Prepared for CBRE Hotels Research by Jack Corgel, Ph.D., Cordial Hotel Property Research
On December 31, 2021, the constant maturity, 10-year U.S. Treasury note (the 10-year) stood at 1.52 percent. The 10-year now hovers around 3.0 percent and the prospects for higher rates appear good. During the data period for the analysis presented below, the 10-year ranged from 0.65 percent to 6.70 percent and last exceeded 5.0 percent in 2006. A concern among commercial real estate investors (especially hotel investors because of the high sensitivity to macroeconomic conditions) is a rate-driven economic slowdown that threatens property income growth. Given the linkages across capital market rates, investors are concerned about the possible upward movement in hotel capitalization rates (cap rates) promoted by increasing 10-year rates. This blog addresses the sensitivity of hotel cap rates to changes in the 10-year.
Are the Two Rates Conceptually Related?
Equation (1) presents a simple capitalization model,
Vt = NOIt / Rt (1)
where Vt is the property value in period t, NOIt represents the property net operating income, and Rt is the capitalization rate. The capitalization rate can be decomposed as follows:
R = rreal + rexpected inflation + rrisk premium - g – rliquidity premium (2)
where rreal is the return associated with demand and supply imbalances in a world without inflation, rexpected inflation represents the return needed to compensate for the loss of future purchasing power due to expected inflation, rrisk premium represents the return component require for taking on credit risk, and g stands for the expected growth in property income (time subscripts not shown).
The risk-free rate includes the first two terms on the right side of this equation (i.e., rreal + rexpected inflation) which is commonly represented by the U.S. Treasury rate – the 10-year at the 10-year point on the Treasury yield curve. Together the two terms are a simplified representation of the Fisher Effect. To conclude, the 10-year, in theory, is a potentially important determinant of hotel cap rates.
Note that the focus here is on the denominator of Equation (1). Nevertheless, no inferences will be drawn about how valuations may adjust because of changes in R resulting from changes in the 10-year. Clearly, increases (decreases) in the net operating income (NOI) also move values as do changes in the other components of R shown in Equation (2).
The U.S. appears to be entering a period of stagflation. If this happens, hotel NOIs will be under pressure, and some or all the components of R could move against valuations. The stability of NOIs depends on sustainable ADR growth which offsets inflation’s influence on expenses. The ability to grow ADRs also may offset some of the increases in R. If this scenario plays out, hotel valuations hold firm.
Are the Two Rates Statistically Related?
To answer this question, I draw upon data from two sources – Real Estate Research Corporation (RERC) and the Federal Reserve Economic Data (FRED) managed by the Federal Reserve Bank of St. Louis. Complete data for all the variables considered here are available from Q1 1997 through Q4 2021. Data for hotel capitalization and 10-year rates extend back to Q1 1992.
Exhibit 1 shows the historical patterns of hotel cap rates and 10-year rates. Both patterns exhibit a similar downward trend since the 1990s. During the past 10 years, hotel cap rates varied around 8.0% - below the long-run (i.e., since 1992) average of 9.3%. Similarly, 10-year rates held at or below 2.0% since 2012 which is about half of long-run average. The volatilities of the two series are about the same as measured by the standard deviation and tests of lag relationships did not reveal evidence of one series leading the other through time.
Addressing the central question about the sensitivity of hotel cap rates to changes in the 10-year rate involves running a series of regressions. Elasticity measured from the two series – the percent change in hotel capitalization rates given the percent change in 10-year rates – encapsulates their sensitivity to one another. By converting both variables to natural logs and regressing one on the other the resulting coefficient is interpreted as the elasticity. I used the following series of regression steps with associated results: (The elasticity interpretations are presented later.)
1. Determining the ‘own’ elasticity (full sample) – Here the log of hotel cap rate serves as the dependent variable and the log of the 10-year rate is the only independent variable. Result:
ER,10yr = .19
2. Determine the ‘own’ elasticity (2009 q1 – 2021 q4) – Same as above. Result:
ER,10yr = .07
3. Determine the elasticity in a multivariate model (full sample, Q1 2009 – Q4 2021) – Here the log of hotel cap rate serves as the dependent variable and the log of the 10-year rate is one of four independent variables specified in accordance with theory developed in Equation (2). The following additional variables enter the regression:
a. The spread between Moody’s Baa bond yield (FRED) and the 10-year rate.
b. The growth rate of hotel RevPar (listed as rents in RERC data).
c. Credit availability measured as real estate loans divided by GDP (both from FRED).
ER,10yr = .15 (full sample)
ER,10yr = .08 (2009 q1-2021 q4))
4. Each of the steps listed above uses nominal rates (i.e., not adjusted for inflation). A similar set of steps were followed using real rates. Not surprisingly, the elasticity estimates are quite low – hovering around .01.
Because the elasticity statistics have values well below 1.0, hotel rates are quite inelastic (i.e., insensitive) relative to 10-year rates. For example, assuming a 3 percent 10-year rate, an 8 percent hotel cap rate, and an elasticity of .07 (a 10 percent change in the 10-yr to 3.3 percent) should result in a hotel caprate of 8.1 percent (rounded).
The elasticity weakened during the past dozen years. The receding sensitivity of hotel cap rates to changes in the 10-year may be due to accommodative fiscal and monetary policy. The sensitivity could revert back to the long-run average as government policies become more restrictive. Additionally, the proper economic interpretation of elasticity is to perform the analyses with real rates. Nominal rates are utilized here because actual valuations by investors relying on cap rates involve nominal values.
If hotel cap rates have a low sensitivity to changes in long-term Treasury notes, then what conditions elicit strong responses? A meaningful contribution comes from the spread between Moody’s Baa bond yield and the 10-year rate (i.e., a risk premium), the growth rate of hotel RevPar, and credit availability. In the multivariate model I use to calculate elasticity each of these variables has the correct sign and is statistically significant. For ease of interpretation a semi-log model also was estimated using the same variables and beta coefficients are reported in Exhibit 2. The standardized (i.e., Beta) coefficients provide general guidance about the relative weights of each member in this variable set. The 10-year and RevPAR growth variables are somewhat more powerful than the Baa spread and credit availability variables. But again, all four variables are economically and statistically important for explaining variation in hotel cap rates.
 The NOI is assumed at stabilization in period t.
 The liquidity premium in Equation (2) is not included in traditional specifications of R, but has been shown to be
statistically significant in some studies.
 The Fisher Effect is an economic theory created by Irving Fisher in the early 1900s that describes the relationship
between inflation and both real and nominal interest rates. Wikipedia and many other sources provide greater