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Asset pricing
In this section, the reports deal with articles on asset pricing: asset pricing models, stochastic discount factors, equity premium puzzle, consumption-based models, habit-persistence models, multi-factor models, pricing anomalies, asset return predictability, credit spreads, credit models etc...

In Search of Distress Risk

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In this article, the authors study the pricing of distress risk in equity returns. They use a set of firm characteristics such as leverage, profitability, market cap, stock returns and volatility, cash holdings, market-to-book ratio and stock price to predict default. 

They use a logit model to estimate the probability of bankruptcy or failure. They use data from Kamakura Risk Information Services, Compustat and CRSP from January 1963 to December 2003.

They find that all the variables are significant with the correct sign. As they extend the horizon of the default forecast, they find that market capitalization and equity volatility become the most important variables. Their reduced form model seems to be more accurate than a structured credit model. 

They proceed to look at the risk and returns on distressed stocks (high likelihood of failure). Previous research has documented that returns are high (Vassalou and Xing 2004, using Merton style distance to default) or low (for instance Dichev 1998 using accounting information). Since they have a better model to predict default they hope to get more robust findings on the effect on equity returns.

Specifically, they look at 12-month equity returns of value-weighted portfolios ranked on their 12-month conditional default probabilities. Stocks with high default risk have lower returns but positively skewed returns. Interestingly, the stocks in the high default risk portfolio are volatile and small.    

The factor loadings on the equity market, the Fama and French (FF) HML and SMB factors are high and positive especially on the SMB factor. Even after controlling for the FF factors, they find the alphas of the portfolios are decreasing with distress risk. Their results do not change when results are first sorted on firm characteristics such as book-to-market, size or distance-to-default.

In their conclusions, they discuss several explanations:

-  Underreaction to negative news

-  Private benefits of shareholders that compensate for the low returns

Preference for positively skewed stocks

- Transition in this sample of asset holdings from individual investors to institutional investors (who prefer “safe’” stocks and probably large stocks)

We think  the institutional explanation is reasonable (large institutional investors cannot load small cap stocks). The preference for lottery stocks (positively skewed distribution) is also a strong contender. The payoff of holding these stocks is similar to holding cheap call options with limited downside and potentially large returns when the stock recovers. 

Campbell, John Y., Hilscher, Jens and Szilagyi, Jan, "In Search of Distress Risk" . Harvard Institute of Economic Research Discussion Paper No. 2081 Available at SSRN:

Dichev , Ilia,  “Is the Risk of Bankruptcy a Systematic Risk?”, The Journal of Finance, Vol. 53, No. 3 (Jun., 1998), pp. 1131-1147

Vassalou, Maria and Yuhang Xing, 2004, “Default risk in equity returns”, Journal of Finance 59:831-868.



A Simple, Unified, Exactly Solved Framework for Ten Puzzles (..)

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A Simple, Unified, Exactly Solved Framework for Ten Puzzles about Stocks, Bonds and Exchange Rates

Xavier Gabaix’s paper is an ambitious piece of work that claims to solve many asset pricing puzzles in one unique, tractable and fully solved framework.  

The author builds on the Rietz-Barro view that small probabilities of large crises or disasters create a risk premium. Barro (2006) documents that disaster probabilities in the twentieth century (1.5%-2% per year) with large declines in per capita GDP (15% to 64%) are high enough to explain the risk premium. This research rehabilitates the Rietz model that was discarded as needing unrealistic assumptions and making implausible predictions (see Barro 2006). 

In Gabaix (2007), the asset losses given the crisis are time varying and therefore cause the risk premium to be also time varying in normal time. The model addresses different puzzles: 

(i)                   the equity premium puzzle (it is too high, already discussed in Barro 2006)

(ii)                 risk-free rate puzzle (it is too low, already discussed in Barro 2006)

(iii)                excess equity volatility puzzle

(iv)                value-growth puzzle (growth stocks underperform value stocks)

(v)                  upward nominal yield curve (but is it a puzzle?)

(vi)                steep yield curve predicts high risk premia in bond returns (Fama-Bliss)

(vii)                corporate bond spread puzzle (it is too high)

(viii)             countercyclical equity premium

(ix)               firm characteristics vs. return covariance puzzle

(x)                 price-dividend ratio and consumption-wealth ratios predict aggregate stock market returns

(xi)               high price of deep out-of-the-money puts

(xii)              forward exchange rate premium puzzle 

In the model, a representative agent has a utility function that depends on a stream of consumption. Consumption grows at a constant rate except in time of crisis when it drops by some percentage amount. Risky assets have similar behaviors:

 -          Stock dividends grow at a stochastic rate around some mean growth rate but falls in value in time of crisis  

-          Bond coupons fall in value at the rate of inflation and in time of crisis fall even more because of inflation shock (in crisis, inflation increases) 

-          Productivity is constant but falls in time of crisis and affects the foreign exchange rate (which is the discounted valued of future productivity levels) 

For the stock price and the foreign exchange rate, Gabaix uses resilience. The “expected resilience” of an asset (or a country) mainly depends on the recovery value of the dividends (or the fall in productivity) and the chance of disaster. 

