قیمت گذاری اوراق بهادار املاک غیر منقول تجاری در طول بحران مالی 2009-2007

We study the relative and absolute pricing of CMBX contracts (commercial real estate derivatives) during the recent financial crisis. Using a structural CMBX pricing model, we find little systematic mispricing relative to REIT equity and options. We do find short-term deviations from this relative pricing relationship that are statistically and economically significant. In particular, the CMBX market temporarily overreacts to news announcements. We provide evidence that this temporary mispricing is caused by price pressure due to hedging activities. Finally, an absolute pricing analysis provides no substantial evidence that CMBX contracts traded at fire sale levels during the crisis.

In this paper we provide a detailed analysis of the pricing of CMBX contracts, which are credit default swaps on a portfolio of Commercial Mortgage-Backed Securities (CMBS). In particular, we study to what extent this asset-backed securities market was affected by the recent financial crisis. While it is well documented how the market for residential mortgage-backed securities has collapsed, with these securities trading at fire sale levels, there is less work on the performance of the market for commercial real estate derivatives during the crisis period. In addition, we study whether investors overpriced senior CMBX tranches before the crisis. Coval, Jurek, and Stafford (2009a) argue that investors overpriced tranched securities because they relied on credit ratings instead of systematic risk. We address these issues in two ways. First, we perform a relative pricing exercise. In contrast to residential mortgage-backed derivatives (like ABX contracts), for CMBX contracts there is a closely related and liquid asset class, Real Estate Investment Trusts (REITs), with both stock and option data. Given that we have reliable daily CMBX price data, this makes the commercial real estate market an ideal place to study the pricing of mortgage-backed securities. We therefore develop a pricing model to evaluate CMBX prices relative to stock and option prices of REITs and the Standard & Poor's (S&P) 500 index, and use this model to empirically test for the existence of relative mispricing. Our relative pricing exercise allows us to test for both long-term and short-term mispricing in the CMBX market, most importantly by analyzing whether CMBX and REIT returns can be predicted by the degree of relative mispricing and by studying mispricing around news announcements. Of course, it is possible that CMBX and REITs are priced “correctly” relative to each other, even when both assets are mispriced in terms of their absolute price levels. Therefore, our second analysis focuses on the absolute pricing of CMBX contracts. To this end, we adjust our CMBX pricing model for potential mispricing of REITs. We do this by using NAVs (net asset values) of REITs as input to the pricing model, instead of equity market values of REITs. In an additional exercise, we study the commercial mortgage default rates that are implied by CMBX prices and compare these to historical default rates. To illustrate the contracts and pricing, consider Fig. 1. The price of a CMBX contract is quoted as $100$100 minus the price of protection on $100$100 notional, and Fig. 1 plots the price for the CMBX 1 AA index, which references a portfolio of 25 CMBS tranches which insure losses between 10.5% and 12.5% on the underlying portfolio. At the lowest price of $19.60$19.60 on April 15, 2009, it cost $80.40$80.40 per $100$100 notional to insure losses on the CMBS bonds.The second key result of this paper is that our pricing model shows that over shorter horizons, there are temporary deviations from this relative pricing relation: the CMBX mispricing predicts subsequent CMBX returns, and a trading strategy that exploits this temporary mispricing earns abnormal returns that are statistically and economically significant. We show that this evidence of short-term inefficiencies is robust to various parameter settings for the pricing model. We also provide evidence that suggests that this temporary CMBX mispricing is due to hedging pressure by banks hedging their commercial real estate exposure. Our third key result is that we do not find evidence for substantial absolute mispricing. This conclusion is reached on the basis of two analyses. First, instead of inserting REIT equity prices into our CMBX pricing model, we use net asset values (NAVs) of REIT equity (as reported by Green Street Advisors). These NAVs are supposed to measure the “fundamental” value of REIT equity, and differ from market prices if REIT equity is mispriced in the market. We find that using the NAV instead of REIT equity prices as input to the model does not lead to very different model prices. The NAV and REIT equity prices do differ substantially during the peak of the crisis, but in this period the model price of the CMBX tranches considered is not very sensitive to the REIT asset value, in a similar way that an out-of-the money option is not very sensitive to changes in the underlying price (low delta). In addition to this NAV-based analysis, we study default rates implied by CMBX prices and find that these are not excessively high compared to historical default rates. In sum, although CMBX prices went down substantially during the crisis period, it does not seem to be the case that these contracts traded at fire sale prices. Interestingly, Stanton