Rare events, financial crises, and the cross-section of asset returns

Francesco Bianchi 22 April 2015

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The most recent financial crisis triggered the longest and most severe recession in the United States since WWII. The possibility of a complete financial meltdown suddenly became a real concern and commentators and policymakers alike feared that the economy could be heading toward a second Great Depression (Krugman 2009). The Great Depression can certainly be considered a rare event in US economic history. It began with a devastating market crash and represents an extreme example of how a financial crisis and a recession can negatively affect each other.

It is therefore not surprising that the Great Depression has received attention in the asset pricing literature. Cogley and Sargent (2007) argue that the fear of a return to the Great Depression might explain the large but declining equity premium observed in the data. In a related but distinct line of research, Barro (2006), following Rietz (1988), shows that rare disasters are potentially important in explaining the equity premium puzzle. In Bianchi (2015), I show that during the early months of the Great Recession, financial markets were on a path consistent with the Great Depression and that this helps to correctly price the cross section of asset returns. Four stylized facts emerge.

1. The unusual characteristics of the Great Depression can be captured by a Great Depression regime. The probability of this regime has remained close to zero for many decades, but spiked for a short period during the Great Recession.

I estimate a Markov-switching vector autoregression (MS-VAR) over the period December 1928 - June 2009. In a MS-VAR the relations between the variables of interest and the size of the shocks are allowed to vary over time based on the regime that is in place.1 Four key financial variables are included in the estimates: the excess market return over a risk free rate; the Term Yield spread; the Price Earnings ratio; and the Value spread. The Term Yield spread summarizes the slope of the term structure of interest rates. The Value spread measures the difference between the log book-to-market ratios of small-value and small-growth stocks and captures the behaviour of the cross section of asset returns, given that it increases when small-growth stocks perform relatively better.

A Great Depression regime emerges from the estimates. As shown in Figure 1, the probability of this regime was very close to one during the Great Depression. For the remainder of the sample, its probability has been generally close to zero, but it spiked for a short period during the Great Recession, crossing the threshold of 50% in February 2009 for the first time since November 1948. However, its probability quickly returned to zero in March 2009.

Figure 1. The Great Depression regime

Notes: The first panel reports the estimated probability of the Great Depression regime together with the evolution of the price-earnings ratio and the value spread (both variables are rescaled to fit in the 0-1 scale). The lower three panels zoom on three key events: The Great Depression; the end of the Information Technology bubble; and the Great Recession.

2. The Great Depression regime is characterised by a collapse of the stock market with a contemporaneous large increase in the Value spread, indicating that growth stocks perform better than value stocks during financial crises.

Figure 2 shows a simulation in which only the most likely path for the regimes is considered (solid blue line) and compares it with the actual data (red dashed line).  Entering the Great Depression regime determines a sharp drop in the stock market and a contemporaneous increase in the Value spread and the Term Yield spread. After a dramatic fall, the stock market partially recovers, while the Value spread and Term Yield spread keep increasing. Once the economy exits the Great Depression regime, the model predicts a quick reversion in the Value spread and the Term Yield spread. The stock market moves in the opposite direction, showing a steady increase and converging to a higher average value.

Figure 2. The Great Depression

Notes: The figure reports a simulation in which regimes follow their most likely path based on the estimated probabilities. The initial values coincide with the actual data. The simulated series are reported with a solid blue line, while the red dashed line corresponds to the data. The two horizontal lines mark the regime-specific conditional steady states. These are the values to which the variables would converge if a regime were in place for a long time.

3. During the early stages of the Great Recession, financial markets were on a path consistent with the Great Depression, explaining why the Great Depression regime probability spiked in February 2009.

Figure 3 considers two simulations. In the first simulation (solid blue line), a counterfactual regime sequence is assumed, meaning that starting from February 2009, the Great Depression regime prevails until the end of the sample. In the second simulation (black dashed line), the most likely regime sequence is assumed, meaning that the economy does not enter the Great Depression regime. The red dotted line corresponds to the data.

Figure 3. The Great Recession

Notes: The figure reports two simulations in which two different paths for the regimes are considered starting from March 2009. In the first simulation (solid blue line) a counterfactual regime sequence is assumed – the Great Depression regime prevails until the end of the sample. In the second simulation (black dashed line) the actual regime sequence is assumed to be in place – the economy does not enter the Great Depression regime. The red dotted line corresponds to the data.

The simulations can be related to the main events that characterized the beginning of the Great Recession. On March 2008, the Federal Reserve had to intervene to prevent the Bear Stearns bankruptcy. From that moment on, the crisis accelerated, with Lehman brothers filing for bankruptcy, unemployment increasing sharply, and the Federal Reserve cutting the federal funds rate to zero. On February 10, the secretary of the Treasury Geithner outlined the plan for the expansion of the government bank rescue effort. The plan was received with some scepticism by financial markets, which fell by 5% (Solomon 2009). A few days later, the newly elected President Obama signed a stimulus package that was judged as insufficient b­y some commentators.

