Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.     

Diagnosing Asset Pricing Models Using the Distribution of Asset Returns

This paper develops a set of diagnostic tests which can shed light on why a particular model is failing and indicate what steps might be taken to make the model consistent with asset returns. Theoretical bounds on the moments of a stochastic discount factor are derived as a function of the moments of observed asset returns. Particular attention is paid to restrictions on moments other than the variance. These bounds can also be used to measure the information about the distribution of the discount factor contained in the moments of various asset returns. As an application of this methodology, bounds on the discount factor are estimated using size-based portfolios, and the results are used to analyze the small firm effect. Empirical results indicate, for the period 1926–1975, that moments of the returns of small firms contain information about the discount factor that is not contained in the moments of the returns of large firms and/or a proxy of the aggregate wealth portfolio. However, this difference disappears when more recent data is included.     

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.     

Using Expectations to Test Asset Pricing Models

Asset pricing models generate predictions relating assets' expected rates of return and their risk attributes. Most tests of these models have employed realized rates of return as a proxy for expected return. We use analysts' expected rates of return to examine the relation between these expectations and firm attributes. By assuming that analysts' expectations are unbiased estimates of market-wide expected rates of return, we can circumvent the use of realized rates of return and provide evidence on the predictions emanating from traditional asset pricing models. We find a positive, robust relation between expected return and market beta and a negative relation between expected return and firm size, consistent with the notion that these are risk factors. We do not find that high book-to-market firms are expected to earn higher returns than low book-to-market firms, inconsistent with the notion that book-to-market is a risk factor.     

The Asset Pricing Palette: Cash Flows, Returns and Trading Behavior

Asset pricing is the topic of the 2001 Eastern Finance Association Symposium and the five papers selected for this collection, which are summarized below, span a broad range of subjects that fall under the umbrella of the determinants of market prices. For example, the Schwartz and Moon article that introduces the symposium uses real options methodology to value firms whose cash flows are subject to multiple sources of uncertainty while the Luders and Peisl and Mixon analytical models that close the selections incorporate dual stochastic processes to derive relationships between information flow, trading volume and price volatility that are consistent with empirical evidence. In between, Mishra and O'Brien present new evidence on the important of index and factor selection when estimating the required return on equity and Spahr and Schwebach revisit the issue of time diversification by reintroducing a statistical construct from earlier times. Each of the works included here makes an important contribution to our understanding of the asset pricing process in a distinct area and opens new doors onto avenues for future research.     

Testing Conditional Asset Pricing Models Using a Markov Chain Monte Carlo Approach

We use Markov Chain Monte Carlo (MCMC) methods for the parameter estimation and the testing of conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors‐in‐variables. Using S&P 500 panel data, we analyse the empirical performance of the CAPM and the Fama and French (1993) three‐factor model. We find that time‐variation of betas in the CAPM and the time variation of the coefficients for the size factor (SMB) and the distress factor (HML) in the three‐factor model improve the empirical performance. Therefore, our findings are consistent with time variation of firm‐specific exposure to market risk, systematic credit risk and systematic size effects. However, a Bayesian model comparison trading off goodness of fit and model complexity indicates that the conditional CAPM performs best, followed by the conditional three‐factor model, the unconditional CAPM, and the unconditional three‐factor model.     

Decimal Pricing and Information-Based Trading: Tick Size and Informational Efficiency of Asset Price

Abstract:  In this study we analyze the effect of tick size on information-based trading. Although prior studies provide extensive evidence on the effect of tick size on market quality measures such as spreads, depths, and return volatility, there is little evidence as to the effect of tick size on the informational efficiency of asset price. Our results indicate that the probability of information-based trading during the post-decimal period is significantly greater than the corresponding figure during the pre-decimal period. We also show that the increase in information-based trading after decimalization cannot be attributed to concurrent changes in stock attributes. We interpret our findings as evidence that the smaller tick size under penny pricing encourages information-based trading and thereby raises the informational efficiency of asset price.     

