DURATION AND INTEREST RATE RISK FOR UNCERTAIN CASH FLOW STREAMS

This paper amends the Hicks-Macaulay-Samuelson duration analysis to allow for uncertainty in asset cash flows. An asset's duration measure then becomes a random variable which may possess no central moments. We show, however, that a transformed version of the duration measure is normally distributed. This can be used to make probability assessments of the sensitivity ofthe present value of an asset's cash flow stream to interest rate movements.     

THE SEARCH FOR A PROPORTIONATE CARE LAW BY FORMULA FUNDING IN THE ENGLISH NHS

Although the National Health Service was created to achieve equity of access to health care in 1948, over twenty years later an 'inverse care law' was seen to operate. The 1976  Report of the Resource Allocation Working Party  laid the principles of formula funding to achieve an equitable distribution of resources, to move, over time, towards the operation of a proportionate care law. These principles have been applied ever since in England. This paper describes the context, governance and subsequent development of formulas and three persistent problems: accounting for populations, their needs and variations in the unavoidable costs of providers. The paper concludes by outlining continuing problems from the past and new challenges of formula funding in England to reduce 'avoidable' inequalities in health.     

OLIVE: A SIMPLE METHOD FOR ESTIMATING BETAS WHEN FACTORS ARE MEASURED WITH ERROR

We propose a simple and intuitive method for estimating betas when factors are measured with error: ordinary least squares instrumental variable estimator (OLIVE). OLIVE performs well when the number of instruments becomes large, whereas the performance of conventional instrumental variable methods becomes poor or even infeasible. In an empirical application, OLIVE beta estimates improve R² significantly. More important, our results help resolve two puzzling findings in the prior literature: first, the sign of average risk premium on the beta for market return changes from negative to positive; second, the estimated value of average zero‐beta rate is no longer too high.     

THE RELATIONSHIP BETWEEN DURATION AND ECONOMIC DEPRECIATION: A NOTE

This note derives an expression for duration in terms of the economic depreciation of a capital budgeting project or financial instrument. By showing how the decline in the value of an asset or liability influences duration, additional insight into the characteristics of this measure is obtained. The new formula shows that duration equals a standard value, which is adjusted for depreciation or appreciation.     

EXPONENTIAL DURATION: A MORE ACCURATE ESTIMATION OF INTEREST RATE RISK

We develop a new method to estimate the interest rate risk of an asset. This method is based on modified duration and is always more accurate than traditional estimation with modified duration. The estimates by this method are close to estimates using traditional duration plus convexity when interest rates decrease. If interest rates rise, investors will suffer larger value declines than predicted by traditional duration plus convexity estimate. The new method avoids this undesirable value overestimation and provides an estimate slightly below the true value. For risk‐averse investors, overestimation of value declines is more desirable and conservative.     

淡泊的周庄

走过周庄,周庄就生在了我的梦里,总想用笔去描绘那份恬淡和美妙,却怕墨迹不能表达内心的惊奇反而惊扰了周庄的宁静。倏忽间,时光流过了几个年头,再回想江南水乡的时候,那份悸动已经变得深沉和安静,于是终于提起笔来,再走一遭周庄。     

DURATION MOMENTS AND YIELD CURVE MOVEMENTS

In this paper we will analyze the relationship between the value and duration moments of a cash flow and movements in the yield curve. We will show that for changes in the yield curve which can be related to tⁿ , the 1st order changes in the net present value of a cash flow are linearly dependent on the n + lth duration moments, and that the 2nd order changes are dependent on the sum of duration moments of order 2 n + 1 and 2 n + 2. We will use this relationship to tilt tracking portfolios so as to protect them against specific changes in the yield curve.     

SINGLE-FACTOR DURATION MODELS: CANADIAN TESTS

Single-factor duration models of bond returns are derived from an underlying stochastic process of the term structure of interest rates. It is shown that beta in these models is a function of the parameters of the stochastic process and of implied measures of duration. Using unsmoothed Canadian monthly prices on default-free government bonds, the single-factor duration model is found to perform well from 1963 to 1986, but the hypothesis of stationarity of the duration-based bond returns model for the period cannot be accepted. Some of the underlying stochastic processes imply stationary models and some of them imply nonstationary bond return models. The models of this paper open the door to a variety of linear bond return models having a strong theoretical support based on a theory of the stochastic motion of the term structure.     

SIMPLE RESOURCE ALLOCATION RULES: A NOTE ON A GENERALISATION

A stream of literature exists on the ability to pick payback hurdles such that use of the payback method replicates decisions based on net present value (NPV) analysis under circumstances where the basic shape of the cash inflow pattern associated with the investment opportunity facing the firm is assumed known. The literature has derived such payback hurdles for specific cash inflow pattern shapes (e.g., level, exponentially increasing/decreasing, arithmetic growth, etc.) The main concern of this note is to identify an expression for a general class of cash inflow pattern shapes (of which the specific shapes in the previous literature are examples) from which can be derived the payback hurdle corresponding to any specific shape belonging to the general class.