Empirical tests on the asset pricing model with liquidity risk: An unobserved components approach

The aim of this paper is to test empirically the conditional liquidity-adjusted capital asset pricing model (L-CAPM) developed by Acharya and Pedersen (2005). Accordingly, we propose to estimate the L-CAPM using unobserved components methodology, which allows us to take into account the main stylized facts characterizing liquidity. Based on a sample of firms listed on the NASDAQ, our empirical analysis reveals several findings. Firstly, we show that liquidity is time-varying and exhibits strong seasonality. Secondly, we highlight the impact of the liquidity level premium on asset prices. Thirdly, we show that the most important liquidity risk is related to the covariance between portfolio illiquidity and market returns. Fourthly, we observe a negative relationship between portfolio returns and market illiquidity. Fifthly, we find that liquidity risk and illiquidity level are not always positively correlated.     

Rational Pessimism, Rational Exuberance, and Asset Pricing Models

The paper estimates and examines the empirical plausibility of asset pricing models that attempt to explain features of financial markets such as the size of the equity premium and the volatility of the stock market. In one model, the long-run risks (LRR) model of Bansal and Yaron, low-frequency movements, and time-varying uncertainty in aggregate consumption growth are the key channels for understanding asset prices. In another, as typified by Campbell and Cochrane, habit formation, which generates time-varying risk aversion and consequently time variation in risk premia, is the key channel. These models are fitted to data using simulation estimators. Both models are found to fit the data equally well at conventional significance levels, and they can track quite closely a new measure of realized annual volatility. Further, scrutiny using a rich array of diagnostics suggests that the LRR model is preferred.     

Risk premia in forward foreign exchange rates: a comparison of signal extraction and regression methods

We investigate possible presence of time-varying risk premia in forward pound, yen, and Euro monthly exchange rates versus the US dollar over the last two decades. We study this issue using regression techniques and separately using a signal plus noise model. Our models account for time-varying volatility and non-normality in the observed series. Our regression model rejects the hypothesis that the forward rate is an unbiased predictor of future spot exchange rate, indicating the existence of time-varying risk premium under rational expectations. Our signal plus noise model reveals a time-varying risk premium component in yen and Euro. The same model provides evidence for the presence of risk premium in pound over a shorter sample period, though not over the entire sample. We conclude that risk premia exist, although we may fail to detect these for some currencies over specific time periods.     

Equity risk premium and time horizon: What do the U.S. secular data say?

We consider a representative investor whose wealth is made up of the equity market portfolio and the riskless asset, and who maximizes the expected utility of his/her future wealth for a given horizon. The solution of this program shows that the equilibrium value of the equity risk premium – the latter being measured by the difference between the expected equity portfolio return and the risk-free interest rate – is given by the product of the price of risk by the expected variance of stock returns. When returns are predictable, these two magnitudes are both time-varying and horizon-dependent. In accordance with this theoretical framework, our paper presents an econometric model of the equity risk premia for two traditional horizons: the one-period-ahead horizon (i.e. the ‘short-term’ premium) and the infinite-time horizon (i.e. the ‘long-term’ premium). Using annual US secular data from 1871 to 2008, and representing the expected returns by mixing the three traditional adaptive, extrapolative and regressive processes, large disparities in the dynamics of the two premia are evidenced. Concerning the determination of the equilibrium values of the two premia, the expected variances depend on the past values of the centered squared returns while the prices of risk (unobservable variables) are estimated according to the Kalman filter methodology, which enables us to capture the influence of hidden variables and of non-directly measurable psychological effects. A spread of interest rates adds to this determination. Possibly due to risky arbitrage and transaction costs, the results show that observed premia gradually converge towards their equilibrium values, this process being described by an error correction model. Overall, our model provides a rather satisfactory representation of ‘short-term’ and ‘long-term’ premia.     