Attention Spillover in Asset Pricing

Exploiting a screen display feature whereby the order of stock display is determined by the stock's listing code, we lever a novel identification strategy and study how the interaction between overconfidence and limited attention affect asset pricing. We find that stocks displayed next to those with higher returns in the past two weeks are associated with higher returns in the future week, which are reverted in the long run. This is consistent with our conjectures that investors tend to trade more after positive investment experience and are more likely to pay attention to neighboring stocks, both confirmed using trading data.     

Asset Pricing with a Bank Risk Factor

This paper studies how the state of the banking sector influences stock returns of nonfinancial firms. We consider a two‐factor pricing model, where the first factor is the traditional market excess return and the second factor is the change in the average distance to default of commercial banks. We find that this bank factor is priced in the cross section of U.S. nonfinancial firms. Controlling for market beta, the expected excess return for a stock in the top quintile of bank risk exposure is on average 2.83% higher than for a stock in the bottom quintile.     

Asset Pricing in a Production Economy with Incomplete Information

This paper analyzes an economy in which investors operate under partial information about technology-relevant state variables. It is shown that for Gaussian information structures under incomplete observations, the consumer's problem can be transformed into an equivalent program with a completely observed state: the conditional expectation of the underlying unobservable state variables. A consequence of this transformation is that classic results in finance remain valid under an appropriate reinterpretation of the state variables.     

Higher Order Expectations in Asset Pricing

We examine formally Keynes' idea that higher order beliefs can drive a wedge between an asset price and its fundamental value based on expected future payoffs. We call this the higher order wedge, which depends on the difference between higher and first order expectations of future payoffs. We analyze the determinants of this wedge and its impact on the equilibrium price in the context of a dynamic noisy rational expectations model. We show that the wedge reduces asset price volatility and disconnects the price from the present value of future payoffs. The impact of the higher order wedge on the equilibrium price can be quantitatively large.     

Conditional Skewness in Asset Pricing Tests

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.     

The US Housing Market: Asset Pricing Forecasts Using Time Varying Coefficients

The US housing market has experienced significant cyclical volatility over the last twenty-five years due to major structural changes and economic fluctuations. In addition, the housing market is generally considered to be weak form inefficient. Houses are relatively illiquid, exceptionally heterogeneous, and are associated with large transactions costs. As such, past research has shown that it is possible to predict, at least partially, the time path of housing prices. The ability to predict housing prices is important such that investors can make better asset allocation decisions, including the pricing and underwriting of mortgages. Most of the prior studies examining the US housing market have employed constant coefficient approaches to forecast house price movements. However, this approach is not optimal as an examination of data reveals substantial sub-sample parameter instability. To account for the parameter instability, we employ alternative estimation methodologies where the estimated parameters are allowed to vary over time. The results provide strong empirical evidence in favor of utilizing the rolling Generalized Autoregressive Conditional Heteroskedastic (GARCH) Model and the Kalman Filter with an Autoregressive Presentation (KAR) for the parameters time variation. Lastly, we provide out-of-sample forecasts and demonstrate the precision of our approach.     

Networks in Production: Asset Pricing Implications

In this paper, I examine asset pricing in a multisector model with sectors connected through an input‐output network. Changes in the network are sources of systematic risk reflected in equilibrium asset prices. Two characteristics of the network matter for asset prices: network concentration and network sparsity. These two production‐based asset pricing factors are determined by the structure of the network and are computed from input‐output data. Consistent with the model predictions, I find return spreads of 4.6% and ?3.2% per year on sparsity and concentration beta‐sorted portfolios, respectively.     

