Efficient Stochastic Modeling for Large and Consolidated Insurance Business: Interest Rate Sampling Algorithms

Abstract

One of the challenges of stochastic asset/liability modeling for large insurance businesses is the run time. Using a complete stochastic asset/liability model to analyze a large block of business is often too time consuming to be practical. In practice, the compromises made are reducing the number of runs or grouping assets into asset categories. This paper focuses on the strategies that enable efficient stochastic modeling for large and consolidated insurance business blocks. Efficient stochastic modeling can be achieved by applying effective interest rate sampling algorithms that are presented in this paper. The algorithms were tested on a simplified asset/liability model ASEM (Chueh 1999) as well as a commercial asset/liability model using assets and liabilities of the Aetna Insurance Company of America (AICA), a subsidiary of Aetna Financial Services. Another methodology using the New York 7 scenarios is proposed and could become an enhancement to the Model Regulation on cash flow testing, thus requiring all companies to do stochastic cash flow testing in a uniform, nononerous manner.     

Agency costs of free cash flow and conditional conservatism

This study investigates whether agency costs of free cash flow (FCF) are associated with conditional conservatism. Prior research documents that conditional conservatism improves ex ante efficient investment decisions and facilitates ex post monitoring of managers’ investment decisions. As conditional conservatism can provide protection from possible managerial expropriation, the demand for conditional conservatism should increase with the agency costs of FCF. Using excess cash as a proxy for the agency costs of FCF, I provide evidence that firms with higher agency costs of FCF incorporate losses in a timelier manner relative to gains compared to their counterparts. Additionally, the association between excess cash and conditional conservatism predictably varies with the presence of alternative monitoring mechanisms that mitigate FCF problems, such as debt or dividend payouts or repurchases. Further investigation suggests that greater conservatism is associated with a lower likelihood of overinvestment among firms bearing high agency costs of FCF, demonstrating the ability of conservatism to reduce agency costs of FCF.     

Implementing Fischer Black's Simple Discounting Rule

Corporate managers typically estimate the value of capital projects by discounting the project's expected future net cash flows at the cost of capital. The capital asset pricing model (CAPM) is generally used to estimate that cost. But, as anyone who has worked on the finance or business development staff of a public company can attest, there are major challenges in applying the CAPM, including largely unresolved questions about what constitutes the “market portfolio,” how to estimate market risk premiums, and how to estimate the betas of projects. In a short article published in Financial Management in 1988, Fischer Black proposed a valuation “discounting rule” that avoids all these problems—one that involves discounting a relatively certain (as opposed to an expected or average) level of operating cash flows at the risk-free rate. But Black's article does not address the question of how to calculate these “certainty equivalent” or “conditional” cash flows. In this article, the authors propose a way of implementing Black's rule that involves estimating the “conditional” cash flows in a three-step procedure:

• • Find a benchmark security that correlates with the project's cash flows;
• • Estimate the percentiles of the distribution in which the benchmark return equals the risk-free rate over different investment horizons;
• • Use information from corporate managers to assess the cash flows that define the same percentiles in the cash flow distributions.

As the authors point out, the virtue of Black's rule is that it shifts the focus of the analyst away from the assessment of discount factors and puts it squarely on the more challenging, and arguably more relevant, problem of estimating the project's cash flows.     

Valuation in Emerging Markets: A Simulation Approach

Most of the foundations of valuation theory have been designed for use in developed markets. Because of the greater, and in some cases different, risks associated with emerging markets (although recent experience might suggest otherwise), investors and corporate managers are often uncomfortable using traditional methods. The typical way of capturing emerging-market risks is to increase the discount rate in the standard valuation model. But, as the authors argue, such adjustments have the effect of undermining some of the basic assumptions of the CAPM-based discounted cash flow model. The standard theory of capital budgeting suggests that estimates of unconditional expected cash flows should be discounted at CAPM discount rates (or betas) that reflect only “systematic,” or “nondiversifiable,” market-wide risks. In practice, however, analysts tend to take what are really estimates of “conditional” expected cash flows—that is, conditional on the firm or its country avoiding a crisis—and discount them at higher rates that reflect not only systematic risks, but diversifiable risks that typically involve a higher probability of crisis-driven costs of default. But there is almost no basis in theory for the size of the increases in discount rates. In this article, the authors propose that analysts in emerging markets avoid this discount rate problem by using simulation techniques to capture emerging-market risks in their estimates of unconditional expected cash flows—in other words, estimates that directly incorporate the possibility of an emerging-market crisis and its consequences. Having produced such estimates, analysts can then discount them using the standard Global CAPM.     

