Capital Allocation for a Sum of Dependent Compound Mixed Poisson Variables: A Recursive Algorithm Approach

The sum of independent compound Poisson random variables is a widely used stochastic model in many economic applications, including non-life insurance, credit and operational risk management, and environmental sciences. In this article we generalize this model by introducing dependence among Poisson frequency variables through a latent random variable in a linear fashion, which can be translated as a common underlying risk factors affecting the frequencies of individual compound Poisson variables. Despite its natural interpretation, this generalization leads to a highly complicated model with no closed-form distribution function. For this dependent compound mixed Poisson sum with an arbitrary severity distribution, we obtain the Laplace transform and further develop a new recursive algorithm to efficiently compute the probability mass function, extending the well-known Panjer recursion. Furthermore, based on this recursion, we derive another recursive scheme to determine the capital allocation associated with the Conditional Tail Expectation, a popular risk management exercise. A numerical example is presented for the illustration of our findings.     

Corporate Diversification: What Gets Discounted?

Prior literature finds that diversified firms sell at a discount relative to the sum of the imputed values of their business segments. We explore this documented discount and argue that it stems from risk–reducing effects of corporate diversification. Consistent with this risk–reduction hypothesis, we find that (a) shareholder losses in diversification are a function of firm leverage, (b) all equity firms do not exhibit a diversification discount, and (c) using book values of debt to compute excess value creates a downward bias for diversified firms. Overall, the results indicate that diversification is insignificantly related to excess firm value.     

Compound mixed Poisson distributions I

The concept of compound mixed Poisson distributions in actuarial science is used to represent such variables as the total amount of claims or losses payable by an insurer. In this paper, comprehensive collections of approximate forms are derived for the compound mixed Poisson distribution. The calculations involve use of several special functions and their properties. We believe that the results will serve as an important reference in actuarial science.     

On the asymptotic distribution of weighted least squares estimators

Abstract

In the ELB (Empirical Linear Bayes)-approach to credibility, the unknown structural parameters are substituted by a set of parameter estimates. The weighted least squares estimators are known to be asymptotically normally distributed when the design variables are independent and identically distributed random variables. It is demonstrated that, with probability one, the conditional asymptotic distribution, given the design, is the same as the unconditional distribution. Estimation of the asymptotic covariance matrix will also be considered.     

Arbitrage Bounds and the Time Series Properties of the Discount on UK Closed-End Mutual Funds

Abstract:  In a dataset of weekly observations over the period since 1990, the discount on UK closed-end mutual funds is shown to be nonstationary, but reverting to a nonzero long run mean. Although the long run discount could be explained by factors like management expenses etc., its short run fluctuations are harder to reconcile with an arbitrage-free equilibrium. In time series terms, there is evidence of long memory in discounts consistent with a bounded random walk. This conclusion is supported by explicit nonlinearity tests, and by results which suggest the behaviour of the discount is perhaps best represented by one of the class of Smooth-Transition Autoregressive (STAR) models.     

Integrating business strategy,organizational configurations and management accounting systems with business unit effectiveness: a fitness landscape approach

This study adopts a fitness landscape approach to test contingency hypotheses about the relationship between business strategy, organizational configurations, management accounting systems, and business unit effectiveness. Central to this approach is the notion of contingent fit between strategic priorities and its contextual variables. Building on Kauffman’s N-locus, two-state additive fitness model, this study predicts that the degree of contingent fit, defined as the weighted sum of independent fitness contributions of each contextual variables, will have a positive association with business unit effectiveness.Based on a mail survey and personal interviews of 106 business unit managers of publicly held companies listed under consumer goods industry, this study indicates that the degree of contingent fit has a positive association with business unit effectiveness. Further analysis reveals that strategic priorities affect the types of controls and management accounting systems used by the business units.     

Value Under Active and Passive Debt Management Policy

The relationship between debt policy and valuation has been extensively analysed in the finance literature; within a Modigliani-Miller framework, the consensus is that valuation is affected by whether debt is managed actively or passively, and that for finite projects with time varying risky cash flows, it is appropriate to use a weighted average discount rate for valuation only if it is assumed that debt is actively managed. In this paper, the relationship between debt policy and valuation is re-examined. In particular, it is shown that, under one of the most plausible forms of passive debt policy, valuation using a simple weighted average discount rate is in fact possible.     