Macroeconomic News in Asset Pricing and Reality

Revisions in successive Greenbook forecasts of quarterly real GDP growth proxy for news of current and expected future economic growth. In the sample 1975 through 2015, news of future growth is slightly negatively related to contemporaneous changes in Treasury bond yields, while news of current growth is strongly positively related to changes in these yields. Both results are difficult to reconcile with a representative agent's bondholding first-order condition. A continuous-time dynamic model of output attributes almost all of the covariation with yields to martingale innovations in log output and a minimal amount to innovations in the conditional drift of log output.     

Coordination of Expectations in Asset Pricing Experiments

We investigate expectation formation in a controlled experimentalenvironment. Subjects are asked to predict the price in a standardasset pricing model. They do not have knowledge of the underlyingmarket equilibrium equations, but they know all past realizedprices and their own predictions. Aggregate demand for the riskyasset depends upon the forecasts of the participants. The realizedprice is then obtained from market equilibrium with feedbackfrom six individual expectations. Realized prices differ significantlyfrom fundamental values and typically exhibit oscillations around,or slow convergence to, this fundamental. In all groups participantscoordinate on a common prediction strategy.     

On a Simple Econometric Approach for Utility-Based Asset Pricing Model

The Journal of Finance has published an important paper entitled A Simple Econometric Approach for Utility-Based Asset Pricing Model by Brown and Gibbon (1985). The main purpose of this paper is to extend the research of Brown and Gibbons (1985) and Karson, Cheng and Lee (1995) in estimating the relative risk aversion (RRA) parameter in utility-based asset pricing model. First, we review the distributions of RRA parameter estimate . Then, a new method to the distribution of is derived, and a Bayesian approach for the inference of is proposed. Finally, empirical results are presented by using market rate of return and riskless rate data during the period December 1925 through December 2001.     

An Empirical Investigation of CDS Spreads Using a Regime-Switching Default Risk Model

Default risk in equity returns can be measured by structural models of default. In this article we propose a credit warning signal (CWS) based on the Merton Default Risk (MDR) model and a Regime-Switching Default Risk (RSDR) model. The RSDR model is a generalization of the MDR model, comprises regime-switching asset distribution dynamics, and thus produces more realistic default probability estimates in cases of deteriorating credit quality. Alternatively, it reduces to the MDR model. Using a dataset of U.S. credit default swap (CDS) contracts around the 2007-8 crisis we construct rating-based indices to investigate the MDR and RSDR implied probabilities of default in relation to the market-observed CDS spreads. The proposed CWS measure indicates an increase in implied default probabilities several months ahead of notable increases in CDS spreads.     

An Investigation of Commodity Futures Prices Using the Consumption-Based Intertemporal Capital Asset Pricing Model

In this paper we extend the multigood futures pricing model of Grauer and Litzenberger 9 to a dynamic discrete time setting. We then test the model using data on futures prices for corn, wheat, and soybeans. The parameter estimates we obtain are similar to those obtained by other researchers using stock return data. The model itself is rejected and we offer some suggestions as to which assumption may be violated. We also give an interpretation to the Hansen-Singleton nonlinear instrumental variables estimation technique used in our empirical work.     

Some Tests of the Risk-Return Relationship Using Alternative Asset Pricing Models and Observed Expected Returns

This study examines the performance of three asset pricing models: the CAPM, the APT and the UAPT using observed expected returns from a three-phase dividend discount model with Value Line analyst estimates of future company-level earnings, dividends and growth rates. Our study is the first we know of to test the three major asset pricing models using observed expected returns. Our results are similar to prior research using ex post (realized) returns in that we find that the UAPT using macroeconomic factors is the best performing model, followed by the APT and the CAPM. However, our results also suggest that the importance of macroeconomic factors is much greater to expected returns than to realized returns, and the corresponding R2 values for models using expected returns are much higher than for models using realized returns. Combining our results for the UAPT with those of Marston and Harris (1993) for the CAPM suggests that these models are more successful in tests using observed expected returns than in tests using realized returns as proxies for expected returns. Unit root tests suggest that monthly observed expected returns follow the classic random walk without drift model while monthly realized returns do not.