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arXiv2011

The efficient index hypothesis and its implications in the BSM model

This note studies the behavior of an index I_t which is assumed to be a tradable security, to satisfy the BSM model dI_t/I_t = μdt + σdW_t, and to be efficient in the following sense: we do not expect a prespecified trading strategy whose value is almost surely always nonnegative to outperform the index greatly. The efficiency of the index imposes severe restrictions on its growth rate; in particular, for a long investment horizon we should have μ\approx r+σ^2, where r is the interest rate. This provides another partial solution to the equity premium puzzle. All our mathematical results are extremely simple.

q-fin.GN↗

arXiv2011

Okun's law revisited. Is there structural unemployment in developed countries?

Okun's law for the biggest developed countries is re-estimated using the most recent data on real GDP per capita and the rate of unemployment. Our results show that the change in unemployment rate can be predicted with a high accuracy. The link needs the introduction of a structural break which might be caused by the change in monetary policy or/and in measurement units. Statistically, the link between the studied variables is characterized by the coefficient of determination between 0.40 (Australia) and 0.84 (the USA). The residual errors can be associated with measurement errors. The obtained results suggest the absence of structural unemployment in the studied developed countries.

q-fin.GN↗

arXiv2011

Employment, unemployment and real economic growth

We have modeled the employment/population ratio in the largest developed countries. Our results show that the evolution of the employment rate since 1970 can be predicted with a high accuracy by a linear dependence on the logarithm of real GDP per capita. All empirical relationships estimated in this study need a structural break somewhere between 1975 and 1995. Such breaks might be caused by revisions to monetary policy (e.g. inflation targeting) or/and changes in measurement units. Statistically, the link between measured and predicted rate of employment is characterized by the coefficient of determination from 0.84 (Australia) to 0.95 (Japan). The model residuals are likely to be associated with measurement errors.

q-fin.GN↗

arXiv2011

The Food Crises: A quantitative model of food prices including speculators and ethanol conversion

Recent increases in basic food prices are severely impacting vulnerable populations worldwide. Proposed causes such as shortages of grain due to adverse weather, increasing meat consumption in China and India, conversion of corn to ethanol in the US, and investor speculation on commodity markets lead to widely differing implications for policy. A lack of clarity about which factors are responsible reinforces policy inaction. Here, for the first time, we construct a dynamic model that quantitatively agrees with food prices. The results show that the dominant causes of price increases are investor speculation and ethanol conversion. Models that just treat supply and demand are not consistent with the actual price dynamics. The two sharp peaks in 2007/2008 and 2010/2011 are specifically due to investor speculation, while an underlying upward trend is due to increasing demand from ethanol conversion. The model includes investor trend following as well as shifting between commodities, equities and bonds to take advantage of increased expected returns. Claims that speculators cannot influence grain prices are shown to be invalid by direct analysis of price setting practices of granaries. Both causes of price increase, speculative investment and ethanol conversion, are promoted by recent regulatory changes---deregulation of the commodity markets, and policies promoting the conversion of corn to ethanol. Rapid action is needed to reduce the impacts of the price increases on global hunger.

q-fin.GN↗

arXiv2011

The Capital Asset Pricing Model as a corollary of the Black-Scholes model

We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is efficient, in the following sense: we do not expect a prespecified self-financing trading strategy whose wealth is almost surely nonnegative at all times to outperform the index greatly. We show that, for a long investment horizon, the appreciation rate of the stock has to be close to the interest rate (assumed constant) plus the covariance between the volatility vectors of the stock and the index. This contains both a version of the Capital Asset Pricing Model and our earlier result that the equity premium is close to the squared volatility of the index.

q-fin.PM↗

arXiv2015

Dynamic Model of Markets of Homogenous Non-Durable

A new microeconomic model is presented that aims at a description of the long-term unit sales and price evolution of homogeneous non-durable goods in polypoly markets. It merges the product lifecycle approach with the price dispersion dynamics of homogeneous goods. The model predicts a minimum critical lifetime of non-durables in order to survive. Under the condition that the supply side of the market evolves much faster than the demand side the theory suggests that unsatisfied demands are present in the first stages of the lifecycle. With the growth of production capacities these demands disappear accompanied with a logistic decrease of the mean price of the good. The model is applied to electricity as a non-durable satisfying the model condition. The presented theory allows a deeper understanding of the sales and price dynamics of non-durables.

