An Empirical Study on the Stock Price Reaction to Earnings Announcements using the Stochastic Discount Factor Approach

In the perfect and unrealistic Black and Scholes (J Polit Econ 81:637–659, 1973) world, the dynamics \((S_{t})_{t\in [0,T]}\) of the risky asset, under the historical probability \(\mathbb{P}\), is given by the following stochastic differential equation: $$\displaystyle{ dS_{t} =\mu S_{t}dt +\sigma S_{t}dW_{t} }$$ where \((W_{t})_{t\in [0,T]}\) is a standard Brownian motion under \(\mathbb{P}\). In this case, there is no ambiguity in the definition the arbitrage-free price of any European contingent claim with maturity T. In fact, in this complete market which is set in continuous time, this value is none other than the value of any replicating portfolio. Moreover, prices may be expressed in terms of conditional expectations under a unique equivalent martingale measure Q whose density with respect to the historical probability is given by the Girsanov theorem $$\displaystyle{ \frac{dQ} {d\mathbb{P}} = e^{-\frac{\mu -r} {\sigma } W_{T}-\left (\frac{\mu -r} {\sigma } \right )^{2} \frac{T} {2} } }$$ where r is the constant and continuously compound risk-free rate. Unfortunately, as we have seen in Sect. 2.1, the restrictive underlying hypotheses (constant volatility, independent increments, Gaussian log-returns, etc…) are questioned by many empirical studies and GARCH models appear as excellent alternative solutions to potentially overcome some well-documented systematic biases associated with the Black and Scholes model.

Hedge Fund Performance Evaluation: A Stochastic Discount Factor Approach

Can Stochastic Discount Factor Models Explain the Cross Section of Equity Returns?

Portfolio Efficiency and Discount Factor Bounds with Conditioning Information: An Empirical Study

Hedge fund strategies, performance &diversification: A portfolio theory & stochastic discount factor approach

Investment Opportunities in Central and Eastern European Equity Markets

Martingalized historical approach for option pricing

We examine the performance of U.K. unit trusts between January 1982 and December 1996 within the stochastic discount factor approach across a wide class of models. No one model dominates the others in correctly pricing passive portfolios or detecting superior performance for hypothetical trading strategies. We find no evidence of significant superior performance by the unit trusts for any model of the stochastic discount factor. Also, the charges of the trust have a mixed effect on trust performance.

Are good-news firms riskier than bad-news firms?

Bond Pricing When the Short Term Interest Rate Follows a Threshold Process

Bond Pricing and Basis Risk when the Short Term Interest Rate Follows a Threshold Process

As shown in the previous section, real estate risk may constitute a priced factor in the framework of the ICAPM. This section reviews the methodological framework used in the empirical analysis of this study. Section 3.1 briefly outlines the asset pricing specifications in the framework of the ICAPM. Section 3.2 reviews the VAR approach to derive innovations in state variables that denote the risk factors in cross-sectional asset pricing tests within the ICAPM. Section 3.3 describes the two asset pricing test methodologies, in particular the traditional beta method and the stochastic discount factor approach.

We assess the profitability of momentum strategies using a stochastic discount factor approach. In unconditional tests, approximately half of the strategies' profitability is explained. In conditional tests we see a further slight decline in profits. We argue that the risk of these strategies should be increasing in the market risk premium. Empirically, while their risk measures estimated relative to the stochastic discount factor behave as predicted, market betas do not; thus capital asset pricing model (CAPM)-like benchmarks may lead to incorrect inferences. Given that our nonparametric risk adjustment explains roughly half of momentum strategy profits, we cannot rule out the possibility of residual mispricing.

Risk Adjustment and Trading Strategies

Hedge Fund Strategies, Performance & Diversification: A Portfolio Theory & Stochastic Discount Factor Approach