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Abstract: Abstract In this paper, we focus on the farmer’s risk income when using commodity futures, when price and output processes are randomly correlated and represented by jump-diffusion models. We evaluate the expected utility of the farmer’s wealth and determine the optimal consumption rate and hedging position at each point in time given the harvest timing and state variables. We find a closed form for the optimal consumption and positioning rate in the case of an investor with CARA utility. This result (see Table 3.3) is a generalization of the result of Ho (J Financ 39:351–376, 1984), which considers the special case in which price and output are diffusion models. PubDate: 2022-05-02
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Abstract: Abstract This paper challenges the use of stocks in portfolio construction, instead we demonstrate that Asian derivatives, straddles, or baskets could be more convenient substitutes. Our results are obtained under the assumptions of the Black–Scholes–Merton setting, uncovering a hidden benefit of derivatives that complements their well-known gains for hedging, risk management, and to increase utility in market incompleteness. The new insights are also transferable to more advanced stochastic settings. The analysis relies on the infinite number of optimal choices of derivatives for a maximized expected utility theory agent; we propose risk exposure minimization as an additional optimization criterion inspired by regulations. Working with two assets, for simplicity, we demonstrate that only two derivatives are needed to maximize utility while minimizing risky exposure. In a comparison among one-asset options, e.g. American, European, Asian, Calls and Puts, we demonstrate that the deepest out-of-the-money Asian products available are the best choices to minimize exposure. We also explore optimal selections among straddles, which are better practical choice than out-of-the-money Calls and Puts due to liquidity and rebalancing needs. The optimality of multi-asset derivatives is also considered, establishing that a basket option could be a better choice than one-asset Asian call/put in many realistic situations. PubDate: 2022-04-28
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Abstract: Abstract This paper studies the general relationship between the gearing ratio of a Leveraged ETF and its corresponding expense ratio, viz., the investment management fees that are charged for the provision of this levered financial service. It must not be possible for an investor to combine two or more LETFs in such a way that his (continuously-rebalanced) LETF portfolio can match the gearing ratio of a given, professionally managed product and, at the same time, enjoy lower weighted-average expenses than the existing LETF. Given a finite set of LETFs that exist in the marketplace, I give necessary and sufficient conditions for these products to be undominated in the price-gearing plane. In an application of the duality theorem of linear programming, I prove a kind of two-fund theorem for LETFs: given a target gearing ratio for the investor, the cheapest way to achieve it is to combine (uniquely) the two nearest undominated LETF products that bracket it on the leverage axis. This also happens to be the implementation with the lowest annual turnover. For completeness, we supply a second proof of the Main Theorem on LETFs that is based on Carathéodory’s theorem in convex geometry. Thus, say, a triple-leveraged (“UltraPro”) exchange-traded product should never be mixed with cash, if the investor is able to trade in the underlying index. In terms of financial innovation, our two-fund theorem for LETFs implies that the introduction of new, undominated 2.5 \(\times \) products would increase the welfare of all investors whose preferred gearing ratios lie between 2 \(\times \) (“Ultra”) and 3 \(\times \) (“UltraPro”). Similarly for a 1.5x product. PubDate: 2022-04-12
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Abstract: Abstract This paper develops a model for optimal portfolio allocation for an investor with quantile preferences, i.e., who maximizes the \(\tau \) -quantile of the portfolio return, for \(\tau \in (0,1)\) . Quantile preferences allow to study heterogeneity in individuals’ portfolio choice by varying the quantiles, and have a solid axiomatic foundation. Their associated risk attitude is captured entirely by a single dimensional parameter (the quantile \(\tau \) ), instead of the utility function. We formally establish the properties of the quantile model. The presence of a risk-free asset in the portfolio produces an all-or-nothing optimal response to the risk-free asset that depends on investors’ quantile preference. In addition, when both assets are risky, we derive conditions under which the optimal portfolio decision has an interior solution that guarantees diversification vis-à-vis fully investing in a single risky asset. We also derive conditions under which the optimal portfolio decision is characterized by two regions: full diversification for quantiles below the median and no diversification for upper quantiles. These results are illustrated in an exhaustive simulation study and an empirical application using a tactical portfolio of stocks, bonds and a risk-free asset. The results show heterogeneity in portfolio diversification across risk attitudes. PubDate: 2022-03-29
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Abstract: Abstract We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical experiments in order to gauge the accuracy of our approximation. PubDate: 2022-03-11
