Optimal Investment Policy Research Articles

Why is Convertible Debt Subordinated? An Investment-Based Agency Theory

This paper offers an agency-based explanation for the junior priority status of convertible bonds. Using a simple economic model, I show that when convertible and straight debt have equal priority, shareholders can prefer value-decreasing projects, which results in wealth transfers from bondholders to shareholders; and I prove that this problem is solved when convertible debt is subordinated. Empirical evidence supports the theory. I find that firms with greater potential for investment-based agency conflicts are more likely to issue subordinated convertible debt, and firms with senior convertible debt are more likely to deviate from the optimal investment policy.

OPTIMAL INVESTMENT AND REINSURANCE IN A JUMP DIFFUSION RISK MODEL

AbstractWe consider an insurance company whose surplus is governed by a jump diffusion risk process. The insurance company can purchase proportional reinsurance for claims and invest its surplus in a risk-free asset and a risky asset whose return follows a jump diffusion process. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equation, closed-form solutions for the value function as well as the optimal investment and proportional reinsurance policy are obtained. We also discuss the effects of parameters on the optimal investment and proportional reinsurance policy by numerical calculations.

Optimal Investment and Premium Policies Under Risk Shifting and Solvency Regulation

Limited liability creates an incentive for insurers to increase the risk of the assets and liabilities at the expense of policyholders. We show that solvency capital requirements restrict the set of feasible investment and premium policies and can thereby improve efficiency under the risk shifting problem. This finding becomes particularly important in light of Solvency II, the forthcoming European risk-based solvency regime for insurers. We provide evidence for Solvency II related efficiency effects in a calibration study for a non-life insurer average portfolio.

Long Horizons, High Risk-Aversion, and Endogenous Spreads

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as the limits of their isoelastic counterparts for high levels of risk aversion. The results are robust with respect to finite horizons, and extend to multiple uncorrelated risky assets. In this setting, we study a Stackelberg equilibrium, led by a risk-neutral, monopolistic market maker who sets the spread as to maximize profits. The resulting endogenous spread depends on investment opportunities only, and is of the order of a few percentage points for realistic parameter values.

Optimal Corporate Investment and Financing Policies: A Simple Quantitative Rule in a Novel General Setting

We aim at obtaining a simple quantitative rule for the joint determining of optimal corporate investment and financing policies in an intertemporal setting. A novel general continuous-time framework, inspired by the optimal portfolio design literature, is first built. We derive the optimal assets-to-equity and debt-to-equity ratios. Novel principles - driven by speculation and hedging motives - for the corporate decision-making process are exposed. The rule is then simplified to offer an easily obtainable quantitative benchmark for the firm’s manager. We eventually show how the proposed behavior can be applied in practice.

Valuation of Contingent Pension Liabilities and Guarantees Under Sponsor Default Risk

This article analyzes the relationship between a pension fund with contingently indexed defined benefit liabilities and its sponsor, using contingent claims analysis. As pension funds generally choose to run a mismatch risk, future surpluses and deficits will occur. Surpluses are divided between beneficiaries and sponsor through contingent indexation of the benefits and refunding. Covering a deficit at the pension fund level is a function of the sponsor's financial ability to do so. This article suggests that this system creates an asymmetric allocation of the residual risk between sponsor and beneficiaries. The optimal investment policy for the pension fund in this context can be found by reverse engineering option valuation formulas. The main conclusion is that sponsor default risk negatively impacts the optimum risk profile and thereby the market value of contingent pension liabilities.

An empirical model of mainframe computer investment

This paper introduces a dynamic model of investment decisions in mainframe computer systems. I estimate and test the model using detailed micro data from a company in the telecommunications industry. The model accounts for ‘technological depreciation’ which distinguishes computers from other investment goods where physical depreciation is typically a key factor underlying replacement investment decisions. The company increased its installed mainframe computer capacity by over 30-fold over the 10-year sample period. Part of this growth was undoubtedly due to the huge increase in performance and the corresponding drop in the per unit cost of processing capacity of mainframes, a consequence of ‘Moore's law’. However, there was also tremendous growth in the need for computers for billing, account processing and other tasks, due to the rapid growth in the telecommunications industry over this same time period. I estimate the unknown parameters of the investment model using a nonlinear least squares–nested fixed-point algorithm (NLS-NFXP), which solves the Bellman equation underlying the dynamic model of investment and replacement of mainframe computers by nonlinear least squares. I demonstrate that it is feasible to estimate this model on an ordinary PC, whereas standard discretization approaches to solving the firm's optimal investment policy might not even be feasible using supercomputers. I show that the estimated model fits the data very well, and accurately captures the large growth in installed mainframe capacity, the timing and magnitude of replacement investment, as well as periodic upgrades of existing mainframe units. I use the model to decompose how much of the 30-fold increase in mainframe computer capacity is due to ‘Moore's law’ (i.e. the huge drop in the unit cost of installed mainframe capacity), and how much is due to the growth in demand for services of mainframes, due to the rapid growth in demand for telecommunications services (particularly cell phone accounts) by the firm's customers. Copyright © 2010 John Wiley & Sons, Ltd.

