Non-Negativity of Nominal and Real Riskless Rates, Arbitrage Theory, and the Null-Alternative Cash

Pragmatic-world nominal riskless rates are non-negative. However, conventional arbitrage theory has yet to develop a theoretical justification of this phenomenon. – We define the null-alternative cash as an investor holding onto cash and refraining from investment and consumption ("doing nothing"); we use the null-alternative cash to prove that both nominal spot and nominal forward rates are non-negative and that prices of zero-coupon bonds do not increase with increasing maturity. In a positive inflation environment, however, both real spot and real forward rates might well become negative, but prices of zero-coupon bonds still do not increase with increasing maturity. --arbitrage theory,inflation,non-negativity of spot and forward rates,short selling constraints

Some economic remarks on arbitrage theory

Today's primarily mathematically oriented arbitrage theory does not address some economically important aspects of pricing. These are, first, the implicit conjecture that there is 'the' price of a portfolio, second, the exact formulation of no-arbitrage, price reproduction, and positivity of the pricing rule under short selling constraints, third, the explicit assumption of a nonnegative riskless interest rate, and fourth, the connection between arbitrage theory (that is almost universal pricing theory) and special pricing theories. Our article proposes the following answers to the above issues: The first problem can be solved by introducing the notion of 'physical' no-arbitrage, the second one by formulating the concept of 'actively' traded portfolios (that is non-dominated portfolios) and by requiring that there is a minimum price for actively traded portfolios and therefore for every admissible portfolio, and the third one by combining the 'invisible' asset 'cash' with the idea of actively traded portfolios - a riskless asset with a rate of return less than zero can never be actively traded in the presence of cash. Finally, the connection between arbitrage theory and special pricing theories ('law-of-one-price-oriented' and 'utility-oriented' pricing) consists in the fact that special pricing theories merely concretize arbitrage theory using different assumptions. --

Portfolio selection with time constraints and a rational explanation of insufficient diversification and excessive trading

Private investors have limited time available for learning about stocks as they need to divide their time between stock analysis and work. This paper analyzes the influence of learning constraintsin the form of time constraints on portfolio selection and derives both optimal portfolio holdings and time allocation. Under time constraints, rational private investors make portfolio choices similar to those ofi nvestors with bounded rationality, i.e., insufficient diversification and excessive trading. Thus, time constraints offer an alternative, fully rational explanation for these real-world investment phenomena, which have to date been interpreted primarily in the light of behavioral finance. --excessive trading,insufficient diversification,learning,portfolio selection,time constraint

Statistically (optimal) estimators of semivariance: A correction of Josephy-Aczel’s proof

Semivariance is an intuitive risk measure because it concentrates on the shortfall below a target and not on total variation. To successfully use semivariance in practice, however, a statistical estimator of semivariance is needed; Josephy and Aczel provide such an estimator. Unfortunately, they have not correctly proven asymptotic unbiasedness and mean squared error consistency of their estimator since their proof contains a mistake. This paper corrects the computational mistake in Josephy-Aczel’s original proof and, that way, allows researchers and practitioners in the field of downside portfolio selection, hedging, downside asset pricing, risk measurement in a regulatory context, and performance measurement to work with a meaningfully specified downside measure

Empirical Business Valuation and Asset Pricing: An Analysis from an Economic Perspective