The “expected resiliences” and the inflation rate follow some approximated linear processes (Linearity-Generating twist) for mathematical convenience. The author can then price the bonds, the stocks and the exchange rate and solve the different puzzles after calibration.

We will discuss a few puzzles and refer the reader to Gabaix (2006) for the other ones. 

First, as in Barro (2006), the equity risk premium is because of the expected loss (or the asset resilience) in case of disaster. Because the loss is stochastic, it produces excess volatility and makes the stock market difficult to predict (close to a random walk). 

Second, the upward slopping nominal yield curve is caused by the possibility of inflation shocks in time of crisis and thus a loss in value for long maturity bonds. 

Third, the stochastic country resilience causes the excess volatility in exchange rates. Also, the short-term interest rate will depend on the country resilience (decreasing) whereas the exchange rate will be increasing with the resilience. Because the exchange rate mean reverts, we will see patterns of low short-term rates with depreciating currencies (forward exchange rate premium). 

We found this paper interesting by the number of puzzles it claims to solve. We are not sure about the elegance of the approach (often the author chooses shortcuts by modeling directly resilience with Linearity Generating processes), and resilience that also embeds the marginal utility of consumption.      

The approach is also similar to fat-tail modeling in asset returns. A disaster is just a systematic jump in asset value. Could a similar model be solved using standard techniques of continuous time finance with affine processes with jumps (the author often uses continuous time for his proofs)? In continuous time, we suspect the  Linearity Generating processes will not be necessary. 

Some extensions would be interesting: 

-          to tie this model with business cycles (with probabilities of recession and expansion),  

-          to incorporate wealth or the agent portfolio in the model (a disaster could simply be a large drop of the value of stock portfolio). 

Gabaix, Xavier (2006), “A Simple, Unified, Exactly Solved Framework for Ten Puzzles about Stocks, Bonds and Exchange Rates”, MIT Working Paper, 

Barro, Robert, (2006), “Rare Disasters and Asset Markets in the Twentieth Century”, Quarterly Journal of Economics, August 2006, Vol. 121, No. 3, Pages 823-866   


Resolving Macroeconomic Uncertainty in Stock and Bond Markets

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In this paper, the authors use data from economic derivatives provided by Goldman Sachs to examine the effect of macroeconomic uncertainty on stock and bond returns 

Investors and traders can trade these derivatives to hedge or speculate on different macro indicators around announcement dates: the nonfarm payrolls (NFP), Institute of Supply Management manufacturing report and US retail sales ex-autos. These derivatives take the form of capped call, put and digital options. With the help of standard derivatives pricing techniques, the authors back up from observed derivatives prices the implied mean and volatility of the NFP indicator. 

The inferred mean is the best forecast of the market for the NFP and the difference measures the surprise.   

They then run a series of regressions of Treasury bond returns (5-year, 10-year and 30-year Treasury bond futures, Eurodollar futures), equity returns (S&P500, cyclical and noncyclical stocks), implied volatility changes of options on treasury futures and the S&P500 on economic news surprises (realization minus expectation divided by the volatility). They select their observations around the NFP announcement dates. 

They find that a positive shock to the NFP increases the bond returns and decreases the bond yields but has a small impact on the S&P500 returns. 

With the inferred mean, they also calculate the implied economic volatility from all the NFP announcements.  They find the drop of fixed-income implied volatility correlates positively with the size of the implied economic volatility. Here again but using the equity implied volatility measure VIX, they document the impact of the equity market is not significant. The impact is however stronger on the volatility of cyclical stocks. 

The authors explore the behavior of market participants by looking at trading volumes and open interests. They find that trading increases with the economic uncertainty. Using changes in open-interest data, they conclude the increase is because of hedging/speculating trades and not to a wait-after the announcement to trade effect (because the open interest falls after announcement). 

This is an innovative paper since it is using data that are not widely available to financial researchers. The market for economic derivatives is still new. We expect the see more theoretical modeling of the interaction between financial and economic uncertainties. 

Beber, Alessandro and Brandt, Michael W., "Resolving Macroeconomic Uncertainty in Stock and Bond Markets" (May 2006). AFA 2007 Chicago Meetings Paper Available at SSRN:



Default Risk Premia and Asset Returns

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In this paper, the authors extract default risk premia (DRP) from observations of credit default swaps and examine whether corporate bonds, stocks and stock options incorporate these premia in their returns.

Previous research has found that default risk alone cannot explain the high level of credit spreads. The authors uses credit default swap rates (CDS) and recovery rates from 2001 to 2005 and expected default frequencies from Moody’s KMV to estimate the DRP factor. The DRP factor explains the comovement of default risk premia across the different reference entities. 