and Wallace (2011) study derivatives based on subprime residential mortgage-backed securities (ABX indexes) and find strong evidence that actual prices were too low and inconsistent with any reasonable choice of mortgage default rates. Our model is set up as follows. The value of a commercial property is driven by exposure to stock market returns, sector-level property returns, and idiosyncratic shocks. The model includes the three main commercial property sectors: retail, apartment, and office. Defaults on commercial mortgage loans occur whenever the property value is below a default threshold at maturity (hence, for simplicity, we abstract from term defaults). We calibrate the model each day to data on stock index (S&P 500) returns and option prices, and REIT equity returns and option prices for 15 REITs in the different sectors. Our calibration approach extends the standard way of calibrating Merton's (1974) firm value model to equity values and volatilities (see, for example, Vassalou and Xing, 2004). We do not use data on the underlying CMBS contracts since these are not liquidly traded. We then price the CMBX contracts. Importantly, we do not calibrate any parameters to the CMBX prices, which allows for a clean and transparent analysis of relative pricing. CMBX contracts are priced by simulating property values for the pool of loans and assessing the loss distribution due to loan defaults. We recalibrate the latent property values, volatilities, correlations, and stock-market exposure each day. We focus our empirical analysis on three liquid CMBX series 1 tranches: the AJ tranche, which insures portfolio losses between 12.5% and 20%, the AA tranche which insures losses between 10.5% and 12.5%, and the A tranche, which insures losses between about 7.7% and 10.5%. We find a close correspondence between market and model prices. The correlation between model and market prices is in the range of 86–96%. We also find that the model does a reasonable job pricing the AJ tranches of series 2 through 5 (which are also liquidly traded), but that there is a modest downward trend in the actual price relative to the model price as one moves to newer series, consistent with a downward trend in underwriting standards, which is (partially) recognized by the market but not accounted for in the model. As a robustness check we consider model extensions with (i) jumps in the asset value dynamics and (ii) a stochastic interest rate process, and find similar results. We do, however, find evidence of short-term episodes of mispricing. We first establish that the model mispricing predicts subsequent CMBX returns with t-statistics between 2.3 and 3.3 across tranches. To assess the economic significance of the predictability in CMBX returns, we analyze a simple trading strategy in CMBX and REIT stocks that exploits the model mispricing. Assuming realistic transaction costs, we find an annualized Sharpe ratio of 2.25 for a strategy based on the AJ, AA, and A tranches. To put this figure in perspective, Duarte, Longstaff, and Yu (2007) analyze five popular fixed-income arbitrage strategies and find a maximum Sharpe ratio of 1.20. We show that the trading strategy earns a significant alpha when we correct for the exposure to several equity and bond market risk factors. Next, we use the model to study the response of the CMBX market to news announcements. We stick to an objective set of news days to prevent data snooping. We find that on the two days following the news day, the CMBX market continues to move (on average) in the same direction as it did on the news day itself (relative to the REIT market). This could be either due to initial underreaction or subsequent overreaction. Our results point to overreaction, since the (average) price reverses within five days of the announcement to a price around the closing level of the announcement day.1 Despite the short sample period, these results are statistically significant. The evidence above raises the question why this apparent market inefficiency is not arbitraged away instantaneously. We argue that the short-term mispricing can occur due to hedging pressure effects. The sample period includes the financial crisis and many banks were very concerned with hedging risk exposure to real estate assets, e.g., to satisfy regulatory value-at-risk requirements. These hedging needs could create a temporary price pressure on the instruments used for hedging, like CMBX. This would explain why we find convincing evidence of predictability for CMBX, and only limited evidence of predictability for REITs. Also, our finding that following news announcements the CMBX market overreacts for two days, seems consistent with banks rebalancing their hedge portfolio in a rush following news. We provide further evidence supportive of this interpretation by regressing the change in CMBX mispricing on the return on a bank stock index (in excess of the market return). We find that CMBX mispricing has a positive exposure to bank stock returns, in line with the hedging pressure hypothesis: as banks get closer to distress, they short CMBX tranches for hedging, pushing down CMBX prices relative to REIT stock and option prices. In line with this hedging hypothesis, we find that most of the abnormal returns of the trading strategy are generated at the height of the crisis period in 2008 and 2009. Our paper builds on a recent literature studying tranched derivative structures. Recent work of Stanton and Wallace (2010) analyzes