Common basis of all empirical accounting-based asset pricing models is their attempt to explain today’s asset prices or returns with accounting characteristics that are observable today. Technically, empirical accounting-based asset pricing is implemented in the literature with a wide variety of statistical methods: regression approaches, method of multiples, and error measures, a fact that results in several problems. First problem Given that regression approaches, method of multiples, and error measures deal with empirical asset pricing, the multitude of conceptually different and non-connected approaches is puzzling and gives rise to two questions: (i) If regression approaches, method of multiples, and error measures are applied empirically, they might lead to vastly different valuation results. Therefore, wouldn’t it be useful to elaborate conceptual similarities and differences between these statistical methods and even find a superordinate category? (ii) With respect to regression approaches, the existing literature uses just a small subset of possible statistical methods for empirical asset pricing, i.e., ordinary least squares, weighted least squares, or quantile regressions. Wouldn’t it be rational to enlarge this subset of regression approaches by using other functions of the residuals, e.g., higher (and not first or second) order of absolute values of residuals or the maximum error? With respect to the method of multiples, wouldn’t it be useful to possess a pricing formula that can integrate different methods of computing means as well as using several accounting figures? With respect to error measures, wouldn’t it be reasonable to have a pricing framework (= objective function) that is consistent with the error measure (= quality assessment). Given these questions, the first objective of this thesis in Chapter II is to analyze which of the existing empirical asset pricing approaches are conceptually similar, i.e., can be summarized to a superordinate category and present statistical methods that can be considered as quasi-natural extensions to existing empirical asset pricing models. Second problem Based on this overview over empirical asset pricing models and the literature, it can be strongly assumed that the chosen factors (numbers and specific selection of explanatory variables) as well as the specific statistical method used (e.g., ordinary least squares regression, quantile regression) have an important influence on the explanatory power of an empirical analysis. Since the only concern of the majority of existing papers is the previously mentioned explanatory power, they can be regarded as dealing with statistical significance of factors/specific statistical methods, whereas the economic relevance is far less analyzed. Since price differences are the decisive aspect of valuation models in practice and not statistical significance, analyzing their economic significance is essential and inevitable. Nobody will pay a higher price for a company just because a specific valuation method produces a high out-of-sample R². Moreover, business decisions should not be based only on whether a p-value passes a specific threshold because statistical significance (p-value) cannot measure the size of an effect or the importance of a result. Therefore, it is the second objective of this thesis in Chapter III to analyze the economic significance of different factors/specific statistical methods. Third problem If, however, different factors/specific statistical methods lead to economically significant differences in value, a model-selection criterion is needed that is based on economic instead of statistical criteria. While arbitrage theory provides a general guideline for economic model evaluation for theoretical asset pricing models (i.e., prices must be a linear function of their future cash flows), empirical asset pricing models do not rely on present values of cash flows, but on assumed relations between accounting characteristics/factor returns and company prices/returns. For that reason, no theoretical guidelines regarding the components of the model exist. In particular, there are neither hints regarding the number and type of explanatory variables nor the specific statistical approach. Given this high need for an economic model evaluation criterion, the third objective of this thesis in Chapter IV is to develop an economic model evaluation criterion and come up with an economic ranking of different empirical models. Fourth problem From the perspective of asset pricing theory such a model evaluation criterion is superfluous because the correct business valuation model is clear: the present value of future cash flows. Practically, forecasts of the future are difficult and, in particular, the determination of discount factors proves problematic. Therefore, it might be better to use a theoretically less convincing but easier applicable model—e.g., use of accounting characteristics—instead of a theoretically superior but inadequately implementable model—present value. However, the superior practicability of existing accounting-based valuations comes at a high cost: a relatively weak foundation in asset pricing theory: (i) Multiples Multiples essentially argue that similar accounting characteristics should result in similar prices. Problems from the perspective of asset pricing theory: While such a valuation statement is intuitive, it is not backed up by asset pricing/arbitrage theory that states: Identical cash flow streams must possess identical prices. In other words, there are three differences between multiples and arbitrage theory. First, accounting characteristics are considered instead of cash flow streams. Second, similar instead of identical positions are examined. Third, one accounting characteristic is regarded as enough to characterize a company completely. (ii) Implementing discounted cash flow models with the help of accounting characteristics In literature, there are discounted cash flow models that use (functions of) accounting figures in order to express cash flows, the horizon value and/or the discount rate. Problems from the perspective of asset pricing theory: Irrespective of the specific inclusion of the accounting characteristics in the discounted cash flow models, they can only serve as an approximation, i.e., the models contain assumptions that do not generally hold in reality. (iii) Empirical accounting-based approaches Empirical accounting-based approaches explain stock prices with the help of accounting characteristics. Problems from the perspective of asset pricing theory: These empirical accounting-based approaches belong to the field of value relevance studies and, thus, are only interested in statistical significance of accounting characteristics, but not economic significance, i.e., they do not derive pricing statements. In principle, the regression coefficients of value relevance studies can also be used to obtain business values. However, valuation differences between different regression approaches are huge and these models have a weak economic backing when contrasted with the economic principle. All these problems underline the trade-off between asset pricing rigor and practicability of models: Present value models are theoretically superior, but their practical implementation in form of constant discount rates and horizon models is far from economically convincing. Accounting-based models are characterized by less asset pricing theory rigor, however, can be implemented without sacrificing much of their theoretical basis. Obtaining better asset pricing models, hence, means either improve the implementation of present value models or the theoretical foundations of accounting-based models. Two reasons favor the improvement of the asset pricing foundation of empirical accounting-based models. On the one hand, the accounting literature so far has not fully exploited the asset pricing potential of accounting-based valuation models: It can be increased visibly without sacrificing practicability. On the other hand, purely empirical models always create a justification problem: Who would pay a higher price for a company because sales multiples result in higher prices than earnings multiples? Who would pay a higher price for a company because a lower discount rate for earnings is used? Who would pay a higher price for a company because an empirical estimation procedure, which possesses a higher R², recommends a higher price than other empirical estimation procedures? Therefore, it is the fourth objective of this thesis in Chapter V to connect the practicability of accounting-based valuation models with the theoretical rigor of asset pricing theory

