Additional Case Study One: Risk Analysis of Home Purchase

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1 Additional Case Study One: Risk Analysis of Home Purchase This case study focuses on assessing the risk of housing investment. The key point is that standard deviation and covariance analysis can be effectively used to evaluate housing investment risk. This case study, prepared by G. Donald Jud, PhD, Stephen E. Roulac, PhD, and Daniel T. Winkler, PhD, can be read in entirety in The Appraisal Journal (Fall 2005), pages While the subject matter is of particular interest to developers, real estate investors, and real estate consultants, the statistical tools employed are of universal interest. This study focuses on an analysis of the non-systemic risk of individual housing investments in Greensboro, North Carolina, and Houston, Texas. The aim of the paper is to demonstrate the application of a simple model for forecasting the risk of individual home ownership. Statistical tools employed include average, standard deviation, coefficient of variation (CV in this study), Jarque-Bera statistic, coefficient of determination (R 2 ), and type two error (ß). BUSI 344 students will be familiar with two of these statistical measures (CV and R 2 ). The Jarque-Bera statistic provides a test of whether or not observed distributions are normally distributed and a type two error happens when you accept the null hypothesis when it is false. Background Although most homeowners consider housing to be a consumption good, it is clear that housing also represents an investment. Although imputed rent is consumed when a homeowner occupies a house, this benefit is excluded from the risk and return analysis in this study. When judged on the basis of movements in aggregate price indexes, housing appears to be a relatively lowrisk investment. When compared to common stocks, over the short-term (five years) housing investment appears to have substantially lower risk. The Coefficient of Variation (CV) is a test statistic commonly used in financial markets to help define risk. Recall from lesson one that the CV, a statistical measure of dispersion, is calculated by dividing standard deviation by the mean such that for the holding period for year 1 on Table 1, for example, CV = 3.2% 5.7% = The CV is used to allow consistent comparisons of variation for two different populations. The outcome of application of this test of risk to compare investments in housing versus the equity markets is shown on the following two tables. In this case, while the stock market delivers higher returns than housing, its clear that the risk (as represented by stock value deviation) of holding stock is considerably higher than housing. Therefore, our general rule is that the lower the CV, the lower the dispersion around the mean, and hence the lower the risk to the investor. UBC Real Estate Division 1

2 In the above tables, the CVs for housing with 7 and 10 year holding periods are higher than the corresponding CVs for stocks. The implication of this is that over the long-term (holding period greater than five years), housing is a riskier investment than stocks. One further note of importance: the risks of home ownership for various holding periods (CV), based on national data, represent the overall or general market risk of home ownership. In other words, the risk associated with changes in interest rates, possibility of inflation or recession, or other macroeconomic factors. In financial terms this risk is referred to as the systemic risk. However, there is an additional risk associated with very specific aspects of individual home ownership such as changes in location influence, neighbourhood influences, and local services. This risk is known as non-systemic or the unique risk associated with a specific investment, in this case, individual homeownership. Methodology In this study, the authors introduce and test the following model for understanding the total risk associated with individual housing investments. Total Housing Risk = Market Risk (systemic) and House Specific Risk (non-systemic) The market risk was identified in Table 1, above, using national data. To understand the non-systemic risk, statistical analysis was conducted for two samples of repeat-sale, single-family homes in two urban centers; Greensboro, NC, and Houston, Texas. The methodology is summarized below and application of the selected statistical tools highlighted. Using sales samples in two different cities, local home ownership risk can be compared to national market risk by means of calculating the annualized capital gain for each sale in the two samples and comparing the annualized average rate of return, risk-assessed by means of standard deviation and CV, to national market risk. Refer to the following figures extracted from the Jud, Roulac, Winkler Appraisal Journal article illustrate the distribution of the capital gains in the two communities studied. UBC Real Estate Division 2

3 Figures 1 & 2, above, show that the data patterns are fairly normal but slightly skewed to the right. They both have a strong central tendency. However, as they are skewed the median may be the best representation of the sample populations. Figure 3, below, shows that the standard deviation of the mean annual return for Greensboro in Year 1 is over 2.5 times greater than standard deviation for Houston, and the corresponding CV for Year 1 is twice as great as CV for Houston. The implication of the foregoing is that investing in home ownership in Greensboro is significantly riskier than in Houston. In addition, this figure shows that over a ten-year holding period, as measured by standard deviation of rate of annual capital gain, risk of investing in the housing market decreases in both cities. For longer holding periods the differential between total and market risk declines, but total risk is still substantially higher than market risk even over a ten-year holding period. UBC Real Estate Division 3

4 Section Two-Models of Housing Returns Linear and Multiple regression analysis is used to further understand the relationship between total risk and market risk. The goal of the analysis was to identify the explanatory variables that contribute to nonsystemic risk for home ownership. Again, relying on data from public records it was possible to create a regression model for forecasting the annual return. The first regression model was an attempt at understanding the general relationship between the annualized rate of return for each property sampled and the national rate of return for housing, stratified by holding period. This relationship is expressed by the following regression equation: ri,t = α + βrnt + έi,t RNt represents the national annualized rate of return έi,t represents the residual (unexplained) error α is the regression constant Table 4 below, shows the outcome of this initial regression analysis. UBC Real Estate Division 4

5 You can see from the low R 2 statistics for each community that the national annualized rate of return for Greensboro 1 and 3 year holding periods explains little of the variation in the individual property rate of return. In the 7 and 10 holding periods, the dependent and independent variable appear to move in the same direction (as shown by the positive β coefficient) and the overall relationship is stronger, given the t and F values (e.g., greater than 2 and 4 respectively) at a confidence level of.01. Notice the negative β coefficient for the Greensboro data relative to the Houston data what can conclude about the relative risk in both communities 1. What else can you conclude about the Houston data? The regression analysis was expanded and more variables introduced to attempt to better explain the variation in the individual housing rate of return. Some of the independent variables which were analyzed for their influence on annual return included: HP or Holding Period CEMP or annual growth in employment HVAL or average value of homes in the neighbourhood AGE or age of the home when purchased SQFT or area of property in square feet Refer to Table 5 in the Jud, Roulac, Winkler Appraisal Journal article for the detailed outcome of this analysis. The main outcome was a low R 2 score, indicating that the introduction of additional variables did not improve the explanatory power of the regression equation (e.g., only improved to 8.1%). At this point the paper, the probability of loss is examined with an advanced methodology (Huber/White Procedure) which is beyond the scope of this course. Summary This study shows that the price risk facing the average homeowner is high and may vary widely among cities in the USA. Use of measures of central tendency, including: mean, standard deviation, and co-efficient of variation, show that the probability of loss on sale in the average housing transaction in the USA is large. This probability, confirmed through ß and R 2 tests, is the result of house-specific risk rather than market risk. One interesting outcome is the application of more complex regression analysis does not necessarily improve the explanation of variation in the dependent variable, even after accounting for other factors impacting this time series data, such as heteroskedasticity (strong random variation in the residual error). 1 Betas less than one indicate that the level of market risk in the respective city is below that for housing markets nationally. The estimated betas, that are all less than one except for Houston s seven-year holding period, suggest that housing investment in Houston has more market risk than in Greensboro except for the ten year period UBC Real Estate Division 5