An optimal portfolio model with stochastic volatility and stochastic interest rate

We consider a portfolio optimization problem under stochastic volatility as well as stochastic interest rate on an infinite time horizon. It is assumed that risky asset prices follow geometric Brownian motion and both volatility and interest rate vary according to ergodic Markov diffusion processes and are correlated with risky asset price. We use an asymptotic method to obtain an optimal consumption and investment policy and find some characteristics of the policy depending upon the correlation between the underlying risky asset price and the stochastic interest rate.

ON PORTFOLIO CHOICE BY MAXIMIZING THE OUTPERFORMANCE PROBABILITY

We consider the problem of optimal portfolio selection for a multidimensional geometric Brownian motion model. We look for portfolios that maximize the probability of outperforming a stochastic benchmark. More specifically, we seek to maximize the decay rate of the shortfall probability and (or) to minimize the decay rate of the outperformance probability in the long run. A simple heuristic enables us to find an asymptotically optimal investment policy. The results provide interesting insights.

A MODEL FOR THE EFFECT OF POLLUTANT ON HUMAN POPULATION DEPENDENT ON A RESOURCE WITH ENVIRONMENTAL AND HEALTH POLICY

In this paper, a nonlinear mathematical model to study the effect of environmental pollution on resource biomass and human populations is proposed and analyzed. In modeling the system, it is considered that there is a limited budget to be spent on environmental cleanup and health policies. An optimal investment policy is also discussed using Pontryagin's Maximum Principle.

Optimal dividend policy, debt policy and the level of investment within a multi-period DCF framework

This paper simultaneously analyses optimal dividend, debt and investment policy within a conventional multi-period DCF framework, and takes account of differential personal taxation over both investors and types of income, the effect of dividends and interest on the level of share issues and hence share issue costs, and the effect of dividends and interest on the level of internally-financed investment. Application of the model to three distinct tax regimes reveals that the value benefit from debt is small at best whilst the value benefit from dividends is substantial even in a regime without dividend imputation.

Optimal investment policy and dividend payment strategy in an insurance company

We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cramér–Lundberg process. The firm has the option of investing part of the surplus in a Black–Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the smallest viscosity solution of the associated second-order integro-differential Hamilton–Jacobi–Bellman equation. We study the regularity of the optimal value function. We show that the optimal dividend payment strategy has a band structure. We find a method to construct a candidate solution and obtain a verification result to check optimality. Finally, we give an example where the optimal dividend strategy is not barrier and the optimal value function is not twice continuously differentiable.

Irreversible capital accumulation under interest rate uncertainty

We consider the optimal sequential irreversible investment policy of a value maximizing firm facing decreasing returns to scale and interest rate uncertainty. We characterize the optimal accumulation policy and its value for a broad class of diffusion models of the short interest rate by focusing on the marginal investment decision and deriving the marginal value of capital explicitly. We also state a set of conditions under which there is a maximal capital stock above which the option to expand productive capacity further in the future becomes valueless. Hence, our results indicate that interest rate uncertainty may limit the size of an optimally investing firm.

The Optimal Investment Policy for the Pension Benefit Guaranty Corporation

The Pension Benefit Guaranty Corporation (PBGC) registers a preoccupying financial condition since 2002. The existing literature has not yet dealt with the definition of the PBGC’s optimal portfolio policy. This paper builds a theoretical framework for defining its optimal asset allocation in a continuous-time stochastic world. We first recognize the PBGC’s put seller nature and derive optimal portfolio rules inspired by the option hedging literature. We then build a model characteristic of any asset-liability manager, like the PBGC or equivalent bodies in other countries, a defined benefit (DB) pension fund or a defined contribution pension fund subject to a guarantee. The model implementation only requires the availability of the given institution’s balance sheets. We propose an application using the PBGC’s reports in the period 1995-2009. The optimal risky asset proportion, composed of the speculative fund and the cash flow and liabilities hedge terms, appears as low, as the second and - especially - third terms exert a downward pressure on the speculative portfolio component. We eventually compare the asset-liability management principles of the PBGC and a DB pension fund and conclude that, though both institutions have a comparable optimal portfolio structure, their asset allocation differs in the effect of the liabilities hedge fund. Due to a different nature of the PBGC’s and DB pension fund’s liabilities, the corresponding hedge fund decreases (increases) the optimal risky asset proportion in the case of the PBGC (DB pension fund).

