Dynamic Correlations Among Asset Classes: REIT and Stock Returns

REITs were excluded from widely followed general stock market indexes until October 2001, when Standard & Poor’s announced that REITs would thenceforth be considered for inclusion in its stock market indices, and specifically that six REITs would be included in one of its three general market indices—the S&P 500, the S&P 400, and the S&P 600—as of October 9. Since then publicly traded REITs have been included in other general stock market indexes on the same basis as non-REIT publicly traded companies. As of September 30, 2008 the aggregate market capitalization of publicly traded U.S. REITs was $305.31 billion, accounting for less than 1.7% of the aggregate market capitalization of the Wilshire 5000 index. Because REITs are now included in general stock market indexes, the correlation between a REIT index and a general stock market index overstates the correlation between REITs and non-REIT stocks; therefore, we use as an alternative stock index proxy the CRSP Cap-Based Portfolio Index, which excludes REITs.

The starting date February 1978 is used for the empirical analysis because a measure of risk-free returns—the Citigroup 1-month Treasury Bill Index—is available as of that date. (A measure of bond returns—the Barclays Capital US Aggregate Bond Index, formerly Lehman Brothers US Aggregate Bond Index—is available as of February 1976.) Equity REITs accounted for almost 95% of the aggregate market capitalization of the publicly traded U.S. REIT industry as of September 30, 2008, but we use the FTSE NAREIT All-REIT Index because its average return and standard deviation—both slightly less than the CRSP Index—make for a more useful illustration of the implications of dynamic correlations for optimal asset allocations. In contrast, the FTSE NAREIT Equity REIT Index dominates the CRSP Index in terms of both average return (1.17% per month vs. 1.05%) and standard deviation (3.92% per month vs. 4.39%), meaning that optimal portfolios are heavily weighted toward equity REITs. Conversely, the FTSE NAREIT Mortgage REIT Index is dominated by the CRSP Index in terms of both average return (0.58% vs. 1.05%) and standard deviation (5.60% vs. 4.39%), meaning that optimal portfolios are heavily weighted toward stocks. It is also worth noting that, while the FTSE NAREIT All-REIT Index encompasses mortgage and hybrid REITs as well as equity REITs, there is certainly more heterogeneity in the CRSP Index as a measure of performance in the broad stock market asset class than there is in the FTSE NAREIT All-REIT Index as a measure of performance in the broad real estate asset class.

We evaluate this comparison relative to a portfolio composed 60% of stocks (CRSP Index) and 40% of bonds (Barclays Capital US Aggregate Bond Index). The no-REITs portfolio has an average monthly return of 0.905% and a standard deviation of monthly returns of 2.868%. The same-volatility portfolio is allocated 40.2% to REITs, 34.4% to stocks, and 25.5% to bonds (with no cash) and has an average monthly return of 0.942%. The same-return portfolio is allocated 34.4% to REITs, 29.4% to stocks, and 36.2% to bonds (with no cash) and has a standard deviation of 2.568%.

See Mera and Renaud (2000) for discussions of the Asian financial crisis focusing on the role of the real estate markets and real estate lending. Note that one long-term mechanism by which the Asian financial crisis may have affected REIT-stock correlations in the U.S. is the development of Asian REITs, which Mera & Renaud point out was a common policy response by Asian governments to the financial crisis. This paper, however, focuses on shorter-term covariances; we leave analysis of the importance of longer-term transmission mechanisms to other researchers.

In another context, Bond et al. (2006) also analyzed correlation dynamics by specifying sub-periods and computing separate correlation coefficients from data for each sub-period, in this case looking at cross-border property market correlations.

In other studies using rolling correlation coefficients, Wilson and Zurbruegg (2003) computed rolling 52-week and 156-week correlations between listed property returns in Hong Kong and Singapore, finding evidence that correlations jumped upward during the 1997 Asian financial crisis. And Young (2000) used rolling 60-month correlations to show that REITs focused on different property types generally became more closely correlated over the study period 1989–1998.

Neither Conover et al. (2002) nor Westerheide (2006) makes clear which MSCI U.S. equity index is used, so it is possible that one or both of these studies may have used a total market index.

Besides the Asian financial crisis, other possible events, such as 1987 stock market crash, which might alter asset correlations, are also included in the analysis. We do not report them, however, because they had no significant effect on the DCC-GARCH estimation.

CRSP Cap-based Portfolio Indices data are a monthly series based on portfolios rebalanced quarterly based on market capitalization. The universe includes all common stocks listed on the NYSE, Alternext, and NASDAQ, and excludes Unit Investment Trusts, Closed-End Funds, REITs, Americus Trusts, foreign stocks, and ADRs.

Because few industry participants use the CRSP Index, we repeated the analysis using the Wilshire 5000 Index, probably the most widely used total-market index of U.S. stocks. The results, which are available on request, are qualitatively identical and numerically very similar.

We use VAR rather than an error correction model because we do not find a significant cointegration between the non-stationary REIT and stock series based on the ADF test for cointegrated variables and the Johansen test.

The results are very similar whether stocks are represented by the Dow Jones Wilshire 5000 (which includes REITs after 2001) or the CRSP Index (which excludes REITs).

Another event sometimes asserted to have started the modern REIT era was the development of the “umbrella partnership REIT” structure, or UPREIT; the first UPREIT, however, occurred in 1992, still following the apparent start of the decline in REIT-stock correlations.

Note the artificiality of this approach, in that the covariance is equal to the product of the two-asset correlation and the two asset-specific standard deviations: we are allowing the covariance and the correlation to fluctuate but forcing the standard deviations to remain constant.

Recall that we have fixed expected returns and standard deviations at their unconditional averages; therefore the illustration takes into account the effect of the 1987 stock market crash on conditional asset return correlations but not on conditional asset returns.

We reduced the target portfolio standard deviation from 2.87% to 2.45%—that is, we increased the assumed risk aversion—because even a 100% stock allocation would not have produced a portfolio standard deviation of 2.87% during some months in 1996–1997 and 2007–2008 using a 60-month rolling model of volatilities and correlations.

Specifically, the standard deviation of dynamic REIT allocations was 13.5% using the DCC-GARCH model compared to 20.6% using the rolling model; the standard deviation of stock allocations was 16.5% vs. 24.4%; for bond allocations it was 7.2% vs. 11.1%; and for cash allocations it was 2.8% vs. 11.4%.