Cash management using multi-stage stochastic programming

We consider a cash management problem where a company with a given financial endowment and given future cash flows minimizes the Conditional Value at Risk of final wealth using a lower bound for the expected terminal wealth. We formulate the optimization problem as a multi-stage stochastic linear program (SLP). The company can choose between a riskless asset (cash), several default- and option-free bonds, and an equity investment, and rebalances the portfolio at every stage. The uncertainty faced by the company is reflected in the development of interest rates and equity returns. Our model has two new features compared to the existing literature, which uses no-arbitrage interest rate models for the scenario generation. First, we explicitly estimate a function for the market price of risk and change the underlying probability measure. Second, we simulate scenarios for equity returns with moment-matching by an extension of the interest rate scenario tree.     

Does free cash flow problem contribute to excess stock return synchronicity?

We investigate whether Jensen’s free cash flow problem contributes to excess stock return synchronicity. We find that low-growth firms with high free cash flow have greater stock return synchronicity. These firms also engage in earnings management to lower their disclosure quality. To the extent that free cash flow for low-growth firms provides corporate insiders an opportunity to extract private control benefit, our findings lend direct and concrete support to Jin and Myers (J Financ Econ, 79:257–292, 2006) prediction that insiders increase opaqueness to capture cash flow beyond the level expected by outsider investors. We identify Jensen’s free cash flow problem as an important driver for stock return synchronicity.     

Minimizing CVaR in global dynamic hedging with transaction costs

This study develops a global derivatives hedging methodology which takes into account the presence of transaction costs. It extends the Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239] framework in two ways. First, to reduce the occurrence of extreme losses, the expected utility is replaced by the conditional Value-at-Risk (CVaR) coherent risk measure as the objective function. Second, the normality assumption for the underlying asset returns is relaxed: general distributions are considered to improve the realism of the model and to be consistent with fat tails observed empirically. Dynamic programming is used to solve the hedging problem. The CVaR minimization objective is shown to be part of a time-consistent framework. Simulations with parameters estimated from the S&P 500 financial time series show the superiority of the proposed hedging method over multiple benchmarks from the literature in terms of tail risk reduction.     

Voluntary Termination of Life Insurance Policies

Abstract

In this paper, one error-correction model (ECM) that is able to avoid the problem of producing noise within traditional multiple cointegration vectors has been employed to explore the dynamics of surrender behavior. The evidence shows that both the emergency fund hypothesis and interest rate hypothesis are sustained in the short run as well as in the long run. A unique cointegration relationship within the surrender dynamics has been validated. In addition, a new hypothesis test that stresses the competition for the withdrawal of life insurance policy cash values has also been conducted. Such a crowding-out effect between policy loans and policy surrenders might be attributed to the motivation that keeps a life policy in force, the existence of surrender charges, and the automatic premium loan provision.     

A Direct Test of the Free Cash Flow Hypothesis: Evidence from Real Estate Transactions

This paper tests (Jensen The American Economic Review, 76, 323–329 1986) free cash flow hypothesis using data on real estate transactions. We find that firms with either higher free cash flow or higher cash reserve pay more fore real estate, which is consistent with the free cash flow hypothesis. We also find that the agency costs of free cash flow associated with real estate transactions are more severe when firms have lower Tobin’s Q. Furthermore, we find that among the commonly used corporate governance measures, only equity compensation is effective in mitigating the agency problem of free cash flow.     

Management accounting innovations for rationalizing the cost of services: The reassessment of cash and accrual accounting

ABSTRACT

Management accounting can be a useful tool in austerity government because it produces information about the costs of public services and can be used for informed decision-making. Spanish local governments are required to submit data on the cost of their services to central government, which publishes this information online. The calculation of costs is based on budgetary cash accounting instead of accrual accounting; therefore cash accounting is being used for decision-making and accrual accounting has no role in this process. This paper critically analyses the innovation from three perspectives: the use assigned to the cost information in the legal framework; the opinion of academics and experts; and the perception of professionals about the usefulness of the information produced with the new system.     