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Abstract: Abstract We investigate whether and how strongly Basel 3 chief innovations jointly affected in different ways individual Eurozone banks’ stability (z-score) across six business models (BMs). We study this issue in the initial years when adaptation was most intense (2011–2014) and the Eurozone underwent a phase with sovereign crises abated by ECB policies easing financial conditions. In parallel, we run this exercise over 2000–2010 data, a time frame over which Basel 3 did not apply yet to see through the eyes of the regulator. Irrespective of BMs, we identify the leverage ratio as the most effective driver of banks’ stability. However, the impact on z-score of Basel 3 chief drivers does not seem to differ significantly on 2011–2014 vs. 2000–2010. Next, interactions with banks’ BMs suggest that Basel 3 innovations improve z-scores the most at traditionally focused banks (cooperative and savings banks), vis-à-vis diversified banks. Our results suggest Basel regulatory decisions were questionable. First, the front loading of the increased minimum capital requirements vs. the backloading of the leverage ratio phasing in may have lured banks from credit to financial assets. Second, our findings support the desirability of revising the current “one-size-fits-all” European prudential framework, which disregards BMs. PubDate: 2022-03-02 DOI: 10.1007/s10436-021-00406-3
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Abstract: Abstract Microlending, where a bank lends to a small group of people without credit histories, began with the Grameen Bank in Bangladesh, and is widely seen as the creation of Muhammad Yunus, who received the Nobel Peace Prize in recognition of his largely successful efforts. Since that time the modeling of microlending has received a fair amount of academic attention. One of the issues not yet addressed in full detail, however, is the issue of the size of the group. Some attention has nevertheless been paid using an experimental and game theory approach. We, instead, take a mathematical approach to the issue of an optimal group size, where the goal is to minimize the probability of default of the group. To do this, one has to create a model with interacting forces, and to make precise the hypotheses of the model. We show that the original choice of Muhammad Yunus, of a group size of five people, is, under the right, and, we believe, reasonable hypotheses, either close to optimal, or even at times exactly optimal, i.e., the optimal group size is indeed five people. PubDate: 2022-03-01
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Abstract: Abstract This paper studies the asset allocation problem for a retiree facing longevity risk and living standard risk. We introduce a risk capacity constraint to reduce the living standard risk in the retirement period. Whether the retiree focuses on intertemporal consumption or inheritance wealth, we demonstrate a unique number to measure the expected lump sum of the spending post-retirement. The optimal portfolio is nearly neutral to the stock market movement if the portfolio’s value is higher than this critical value; otherwise, the retiree actively invests in the stock market. As a comparison, we consider a dynamic leverage constraint and show that the corresponding optimal portfolio would lose significantly in stressed markets. PubDate: 2022-01-31 DOI: 10.1007/s10436-021-00404-5
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Abstract: Abstract This paper analyzes the relation between commodity spot, forward prices, and convenience yield under incomplete markets. Since production is a necessary process for commodity markets, we include firms that use inputs and produce outputs in our model. Thus, we show a financial pricing model of spot and forward commodity in an explicit fashion with production under incomplete markets. One of the most important results of this paper is the difference between commodity spot and forward equilibrium price can be explained by the discounted shadow price of storage constraint minus the discounted marginal storage cost and it can be interpreted as the net convenience yield in the existing literature. Here the discounted factor is affected by the incompleteness of the markets. We prove the generic existence of the equilibrium and thus the obtained spot forward price relation is the equilibrium price formula. We also derive the firm’s optimal production plan and trading strategy. PubDate: 2022-01-17 DOI: 10.1007/s10436-021-00402-7
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Abstract: Abstract This paper focuses on valuing R&D projects using a twofold compound real option by including two knock-out barriers. However, the valuation of R&D projects is not a simple task, since they are characterised by various risks and sequential decision-making. Specifically, we embed a double-barrier in the multi-stage real option in order to mitigate the risk of huge losses for the investor. In this way, our model incorporates the opportunity to abandon a project if its profitability falls below a benchmark level. We contribute to the existing literature in these ways: first we present a closed formula that allows evaluating this kind of project assuming the technical uncertainty of each research phase; secondly, we consider the scenario in which the volatility and the interest rate are both stochastic. Finally, we provide an application for a wind farm case. PubDate: 2022-01-08 DOI: 10.1007/s10436-021-00403-6
