presents a univariate threshold that measures mean reversion in Australian suburb house prices. The threshold uses a single variable: cumulative median house price growth over the preceding 10 years. Suburbs where prices grew less than 44% over the past decade are classified as "top tier" and tend to outperform in the next four years. Suburbs where prices grew more than 91.9% are classified as "bottom tier" and tend to underperform.

The top tier outperformed the national median by +1.14 percentage points per year over rolling 4-year windows. The bottom tier underperformed by -1.88 percentage points. The total spread is 3.02 percentage points per year. This was measured across 825,392 property sales from 2008 to 2021.

The signal was tested across 55 quarterly periods and 28 individual sample dates. It held at every single quarter and every single sample date. This is a 100% consistency rate. No other threshold in the Microburbs research programme achieves this level of temporal consistency. The t-statistic is 251.87 and the p-value is effectively zero.

The signal was tested across 15 GCCSA regions. It produced a positive spread in 12 of 15 regions. The three regions where it inverted are resource-driven markets (Perth, Darwin, and Rest of NT) where mining boom prices did not fully revert.

2. Methodology

2.1 Variable Construction

The mean reversion threshold uses a single variable: the cumulative percentage change in a suburb's median house price over the preceding 10 years. This is calculated as:

For example, if a suburb's median house price was $300,000 ten years ago and is $420,000 today, the past growth is 40%. This suburb would fall into the top tier (below 44%). If another suburb's median was $250,000 and is now $500,000, the past growth is 100%. This suburb would fall into the bottom tier (above 91.9%).

2.2 Threshold Calibration

The thresholds were calibrated using property sales data spanning 2008 to 2021. The top tier threshold is 44% past 10-year growth. The bottom tier threshold is 91.9%. Suburbs between these two thresholds fall into the middle tier.

These thresholds were optimised to maximise the spread between the top and bottom tiers while maintaining statistically significant sample sizes in each tier.

2.3 Performance Metric

The primary metric is the difference in median annualised 4-year growth between each tier and the national median. Statistical significance is assessed using a two-sided t-test against the null hypothesis that the tier's mean growth equals the national mean.

2.4 Inverted Logic

This threshold is inverted relative to most other indices. The "top tier" contains suburbs with LOW past growth. These are the suburbs that outperform in the future. The "bottom tier" contains suburbs with HIGH past growth. These are the suburbs that underperform in the future.

This inversion is the defining characteristic of mean reversion. Markets that have run hard tend to cool. Markets that have lagged tend to catch up.

3. Tier Performance

The model sorts suburbs into three tiers based on their past 10-year median house price growth. Each tier has a distinct forward growth profile.

4. Temporal Analysis

A signal that works at one point in time could be a fluke. We tested the mean reversion threshold across every quarter from 2008-Q1 to 2021-Q3. The chart below tracks the 4-year annualised growth rate for low-past-growth suburbs (top tier) and high-past-growth suburbs (bottom tier) over time.

4.1 Date-by-Date Consistency

We tested the top tier's outperformance at 28 individual sample dates between 2008 and 2021. At each date, the model was evaluated independently. The result was positive at all 28 dates. Every single date showed the top tier outperforming the bottom tier.

5. Regional Robustness

A signal that works only in one city is less useful than one that works nationally. We tested the mean reversion threshold across all 15 GCCSA (Capital City Statistical Area) regions in Australia.

5.1 Full Regional Table

All growth rates are annualised over 4 years. The spread column shows the difference between the top tier (low past growth) and bottom tier (high past growth) forward growth rates.

6. Defence of Method

6.1 Why Mean Reversion Works

Mean reversion in property markets is well documented in academic literature. The mechanism is straightforward. Suburbs that have grown quickly become relatively expensive. Buyers start looking at cheaper alternatives. Capital flows shift toward undervalued areas. Over time, the gap between expensive and cheap suburbs narrows.

This is not a new idea. What is new is the precision of the threshold calibration (44% and 91.9%), the scale of testing (825,392 sales), and the perfect temporal consistency (100% of dates).

6.2 Statistical Significance

The t-statistic is 251.87. This is not borderline. The probability of observing a +3.02% spread across 825,392 sales by random chance is effectively zero. For context, a p-value below 0.05 is the standard threshold for statistical significance. The mean reversion threshold exceeds this by hundreds of orders of magnitude.

6.3 Consistency Over Time

The signal was positive at all 28 sample dates spanning 14 years. It was positive in 100% of 55 quarterly observations. No other threshold in the Microburbs research programme achieves this level of temporal consistency. This is not a signal that works "most of the time." It works every time, in the data tested.

6.4 Geographic Breadth

The spread is positive in 12 of 15 GCCSA regions. It works in rising markets (Sydney, Hobart) and falling markets (Rest of WA). The three exceptions are resource-driven markets where mining booms created unusual price dynamics. In these markets, suburbs that boomed during the mining cycle did not fully revert. This is a known feature of commodity-linked economies.

6.5 Practical Use

The mean reversion threshold provides a simple screen for suburb selection. Look for suburbs where the median house price grew less than 44% over the past decade. Avoid suburbs where it grew more than 91.9%. This is a filter, not a final answer. Combine it with other Microburbs signals for a more complete picture.

7. Limitations

7.1 Resource Markets

The signal inverts in three resource-driven regions: Perth, Darwin, and Rest of NT. In these markets, suburbs that boomed during mining cycles did not fully revert. Investors in Western Australia and the Northern Territory should not rely on this threshold alone.

7.2 Backward-Looking Model

The model was calibrated on historical data from 2008 to 2021. Past patterns do not guarantee future results. The relationship between past growth and future growth could change if the underlying market dynamics shift. However, mean reversion is a fundamental economic principle, not an artefact of a specific time period.

7.3 Individual Suburb Variation

Even within the top tier, individual suburb outcomes vary widely. The threshold provides a statistical edge across large numbers of purchases, not a guarantee for any single suburb.

7.4 Threshold Stability

The thresholds (44% and 91.9%) were calibrated on a specific data sample. Different calibration periods might produce slightly different thresholds. The underlying principle (low past growth predicts strong future growth) is well supported, but the exact cutoff values may shift over time.

7.5 Confounding Variables

Suburbs with low past growth may share other characteristics (regional location, housing stock type, demographic profile) that also predict future growth. The mean reversion effect may be partially explained by these confounders. This paper documents a correlation, not a causal mechanism.

7.6 Sample Composition

The top tier contains 367,662 sales and the bottom tier contains 205,557 sales. These are large samples. However, the composition of suburbs within each tier shifts over time as past growth rates change. A suburb can move between tiers as its 10-year growth window updates.