Part 2 of 2
Target Audience: New Graduates/Analysts
Time Adjustment in AVM (Quick Review):
Automated valuation models (AVMs)
involve adjusting sale prices to account for changes in market conditions
between a property's sale and valuation dates, considering real estate markets
fluctuate, meaning that a house sold last year may not be directly comparable
to an identical house sold today. Here is why time adjustment is needed:
1. Adjusting sale prices to
reflect the market conditions at the valuation date allows the model to provide
a more accurate estimate of the property's value on the target valuation date.
This precision, achieved through diligent time adjustments, inspires confidence
in the reliability of the AVM.
2. Time-adjusted sale prices improve
model accuracy by ensuring that the model considers market trends, leading to
more reliable valuations.
3. Consistent time adjustment
across all comparable properties enhances model consistency, allowing the model
to compare "apples to apples" when estimating the value of the
subject property.
By incorporating time-adjusted
sale prices as the dependent variable instead of the raw sale prices in the
regression-based AVM, the model can produce more realistic and reliable
property valuations that reflect the market conditions at the valuation date.
Using an Extended Time Series dataset
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Suppose you are developing an AVM using a
single-family home sales dataset sample from a specific county, with sales from
the previous nine quarters (Q1-2022 to Q1-2024). The target is to value
properties on April 1, 2024. So, the regression model's dependent variable
(sale price) must be adjusted to the target valuation date.
There are two common
median-based methods for time-adjusting sales prices:
1) Sale price adjustment: This method adjusts the entire sales price for changes in the market over time. It calculates a percentage change in the median sale price from the sale date to the target valuation date, which is then applied to the individual sales prices to adjust them to the target valuation date.
· Advantages:
o
Easier
to understand and interpret by users of the AVM.
o Less susceptible to outliers caused by unusually large or small homes because it considers the whole property, not just the price per square foot.
Disadvantages:
o It doesn't account for size differences between houses. A few large, expensive homes in an affluent neighborhood can skew the median up, making it a less accurate reflection of the value of smaller homes.
2) SP/SF adjustment: This method adjusts the sales price per square foot (SP/SF) for changes in the market over time. It calculates a percentage change in the median SP/SF from the sale date to the target valuation date, which is then applied to the individual SP/SF figures to adjust to the target valuation date.
Advantages:
o
Takes
into account the size of the property, providing a more standardized measure of
price.
o This can be particularly important in areas with a mix of large and small houses.
Disadvantages:
o It can
be more difficult for users to understand the metric's meaning, especially
if they are recent graduates unfamiliar with real estate valuation.
o
More
susceptible to outliers caused by unusually high or low prices per square foot.
Analyzing the two methods – Median Sale Price and Median Sale
Price per Square Foot (SP/SF) – for adjusting the dependent variable in the
regression model for the AVM using the single-family home sales data requires a
comparative evaluation based on the averages, standard deviations, and
coefficient of variations (CV).
1.
Median
Sale Price Method:
o Average Median Sale Price: $394,139
o Standard Deviation of Median Sale
Price: $11,567
o Coefficient of Variation (CV) for
Median Sale Price: 2.93%
2.
Median
Sale Price per Square Foot (SP/SF) Method:
o Average Median SP/SF: $210.00
o Standard Deviation of Median SP/SF:
$5.84
o Coefficient of Variation (CV) for
Median SP/SF: 2.78%
Comparative Analysis:
- The Coefficient of Variation (CV) for the Median Sale Price method is slightly higher than that for the Median SP/SF method, suggesting that the Median Sale Price has slightly higher relative variability.
- The Median Sale Price per Square Foot method could be more robust due to the lower Standard Deviation and CV, implying that the SP/SF values are less dispersed around the average than the Median Sale Price.
Considering the
comparative analysis, the Median Sale Price per Square Foot
(SP/SF) method may be preferable for adjusting the dependent variable in the
AVM model. The lower variability and CV suggest that using SP/SF as a measure
may provide more stability and consistency in estimating property values for
the target month of April 2024. This method could offer more reliable and accurate valuation predictions than the Median Sale Price
method.
Alternative Method – Two-quarter Moving Averages
Using a two-quarter moving average can help smooth out the
quarter-to-quarter volatility in the data and potentially provide a more stable
trend for analysis. It can help reduce the impact of short-term fluctuations
and noise in the data, making it easier to identify underlying patterns and
trends.
Calculating a moving average of the sales data over two quarters can create a more stable trend line that captures the market's medium-term changes rather than its short-term ups and downs. This can be
particularly useful when the data exhibits high volatility or
seasonality.
In terms of statistical significance, a moving average can help
reveal longer-term patterns and trends that may not be as apparent when looking
at the unadjusted quarterly medians. By smoothing out the data, you can identify more meaningful relationships and patterns that can be
statistically significant.