Financial market integration: Theory and empirical results

In this article, we introduce a new theoretical international asset pricing model which accounts for partial financial market segmentation. We show that if some investors do not hold all international assets because of implicit and/or explicit segmentation factors, the world market portfolio is not efficient and the classic ICAPM must be augmented by a new factor reflecting the local risk undiversifiable internationally. We test this model empirically for a sample of emerging markets. Our findings show that the degree of market integration is time-varying and that the premium associated with the domestic risk factors is the most important component of the total risk premium. However, our results also show that most of the emerging markets we study have become more integrated in the end of our sample period as a result of liberalization and reforms.     

Analysing the risk premium in the Italian stock market: ARCH-M models versus non-parametric models

This Paper investigates the variability of the risk premium in the Italian stock market, over the period 1978–89. We have modelled voatility using two different approaches: ARCH-M models and non-parametric models. The estimate of the ARCH-M models confirm the existence of both an ARCH process in the variance and a time-varying risk premium. Also the non-parametric specification confirms the existence of a time varying risk premium. Moreover in both models the acceleration in the inflation rate has a negative effect on stock prices.     

Liquidity and asset prices in rational expectations equilibrium with ambiguous information

The quality of information in financial asset markets is often hard to estimate. Reminiscent of the famous Ellsberg paradox, investors may be unable to form a single probability belief about asset returns conditional on information signals and may act on the basis of ambiguous (or multiple) probability beliefs. This paper analyzes information transmission in asset markets when agents?? information is ambiguous. We consider a market with risk-averse informed investors, risk-neutral competitive arbitrageurs, and noisy supply of the risky asset, first studied by Vives (Rev Financ Stud 8:3?C40, 1995a, J Econ Theory 67:178?C204, 1995b) with unambiguous information. Ambiguous information gives rise to the possibility of illiquid market where arbitrageurs choose not to trade in a rational expectations equilibrium. When market is illiquid, small informational or supply shocks have relatively large effects on asset prices.     

Product line pricing in a vertically differentiated oligopoly

Abstract This paper examines the joint pricing decision of products in a firm’s product line. When products are distinguished by a vertical characteristic, those with higher values of that characteristic will command higher prices. We investigate whether, holding the value of the characteristic constant, there is an additional price premium for products on the industry and/or the firm frontier, that is, for the products with the highest value of the characteristic in the market or in a firm’s product line. We also investigate the existence of price premia for lower‐ranked products and other product line pricing questions. Using personal computer price data, we show that prices decline with the distance from the industry and firm frontiers, even after holding absolute quality constant. We find evidence that consumer tastes for brands is stronger for the consumers of frontier products (and thus competition between firms weaker in the top end of the market). There is also evidence that a product’s price is higher if a firm offers products with the immediately faster and immediately slower computer chip (holding the total number of a firm’s offerings constant), possibly as an attempt to reduce cannibalization. Finally, a product’s price declines with the time it is offered by a firm, suggesting intertemporal price discrimination.     

Risk, ambiguity, and state-preference theory

The state-preference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling ??smooth?? ambiguity-averse preferences. It does not require reference to objective probabilities, personalistic consequences, or counterfactual acts, and it allows for state dependence of utility and unobservable background risk. The decision maker??s local revealed beliefs are encoded in her risk-neutral probabilities (her relative marginal rates of substitution between states) and her local risk preferences are encoded in the matrix of derivatives of the risk-neutral probabilities. This matrix plays a central but generally unappreciated role in the modeling of risk attitudes in the state-preference framework. It can be computed by inverting a bordered Slutsky matrix and vice versa, it generalizes the Arrow?CPratt measure for approximating local risk premia, and its structure reveals whether the decision maker??s risk preferences are ambiguity averse as well as risk-averse. Two versions of the smooth ambiguity model are analyzed??the source-dependent risk aversion model and the second-order uncertainty (KMM) model??and it is shown that in both cases, the overall premium for local uncertainty can be decomposed as the sum of a risk premium and an ambiguity premium.     

On the effects of rare disasters and uncertainty shocks for risk premia in non-linear DSGE models

This paper studies how rare disasters and uncertainty shocks affect risk premia in DSGE models approximated to second and third order. Based on an extension of the results in Schmitt-Grohé and Uribe (2004) to third order, we derive propositions for how rare disasters, stochastic volatility, and GARCH affect any type of risk premia in a wide class of DSGE models. To quantify the effects, we set up a standard New Keynesian DSGE model where total factor productivity includes rare disasters, stochastic volatility, and GARCH. We find that rare disasters increase the level of the 10-year nominal term premium, whereas a key effect of uncertainty shocks, i.e. stochastic volatility and GARCH, is an increase in the variability of this premium.     