Asset Pricing on Segmented Markets: A Synthesis, an Extension and an Application to Islamic Financial Markets

The starting point for this thesis was that although Islamic financial assets and Islamic financial intermediaries have grown into relevant players, they are highly dependent on one another since funding of financial intermediaries has typically been achieved through Islamic investment accounts, which are profit-sharing-based contracts and represent 67% of Islamic banks’ funding. This reliance on profit-sharing-based contracts—that do not guarantee fixed interest payments—comes at a cost, namely, the risk that inadequate rates of return could lead to massive withdrawals that may reach systemic proportions and cause concern on the part of supervisory authorities as expressed in IFSB Guidance Note 3, Article 9. Consequently, the main objective of this thesis was to develop an asset pricing (valuation) formula for Islamic financial assets that captures the segmented market nature of financial markets where Islamic banks operate and solves their adequate returns benchmark problem. In the second chapter, we analyzed the cash flows and risks involved in Islamic financial contracts and found in the case of Islamic investment accounts and Sukuk that their cash flows and risks depend on a two-stage structure. On the one hand, their cash flows and risks hinge on their underlying contracts (first stage). Mark-up contracts are able to secure riskless cash flows while profit-sharing contracts are unable to do so. On the other hand, these cash flows are then subject to a number of transformations (second stage) such as smoothing, management fees, reserve creation, and pooling of different investments. These transformations may alter the stochasticity of the cash flows distributed to depositors/Sukuk holders in a sense that individually riskless contracts become slightly risky and individually risky contracts become slightly less risky. In the third chapter, we obtained four main results: First, we successfully derived valuation formulas for all assets available (including Islamic financial assets) on different levels of market segmentation. The required expected return on common assets (Islamic financial assets and Islamic stocks) is computed in an identical way as the classical CAPM with the exception that rather than taking a single riskless rate as the return on riskless assets, a mixture (weighted by the aggregated risk preference parameters of both investor groups) of the riskless rates available to Conventional investors and Islamic investors (assumed to be an interest rate of zero in our model) should be used. The required expected return on the restricted asset class (non-Islamic stocks) consists of a single riskless rate, namely that of the unrestricted group (Conventional investors) plus a risk correction that is based on the risk preferences of the unrestricted group and an additional term that reflects the demand frictions caused by the fact that Islamic investors cannot invest in non-Islamic stocks (a demand-effect term). Second, valuation formulas that contain unobservable quantities (risk preference parameters) and an explicit reference to the riskless rate cannot be used to value Islamic financial assets in practice. Hence, we express the valuation formulas only in market-observable quantities independent of the riskless rate. Using the reformulated valuation formulas, we can show that the valuation for common assets is no longer a linear function of the expected return of the market portfolio as is the case in the classical CAPM; instead, we observe a linear two-factor valuation model for Islamic assets and Islamic stocks. For the restricted assets (non-Islamic stocks), the linear market portfolio structure breaks down completely resulting in a non-linear two-factor model of valuation. Third, statistical significance analysis found that the security market lines of the valuation formulas that overlook the segmented market framework are never identical to those of the theoretically correct valuation formula. For the valuation of specific assets, however, there are exceptions: Assets whose covariance/risk lies exactly at the intersection point of the security market lines for segmented (correct) and unsegmented (incorrect) markets have the same required expected return. We conveniently call this effect of an accidentally correct valuation result even if a wrong valuation formula is used the “double error compensation effect”. Fourth, we test the economic significance, i.e., whether valuation errors from using an incorrect valuation model are large enough to induce economic consequences. For this analysis we use a sample of representative sub-market portfolios as examples of specific assets. We find that the differences in the required expected returns between the theoretically exact segmented model and the unsegmented market model are nearly always economically significant when transaction costs are used as benchmarks. With other benchmarks mixed results are obtained. Finally, in the fourth chapter, we obtained two results. Our first result is that we determine over-, correct, and undervaluation for both short- and long-term using full-sample and a five-year rolling estimation window for 81 Islamic banks in 16 countries. Based on these valuations—second results—we develop recommendation for practical application. On the one hand, a traffic light system for private investors is developed that translates valuation result into withdraw, hold, and deposit funds recommendations. On the