A note on relative efficiency and risk aversion

Stochastic dominance rules have recently been suggested as criteria for efficient choice under uncertainty. However, the aspect of relative efficiency has been neglected, i.e., given any specific utility function u₀, find the conditions imposed on F and G such that $\text{E}{}_{\mathrm{F}}\text{u≧E}{}_{\mathrm{G}}\text{u}$ for all u?U (u₀), where U(u₀)={u| ? u′/u′ ≥ ? u″₀/u′₀}. This note suggests a necessary and sufficient condition for relative efficiency in the case that F and G cross other only once. Some applications are discussed.     

Explicit solutions to some single-period investment problems for risky log-stable stocks

Numerical approximations are presented for the expected utility of wealth over a single time period for a small investor who proportions her or his available capital between a risk-free asset and a risky stock. The stock price is assumed to be a log-stable random variable. The utility functional is logarithmic or isoeleastic ($\text{y}{}^{\mathrm{a}}\text{q}$, q < 0). Analytic results are presented for special choices of model parameters, and for large and small time periods.     

R2

Even with hindsight, the ability to explain stock price changes is modest. $R^2$s were calculated for the returns of large stocks as explained by systematic economic influences, by the returns on other stocks in the same industry, and by public firm-specific news events. The average adjusted $R^2$ is only about .35 with monthly data and .20 with daily data. There is little relation between explanatory power and either the firm's size or its industry. There is little improvement in $R^2$ from eliminating all dates surrounding news reports in the financial press. However, the sample kurtosis is quite different when such news events are eliminated, thereby revealing a mixture of return distributions. Non-news dates also indicate the presence of a distributional mixture, perhaps due to traders acting on private information.     

Patterns of Productivity in the Finance Literature: A Study of the Bibliometric Distributions

This study finds a bibliometric regularity in the finance literature that the number of authors publishing n papers is about $1/n^c$ of those publishing one paper. We find that the finance literature conforms very well to the inverse square law $(c=2)$ if data are taken from a large collection of journals. When applied to individual finance journals, we find that values of c range from 1.95 to 3.26. We also find that top-rated journals have higher concentrations among their contributors. This implies that the phenomenon “success breeds success” is more common in higher quality publications.     

Eksamen i Forsikringsvidenskab og Statistik ved Københavns Universitet

Abstract

Let X ₁, X ₂,... be a sequence of independent, identically distributed random variables with P(X?0)=0, and such that pκ = ?₀ ^∞ x ^κ dP(x)<∞, k= 1, 2, 3, 4. Assume that {N(t), t?0} is a Poission stochastic process, independent of the X ₁ with E(N(t))=t. For λ ? 0, let Z _T= max {Σ _t?1 ^N(t) X _t ?t(p ₁+λ)}. Expressions 0 ?t?T for E(Z _T ), E(Z _T ²), and P(Z _T =0) are derived. These results are used to construct an approximation for the finite-time ruin function Ψ(u, T) = P(Z _T >u) for u?0. An alternate method of approximating Ψ(u, T) was presented in [10] by Olof Thorin and exemplified in [11] by Nils Wikstad. One of the purposes of this paper is to compare the two methods for two distributions of claims where the number of claims is a Poisson variate. The paper will also discuss the advantages and disadvantages of the two methods. We will also present a comparison of our approximate figures with the exact figures for the claim distribution      

Assessing Specification Errors in Stochastic Discount Factor Models

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on ${\chi }^2$ statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.     

Assessing Goodness-of-Fit of Asset Pricing Models: The Distribution of the Maximal R2

The development of asset pricing models that rely on instrumental variables together with the increased availability of easily-accessible economic time-series have renewed interest in predicting security returns. Evaluating the significance of these new research findings, however, is no easy task. Because these asset pricing theory tests are not independent, classical methods of assessing goodness-of-fit are inappropriate. This study investigates the distribution of the maximal $R^2$ when k of m regressors are used to predict security returns. We provide a simple procedure that adjusts critical $R^2$ values to account for selecting variables by searching among potential regressors.     

Predictive Regressions: A Present‐Value Approach

We propose a latent variables approach within a present‐value model to estimate the expected returns and expected dividend growth rates of the aggregate stock market. This approach aggregates information contained in the history of price‐dividend ratios and dividend growth rates to predict future returns and dividend growth rates. We find that returns and dividend growth rates are predictable with $R^2$ values ranging from 8.2% to 8.9% for returns and 13.9% to 31.6% for dividend growth rates. Both expected returns and expected dividend growth rates have a persistent component, but expected returns are more persistent than expected dividend growth rates.     

A Theoretical Framework for Evaluating the Impact of Universal Reserve Requirements

This paper provides an appropriate framework to evaluate the impact of the universal reserve requirements called for by the new DIDMC Act of 1980. We derived the optimal reserve ratios for a dual banking system under the objective of controlling the monetary aggregates and the level of output. Then optimal reserve requirements were calculated from illustrative money market and macroeconomic parameters since the usual comparative statics were not useful. The results, generally, suggested optimal reserve ratios which were significantly higher than the old dual or the new universal reserve regimes for all targets. However, the calculation of values for the loss functions under various reserve regimes suggests that attainment of $r_1^{*},r_2^{*}$ and $t^{*}$ may not be imperative, since the discrepancy between losses for optimal and various nonoptimal reserve schemes were not large. A major result of this paper, observed for both monetary and real targets, was that the differences in the instability of the targets for the old dual reserve ratios and the Fed's new universal reserve scheme were small. This result clearly suggests that although the DIDMC Act may solve the Federal Reserve's membership problem, it will not significantly enhance the Fed's effectiveness in controlling monetary or real sector aggregates.     