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Abstract: Abstract We study the behavior of permutation-weighted portfolios, portfolios with weights that are proportional to a permutation of the current market weights. For markets with more than two assets, these portfolios are not functionally generated (except for the identity permutation), so we use rank-based methods to analyze their behavior. The reverse-wighted portfolio is the permutation-weighted portfolio with weights proportional to the market weights, but reversed by rank. We show that in a market represented by a first-order model with rank-symmetric variance parameters, the reverse-weighted portfolio will outperform the market portfolio over the long term. This result carries over to a commodity futures market with rank-based parameters similar to those of such a first-order model. In this market we find that the reverse-weighted portfolio outperforms the price-weighted market portfolio from 1977–2018. PubDate: 2022-01-03 DOI: 10.1007/s10436-021-00401-8
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Abstract: Abstract This paper investigates the effect of model uncertainty on the performance of commodity-based portfolios. We consider a constant relative risk aversion (CRRA) utility maximizer investor in a complete market, with independent ambiguity-aversion levels for the three factors explaining the term structure of future prices, namely, spot prices, convenience yield (CY) and interest rates (IRs), as proposed in the seminal work of Schwartz (J Finance 52(3): 923–973, 1997). This generic investor is interested in the speculative component of the investment rather than possessing/consuming the physical commodity. We obtain closed-form solutions for optimal investments, optimal perturbations (alternative model) and value functions in line with the robust portfolio setting of Maenhout (Rev Financial Stud 17(4): 951–983, 2004). Our main focus is on the effect of convenience yield’s uncertainty on the optimal analysis. We estimate the model by applying a combination of maximum likelihood estimation (MLE) and Kalman Filter (KF) techniques, to two commodities: West Texas Intermediate (WTI) and copper future prices. The analysis demonstrates that uncertainty on the CY factor could be the largest contributor to the under-performance of a commodities portfolio, with wealth equivalent losses (WELs) in the ranges of 33% to 88% (WTI), and 7% to 31% (copper). Moreover, small variations, of up 25%, on CY’s covariance parameters could lead to a WEL of up to 40% (WTI, lesser volatility of CY). PubDate: 2021-12-01 DOI: 10.1007/s10436-021-00393-5
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Abstract: Abstract We study the consequences and optimal design of bank deposit insurance and reinsurance in a general equilibrium setting. The model involves two production sectors, financed by bonds and bank loans, respectively. Financial intermediation by banks is required in the model as we assume that one of the production sectors is risky and requires monitoring by banks. Households fund banks through deposits and equity. Deposits are explicitly insured and banks pay a premium per unit of deposits. Any remaining shortfall is implicitly guaranteed by the government. Two types of equilibria emerge: One type of equilibria supports the Pareto optimal allocation. In the other type, bank lending and the default risk are excessively large. The intuition is as follows: the combination of financial intermediation by banks, limited liability of bank shareholders, and deposit insurance makes deposits risk-free from the individual households’ perspective, although they involve risk from the societal point of view. This distorts investment choices and the resulting input allocation to production sectors. We show, however, that a judicious combination of deposit insurance and reinsurance eliminates all non-optimal equilibrium allocations. Our paper thus may provide a benchmark result for policy proposals advocating deposit insurance cum reinsurance. PubDate: 2021-12-01 DOI: 10.1007/s10436-021-00387-3
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Abstract: Abstract In this paper, we introduce and analyze the fractional Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. The proposed model is based upon two desirable properties of the long-term variance process suggested by the empirical data: long-term memory and jumps. The proposed model incorporates the long-term memory and positive autocorrelation properties of fractional Brownian motion with \(H>1/2\) , and the jump properties of the BN-S model. We find arbitrage-free prices for variance and volatility swaps for this new model. Because fractional Brownian motion is still a Gaussian process, we derive some new expressions for the distributions of integrals of continuous Gaussian processes as we work towards an analytic expression for the prices of these swaps. The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed. The amount of derivatives required to minimize a quadratic hedging error is obtained. Finally, we provide some numerical analysis based on the VIX data. Numerical results show the efficiency of the proposed model compared to the Heston model and the classical BN-S model. PubDate: 2021-12-01 DOI: 10.1007/s10436-021-00394-4