RECOGNIZING MACROECONOMIC FLUCTUATIONS IN VALUE BASED MANAGEMENT

Value Based Management (VBM) has become a common tool for evaluating corporate strategies and projects from the perspective of shareholder value maximization, and can be an important input for corporate compensation systems. But traditional VBM frameworks make no systematic effort to distinguish between changes in performance attributable to macroeconomic fluctuations beyond management's control and changes in performance that reflect the intrinsic competitive position of the firm.
The authors have developed an approach for "filtering out" the impact of macroeconomic fluctuations on cash flows for purposes of performance evaluation. Such fluctuations are captured by changes in exchange rates, interest rates, and aggregate price levels (both domestically and abroad) that are significantly correlated with a particular company's cash flows. The authors also provide a method for distinguishing between expected and unanticipated cash flow effects of macro events and recommend insulating managers' performance only from the changes they cannot anticipate and manage. In applying the framework to Electrolux, a Swedish multinational, the authors show that unanticipated changes in the krona/pound exchange rate and various interest rates contribute significantly to the variability of the firm's cash flows; and with the help of the sensitivity coefficients used to measure such exposures, they calculate measures of "intrinsic" cash flow that are purged of such macro effects.     

Authors’ Reply: Credit Standing and the Fair Value of Liabilities: A Critique - Discussion by Marsha Wallace

Abstract

As investment plays an increasingly important role in the insurance business, ruin analysis in the presence of stochastic interest (or stochastic return on investments) has become a key issue in modern risk theory, and the related results should be of interest to actuaries. Although the study of insurance risk models with stochastic interest has attracted a fair amount of attention in recent years, many significant ruin problems associated with these models remain to be investigated. In this paper we consider a risk process with stochastic interest in which the basic risk process is the classical risk process and the stochastic interest process (or the stochastic return-on-investmentgenerating process) is a compound Poisson process with positive drift. Within this framework, we first derive an integro-differential equation for the Gerber-Shiu expected discounted penalty function, and then obtain an exact solution to the equation. We also obtain closed-form expressions for the expected discounted penalty function in some special cases. Finally, we examine a lower bound for the ruin probability of the risk process.     

Cash Flow Risk Management in the Property/Liability Insurance Industry: A Dynamic Factor Modeling Approach

This study proposes and demonstrates a dynamic factor model that can be empirically carried out by the utilization of a factor-augmented autoregressive technique to explain and forecast the time-varying patterns of cash flows of insurance companies in the United States. A principal component approach is employed in the Factor-Augmented Autoregressive Model (FAARM) to capture the augmented factors that are to be utilized for forecasting. We describe the cash flow statistical model by a dimension-reduction technique that can depict the dynamic patterns of the cash flows of insurance firms and then measure the FAARM model. Results from the first step (principal component analysis) help capture the macroeconomic variables and the variables pertaining to insurance companies' cash flows, namely, cash flows from investment, underwriting, and risk management activities. Results from the second step offer evidence supporting that the FAARM improves the out-of-sample forecasting accuracy assessed by a forecasted root-mean-squared error (FRMSE). This article presents a set of feasible FAAR models from which an insurance firm can choose one that can be a better fit to the firm corresponding to its specific firm characteristics, such as firm size. Consequently, the chosen FAARM(s) can improve the accuracy of cash flow forecasting and thus can help insurers to manage risk via cash-flow–matching techniques.     

The persistence of current and proposed measures of operating cash flow

The measurement of operating cash flow using U.S. generally accepted accounting principles (GAAP) currently requires deductions for interest and income tax payments, and prohibits deductions for capital expenditures. In contrast, the IASB and the FASB are jointly proposing a new measure of operating cash flow which prohibits deductions for interest and income tax payments, and requires deductions for capital expenditures. This study compares the persistence of the current and proposed measures of operating cash flow, and the industry-specific results indicate that there is no significant difference between the persistence of the two measures for more than three-fourths of the industries in the sample. Moreover, the Boards’ constituents are recommending the use of a subtotal of operating cash flow prior to capital expenditures, and the results of this study suggest that this subtotal is more persistent for a limited number of industries than the current measure. Overall, the results of this study suggest that the predictive ability of operating cash flow will not change significantly for most industries.     