Liquidity shocks and equilibrium liquidity premia

We study an equilibrium in which agents face surprise liquidity shocks and invest in liquid and illiquid riskless assets. The random holding horizon from liquidity shocks makes the return of the illiquid security risky. The equilibrium premium for such risk depends on the constraint that agents face when borrowing against future income; it is insignificant without borrowing constraint, but can be very high with borrowing constraint. Illiquidity, therefore, can have large effects on asset returns when agents face liquidity shocks and borrowing constraints. This result can help us understand why some securities have high liquidity premia, despite low turnover frequency.     

Trade, Technology and UK Wage Inequality

This paper examines the impact of international trade and technical change on changes in the UK skill premium. We first measure trade as changes in product prices and technical change as TFP growth. Then we relate price and TFP changes to a set of underlying forces. Among our results are (a) changes in prices, not TFP, were the major force behind the rise in inequality in the 1980s; (b) changes in OECD prices and UK tariffs significantly raised 1980s skill premia through their effects on prices, and that industry concentration significantly raised 1980s skill premia through its effect on TFP.     

The relationship between risk-neutral and actual default probabilities: the credit risk premium

The study investigates empirically the relationship between the risk-neutral measure Q and the real-world measure P. We study the ratio between the risk-neutral and actual default intensities, which we call the coverage ratio or the relative credit risk premium. Actual default intensities are derived from rating agencies annual transition matrices, while risk-neutral default intensities are bootstrapped from CDS quotes of European corporates. We quantify the average risk premium and its changes over time. Compared to related literature, special attention is given to the effects of the recent financial and European sovereign crises. We find that average credit risk premia rose substantially and that post-crisis levels are still higher than those observed before the financial crisis. This observation is especially true for high-quality debt and if it persists, it will have an impact on corporates funding costs. The quantification and revision of risk premia contributes to the discussion of the credit spread puzzle and could give extra insights in valuation models that start from real-world estimates. Our work is furthermore important in the context of state aid assessment. The real economic value (REV) methodology, applied by the European Commission to evaluate impaired portfolios, is based on a long-term average risk premium.     

On the role of liquidity in emerging markets stock prices

This paper investigates the impact of liquidity on emerging markets' stock prices. Particular attention is given to the estimation of Jensen's alpha and the quantity of risk. Our empirical analysis gives rise to two main issues. The first is related to the presence of an extra premium, i.e. “alpha puzzle”. The second is the time-varying component of the quantity of risk, i.e. “beta puzzle”. We find that local liquidity factors do not explain the presence of positive and statistically significant alphas. This puzzle is solved by means of transaction costs. In addition, we show that global liquidity factors, such as VIX and Open Interest, statistically affect the market price of risk. Our empirical finding proves the time varying nature of the global risk factors. Finally, we argue that standard asset pricing models cannot solve the two puzzles simultaneously.     

Financial Deregulation And The Relationship Between The Economy And The Share Market In Australia

In this paper we investigate the effect of financial deregulation on the relationship between the macro-economy and the share market within the framework of a VAR using quarterly Australian data for four variables – aggregate share prices, real output, the term premium and the default premium. After an analysis of stationarity and cointegration of the variables, we specify the VAR in the first differences of the logs of share prices and output and the levels of the premia. We identify December 1983 as the most appropriate date for testing for a structural break in our model due to financial deregulation and find strong evidence supporting our hypothesis of a break at this date. We go on to estimate and simulate the model separately over two sub-samples: 1978(1)–1983(4) and 1984(1)–2001(2). While our results are not clear-cut, we find that, if anything, the deregulation of financial markets weakened the relationship between the share market and the rest of the economy.     

