Institutional investors, such as pensions and insurers, are typically constrained to hold enough wealth to be able to make their contractually promised payments to fund beneficiaries. This creates an additional risk in the economy, namely the risk of funding-shortfall. We seek to explore the optimal asset allocation strategies for institutions facing this risk, and its effects on asset prices. The constraint introduces two distinct regions in the economy, characterising unconstrained and constrained regions, with the possibility of transitioning from the constrained to unconstrained regime, which leads to a two-factor asset pricing model. The funding-shortfall risk increases the conditional equity premium and Sharpe ratio, which evolve counter-cyclically, but decreases the conditional volatility of equity returns, which evolves cyclically. The constrained institution may optimally an under-diversified portfolio, and simultaneously increases its demand for the riskfree and higher-risk assets relative to medium-risk assets, inducing a bubble-like behaviour in the prices of higher-risk assets. The dynamics of contractually promised payments affect the dynamics of conditional moments of asset return distributions, and may lead to predictability. The term structure of interest rates is predominantly upward sloping, but can change shape upon shocks to the growth rate of aggregate dividend relative to the growth rate of minimum payouts. Implied volatility exhibits a time-varying volatility smile, and the term structure of implied volatility can be both upward or downward sloping, depending on the relative growth rates of aggregate dividends and promised institutional payouts. These results may have implications for the design of optimal regulatory requirements.
{"title":"Funding Shortfall Risk and Asset Prices in General Equilibrium","authors":"M. Hasan","doi":"10.2139/ssrn.2787573","DOIUrl":"https://doi.org/10.2139/ssrn.2787573","url":null,"abstract":"Institutional investors, such as pensions and insurers, are typically constrained to hold enough wealth to be able to make their contractually promised payments to fund beneficiaries. This creates an additional risk in the economy, namely the risk of funding-shortfall. We seek to explore the optimal asset allocation strategies for institutions facing this risk, and its effects on asset prices. The constraint introduces two distinct regions in the economy, characterising unconstrained and constrained regions, with the possibility of transitioning from the constrained to unconstrained regime, which leads to a two-factor asset pricing model. The funding-shortfall risk increases the conditional equity premium and Sharpe ratio, which evolve counter-cyclically, but decreases the conditional volatility of equity returns, which evolves cyclically. The constrained institution may optimally an under-diversified portfolio, and simultaneously increases its demand for the riskfree and higher-risk assets relative to medium-risk assets, inducing a bubble-like behaviour in the prices of higher-risk assets. The dynamics of contractually promised payments affect the dynamics of conditional moments of asset return distributions, and may lead to predictability. The term structure of interest rates is predominantly upward sloping, but can change shape upon shocks to the growth rate of aggregate dividend relative to the growth rate of minimum payouts. Implied volatility exhibits a time-varying volatility smile, and the term structure of implied volatility can be both upward or downward sloping, depending on the relative growth rates of aggregate dividends and promised institutional payouts. These results may have implications for the design of optimal regulatory requirements.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2016-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89938524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Determining the yield to maturity of a coupon bond with more than four coupon periods is a two-step process. The first step uses an approximation formula to obtain a first approximation of the true yield. The second step uses an algorithm to advance the first approximation closer to the bond's true yield. Newton's Method is the algorithm used in applications such as Microsoft's Excel "YIELD" function. This paper evaluates some commonly used approximation formulae before demonstrating a solution algorithm that generally outperforms Newton's Method.
{"title":"Superseding Newton with a Superior Yield Algorithm","authors":"Chris Deeley","doi":"10.2139/SSRN.1253166","DOIUrl":"https://doi.org/10.2139/SSRN.1253166","url":null,"abstract":"Determining the yield to maturity of a coupon bond with more than four coupon periods is a two-step process. The first step uses an approximation formula to obtain a first approximation of the true yield. The second step uses an algorithm to advance the first approximation closer to the bond's true yield. Newton's Method is the algorithm used in applications such as Microsoft's Excel \"YIELD\" function. This paper evaluates some commonly used approximation formulae before demonstrating a solution algorithm that generally outperforms Newton's Method.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2008-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77434149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Asynchronous annuities are defined as those in which the frequency of cash flows differs from the frequency of interest compounding. The conventional approach to calculating the present and future values of such annuities is to impute a rate of interest (or return) to a cash flow period, which is then inserted into standard annuity equations. The method produces inaccurate results when the frequency of cash flows exceeds the frequency of interest compounding. After identifying the source of those inaccuracies, this paper develops and demonstrates a new approach to accurately solving annuity problems when the frequency of cash flows exceeds the frequency of interest compounding.
{"title":"Mathematics of Asynchronous Annuities","authors":"Chris Deeley","doi":"10.2139/ssrn.1001145","DOIUrl":"https://doi.org/10.2139/ssrn.1001145","url":null,"abstract":"Asynchronous annuities are defined as those in which the frequency of cash flows differs from the frequency of interest compounding. The conventional approach to calculating the present and future values of such annuities is to impute a rate of interest (or return) to a cash flow period, which is then inserted into standard annuity equations. The method produces inaccurate results when the frequency of cash flows exceeds the frequency of interest compounding. After identifying the source of those inaccuracies, this paper develops and demonstrates a new approach to accurately solving annuity problems when the frequency of cash flows exceeds the frequency of interest compounding.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2007-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80262823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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