Exchange Rates and Fundamentals: A General Equilibrium Exploration

Engel and West (2005) show that the observed near random‐walk behavior of nominal exchange rates is an equilibrium outcome of a partial equilibrium asset approach when economic fundamentals follow exogenous first‐order integrated processes and the discount factor approaches one. In this paper, I argue that the unit market discount factor creates a theoretical trade‐off within a two‐country general equilibrium model. The unit discount factor generates near random‐walk nominal exchange rates, but it counterfactually implies perfect consumption risk sharing and flat money demand. Bayesian posterior simulation exercises, based on post‐Bretton Woods data from Canada and the United States, reveal difficulties in reconciling the equilibrium random‐walk proposition within the canonical model; in particular, the market discount factor is identified as being much smaller than one. A relative money demand shock is identified as the main driver of nominal exchange rates.     

SOME FORMAL CONNECTIONS BETWEEN ECONOMIC VALUES AND YIELDS AND ACCOUNTING NUMBERS

This paper reports a number of results concerning the relationship between accounting numbers and economic values and yields. Some of the results have appeared previously in the literature and some are new. They have been collected together in a common analytical framework in order to demonstrate their formal, mathematical character. It is shown that present value can be obtained by discounting almost any profit numbers; that accounting rates of return define a discount function directly analagous to the term structure and the internal rate of return; and that the internal rate of return can be expressed as a linear weighted sum of accounting rates of return.     

How much of the diversification discount can be explained by poor corporate governance?

We investigate whether the diversification discount occurs partly as an artifact of poor corporate governance. In panel data models, we find that the discount narrows by 16% to 21% when we add governance variables as regression controls. We also estimate Heckman selection models that account for the endogeneity of diversification and dynamic panel generalized method of moments models that account for the endogeneity of both diversification and governance. We find that the diversification discount persists even with these controls for endogeneity. However, in selection models the discount disappears entirely when we introduce governance variables in the second stage, and in dynamic panel GMM models the discount narrows by 37% when we include governance variables.     

A Re-Examination of the Joint Mortality Functions

Abstract

Mortality analysis involving multiple lives is easily one of the more complicated aspects in the theory of life contingencies. In this paper, we re-investigate joint mortality functions and in particular, we examine an assertion that relates the joint-life and last-survivor random variables. This common assertion states that the sum of the lifetimes of the joint-life and the last-survivor statuses is equal to the sum of the lifetimes of the single statuses. However, we show that this assertion is not precisely correct. We therefore offer a modification to the statuses definitions so that this common assertion holds.     

A characterization of the distributions that imply existence of linear equilibria in the Kyle-model

The existence of a linear equilibrium in Kyle’s model of market making with multiple, symmetrically informed strategic traders is implied for any number of strategic traders if the joint distribution of the underlying exogenous random variables is elliptical. The reverse implication has been shown for the case in which the random variables are independent and have finite second moments. Here we extend this result to the case in which the underlying random variables are not necessarily independent and their joint distribution is determined by its moments. We thank two anonymous referees for their comments. Financial support by the Deutsche Forschungsgemeinschaft, SFB-TR 15, is gratefully acknowledged.     

¿Influyen las Normas Internacionales de Información Financiera en el riesgo de las acciones?

The present research has two objectives. First, we study the determinants of stock risk. Second, we analyze whether International Financial Reporting Standard (IFRS) implemented in the Spanish market in 2005 has affected these determinants. It is quite important for both entrepreneurs and management professionals to understand the accounting information and macroeconomic factors that explain stock risk, since it suggests which factors can be used to estimate this risk, and hence, to analyze the evolution of cost of capital or discount rate. The discount rate plays an important role in wide range of financial decisions; whose value depends on the risk among other factors. Therefore, it is significant to obtain an objective estimation of discount rate, which is difficult to handle specifically in the context of small and medium sized enterprises (SMEs). Effective management involves the ability to forecast future changes, capture positive effects, and minimize negative ones. Once we find out the variables that can be utilized to explain the risk, we can observe and analyze their evolution to anticipate future changes in the discount rate.     

