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Concept# Average

Résumé

In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often given as the median—the number below which are 50% of personal incomes and above which are 50% of personal incomes—because the mean would be higher by including personal incomes from a few billionaires. For this reason, it is recommended to avoid using the word "average" when discussing measures of central tendency.
General properties
If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each of the many types of average.
Another universal property is monotonicity: if two lists of numbers A and

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In this thesis, we treat robust estimation for the parameters of the Ornstein–Uhlenbeck process, which are the mean, the variance, and the friction. We start by considering classical maximum likelihood estimation. For the simulation study, where we also investigate the choice of the time lag, we use the method of moment (MoM) estimator as initial estimator for the friction parameter of the maximum likelihood estimator (MLE). However, in several aspects the MLE is not robust. For robustification, we first derive elementary M-estimates by extending the method of M-estimation from Huber (1981). We use an intuitively robustified MoM estimate as initial estimate and compare by means of simulation the M-estimate with the MLE. This approach is, however, only ad-hoc since Huber’s minimum Fisher information and minimax asymptotic variance theory remains incomplete for simultaneous location and scale, and does not cover more general models (as for example the Ornstein–Uhlenbeck process). A more general robustness concept due to Kohl et al. (2010), Rieder (1994), and Staab (1984) is based on local asymptotic normality (LAN), asymptotically linear (AL) estimates, and shrinking neighborhoods. We then apply this concept to the Ornstein–Uhlenbeck process. As a measure of robustness, we consider the maximum asymptotic mean square error (maxasyMSE), which is determined by the influence curve (IC) of AL estimates. The IC represents the standardized influence of an individual observation on the estimator given the past. For two kind of neighborhoods (average and average square neighborhoods) we obtain optimally robust ICs. In case of average neighborhoods, their graph exhibits surprising, redescending behavior. For average square neighborhoods the graph is between the one of the elementary M-estimates and the MLE. Finally, we discuss the estimator construction, that is, the problem of constructing an estimator from the family of optimal ICs. We carry out in our context the One-Step construction dating back to LeCam and use both an intuitively robustified MoM estimate and the elementary M-estimate as initial estimate. This results in optimally AL estimates (for average and average square neighborhoods). By means of simulation we then compare the different estimators: MLE, elementary M-estimates, and optimally AL estimates. In addition, we give an application to electricity prices.

Christoph Helmut Peter Herpfer

This thesis contains four chapters, each of which utilizes new or unusual data sources to analyze a different area of financial economics. In the first chapter, I construct a novel dataset linking individual bankers to large borrowers in the U.S. syndicated loan market to analyze the impact of bankers on bank lending. I find that time invariant banker fixed effects have at least as much explanatory power as bank fixed effects across key loan outcome variables. One channel through which bankers impact lending is through personal relationships with borrowers. I address the endogenous nature of relationship formation by exploiting shocks to relationships from the departure of bankers and find that stronger personal relationships are associated with significantly lower interest rates charged to clients. Reduced interest rates of relationship loans reflect superior information of bankers, rather than nepotism. Loans issued by bankers that have stronger personal relationships with borrowers are associated with fewer bankruptcies and no more beneficial terms upon renegotiation. The second chapter, which is joint work with Stefano Colonnello, exploits a U.S. Supreme Court ruling on diversity of citizenship in legal disputes to estimate the contribution of the court system to firm value. In an event study, we find that an increase in state court quality from bottom to top tercile is associated with an average increase in equity value of 0.45%, or about $8.7 million on the event day. This effect appears to be driven by courts¿ attitude towards businesses more than by their competency and is more pronounced for firms in industries with high litigation risk. We also test whether firms benefit from the ability to steer lawsuits into friendly courts, so called forum shopping. We provide evidence that a reduction in firms¿ ability to forum shop decreases firm value, whereas a reduction in plaintiffs¿ ability to forum shop increases firm value. We further document that the ruling had significant real effects. Firms which previously stayed out of regions with potentially problematic courts subsequently increased their operations in those regions. The third chapter is coauthored with Matthias Effing, Rüdiger Fahlenbrach, and Philipp Krüger and examines the impact of a sudden home currency appreciation on the valuation and behavior of corporations in a developed economy. The Swiss National Bank surprisingly repealed the minimum exchange rate of 1.2 Swiss francs per Euro on January 15, 2015. On that day the franc appreciated by 15% and the main stock market index dropped by 8.7%. The impact was largest for export oriented firms with high domestic costs. These firms experienced 5% lower announcement returns, subsequently faced economically sizeable reductions in sales and profitability, and responded by reducing investment by 8.1% while only slightly reducing employment. In the fourth chapter, which is joint work with Cornelius Schmidt and Aksel Mjøs, we exploit exogenous shocks to the distance between corporate borrowers and banks to analyze the role of distance in commercial bank lending. We find that a reduction in travel time due to improved infrastructure increases the likelihood of initiating a new borrowing relationship, evidence that closer distance creates a surplus from lower transaction costs. In existing lending relationships, however, banks capture a fraction of this surplus by increasing interest rates.

In the first chapter of this thesis, I empirically show that the time delay firms face in raising outside capital affects cash holdings. I exploit the 2005 US Securities Offering Reform (the Reform) as a quasi-natural experiment. For a subset of large public US firms, the Reform relaxed the requirement to undergo the standard review process with the Securities and Exchange Commission (SEC) before raising new public capital, leading to a reduction in regulatory delay of approximately 1-1.5 months on average and exceeding half a year in extreme cases. Difference-in-differences estimates based on the event suggest a causal channel from time delay to cash holdings. Over the course of the year following the Reform, affected firms reduced their cash holdings by approximately 2-3% as a fraction of book assets relative to unaffected control-group firms. As predicted by theory, the effect is strongest among firms in cash flow volatile industries. The second chapter investigates whether seasoned equity offerings (SEOs) are accompanied by price pressure effects that models of investor inattention and slow-moving capital predict. In line with theoretical predictions, I find that the share prices of issuing firms exhibit a drop in the pre-offer week, and a positive trend in the first four to eight weeks thereafter. The pattern is systematically related to the size of an offering and to measures of the amount of attention the issuing firm receives by market participants. The resulting costs to the issuing firm are on the order of 2% as a fraction of offer proceeds for the average firm, and nearly twice as large for the tercile of firms issuing the largest quantities of illiquid stock. The price impact is so sizable and long-lasting that simple monthly trading strategies that purchase SEO stocks in the first calendar month after an offering yield monthly five-factor alphas exceeding 1.5 percentage points. The abnormal returns are most pronounced in periods of low aggregate stock market liquidity, as measured by the Pástor and Stambaugh (2003) liquidity index. The results are consistent with the interpretation that the return pattern represents a compensation to temporary liquidity providers, who require the largest compensation during periods in which funding liquidity is scarce. The third chapter is joint work with Cornelius Schmidt from the University of Lausanne. We propose a novel setting to test how the presence of attention constraints affects stock prices. Our setting exploits the particular industry exposure of vertically integrated firms. Because of inter-segment sales of goods, the relative size of individual segments within such firms, in an accounting sense, is a misleading indicator for the firm's overall exposure to industry shocks. We hypothesize that attention constrained investors will tend to neglect this detail, leading to systematic pricing mistakes after confounding, industry-specific news shocks. In line with this hypothesis, we find evidence of predictable price corrections in post-news periods – in particular in the time around firms' earnings announcements. A fully implementable long-short equity strategy based on the phenomenon leads to significant risk-adjusted excess returns. Security analysts' earnings forecasts exhibit a predictable error in the same direction as stock prices.