Hedging and Reserving for Single-Premium Segregated Fund Contracts

Abstract

Three methods for determining suitable provision for maturity guarantees for single-premium segregated fund contracts are compared. Actuarial reserving assumes funds are held in risk-free assets, to give a prescribed probability of meeting the guarantee liability. Dynamic hedging uses the Black-Scholes framework to determine the replicating portfolio. Static hedging assumes a counterparty is willing to sell the options required to meet the guarantee. Using a stochastic cash flow projection, we consider how to assess which approach is most profitable. The example given assumes a typical Canadian segregated fund contract.     

A diffusion approximation for the ruin function of a risk process with compounding assets

Abstract

The traditional theory of collective risk is concerned with fluctuations in the capital reserve {Y(t): t ?O} of an insurance company. The classical model represents {Y(t)} as a positive constant x (initial capital) plus a deterministic linear function (cumulative income) minus a compound Poisson process (cumulative claims). The central problem is to determine the ruin probability ψ(x) that capital ever falls to zero. It is known that, under reasonable assumptions, one can approximate {Y(t)} by an appropriate Wiener process and hence ψ(.) by the corresponding exponential function of (Brownian) first passage probabilities. This paper considers the classical model modified by the assumption that interest is earned continuously on current capital at rate β > O. It is argued that Y(t) can in this case be approximated by a diffusion process Y*(t) which is closely related to the classical Ornstein-Uhlenbeck process. The diffusion {Y*(t)}, which we call compounding Brownian motion, reduces to the ordinary Wiener process when β = O. The first passage probabilities for Y*(t) are found to form a truncated normal distribution, which approximates the ruin function ψ(.) for the model with compounding assets. The approximate expression for ψ(.) is compared against the exact expression for a special case in which the latter is known. Assuming parameter values for which one would anticipate a good approximation, the two expressions are found to agree extremely well over a wide range of initial asset levels.     

Managerial entrenchment and the value of dividends

This study examines the effects of takeover defenses on the value implication of dividends. Using the framework of Fama and French in J Finance 53(3): 819–843 (1998), the paper shows that dividends paid by managers with strong managerial power resulting from takeover protection measures are more valued in the stock market. The results are consistent with the hypothesis of the agency costs of free cash flow built on by Jensen in Am Econ Rev 76(2): 323–329 (1986) in the sense that dividends are important to determine firm value by reducing the free cash flow that would otherwise be deployed for private benefits by entrenched managers. This paper also examines whether the incremental value effect of dividends in entrenched firms is attributable to a numerator effect (changes in the future cash flow) or a denominator effect (changes in the discount rate). The empirical results show that the dividend payout of such firms is more positively related to future performance and more negatively related to information risk, which supports both numerator and denominator effects.     

Divisional Informativeness Gap and Value Creation from Asset Sales

Nanda and Narayanan (1999) show that the information asymmetry between the managers and market participants regarding divisional cash flows helps explain the value creation on asset sales. Based on their theoretical framework, the divisional informativeness gap hypothesis predicts that the announcement‐period return increases with the difference in cash‐flow informativeness of retained and divested divisions prior to the divestiture. Our results, using industry‐average earnings response coefficient as a proxy for cash‐flow informativeness of a division, support this prediction. The effect is stronger when a conglomerate retains the division with relatively greater growth opportunities.     

Correlated interest rate risk and funding strategies for nonfinancial firms

This paper considers appropriate funding strategies for nonfinancial firms when operating cash flows are correlated with interest rates. An example expression is provided for the optimal funding position when the firm has a two-period investment horizon. The conclusion is that matching will be the best strategy if the unbiased expectations hypothesis of the term structure holds and operating cash flows are uncorrelated with interest rates. Since the optimal funding position will be the minimum-risk one if the expectations hypothesis holds, the properties of the minimum-risk funding strategy are also investigated. The primary result is that maturity matching will not necessarily be the optimal funding strategy even when, on average, the cost of long- and short-term funds is the same. Finally, some empirical estimates of minimum risk funding positions for nonfinancial firms are provided using data from the Quarterly CompuStat files. The data indicate that changes in corporate operating earnings are, on average, significantly positively correlated with changes in short-term interest rates, but that there is substantial cross-sectional variation across companies in our sample.