Measuring the risk level in a portfolio of real estate assets relative to the overall market is challenging because there are many factors that need to be accounted for, such as the appreciation of the housing market, the correlation of various geographic areas and the geographic concentration of the portfolio.
“Beta” is a metric derived from the Capital Asset Pricing Model^{1} (CAPM) and is often used in equity markets to measure the exposure of a single stock or a portfolio of stocks to the overall market. Generally speaking, if beta is less than zero, then the stock moves in the opposite direction of the market; if beta is between zero and one, the stock moves in the same direction as the market, but is less volatile than the market; if beta is greater than one, the stock not only moves in the same direction as the market, but it moves faster than the market.
Real estate assets can be included in the CAPM framework, although the expected return and risk are difficult to calculate for a single property due to the uniqueness of each property and the infrequent transactions associated with each. Still, the expected return and risk of a portfolio can be approximated by using the return calculated based on the CoreLogic Home Price Index (HPI). As a result, the concept of CAPM and beta can be used in the residential real estate market to evaluate the exposure of a portfolio to the market.
The following example illustrates this concept using the CoreLogic national and statelevel HPI. Consider a hypothetical portfolio that consists of 50 properties from California, 50 properties from Florida, 100 properties from Georgia and 100 properties from Texas. The aggregate value for these properties by state is listed in Figure 1.
While prices for properties in “sand states” are generally more volatile, it’s difficult to quantify this portfolio’s exposure or sensitivity to the whole housing market. We’d like to be able to answer questions such as: If the U.S. housing market appreciates 10 percent in the next five years, how much will this portfolio likely appreciate? What will happen to the value of this portfolio if the U.S. housing market declines 10 percent in the next five years?
However, what if we could bring additional insight to the problem? Figure 2 shows the CoreLogic HPI for California, Florida, Georgia, Texas and the U.S. Is it possible to use this information to determine how the hypothetical portfolio will perform relative to the market? The answer is yes, but the solution requires tapping into the concepts of CAPM and beta along with some simple math.
In the CAPM framework, beta is the covariance of the return on an asset and the return on the market, divided by the variance of the return on the market, as described in the following equation:
The CoreLogic national HPI can be used to approximate the return for the U.S. real estate market since it measures the appreciation or depreciation of the housing market for a given time period. This is analogous to using the return for the S&P 500 Index as a proxy to understand potential return for the entire stock market. Similarly, the movement of CoreLogic state indexes can represent the return for each state’s housing market. With these additional insights, the beta for California, Florida, Georgia and Texas can be calculated for the period of time from January 2000 to November 2014. The results are listed in Figure 3.
Figure 3: 
State 
Beta 
CA 
1.241 
FL 
1.177 
GA 
0.779 
TX 
0.407 
Once the beta for each of the states is obtained, the beta for the portfolio can be calculated since beta is additive. Multiplying each beta by the percentage of the portfolio that the properties in each state represent yields the weighted beta (e.g., the properties in California comprise 21 percent of the portfolio, and hence have a weighted beta of 1.241 times 21 percent). Adding all of the weighted betas together yields the portfolio’s overall beta, which, in this case, is 0.801. The weighted beta for the properties in each state and the overall portfolio beta are shown in Figure 4.
Figure 4: 
State 
Number of Properties 
Aggregate Value 
Percentage 
Beta 
Weighted Beta 
CA 
50 
$12,500,000 
21.37% 
1.241 
0.265 
FL 
50 
$7,500,000 
12.82% 
1.177 
0.151 
GA 
100 
$18,500,000 
31.62% 
0.779 
0.246 
TX 
100 
$20,000,000 
34.19% 
.407 
0.139 
Sum 
300 
$58,500,000 


0.801 
Depending on a portfolio manager’s risk appetite, the portfolio will be adjusted accordingly. If the portfolio manager is a risk taker, positions in California, Florida, or other states with a high beta may be increased to capitalize on potential market appreciation. On the other hand, if the portfolio manager is risk adverse, a lower beta could be obtained by selling positions in California and Florida and increasing positions in Texas or other states with a low beta.
Additionally, a portfolio’s beta approximates its concentration risk, since it accounts for the covariance of each asset and the market and its relative position. For instance, a portfolio with a high beta must be concentrated in areas that are more volatile, and a portfolio with a low beta must be concentrated in areas that are relatively less volatile. Geographic concentration risk can be evaluated by ranking the portfolio beta together with the beta of different geographic areas.
In the above calculation, the return for the statelevel CoreLogic HPI is used to approximate the return for properties in each state. The underlying assumption is that the properties in the portfolio represent each state, which may not always be true, and more granular HPI can be used instead. Of course, the ideal scenario is to know the beta for individual properties. In a future blog, I’ll discuss the beta for an individual property and its application.
^{1}References:
 Black, Fischer, Michael C. Jensen, and Myron Scholes (1972). The Capital Asset Pricing Model: Some Empirical Tests, pp.79–121, Michael C. Jensen, Studies in the Theory of Capital Markets. Praeger Publishers Inc..
 Mossin, Jan (1966). Equilibrium in a Capital Asset Market, Econometrica, 34(4), pp. 768–783.
 Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425–442
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