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Abstract: Abstract We show that the standard notion of residual income (RI) does not fulfill additive coherence. This gives rise to ambiguities and inconsistencies. The pitfall resides in the capital charge, which blends a non-market value with a market rate. We solve the problem by using a capital charge based on economic return, obtained as the product of a market value and a market rate. The resultant economic RI enjoys additivity. The economic RI is naturally associated to the average Return on Investment (ratio of total income to total invested capital). Subtracting the respective cost of capital (ratio of total economic return to total invested capital) the marginal economic efficiency of the capital is correctly captured. Economic RI guarantees consistency among the various sets of incomes, book values, economic values, accounting rates, and costs of capital, under an investment perspective as well as a financing one, both at a period level and at an aggregate level, either assuming time-invariant or time-varying costs of capital. Therefore, the economic RI offers a coherent tool for the assessment of a project’s or firm’s economic efficiency. PubDate: 2021-12-01 DOI: 10.1007/s10436-021-00388-2
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Abstract: Abstract This study explores the welfare implications of mitigating investment uncertainty in the context of Easley and O’Hara (Rev Financ Stud 22:1817–1843, 2009) While one may expect welfare gains by encouraging participation in financial markets by ambiguity-averse investors, we formally show that it hurts other investors and thus is not Pareto-improving without appropriate income transfers. We also examine the welfare effects of income redistribution among heterogeneous investors and government spending on investor education. PubDate: 2021-12-01 DOI: 10.1007/s10436-021-00395-3
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Abstract: Abstract We study the problem of dynamically trading multiple futures contracts on different underlying assets subject to portfolio constraints. The spreads between futures and spot prices are modeled by a multidimensional scaled Brownian bridge to account for their convergence at maturity. Under this stochastic basis model, we apply the stochastic control approach to rigorously derive the optimal trading strategies via utility maximization. This leads to the analysis of the associated system of Hamilton-Jacobi-Bellman equations, which are reduced to a system of ODEs. A series of numerical examples are provided to illustrate the optimal strategies and wealth distributions under different portfolio constraints. PubDate: 2021-11-07 DOI: 10.1007/s10436-021-00398-0
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Abstract: Abstract This paper seeks to examine the unidirectional versus bidirectional Granger causality between investors’ sentiment and momentum strategies. It is based on the full sample Granger causality test and the recent rolling-window bootstrap approach. We also applied a probit model to the extent to which the probability that investors’ sentiment and momentum strategies influence each other. Our results suggest bidirectional Granger causality between investor sentiment and momentum strategy with unstable causality dynamics over time. We find that ADS and VIX positively affect the likelihood that investor sentiment Granger causes momentum strategy and negatively impact the probability that momentum strategy Granger causes investor sentiment. Gold harms the likelihood that investors’ sentiment and momentum strategies affect each other. The research design is unique to combine bootstrap rolling-window Granger causality tests between Sentiment and Momentum to assess investors’ implications in terms of confidence, uncertainty, aggressiveness, or optimism versus Pessimism. PubDate: 2021-10-26 DOI: 10.1007/s10436-021-00399-z
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Abstract: Abstract Using data from Italian banks over the period 2011–2017, we study how negative interest rate policy and prudential regulation impact on bank business models. We report four key findings. First, banks shifted into retail- and market-oriented business models. Second, high- and low-deposit banks reduced loans and increased security/liquid assets; only market-oriented banks expanded lending. Third, interest rate income compression induced by negative rates has been substantial for the Italian banking system as a whole, although retail banks seem to have suffered less. Fourth, non-interest incomes played a compensatory effect. The portfolio reshuffling, as we observed for wholesale and retail banks (less lending and more securities/liquid assets), is related to the goal of reducing risk exposures and, in turn, the connected capital absorption required by prudential regulation. PubDate: 2021-10-13 DOI: 10.1007/s10436-021-00397-1
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Abstract: Abstract We calibrate several advanced stock price models to a time series of real market data of European options on the DAX. Via a Monte Carlo simulation, we price barrier down-and-out call options for all models and compare the modeled prices to given real market data of the barrier options. The Bates model reproduces barrier option prices very well. The BNS model overvalues and Lévy models with stochastic time-change and leverage undervalue the exotic options. The Heston model and a local volatility model undervalue the barrier option prices by about 5–6%. A heuristic analysis suggests that the different degree of fluctuation of the random paths of the models are responsible of producing different prices for the barrier options. Higher margins or additional risks like liquidity, calibration or model risk might economically explain why many advanced models undervalue barrier options. PubDate: 2021-08-28 DOI: 10.1007/s10436-021-00396-2
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