However, it's essential to note that using a moving average
involves a trade-off between responsiveness to changes and smoothing out
volatility. A two-quarter moving average may not capture rapid shifts in the
market as effectively as using the unadjusted quarterly medians, but it can
provide a more stable and easier-to-interpret trend for analysis.
Overall, using a two-quarter moving average can be a valuable approach to reducing noise and volatility in the data and uncovering more
statistically significant trends and patterns when analyzing single-family home
sales data over time.
Simple
Moving Average vs. Exponential Moving Average
In
a two-quarter Simple Moving Average (SMA) calculation, you typically
average the values of the current quarter and previous quarters' values. This method
helps smooth out data fluctuations and gives you a clearer trend over
time.
To
calculate a two-quarter SMA, you would sum the current quarter's and previous quarters' values and then divide by 2. This would give you the moving
average for that particular quarter.
If
you were to average the current quarter and the prior moving average, it would
be a different type of moving average calculation known as an Exponential Moving
Average (EMA), which gives more weight to recent data points.
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1. SMA
(Simple Moving Average):
- SMA calculates the average of a given set
of prices over a specific period by equally weighting each price.
- When comparing the SMA to the Median Sale
Price (MSP), we find that the SMA values tend to track closer to the MSP but may lag behind significant price changes.
- The percentage difference between SMA and
MSP ranges from 96.06% to 102.60%, indicating some volatility in the SMA
values compared to the MSP.
- SMA generally irons out short-term
fluctuations and is suitable for identifying trends over time. However,
its responsiveness to recent price changes may be slower than that of EMA.
2. EMA
(Exponential Moving Average):
- EMA places more weight on recent prices,
making it more responsive to recent price changes than SMA.
- The EMA values tend to be more separated from the
MSP and demonstrate increased volatility compared to the SMA. The
percentage difference between EMA and MSP ranges from 94.10% to 102.29%,
showing more fluctuation in EMA values.
The percentage
differences between the EMA and MSP values are higher than between the SMA and MSP values. This means the EMA values exhibit more fluctuation relative to
the MSP than the SMA values.
Therefore, based on this
analysis, we can conclude that the SMA method produces smoother and less
volatile values that are more suitable for adjusting raw sales prices to create
a time-adjusted sale price for use as the dependent variable in a
regression-based AVM in this particular scenario.
Monthly vs. Quarterly Adjustments
(Extended Time Series)
Monthly adjustments can introduce
more noise and volatility into the data, making the dependent variable less stable when compared to quarterly adjustments. Monthly data often
reflect short-term fluctuations and can be influenced by factors such as
seasonality, irregular events, or other short-term variations.
This inherent noise and
volatility in monthly data can make it challenging to accurately identify and interpret underlying trends. It may also lead to a less stable dependent
variable when constructing AVMs, where the goal is to predict property values
based on historical sales data.
By using quarterly adjustments
instead of monthly ones, you can smooth out some short-term fluctuations
and reduce the noise in the data. Quarterly adjustments provide a more
aggregated and stable representation of trends over time, which can help create
a more reliable and robust dependent variable for modeling purposes.
Ultimately, the choice between
monthly and quarterly adjustments should be guided by the specific
characteristics of the data, the objectives of the analysis, and the trade-offs
between noise reduction and capturing short-term dynamics. It's essential to
carefully consider the implications of using different adjustment intervals (e.g.,
consider 3-quarter moving averages if you are using three years of sales) and
choose the approach that best aligns with the goals of the analysis.
Conclusion
This
blog post illustrates the importance of time-adjusting sale prices to create a
reliable and stable dependent variable for regression-based AVMs. By utilizing
sales data over multiple quarters and employing methodologies such as Quarterly
Median Sale Price per Square Foot and Simple Moving Average, the benefits of
smoothing out volatility and creating a more consistent time-adjusted sale
price variable have been demonstrated.
The
examples show that the Quarterly Median Sale Price per Square Foot and the
Simple Moving Average methods provide smoother and less volatile values, making
them ideal choices for time adjustment in an AVM. However, it is crucial to
exercise caution and ensure that the selected methodology aligns with the
specific characteristics of the analyzed real estate market. This
responsibility is critical to mitigating potential risks.
By
incorporating these time-adjusted sale prices into the valuation process,
analysts and new graduates can enhance the accuracy and reliability of their
regression models, ultimately producing more robust and dependable property
valuations.
Disclaimer: This blog post serves as a
starting point. As you gain experience with AVMs, you can explore more advanced
time-adjustment techniques and refine your model for optimal performance.
Remember, continuous learning is a journey, and support and encouragement are
available along the way.
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