Accounting‐based Risk Management and the Capital Asset Pricing Model: An Empirical Comparison

Accounting‐based risk management (ABRM) is a theoretically consistent and practical tool for calculating the cost of capital from underlying financial ratios. In this paper, a sample of ABRM‐generated discount factors is used to generate risk‐adjusted returns, which are compared to CAPM equivalent discount factors. In view of the debates about CAPM's validity, alternative models, the nature and scale of the equity risk premium, and the importance of discount rates in capital budgeting and asset valuation, ABRM's characteristics and resulting discount rates offer a potentially useful alternative. Results suggest that although average discount rates are comparable, their cross‐sectional distributions are dissimilar, so that investors in an average risky firm are overcompensated for systematic risk when using CAPM discount rates, because CAPM discount factors overestimate risk arising from fixed costs in most firms.     

Tax-Adjusted Discount Rates with Investor Taxes and Risky Debt

This paper derives a tax-adjusted discount rate formula with a constant proportion leverage policy, investor taxes, and risky debt. The result depends on an assumption about the treatment of tax losses in default. We identify the assumption that justifies the textbook approach of discounting interest tax shields at the cost of debt. We contrast this with an alternative assumption that leads to the Sick (1990) result that these should be discounted at the riskless rate. These two approaches represent polar cases. Each generates its results by using a different simplifying assumption, and we explain what determines the correct treatment in practice. We also discuss implementation of the valuation procedure using the capital asset pricing model.     

Binomial option pricing with stochastic parameters: A beta distribution approach

This research extends the binomial option-pricing model of Cox, Ross, and Rubinstein (1979) and Rendleman and Barter (1979) to the case where the up and down percentage changes of stock prices are stochastic. Assuming stochastic parameters in the discrete-time binomial option pricing is analogous to assuming stochastic volatility in the continuous-time option pricing. By assuming that the up and down parameters are independent random variables following beta distributions, we are able to derive a closed-form solution to this stochastic discrete-time option pricing. We also derive an upper and a lower bounds of the option price.     

An Interest Rate Model with Upper and Lower Bounds

We propose a new interest rate dynamicsmodel where the interest rates fluctuate in a bounded region. The model ischaracterised by five parameters which are sufficiently flexible to reflect theprediction of the future interest rates distribution. The interest rate convergesin law to a Beta distribution and has transition probabilities which arerepresented by a series of Jacobi polynomials. We derive the moment evaluationformula of the interest rate. We also derive the arbitrage free pure discountbond price formula by a weighted series of Jacobi polynomials. Furthermore wegive simple lower and upper bounds for the arbitrage free discount bond pricewhich are tight for the narrow interest rates region case. Finally we show thatthe numerical evaluation procedure converges to the exact value in the limitand evaluate the accuracy of the approximation formulas for the discount bondprices.     

Minimizing the Risk of a Financial Product Using a Put Option

In this article, we elaborate a method for determining the optimal strike price for a put option, used to hedge a position in a financial product such as a basket of shares and a bond. This strike price is optimal in the sense that it minimizes, for a given budget, a class of risk measures satisfying certain properties. Formulas are derived for one single underlying as well as for a weighted sum of underlyings. For the latter we will consider two cases depending on the dependence structure of the components in this weighted sum. Applications and numerical results are presented.     

An arbitrage model of the term structure of interest rates

A formula for the price of default-free discount bonds of all maturities is found using a Black- Scholes type of arbitrage model which is based on the assumption that a portfolio of three default-free discount bonds of distinct maturities can be managed to be a perfect substitute for any other default-free discount bond. The formula relates the price of bonds to the real rate of interest, the anticipated rate of inflation and the equilibrium prices of interest rate and inflation risks. Bond prices are shown to be the expected value of the sure nominal proceeds of the bond discounted to the present at a random discount rate. It is shown that the unbiased expectations hypothesis is in general inconsistent with this model.