Option-implied preferences adjustments, density forecasts, and the equity risk premium

The main objective of this paper is to analyse the value of information contained in prices of options on the IBEX 35 index at the Spanish Stock Exchange Market. The forward looking information is extracted using implied risk-neutral density functions estimated by a mixture of two-lognormals and several alternative risk adjustments. Our results show that, between October 1996 and March 2000, we can reject the hypothesis that the risk-neutral densities provide accurate predictions of the distributions of future realisations of the IBEX 35 index at 4- and 8-week horizons. When forecasting through risk-adjusted densities the performance of this period is statistically improved and we no longer reject that hypothesis. We show that risk adjustments based on a power specification for the stochastic discount factor—which is the approach used so far in the literature that derives the objective density function from option prices- generates an excessive volatility of risk premia. We use alternative risk adjustments and find that the forecasting performance of the distribution improves slightly in some cases when risk aversion is allowed to be time-varying. Finally, from October 1996 to December 2004, the ex-ante risk premium perceived by investors and that are embedded in option prices is between 12 and 18% higher than the premium required to compensate the same investors for the realised volatility in stock market returns.      

Junior is rich: bequests as consumption

We explore the consequences for asset pricing of admitting a bequest motive into an otherwise standard overlapping generations economy where agents trade equity, a risk free asset and consol bonds. With low risk aversion, the calibrated model produces realistic values for the mean equity premium and the risk free rate, the variance of the equity premium, and the ratio of bequests to wealth. However, the variance of the risk free rate is unrealistically high. Security prices tend to be substantially higher in an economy with bequests as compared to an otherwise identical one where bequests are absent. We are able to keep the prices sufficiently low to generate reasonable returns and premia by stipulating that a portion of the bequests skips a generation and is received by the young.

“You never actually own a Patek Philippe. You merely take care of it for the next generation.” Patek Philippe & Co.

We thank John Cox, Jean Pierre Danthine, Felix Kubler, Edward Prescott and seminar participants at The Bank of Italy, Columbia, Lausanne, Mannheim, MIT, Lugano, SIFR, the University of New South Wales, USC, Yale and the University of Zurich for insightful xcomments. The usual caveat applies.     

Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs

The aim of this paper is to analyse the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, is shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risk tolerance weighted average of the individual beliefs, and the discount factor is proportional to beliefs dispersion. This discount factor makes the heterogeneous beliefs setting fundamentally different from the homogeneous beliefs setting, and it is consistent with the interpretation of beliefs heterogeneity as a source of risk.
We then use our construction to rewrite in a simple way the equilibrium characteristics (market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyse the impact of beliefs heterogeneity. Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia and lower risk-free rates.     

The cross-section and time-series effects of individual stock sentiment on stock prices

In this article, we construct an individual stock sentiment index by using the principal component analysis method. We empirically study the cross-section and time-series effects of investor sentiment on the stock prices based on the panel data model with dummy variable. The results indicate that individual stock sentiment has greater impact on small-firm stock prices than big-firm stock prices, which presents obvious cross-section effect. Moreover, individual stock sentiment leads to much sharper ?uctuations of stock prices in the stock market downturn than in the stock market expansion, which shows obvious time-series effect. Specifically, the individual stock sentiment has the greatest impact on small-firm stock prices under the stock market downturn, exerting significant dual asymmetric effect. Our results are helpful to understanding the micro-mechanism of sentiment effect.     

Determinants of the premium in forward contracts

Whilst the benefits of forward contracting for goods and services have been extensively researched in terms of mitigating market power effects in spot markets, we analyse how the risk in spot price formation induces a counteracting premium in the contract prices. We consider and test a wide-ranging set of propositions, involving fundamental, behavioural, dynamic, market conduct and shock components, on a long data set from the most liquid of European electricity forward markets, the EEX. We show that part of what is conventionally regarded as the market price of risk in electricity is actually that of its underlying fuel commodity, gas; that market power has a double effect on prices, insofar as it increases spot prices and induces a forward premium; that oil price sentiment spills over and that the premium reacts to scarcity and the higher moments of spot price uncertainty. We observe that considerations of the scale and determinants of the forward premium are at least as important as the market power effects in spot market price formation when evaluating the efficiency of wholesale power trading.