A new approach to assessing model risk in high dimensions

A central problem for regulators and risk managers concerns the risk assessment of an aggregate portfolio defined as the sum of d individual dependent risks $X_i$. This problem is mainly a numerical issue once the joint distribution of $\left(X_1\text{,}{X}_2\text{,}\dots \text{,}{X}_d\right)$ is fully specified. Unfortunately, while the marginal distributions of the risks $X_i$ are often known, their interaction (dependence) is usually either unknown or only partially known, implying that any risk assessment of the portfolio is subject to model uncertainty.Previous academic research has focused on the maximum and minimum possible values of a given risk measure of the portfolio when only the marginal distributions are known. This approach leads to wide bounds, as all information on the dependence is ignored. In this paper, we integrate, in a natural way, available information on the multivariate dependence. We make use of the Rearrangement Algorithm (RA) of Embrechts et al. (2013) to provide bounds for the risk measure at hand. We observe that incorporating the information of a well-fitted multivariate model may, or may not, lead to much tighter bounds, a feature that also depends on the risk measure used. In particular, the risk of underestimating the Value-at-Risk at a very high confidence level (as used in Basel II) is typically significant, even if one knows the multivariate distribution almost completely.Our results make it possible to determine which risk measures can benefit from adding dependence information (i.e., leading to narrower bounds when used to assess portfolio risk) and, hence, to identify those situations for which it would be meaningful to develop accurate multivariate models.     

Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads

This paper explores the nature of default arrival and recovery implicit in the term structures of sovereign CDS spreads. We argue that term structures of spreads reveal not only the arrival rates of credit events ${(\lambda }^{?})$, but also the loss rates given credit events. Applying our framework to Mexico, Turkey, and Korea, we show that a single‐factor model with ${\lambda }^{?}$ following a lognormal process captures most of the variation in the term structures of spreads. The risk premiums associated with unpredictable variation in ${\lambda }^{?}$ are found to be economically significant and co‐vary importantly with several economic measures of global event risk, financial market volatility, and macroeconomic policy.     

Asset-pricing Tests under Alternative Distributions

Given the normality assumption, we reject the mean-variance efficiency of the Center for Research in Security Prices value-weighted stock index for three of the six consecutive ten-year subperiods from 1926 to 1986. However, the normality assumption is strongly rejected by the data. Under plausible alternative distributional assumptions of the elliptical class, the efficiency can no longer be rejected. When the normality assumption is violated but the ellipticity assumption is maintained, many tests tend to be biased toward overrejection and both the accuracy of estimated beta and $R^2$ are usually overstated.     

American and European options in multi-factor jump-diffusion models,near expiry

We derive a general formula for the time decay θ for out-of-the-money European options on stocks and bonds at expiry, in terms of the density of jumps F(x,dy) and the payoff g ₊: −θ(x)=∫ g(x+y)₊ F(x,dy). Explicit formulas are derived for the standard put and call options, exchange options in stochastic volatility and local volatility models, and options on bonds in ATSMs. Using these formulas, we show that in the presence of jumps, the limit of the no-exercise region for the American option with the payoff (−g)₊ as time to expiry τ tends to 0 may be larger than in the pure Gaussian case. In particular, for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is separated from the strike price by a nonvanishing margin on the interval [0,T), where T is the maturity date.      

A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market

In an efficient market, the fundamental value of a security fluctuates randomly. However, trading costs induce negative serial dependence in successive observed market price changes. In fact, given market efficiency, the effective bid-ask spread can be measured by $\text{Spread}=2\sqrt{?\text{cov}}$ where “cov” is the first-order serial covariance of price changes. This implicit measure of the bid-ask spread is derived formally and is shown empirically to be closely related to firm size.     

Portfolio Inefficiency and the Cross-section of Expected Returns

The Capital Asset Pricing Model implies that (i) the market portfolio is efficient and (ii) expected returns are linearly related to betas. Many do not view these implications as separate, since either implies the other, but we demonstrate that either can hold nearly perfectly while the other fails grossly. If the index portfolio is inefficient, then the coefficients and $R^2$ from an ordinary least squares regression of expected returns on betas can equal essentially any values and bear no relation to the index portfolio's mean-variance location. That location does determine the outcome of a mean-beta regression fitted by generalized least squares.     

Growth Opportunities and Risk-Taking by Financial Intermediaries

We show that growth opportunities which cannot be converted to cash under conditions of financial distress $\left(G_z\right)$ are a critical determinant of an intermediary's choice of risk. Financial institutions in which $G_z$ is a low proportion of total assets will be much more likely to engage in go-for-broke behavior. The model leads to a reevaluation of the effectiveness of several traditional remedies for dealing with banks that take excessive risks such as raising insurance premiums, intervening before capital is depleted, and restricting investment options. The model also has implications about a new approach to the examination of financial intermediaries.