Elsevier

Journal of Banking & Finance

Volume 36, Issue 12, December 2012, Pages 3227-3238
Journal of Banking & Finance

Short-horizon regulation for long-term investors

https://doi.org/10.1016/j.jbankfin.2012.04.009Get rights and content

Abstract

We study the effects of imposing repeated short-horizon regulatory constraints on long-term investors. We show that Value-at-Risk and Expected Shortfall constraints, when imposed dynamically, lead to similar optimal portfolios and wealth distributions. We also show that, in utility terms, the costs of imposing these constraints can be sizeable. For a 96% funded pension plan, both an annual Value-at-Risk constraint and an annual Expected Shortfall constraint can lead to an economic cost of about 2.5–3.8% of initial wealth over a 15-year horizon.

Introduction

This paper investigates the economic consequences of a difference in the planning horizon of an institutional investor pursuing long-term investment strategies and a regulator enforcing prudential standards and practices on a repeated short-term basis. Such a misalignment of horizons is likely to exist in most developed financial markets and affect, for example, banks, insurance companies, and, notably, pension funds.

Consider, for example, a pension fund which typically faces long-term pension liabilities with maturities of 15 years or more. However, standard regulatory frameworks impose short-term solvency constraints. A recent example can be observed in the Netherlands where a pension regulatory regime (“Financieel Toetsings Kader”, FTK) is effective as of January 2007. According to the Dutch regulation, pension funds should always keep the probability of underfunding 1 year ahead below 2.5%. Underfunding refers to the situation where the market value of a pension fund’s assets falls below the market value of the pension fund’s liabilities. In the Netherlands these liabilities are, for now, taken as nominally guaranteed pensions. This will likely change in the near future where pensions are no longer considered to contain guaranteed minimal payments. Other examples of such a misalignment include Basel II regulation for banks and the newly proposed Solvency II regulation for insurance companies.

The existence of such funding constraints can be understood in light of the recent experience of a simultaneous decrease in pension assets due to a poor stock market performance and an increase in pension liabilities due to low interest rates. For the UK, KPMG estimated the aggregate funding deficit of the FTSE-100 companies reaches GBP 40 billion at the end of 2008. De Nederlandsche Bank (the Dutch regulator) reports that the average Dutch pension funding ratio dropped from 144% in 2007 to 99% in the third quarter of 2010. Of all Dutch pension funds, around 68% has a funding ratio below 105%. The situation in the US is even more alarming. The funding deficit in America’s corporate pension funds is estimated to be USD 350 billion (Jørgensen, 2007).

A Value-at-Risk-type (hereafter, VaR-type) constraint aims to limit the probability that the institutional investor generates a portfolio wealth loss and an Expected Shortfall-type constraint aims to control the expected loss given default. Despite the theoretical shortcomings (c.f., Artzner et al., 1999, concerning the VaR-type constraint), both types of regulatory constraints are widely adopted within the current international regulatory regimes, e.g., Basel II and Solvency II.

This paper compares the optimal portfolio wealth and the economic costs of dynamically imposed regulation when the regulatory horizon is as long as the investment horizon and when the regulatory horizon is shorter than the investment horizon. In the latter case, within the investor’s investment horizon, there are a number of subsequent and non-overlapping regulatory checks and the investment horizon is divided into a few equal-length sub-periods. In general, the investor has to insure his portfolio against the bad performance of the financial market to guarantee that (1) the current period’s regulatory constraint is satisfied and (2) there is enough wealth to fulfill next periods’ regulatory constraints. To do so, the investor has to hold more risk-free assets and less risky assets, thus, his ability to profit from favorable financial market performance is limited. The economic costs are measured by the equivalent amount of wealth lost due to the regulatory constraints.

We show that, for both types of regulatory constraints, a short regulatory horizon can prevent portfolio wealth loss very effectively but at the same time also introduces a large opportunity cost by limiting the investor’s ability to invest in risky assets and profit from favorable stock market performance. We also reconfirm the well-known result (see below) that, when the regulatory horizon is as long as the investment horizon, different types of regulation result in a very different optimal portfolio wealth and investment strategy. However, when the regulatory horizon is actually shorter than the investment horizon and regulation is enforced repeatedly, both types of regulatory constraints lead to very similar portfolio wealth distributions and economic cost due to the fact that both types of regulation require the institutional investor to hold enough wealth to satisfy future regulatory constraints. It is important to note that, for insurance companies, regulation aims at minimizing the risk of (partial) default while obviously the induced costs are borne by the management and/or shareholders.

The strategic asset allocation problem has been studied extensively. For example, Kim and Omberg, 1996, Wachter, 2002 study the optimal portfolio allocation where the price of risk is mean-reverting. Bajeux-Besnainou et al., 2003, Sørensen, 1999 solve the optimal investment problem when interest rates are stochastic. This paper is related to the literature studying the optimal portfolio trading strategy under constraints. Grossman and Vila (1992) provide explicit solutions to optimal portfolio problems containing leverage and minimum portfolio return constraints. Basak, 1995, Grossman and Zhou, 1995 focus on the impact of a specific VaR constraint, the portfolio insurance,1 on asset price dynamics in a general equilibrium model. Van Binsbergen and Brandt (2009) assess the influence of ex ante (preventive) and ex post (punitive) risk constraints on dynamic portfolio trading strategies. Ex ante risk constraints include, among others, VaR and short sell constraints. