From Standard Deviation to SEE: Quantifying Real Estate Risk

From Standard Deviation to SEE: Quantifying Real Estate Risk

Introduction: Beyond Traditional Risk Measures

Real estate investment, by its very nature, is subject to various forms of risk. While simple metrics like historical standard deviation offer a rudimentary view, they often fall short in capturing the nuances and complexities of real estate cycles and market dynamics. This section explores the limitations of standard deviation and introduces the Standard Error of the Estimate (SEE) as a more robust, forward-looking measure of risk, particularly within the context of econometric forecasting.

The Limitations of Standard Deviation as a Risk Proxy

Traditionally, the standard deviation has been used as a shorthand for the risk of an asset. This practice stems from models❓, where price changes are perceived as following a random walk. In a random walk with drift, the historical standard deviation of growth genuinely reflects the risk, and the forecast is the historical mean growth. However, this approach has several critical limitations when applied to real estate:

• Real Estate Cycles: Unlike stocks, real estate is characterized by long-term cycles. Simply extrapolating historical volatility may not adequately capture the impact of cyclical patterns, autorelation or mean reversion.
• Long-Term Forecasting: Standard deviation is a backward-looking metric, while real estate investment decisions rely on long-term forecasts that attempt to understand the real estate cycle.
• Oversimplification: Using standard deviation as the sole risk measure ignores potential interdependencies between various factors influencing real estate value.
• Data Limitations: Relying solely on historical data ignores potential structural shifts in the market or emerging risks not present in the historical record.

“The use of standard deviation as synonymous with risk can also form the foundation of a simulation that can be used to answer questions via a method that in some ways is more robust than a scenario analysis. Monte Carlo simulation uses mean and standard deviations of value change (or any choice of variable) to create an array of forecasts.”

While Monte Carlo simulation can use the mean and standard deviation of value changes to create a multitude of forecasts, these simulations are only as good as the assumptions of the underlying distribution. When used for long-term investment decisions, the random walk approach to determine the distribution produces wide variances of results that may not be helpful. Furthermore, real estate data is often quarterly with short histories which may be insufficient to calculate distributions.

Introducing the Standard Error of the Estimate (SEE)

The Standard Error of the Estimate (SEE) offers a more refined approach to quantifying real estate risk, especially when econometric forecasts are employed. Unlike the historical standard deviation, the SEE considers the cyclical dynamics captured by econometric models. The formula for SEE in a regression model is:

SEE = sqrt( sum((Y - Y')^2) / (n - p) )

Where:
* Y is the actual value.
* Y' is the predicted value from the model.
* n is the number of observations.
* p is the number of parameters in the model.

Key differences between SEE and standard deviation:

• Forecast Incorporation: The SEE acknowledges that the forecast itself attempts to capture a significant portion of the predictable volatility (the cycle).
• Equation Interaction: In a system of equations, the SEE accounts for the interaction between variables, preventing uniformly expanding standard deviation over time. Real estate returns demonstrate autocorrelation and mean reversion over longer periods.
• Forward-Looking: SEE is a forward-looking measure reflecting current market conditions and near-term factors. For instance, low vacancy rates suggest a higher probability of rent and value increases.

Structured Vector Autoregressive Model (VAR)

To obtain such errors requires the system to be converted to a structured vector-autoregressive model (VAR).

• VAR models: Capture the interdependencies between multiple time series.
• SEE derivation: Errors are calculated for each equation within the VAR system, reflecting the uncertainty associated with each forecast variable.

Advantages of the SEE Approach

• Captures Cyclical Dynamics: Incorporates the cyclical nature of real estate, providing a more realistic assessment of risk.
• Accounts for Interdependencies: Considers the interaction of various factors influencing real estate values.
• Forward-Looking Perspective: Integrates current market conditions and near-term forecasts for a more timely risk assessment.
• Beyond Historical Data: Avoids being constrained by historical data limitations. The model at the heart of the SEE approach can avoid this limitation if the inputs to the model have a longer history (for example, employment) than what is being varied and will dictate how bad the downside can get.
• Captures Autocorrelation and Mean Reversion: Accounts for the tendency of real estate returns to exhibit autocorrelation and, over longer periods, mean reversion.

Disadvantages of the SEE Approach

• Complexity: Implementing the SEE approach requires sophisticated econometric modeling and statistical expertise.
• Model Conversion: Converting complex models into a structured VAR form can be challenging.
• Software Requirements: Specialized software is necessary to produce and decompose the forecast errors.
• Transparency Issues: The use of errors from the equation is less transparent to investors when the forecasting process is outsourced.

Practical Applications and Examples

• Investment Analysis: The SEE can be used to create a distribution of potential outcomes, allowing investors to assess the probability of achieving specific investment goals.
• Risk Management: The SEE can help identify potential downside risks and develop strategies to mitigate them.
• Scenario Planning: The SEE can be integrated with scenario analysis to evaluate the impact of specific economic or market events on real estate investments.

combining❓ Approaches: Scenario Analysis and VaR

One method of risk management is to tie scenario analysis to a Value at Risk (VaR) stress level. In cases where a GDP or unemployment scenario is specified, pre-existing SEE results can be used to determine the intersection point with the VaR distribution for a particular time period. For a normal or pseudo-normal distribution, the scenario intersection point can be used and from there the standard deviations from the base forecast can be calculated. The amount of standard deviations can then be converted into a VaR level using an inverse normal distribution function.

Integrating Historical Standard Deviation with Forecasts

While the SEE is a more appropriate measure of risk, combining the use of forecasts with the historical standard deviation should be approached with caution.

• Historical Standard Deviation: The error of a simple autoregressive model.
• SEE: The error of a more complex model with different errors.
• Conservative Estimate: The historical standard deviation can be thought of as a conservative estimate of the error around the forecast, as it is often larger than the SEE.

Converting Forecast Distributions to Probability of Equity Loss

The VaR approach of calculating appropriate capital levels may not be intuitive for equity investors. Therefore the distributions in Monte Carlo and SEE can be converted to a probability of achieving a goal or avoiding a catastrophe. The distribution around the forecast can be used to take an intersection point in a particular period and then calculating the percentage of the distribution above or below that point. Also, leverage increases both the expected return and its standard deviation. An analysis of this type would have caused more investors to pass on the excesses offered by the frenzied debt market of 2005 to 2007.

Conclusion

Quantifying real estate risk requires careful consideration of the chosen methodology. While standard deviation provides a basic measure, the SEE offers a more comprehensive and forward-looking assessment, particularly when integrated with econometric forecasting. Combining the SEE with scenario analysis and VaR methodologies can provide a robust framework for managing risk in real estate investments.