stat.AP↗

arXiv2011

Pricing stocks with yardsticks and sentiments

Human decision making by professionals trading daily in the stock market can be a daunting task. It includes decisions on whether to keep on investing or to exit a market subject to huge price swings, and how to price in news or rumors attributed to a specific stock. The question then arises how professional traders, who specialize in daily buying and selling large amounts of a given stock, know how to properly price a given stock on a given day? Here we introduce the idea that people use heuristics, or "rules of thumb", in terms of "yard sticks" from the performance of the other stocks in a stock index. The under- /over-performance with respect to such a yard stick then signifies a general negative/positive sentiment of the market participants towards a given stock. Using empirical data of the Dow Jones Industrial Average, stocks are shown to have daily performances with a clear tendency to cluster around the measures introduced by the yard sticks. We illustrate how sentiments, most likely due to insider information, can influence the performance of a given stock over period of months, and in one case years.

q-fin.GN↗

arXiv2011

Identification of Demand through Statistical Distribution Modeling for Improved Demand Forecasting

Demand functions for goods are generally cyclical in nature with characteristics such as trend or stochasticity. Most existing demand forecasting techniques in literature are designed to manage and forecast this type of demand functions. However, if the demand function is lumpy in nature, then the general demand forecasting techniques may fail given the unusual characteristics of the function. Proper identification of the underlying demand function and using the most appropriate forecasting technique becomes critical. In this paper, we will attempt to explore the key characteristics of the different types of demand function and relate them to known statistical distributions. By fitting statistical distributions to actual past demand data, we are then able to identify the correct demand functions, so that the the most appropriate forecasting technique can be applied to obtain improved forecasting results. We applied the methodology to a real case study to show the reduction in forecasting errors obtained.

stat.AP↗

arXiv2011

Quis pendit ipsa pretia: facebook valuation and diagnostic of a bubble based on nonlinear demographic dynamics

We present a novel methodology to determine the fundamental value of firms in the social-networking sector based on two ingredients: (i) revenues and profits are inherently linked to its user basis through a direct channel that has no equivalent in other sectors; (ii) the growth of the number of users can be calibrated with standard logistic growth models and allows for reliable extrapolations of the size of the business at long time horizons. We illustrate the methodology with a detailed analysis of facebook, one of the biggest of the social-media giants. There is a clear signature of a change of regime that occurred in 2010 on the growth of the number of users, from a pure exponential behavior (a paradigm for unlimited growth) to a logistic function with asymptotic plateau (a paradigm for growth in competition). We consider three different scenarios, a base case, a high growth and an extreme growth scenario. Using a discount factor of 5%, a profit margin of 29% and 3.5 USD of revenues per user per year yields a value of facebook of 15.3 billion USD in the base case scenario, 20.2 billion USD in the high growth scenario and 32.9 billion USD in the extreme growth scenario. According to our methodology, this would imply that facebook would need to increase its profit per user before the IPO by a factor of 3 to 6 in the base case scenario, 2.5 to 5 in the high growth scenario and 1.5 to 3 in the extreme growth scenario in order to meet the current, widespread, high expectations. To prove the wider applicability of our methodology, the analysis is repeated on Groupon, the well-known deal-of-the-day website which is expected to go public in November 2011. The results are in line with the facebook analysis. Customer growth will plateau. By not taking this fundamental property of the growth process into consideration, estimates of its IPO are wildly overpriced.

q-fin.GN↗

arXiv2011

Integration and Contagion in US Housing Markets

This paper explores integration and contagion among US metropolitan housing markets. The analysis applies Federal Housing Finance Agency (FHFA) house price repeat sales indexes from 384 metropolitan areas to estimate a multi-factor model of U.S. housing market integration. It then identifies statistical jumps in metropolitan house price returns as well as MSA contemporaneous and lagged jump correlations. Finally, the paper evaluates contagion in housing markets via parametric assessment of MSA house price spatial dynamics. A R-squared measure reveals an upward trend in MSA housing market integration over the 2000s to approximately .83 in 2010. Among California MSAs, the trend was especially pronounced, as average integration increased from about .55 in 1997 to close to .95 in 2008! The 2000s bubble period similarly was characterized by elevated incidence of statistical jumps in housing returns. Again, jump incidence and MSA jump correlations were especially high in California. Analysis of contagion among California markets indicates that house price returns in San Francisco often led those of surrounding communities; in contrast, southern California MSA house price returns appeared to move largely in lock step. The high levels of housing market integration evidenced in the analysis suggest limited investor opportunity to diversify away MSA-specific housing risk. Further, results suggest that macro and policy shocks propagate through a large number of MSA housing markets. Research findings are relevant to all market participants, including institutional investors in MBS as well as those who regulate housing, the housing GSEs, mortgage lenders, and related financial institutions.

