The problem of characterizing the least expensive bond portfolio that enables one to meet his/her liability to pay C dollars K years from now is dealt with in this article. Bond prices are allowed to be either overpriced or underpriced at the purchase time, while at the sale time the bonds are suppose to be fairly priced. Assuming shifts in spot rates to occur instantly after the acquisition of a bond portfolio Z and to follow fairly general type of behavior described by the condition (2), we give both necessary and sufficient conditions for Z to solve the immunization problem above. Our model is general enough to cover situations with twists in the yield curve. Making use of the K-T conditions, we explain in remark 7 why we focus on search of an optimal portfolio in the class of barbell strategies. Finally, by means of the K-T conditions we find an optimal bond portfolio which solves the immunization problem.

Abstract:In the following, we offer a theoretical approach that attempts to explain (Comments 1-3) why and when the Macaulay duration concept happens to be a good approximation of a bond's price sensitivity. We are concerned with the basic immunization problem with a single liability to be discharged at a future time q. Our idea is to divide the class K of all shifts a(t) of a term structure of interest rates s(t) into many classes and then to find a sufficient and necessary condition a given bond portfolio, dependent on a class of shifts, must satisfy to secure immunization at time q against all shifts a(t) from that class. For this purpose, we introduce the notions of dedicated duration and dedicated convexity. For each class of shifts, we show how to choose from a bond market under consideration a portfolio with maximal dedicated convexity among all immunizing portfolios. We demonstrate that the portfolio yields the maximal unanticipated rate of return and appears to be uniquely determined as a barbell strategy (portfolio) built up with 2 zero-coupon bearing bonds with maximal and respective minimal dedicated durations. Finally, an open problem addressed to researchers performing empirical studies is formulated.Keywords: barbell strategy, convexity, dedicated duration, Macaulay duration, unanticipated rate of return. IntroductionConsider an investor who possessing C dollars today must achieve an investment goal of L dollars (L > C) q years from now by means of a purchase of appropriately selected bond portfolio (BP). If not successful, he/she will incur a penalty, while achieving more than L dollars will result in practically no rewards. Such investors are called bond immunizers. It is natural to assume that C is the present value of L dollars.By the term structure of interest rates, one understands a schedule of spot interest rates s(t) which is estimated from the yields of all coupon-bearing bonds available on a given debt market M under consideration. The basic immunization problem (BIP) relies on a construction of such a bond portfolio BP with the present value of C dollars that the single liability to pay L dollars (L is the future value of C) q years from now will be discharged by means of the inflows c(t) generated by portfolio BP, no matter what shocks/shifts a(t) of s(t) will occur.The new term structure is always of the form:with a(t) standing for a shift / shock of our term structure s(t), which satisfies Assumption 1 only. The function s(t) can exhibit various behaviors, for example, it can be flat, rising, declining, humped, or twisted. The classical results refer to flat shifts a(t) and flat term structures s(t), and they go back as far as to the pioneering work of Macaulay (1938), Redington (1952), andFisher (1971).In this paper, we approach the BIP by dividing the set K of all possibly shits a(t) into infinitely many classes K v and then solve BIP for each of these classes separately, with durations D v accordingly tailored to the specifics of the class K v . Similar to Zheng in (2002) and (20...

No abstract

No abstract

No abstract

No abstract

The paper presents result of an empirical study in which presence of values among workers of two mining squads characterized by different level of work performance has been compared. Values have been measured by two scales: Mining Values Scale (MVS) and Organizational Culture Assessment Instrument (OCAI). The squad with higher performance had significantly higher level of five out of nine values measured by (MVS); while none of the values measured by OCAI have been differentiating the squads with a statistical significance. The results suggest that Managing by Values (MBV) model for a mining corporation should rather be based on values specific for the mining industry rather than general management value set proposed by OCAI. Research results suggest also an association between presence of certain values and work satisfaction among workers.

Abstract:In this paper, we present a 1-period model of the Polish financial market from the view point of KGHM, the Polish largest listed company that suffered huge declines in share prices from 125 PLN in August 2015 to 60 PLN in January 2015. Our goal is to show how KGHM might create a portfolio (with practically zero cost), which would fully compensate the abovementioned declines. The methodology presented below may be equally well employed by many other listed companies and investment funds, as well. We create here a matrix model of the Polish financial market and employ the BlackScholes formula to valuate portfolios compensating potential declines of KGHM's shares prices. To give more insight to practitioners wishing to apply the results presented here to other listed companies, we distinguish two cases. In one of them, volatility of KGHM's share prices is 20%, and in the other case it equals 33%.