Two sided efficient frontiers at multiple time horizons

IF 0.8 Q4 BUSINESS, FINANCE Annals of Finance Pub Date : 2022-06-06 DOI:10.1007/s10436-022-00411-0
Dilip B. Madan, King Wang
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Abstract

Two price economy principles motivate measuring risk by the cost of acquiring the opposite of the centered or pure risk position at its upper price. Asymmetry in returns leads to differences in risk charges for short and long positions. Short risk charges dominate long ones when the upper tail dominates the comparable lower tail for charges based on distorted expectations. Positive mean return targets acquire long positions with negative mean return targets taking short positions. In each case the appropriate risk charge is minimized to construct two frontiers, one for the positive, and the other for negative, mean return targets. Multivariate return distributions reflect limit laws given by Q self-decomposable laws displaying decay rates in skewness and excess kurtosis slower than those for processes of independent and identically distributed returns. Frontiers at longer horizons display greater efficiency reflected by lower risk charges for comparable mean return targets. The short side frontiers also display greater risk charges than their long side counterparts. All efficient portfolios deliver asset pricing equations whereby required returns in excess of a reference rate are a market price of risk times a risk gradient evaluated at the efficient portfolio. Variations in frontiers and points on the frontier induce differences in reference rates, risk gradients, and the market prices of risk that can yet lead to comparable required returns.

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在多个时间范围内的双边有效边界
两个价格经济学原理通过以较高价格获得中心或纯粹风险头寸的对立面的成本来激励衡量风险。回报的不对称导致空头和多头头寸的风险费用存在差异。对于基于扭曲预期的费用,当上尾部主导可比下尾部时,短期风险费用主导长期风险费用。正平均收益目标获得多头头寸,负平均收益目标持有空头头寸。在每种情况下,适当的风险费用都被最小化,以构建两个边界,一个用于正的,另一个用于负的,平均回报目标。多元收益分布反映了Q自分解定律给出的极限定律,该定律显示出比独立和同分布收益过程慢的偏度和过度峰度衰减率。长期的前沿表现出更高的效率,这反映在可比平均回报目标的风险费用较低。短边边界也比长边边界显示出更大的风险。所有有效的投资组合都提供资产定价方程,其中超过参考利率的所需回报是风险的市场价格乘以在有效投资组合中评估的风险梯度。边界和边界上点的变化会导致参考利率、风险梯度和风险市场价格的差异,这些差异可能会导致可比的所需回报。
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来源期刊
Annals of Finance
Annals of Finance BUSINESS, FINANCE-
CiteScore
2.00
自引率
10.00%
发文量
15
期刊介绍: Annals of Finance provides an outlet for original research in all areas of finance and its applications to other disciplines having a clear and substantive link to the general theme of finance. In particular, innovative research papers of moderate length of the highest quality in all scientific areas that are motivated by the analysis of financial problems will be considered. Annals of Finance''s scope encompasses - but is not limited to - the following areas: accounting and finance, asset pricing, banking and finance, capital markets and finance, computational finance, corporate finance, derivatives, dynamical and chaotic systems in finance, economics and finance, empirical finance, experimental finance, finance and the theory of the firm, financial econometrics, financial institutions, mathematical finance, money and finance, portfolio analysis, regulation, stochastic analysis and finance, stock market analysis, systemic risk and financial stability. Annals of Finance also publishes special issues on any topic in finance and its applications of current interest. A small section, entitled finance notes, will be devoted solely to publishing short articles – up to ten pages in length, of substantial interest in finance. Officially cited as: Ann Finance
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