Real options with unknown-date events

The real options literature has provided new insights on how to manage irreversible capital investments whose payoffs are uncertain. Two of the most important predictions from such theory are: (i) greater risk delays a firm’s investment timing, and (ii) greater risk increases the option value of waiting. This paper challenges such conclusions in a setting in which the relevant random variable is the arrival time of an unfavorable event. In particular, we model situations in which a firm must choose the time at which to invest in a project whose profit grows at a known rate until a random date is reached and decays thereafter, which may be representative of stochastic product or industry life cycles. This is a novel framework in which a firm can update its beliefs about the profitability of an investment opportunity by simply waiting to invest. Thus, a wait-and-see approach allows the firm to capitalize on favorable market evolutions and avoid adverse ones to some extent. Our framework is simple and does not require using stochastic calculus, which allows for an economic interpretation of optimal investment policies for the cases of one-time and sequential investments.

Cash Flow Multipliers and Optimal Investment Decisions

Valuation multipliers are frequently used in practice. By postulating a simple stochastic process for the firm's cash flows in which the drift and the variance of the process depend on the investment policy, we develop a stylized model that links the cash flow multiplier to the optimal investment policy. Our model implies that the multiplier increases with investment at a decreasing rate. On the other hand, the multiplier is inversely related to discount rates. Using an extensive data set we examine the implications of our model. We find strong support for the variables postulated by the model.

Ruin probabilities under optimal investment and proportional reinsurance policy in jump diffusion risk process

Ruin probabilities under optimal investment and proportional reinsurance policy in jump diffusion risk process

Optimal Investment Policy with Fixed Adjustment Costs and Complete Irreversibility

We develop and characterize analytically an investment model in discrete-time with a fixed adjustment cost not proportional to existing capital and complete irreversibility that reproduces the lumpiness of investment at the micro-level. In agreement with the empirical evidence, as firm size increases, investment becomes less lumpy and the investment sensitivity to cash-flows decreases. The optimal policy is of the generalized (S, s) form and it depends on both the marginal q and the average q. We impose a minimal set of restrictions on technology and uncertainty. Proofs use the concept of K-concavity introduced by Scarf (1960). Despite the discontinuity in the profit function due to the fixed cost, the value function is differentiable everywhere except at the investment threshold.

Real Options Games in Complete and Incomplete Markets with Several Decision Makers

We consider optimal investment policies for irreversible capital investment projects under uncertainty in a monopoly situation and in a Stackelberg leader-follower game. We consider two types of payoffs: lump-sum and cash flows. The decisions are the times to enter into the market. The problems belong to the class of optimal stopping times, for which the right approach is that of variational inequalities (V.I.s). In the case of complete markets, payoffs are expected values with respect to the risk-neutral probability. In the case of incomplete markets, the risk-neutral probability is not defined. We consider an investor maximizing his/her utility function, and we consider the investment in the project as an additional decision, besides portfolio investment and consumption decisions. This decision remains a stopping time, conversely to the portfolio investment and consumption decisions (continuous controls). The game problem raises new difficulties. The leader's V.I. has a nondifferentiable obstacle. The weak formulation of the V.I. handles this difficulty. In some cases, the solution of the V.I. may be continuously differentiable although the obstacle is not. An additional difficulty occurs for lump-sum payoffs in the case of incomplete markets. We cannot compare gains and losses at different times. We propose an alternative approach, using equivalence (indifference) considerations. In the case of payoffs characterized by cash flows, this difficulty does not exist, but an intermediary problem arises which has a nice interpretation as a differential game. The solutions thus obtained for the Stackelberg game are not intuitive. Therefore, competition has important consequences on investment decisions.

Optimal Dividends and ALM Under Unhedgeable Risk

In this paper we develop a framework for optimal investment decisions for insurance companies in the presence of (partially) unhedgeable risk. The perspective that we choose is from an insurance company that maximises the stream of dividends paid to its shareholders. The policy instruments that the company has are the dividend policy and the investment policy. Using stochastic control theory, we derive simultaneously the optimal investment policy and the optimal dividend policy, taking the insurance risks to be given. We study the trade off between investing in the optimal hedge portfolio and the fully diversified portfolio. We show next how the pricing of unhedgeable risk can also be embedded in our framework. Finally, we derive the distribution of the time of bankruptcy and demonstrate its usefulness in calibrating the model.