q-fin.GN↗

arXiv2011

A framework for analyzing contagion in banking networks

A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between banks, the possibility of disassortative edge probabilities (an above average tendency for small banks to link to large banks) is explicitly incorporated. We give a probabilistic analysis of the default cascade triggered by shocking the network. We find that the cascade can be understood as an explicit iterated mapping on a set of edge probabilities that converges to a fixed point. A cascade condition is derived that characterizes whether or not an infinitesimal shock to the network can grow to a finite size cascade, in analogy to the basic reproduction number $R_0$ in epidemic modeling. It provides an easily computed measure of the systemic risk inherent in a given banking network topology. An analytic formula is given for the frequency of global cascades, derived from percolation theory on the random network. Two simple examples are used to demonstrate that edge-assortativity can have a strong effect on the level of systemic risk as measured by the cascade condition. Although the analytical methods are derived for infinite networks, large-scale Monte Carlo simulations are presented that demonstrate the applicability of the results to finite-sized networks. Finally, we propose a simple graph theoretic quantity, which we call "graph-assortativity", that seems to best capture systemic risk.

q-fin.GN↗

arXiv2011

Fundamental Measurements in Economics and in the Theory of Consciousness

A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. Elementary (indivisible) technology, in which the object's consumer values are variable, in this case can be formalized as a generalized economic measurement. The algebra of such measurements has been constructed. It has been shown that in the general case the quantum-mechanical formalism of the theory of selective measurements is required for description of such conditions. The economic analogs of the elementary slit experiments in physics have been created. The proposed approach can be also used for consciousness modeling.

physics.gen-ph↗

arXiv2011

Fundamental Measurements in Economics and in the Theory of Consciousness (Manifestation of quantum-mechanical properties of economic objects in slit measurements)

A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were also able to obtain the classical interpretation of the quantum-mechanical law of addition of probabilities by introducing a number of new notions. The principle of "local equity" assumes the transaction completed (regardless of the result) of the states of transaction partners are not changed in connection with the reception of new information on proposed offers or adopted decisions (consent or refusal of the transaction). However it has no relation to the paradoxes of quantum theory connected with non-local interaction of entangled states. In the economic systems the mechanism of entangling has a classical interpretation, while the quantum-mechanical formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness.

physics.gen-ph↗

arXiv2011

Entrepreneurship: what's happening?

Much has been said lately about entrepreneurship, so it seems important to leave here some personal analysis on this topic. The issues outlined here result from a work in about a year in which because a personal and professional obligations it was doing some research on these issues. This is an interesting topic that has not yet expired and on which there is much to research, do it is an area where there are many challenges.

q-fin.GN↗

arXiv2011

Entrepreneurship: some considerations

In this work it is presented some considerations about entrepreneurship. Most of these questions are linked with Portuguese context. Portugal has some particularities, namely because the asymmetries between the littoral and the interior. This situation carried out some problems that complicate and prevent the appearance of new innovated business. In a situation of crisis like that we have today this context can become a really problem to solve some questions.

q-fin.GN↗

arXiv2011

Agglomeration and Interregional Mobility of Labor in Portugal

The aim of this paper is to analyze the relationship between inter-industry, intra-industry and inter-regional clustering and demand for labor by companies in Portugal. Is expected at the outset that there is more demand for work where the agglomeration is greater. It should be noted, as a summary conclusion, the results are consistent with the theoretical developments of the New Economic Geography, namely the demand for labor is greater where firms are better able to cluster that is where transport costs are lower and where there is a strong links "backward and forward" and strong economies of agglomeration.

q-fin.GN↗

arXiv2011

The Importance of Increasing Returns to Scale in the Process of Agglomeration in Portugal: A Non-linear Empirical Analysis

With this work we try to analyse the agglomeration process in the Portuguese regions, using the New Economic Geography models. In these models the base idea is that where has increasing returns to scale in the manufactured industry and low transport costs, there is agglomeration. Of referring, as summary conclusion, that with this work the existence of increasing returns to scale and low transport cost, in the Portuguese regions, was proven and as such the existence of agglomeration in Portugal.

q-fin.GN↗

arXiv2011

The Verdoorn Law in the Portuguese Regions: A Panel Data Analysis

This work aims to test the Verdoorn Law, with the alternative specifications of (1)Kaldor (1966), for five regions (NUTS II) Portuguese from 1986 to 1994 and for the 28 NUTS III Portuguese in the period 1995 to 1999. Will, therefore, to analyze the existence of increasing returns to scale that characterize the phenomena of polarization with circular and cumulative causes and can explain the processes of regional divergence. It is intended to test, even in this work, the alternative interpretation of (2)Rowthorn (1975) Verdoorn's Law for the same regions and periods. The results of this work will be complemented with estimates of these relationships to other sectors of the economy than the industry (primary and services sector), for each of the manufacturing industries operating in the Portuguese regions and for the total economy of each region (3)(Martinho, 2011).

q-fin.GN↗