They first assume some dynamics for the risk-neutral and physical default intensities for each individual firm (they follow a Black-Karasinski model, a simple Ornstein-Uhlenbeck process applied to the logarithm).

They estimate the parameters of the dynamics using time series of EDFs (for the risk-neutral intensities) and CDS and recovery rates (for the physical intensities). They then calculate the model implied values of the intensities.  The difference between the risk-neutral and the physical intensities is then a measure of default risk premia.

They use these intensities to estimate the credit returns unexplained by default risk alone and estimate an OLS regression on the panel data of credit returns to find the DRP factor. The regression explains the credit returns with the Fama and French factors, the momentum factor, a firm specific and a time specific effects.

The DRP factor is the loading of the time dummy plus the average across issuers of the constants in the panel data regression.  

After identifying the DRP factor, they perform a series of asset pricing tests on corporate bond returns (high-grade and high yield), on equity portfolios and equity options. 

They use Fama-McBeth regressions to estimate the risk premium of different factors (equity market, equity size factor, equity value factor, equity momentum factor, corporate debt market factor, treasury bond market factor and the DRP factor). These regressions are time series regression of excess returns on the factors to calculate the betas on the factors and then cross-sectional regressions at each time period to identify the factor risk premia.  

They apply their analysis to equity portfolios sorted by size and book-to-market equity and to corporate bond high-grade and high yield indexes and to corporate portfolios sorted by rating, maturity, and industry. The DRP factor appears significant in time series regression of corporate bond returns especially for low-rated bonds. Higher returns are associated with higher loading the DRP factor. High-expected returns seem therefore to compensate for higher default risk. The results are robust even after controlling for firms characteristics or sectors.  

The authors do not find similar results for equity portfolios. Higher equity returns do not come with higher exposure to the DRP factor. The DRP factor is not priced in the equity market. Using put options on the S&P500, they find that far-out-the-money options returns increase with the exposure to the DRP factor. The results are however not statistically significant. 

They construct a model that includes a market-wide default event risk priced both in the equity and bond returns. It is not clear from their model why the DRP factor is not empirically significant for equity returns. 

Overall, we found that the authors did an excellent job using the default swap data to estimate the DRP factor. We note however that the main movement of the factor happens only in 2002 during the credit downturn. The sample might not be long enough to draw any strong conclusions on the DRP factor. Their findings on options are also not statistically significant so it is not clear that the DRP factor is a proxy for a systematic jump to default risk. They have not used a liquidity factor (such as a portfolio long illiquid bonds vs. liquid bonds) that could better explain some of the residual returns.  

Berndt, Antje, Lookman, Aziz A. and Obreja, Iulian, "Default Risk Premia and Asset Returns" (December 18, 2006). AFA 2007 Chicago Meetings Paper Available at SSRN:



Dispersion in Analysts' Earnings Forecasts and Credit Rating

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In this paper, the authors revisit the negative correlation between earnings forecast dispersion and equity returns documented by Diether, Malloy, and Scherbina (2002). They find that this effect mostly exists only among low credit quality firms and that controlling for the credit quality, it is not statistically significant. This is consistent with the finding that credit risky firms earn a lower equity return as Avramov et al. (2007) have documented. There is therefore a negative risk premium for default risk.



The study uses over 3000 firms from AMEX, NYSE and NASDAQ with data from CRSP, COMPUSTAT, IBES and S&P ratings. 

The authors find that earnings dispersion-return relationship is concentrated among firms that represent 5% de total market capitalization but these firms are not necessarily the smallest ones. They confirm the robustness of their results by controlling for systematic common factors, industry effects and firm characteristics (leverage, turnover, idiosyncratic volatility and size).Credit rating takes over earnings dispersion in all their tests.   

Across time, they find that the negative correlation between credit risk and equity returns is significant only in periods of rating downgrades. They believe that this reflects the weakening of fundamentals among low-rated companies. 

After reading this paper, we have a couple of questions: why is the worsening of fundamentals not priced in the equity? Why do credit ratings have such effect when we know that these measures are often stale and can be dominated by equity-based signals such as EDFs?


Avramov, Doron, Chordia, Tarun, Jostova, Gergana and Philipov, Alexander, "Dispersion in Analysts' Earnings Forecasts and Credit Rating" (March 23, 2007). Available at SSRN: 

Avramov, Doron, Chordia, Tarun, Jostova, Gergana and Philipov, Alexander, "Credit Ratings and the Cross-Section of Stock Returns" (February 16, 2007). Available at SSRN: 

Diether, Karl, Christopher J. Malloy and Anna Scherbina , “Differences of Opinion and the Cross-Section of Stock Returns”, Journal of Finance, Vol. 57, No. 5, October 2002


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