Over this entire period, the Value spread was on an upward trajectory, while the Price Earnings ratio kept falling. The stock market reached a 12 year minimum in February 2009, when concerns that the US might be heading toward a second Great Depression were already real. This is when the probability of the Great Depression regime crossed 50%. The first simulation highlights that if, starting in February 2009, the economy had in fact entered the Great Depression regime, the Price Earnings ratio and the Value spread would have kept moving in exactly the same fashion, while excess returns would have stayed negative. In other words, until February 2009 financial markets were on a path consistent with the Great Depression regime.

In March 2009, these dynamics reversed. Excess stock market returns increased, the Price Earnings ratio recovered, and the Value spread declined. The second simulation shows that moving away from the Great Depression regime implies these changes. March 2009 is when more encouraging economic data were released and details of the rescue plan were disclosed. Arguably, this had a positive effect on financial markets and a second Great Depression was avoided, at least from the point of view of financial markets.

4. The risk-adjusted low performance of Growth stocks during regular times are compensated by their behaviour during financial crises.

Growth stocks are often found to have returns that are too low when controlling for their market betas. To account for this puzzle, I extend the Bad Beta, Good Beta Intertemporal CAPM (ICAPM) proposed by Campbell and Vuolteenaho (2004) to take into account the possibility of regime changes. The model is tested on the 25 Fama-French portfolios sorted with respect to size and book-to-market ratios by using moving windows of 35 years. Figure 4 reports the evolution of the R2 for the cross-sectional regressions.2 During the early years of the sample, the ICAPM performs well, but as the data window moves away from the Great Depression, its explanatory power declines. However, as the window approaches the most recent financial crisis, the explanatory power increases steeply, and the R² touches 60%, a value that was last reached at the end of 1978. It can be shown that these changes in the R² reflect the fact that during the 1980s and 1990s the returns of growth stocks were too low in light of their ICAPM betas. This anomaly was largely corrected during the Great Recession, suggesting that the low returns of growth stocks during regular times are compensated by their performance during financial crises.

Figure 4. Explanatory power of the ICAPM over moving windows

Notes: The figure reports the R² for the cross sectional regressions used to test the Intertemporal CAPM over moving windows of 35 years. The horizontal axis reports the ending date of the rolling window. For example 1965 corresponds to the sample February 1930-January 1965. The dependent variables are the average returns of the 25 Fama-French portfolios.

Conclusions

The opposite behaviour of the Value spread and the stock market relates the Great Depression to the early stages of the Great Recession. This pattern was absent during another important market decline, the burst of the Information Technology bubble, implying that market declines that are associated with financial crises are inherently different and that monitoring the behaviour of the cross section of asset returns during these events might be useful in understanding where markets are headed.

References

Barro, R J (2006) “Rare disasters and asset markets in the Twentieth Century”, Quarterly Journal of Economics, 121, 823-866.

Bianchi, F (2015) “Rare events, financial crises, and the cross-section of asset returns”, CEPR Discussion Paper 10520, NBER WP 21056.

Cogley, T and T J Sargent (2007) “The market price of risk and the equity premium: A legacy of the Great Depression?”, Journal of Monetary Economics, 55(3), 454-476.

Hamilton, J D (1989) “A new approach to the economic analysis of nonstationary time series and the business cycle”, Econometrica, 57, 357-384.

Krugman, P R (2009) “Fighting Off Depression”, The New York Times OP-ED, January 4, 2009.

Solomon, D (2009) “Market pans bank rescue plan”, The Wall Street Journal, 11 February.

Rietz, T A (1988) “The equity risk premium: A solution”, Journal of Monetary Economics, 22, 117-131.

Sims, C A and T Zha (2006) “Were there regime switches in US monetary policy?”, The American Economic Review, 91(1), 54-81.

Footnotes

1 Formally we have: where  is a vector of variables,  a vector with the regime specific intercepts,  is a matrix that controls the autoregressive parameters,  is a matrix that controls the size of the shocks,  a vector of Gaussian innovations. Notice that the parameters are allowed to evolve over time based on the values assumed by  and . These two hidden variables evolve according to two distinct Markov chains controlled by the transition matrices  and . The goal of the econometrician is twofold. First, we want to learn the parameters of the model conditional on a regime combination. Second, we want to learn which regime was in place at each point in time. Details on how this can be accomplished can be found in Bianchi (2015), Sims and Zha (2006), and Hamilton (1989).

2 The R² is computed as 1-RSS/RSM where RSS is the residual sum of squares and RSM is the residual sum of squares when only the constant is used as a regressor.

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Topics:  Economic history Financial markets

Tags:  Great Depression, Great Recession, financial crises, assets, US

Associate Professor of Economics, Duke University; CEPR; NBER

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