Restricted maximum likelihood estimation under Eisenhart model Ill

For a balanced two-way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non-negativity requirements of the variance components by L ee and K apadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non-negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.     

Delta-Hedged Gains and the Negative Market Volatility Risk Premium

We investigate whether the volatility risk premium is negativeby examining the statistical properties of delta-hedged optionportfolios (buy the option and hedge with stock). Within a stochasticvolatility framework, we demonstrate a correspondence betweenthe sign and magnitude of the volatility risk premium and themean delta-hedged portfolio returns. Using a sample of S&P500 index options, we provide empirical tests that have thefollowing general results. First, the delta-hedged strategyunderperforms zero. Second, the documented underperformanceis less for options away from the money. Third, the underperformanceis greater at times of higher volatility. Fourth, the volatilityrisk premium significantly affects delta-hedged gains, evenafter accounting for jump fears. Our evidence is supportiveof a negative market volatility risk premium.     

Mean squared error efficient estimators of the variance components

Summary Pseudo Bayesian estimators for the variance components based on Jeffrey’s Rule are derived for the mixed balanced incomplete block design and are compared with the usual analysis of variance estimators in terms of mean squared error (MSE) efficiency. Numerical results show that Pseudo-Bayesian estimators are more efficient in numerical results.     

Minimal sufficient statistics for the group divisible partially balanced incomplete block design (GD-PBIBD) with interaction under an Eisenhart Model II

Summary In this paper, an Eisenmhart Model II with interaction for a GD-PBIB design withp replicates per cell is considered. Specifically the Model Y_ijl=µ+_i+_j+()_ij+e_ijl is assumed, wherei=1, 2, ...,b; j=1, 2, ...,t andl=0, 1, 2, ...p s _ij wheres _ij=1, if treatmentj appears in blocki, 0, otherwise.If _i, _j, ()_ij ande _ijl are normally and independently distributed, then a minimal sufficient (Vector-valued) statistic for the class of densities for this model is found, together with the distribution of each component in the minimal sufficient statistic. It is also shown that the minimal sufficient statistic for this class densities is not complete. Hence the solution of the problem of finding minimum variance unbiased estimators of the variance components is not straightforward.     

Complexity, concentration and contagion

This paper develops a network model of interbank lending in which unsecured claims, repo activity and shocks to the haircuts applied to collateral assume centre stage. We show how systemic liquidity crises of the kind associated with the interbank market collapse of 2007–2008 can arise within such a framework, with funding contagion spreading widely through the web of interlinkages. Our model illustrates how greater complexity and concentration in the financial network may amplify this fragility. The analysis suggests how a range of policy measures – including tougher liquidity regulation, macro-prudential policy, and surcharges for systemically important financial institutions – could make the financial system more resilient.     

Death and jackpot: Why do individual investors hold overpriced stocks?

Campbell, Hilscher, and Szilagyi (2008) show that firms with a high probability of default have abnormally low average future returns. We show that firms with a high potential for default (death) also tend to have a relatively high probability of extremely large (jackpot) payoffs. Consistent with an investor preference for skewed, lottery-like payoffs, stocks with high predicted probabilities for jackpot returns earn abnormally low average returns. Stocks with high death or jackpot probabilities have relatively low institutional ownership and the jackpot effect we find is much stronger in stocks with high limits to arbitrage.     

Limited arbitrage between equity and credit markets

We document that short-horizon pricing discrepancies across firms' equity and credit markets are common and that an economically significant proportion of these are anomalous, indicating a lack of integration between the two markets. Proposing a statistical measure of market integration, we investigate whether equity–credit market integration is related to impediments to arbitrage. We find that time variation in integration across a firm's equity and credit markets is related to firm-specific impediments to arbitrage such as liquidity in equity and credit markets and idiosyncratic risk. Our evidence provides a potential resolution to the puzzle of why Merton model hedge ratios match empirically observed stock-bond elasticities (Schaefer and Strebulaev, 2008) and yet the model is limited in its ability to explain the integration between equity and credit markets (Collin-Dufresne, Goldstein, and Martin, 2001).     

Firm-specific risk and equity market development

We show that the increase in firm-specific risk in the US stock market is the result of new listings by riskier companies. In addition, our results explain why prior researchers have found that growth opportunities, profit margin, firm size, and industry composition (among other factors) are related to increases in firm-specific risk. The new listing effect is not driven by small companies becoming riskier but instead by a riskier sub-sample of the economy becoming publicly traded. These results are consistent with prior research that documents time trends in financial market development.     

Do idiosyncratic jumps matter?

We show that idiosyncratic jumps are a key determinant of mean stock returns from both an ex post and ex ante perspective. Ex post, the entire annual average return of a typical stock accrues on the four days on which its price jumps. Ex ante, idiosyncratic jump risk earns a premium: a value-weighted weekly long-short portfolio that buys (sells) stocks with high (low) predicted jump probabilities earns annualized mean returns of 9.4% and four-factor alphas of 8.1%. This strategy’s returns are larger when there are greater limits to arbitrage. These results are consistent with investor aversion to idiosyncratic jump risk.