CMBS contracts before and during the recent financial crisis, and finds that the collapse of this market was mainly caused by rating agencies who gradually lowered subordination levels to levels that provided insufficient protection given the assigned rating. They do not use a formal pricing model, but regress CMBX returns on variables such as default dynamics and REIT returns and find that these “fundamentals” explain most of the CMBX return variation, which is consistent with our findings. Using an equity- and option-based pricing model for corporate collateralized debt obligations (CDOs), Coval, Jurek, and Stafford (2009a) show that prices of senior tranches on a pool of credit default swaps were higher than model-based predictions before the crisis. Coval, Jurek, and Stafford (2009b) find that model and market prices became more in line during the crisis. Diamond and Rajan (2009) argue that the short-term incentives of traders led them to invest in products with substantial tail risk, which is a key feature of tranched securities. Keys, Mukherjee, Seru, and Vig (2010) provide evidence that securitization led to lax screening of residential mortgage loans. In contrast, for the CMBX market we find no evidence that investors overpriced senior tranches before the crisis. Much of the attention in this recent literature has been devoted to tranched products based on corporate loans, credit default swaps, and residential mortgage loans.2 We complement these various papers by looking at tranched derivative products in the market for commercial real estate loans (CMBX). This is interesting for several reasons. First, because CMBX are derivative contracts on commercial property values, we can study their relative value to other liquid assets that are also directly dependent on commercial property values, like REIT stock and options.3 Second, while by now it is widely accepted that large losses on subprime securities will materialize, the jury is still out on CMBX. For example the delinquency rate on the CMBS deals referenced by CMBX 1 was only 4.50% per March 2010; in contrast, the delinquency rate for subprime deals referenced by the ABX 06-01, issued around the same time as the CMBX 1 series, was 41.61% per March 2010.4 Third, we study the market development before, during, and after the crisis period. This allows us to see whether the crisis led to fire sales or market breakdowns, and whether investors updated their beliefs concerning tranched securities, leading to more accurate pricing in this market. Fourth, we analyze the time series of mispricing of CMBX contracts in detail and report several short-term inefficiencies. Our paper also builds on the literature applying the Merton (1974) contingent-claim approach for pricing bonds. Titman and Torous (1989) and Childs, Ott, and Riddiough (1996) apply such an approach to CMBS contracts, while Christopoulos, Jarrow, and Yildirim (2008) test the pricing of CMBS contracts using a reduced-form approach. Downing, Stanton, and Wallace (2007) use the Titman and Torous (1989) model to analyze CMBS over the 1996–2005 period and provided an early warning that subordination levels were decreasing over time, while implied volatility estimates remained roughly constant. Kau, Keenan, and Yildirim (2009) study CMBS default probabilities using REIT property-type indexes. Also, there is a large literature studying the empirical determinants of commercial mortgage defaults, including VanDell, Barnes, Hartzell, Kraft, and Wendt (1993), Follain and Ondrich (1997), Ciochetti, Deng, Gao, and Yao (2002), Ambrose and Sanders (2003), and Ciochetti, Deng, Lee, Shilling, and Yao (2003). To the best of our knowledge, none of these papers study the CMBX derivative contract, nor do they test the efficiency of the commercial real estate market during the 2007–2009 financial crisis, like this paper does. The paper proceeds as follows. In Section 2 we discuss the CMBS and CMBX market. In Section 3 we present the option model, and in Section 4 we discuss the data and calibration results. Section 5 presents results on pricing CMBX contracts, several empirical tests for inefficiencies, and a test of the hedging pressure hypothesis. In Section 6 we discuss the main news events that affected the CMBS market and we analyze the CMBX market response to those announcements. Section 7 explores the absolute pricing of CMBX and REITs. Section 8 concludes.

We analyze the efficiency of the CMBX market during the recent financial crisis. We do this by comparing actual CMBX prices with prices from a Merton-style structural option pricing model. This model is calibrated to stock and option prices for the S&P 500 index and several REITs, and not to CMBX prices, which allows for a clean relative pricing analysis. We find that, on the one hand, the general price swings experienced by the CMBX indexes are largely explained by our structural option model. On the other hand, at shorter horizons, we find predictability in CMBX prices relative to REIT prices that is both statistically significant and economically meaningful, as evidenced by significant abnormal returns from a model-based trading strategy. We provide evidence that this temporary mispricing of CMBX contracts is caused by hedging pressure of banks. In addition to this relative pricing analysis, we also study the absolute pricing of CMBX contracts, and do not find strong evidence that these assets were substantially mispriced before or during the crisis period.