other hand, for institutional investors no standardized system like a traffic light system is needed in general because institutional investors are assumed to possess a high degree of financial literacy. Therefore, only the necessary input data required for computations are provided. Only if the regulator is concerned about systemic risk of the Islamic financial system, the regulator might wish to assure that Islamic banks do not invest in overvalued Islamic investment accounts. In that case, a traffic light system might come into play. Finally, since transparency is connected with the reliability of the Islamic financial system, the traffic light system must be reliable as well. Consequently, regulators or central banks publishing the traffic-lights-system should do so periodically and include the valuation on one (web)page because only then comparisons of different banks’ Islamic investment accounts will become possible. Our results have a number of practical implications. The first one relates to empirical research in connection with asset pricing models in general and segmented markets in particular. Our asset pricing formulas show that valuation formulas on segmented markets that consist of observable quantities only comprise at least two market factors. Therefore, required expected returns cannot be determined using regressions that contain just one market factor (even when combined with Fama/French and Carhart factors); instead, at least a second market factor must be integrated into the analysis. Even then, the factor loadings of the segmented markets asset pricing models are not identical to regression coefficients in general. Only if a specific model of asset returns is used, namely asset returns that are a linear function of the return of the market portfolio and another factor that is uncorrelated with the market portfolio’s return, will regression coefficients result (see Errunza/Losq (1985) for such a model). Second, our pricing formulas contain a valuation model for Islamic financial assets that does not contain any reference to the riskless interest rate r, thus, are indeed Shariah-compliant. In other words, Equation (7b) is the asset pricing formula for Islamic financial assets that has been missing in the literature so far. In particular, it offers an alternative valuation of Islamic financial assets that does not rely on mimicking Conventional rates. Hence, it takes into account the criticism of the recent AAIOFI Standard 27 on Indices, Clause 7 as well as decision number 76 (7) of the 8th conference of the International Islamic Fiqh Academy of Saudi Arabia, which took place in Brunei 1993 that Conventional interest rates should not be used as a benchmark for Islamic assets (International Islamic Fiqh Academy, 1993; AAOIFI, 2010: 489). We highlight the notion that a country-wide Islamic returns benchmark is not a very reliable index for valuation since it does not take into consideration the unique risk profile of each individual Islamic asset i, which would result in a unique required expected return for each Islamic financial asset. Third, we provide financial institutions with an alternative to tweaking the returns of profit-sharing products. Consequently, there remains no need to smoothen the returns and mimic those of Conventional deposits and bonds which was done in order to remain competitive or to avoid mass withdrawals by depositors. These return transformation techniques came at a high cost: (i) mimicking the returns of conventional deposits violates the spirit of Shariah conformity (International Islamic Fiqh Academy, 1993; AAOIFI, 2010: 489) and is therefore not sustainable in the long-term; (ii) it exerts additional pressure on the bank by forcing them to meet the returns of Conventional deposits if the returns on actual investments were not high enough; (iii) they give rise to displaced commercial risk which is “the risk arising from assets managed on behalf of IAH (investment account holders) which is effectively transferred to the (bank’s) own capital because the (bank) follows the practice of (smoothing) when it considers this necessary as a result of commercial and/or supervisory pressure” (IFSB GN-3: 3); (iv) smoothing practices have inherent inter-generational reserve problems: Reserves that have been built up in the past and are used today for the benefit of the current investment account holders, who may be different than those who contributed to the reserves in the past; (v) smoothing conceals the actual returns achieved by bank management and removes the ability of regulators and depositors to evaluate the quality of investment management at the bank, (vi) smoothing only hides the problem of fluctuations in the returns of investment accounts from the depositors’ perspective, yet the banks must deal with these fluctuations and must determine the correct amount of smoothing and return transformation to apply. By removing the need for smoothing, transparency regarding Islamic investment accounts can be guaranteed and might help supervisors to monitor the stability of the Islamic financial system. On the one hand, Islamic banks who offer overvalued Islamic investment accounts might be confronted with withdrawal risk in the future or, at least, will have problems getting enough funding in the future. On the other hand, Islamic banks are closely connected since they invest funds in Islamic investment accounts of other banks. A repeated investment in overvalued Islamic investment accounts by some banks might indicate a potentially dangerous investment chain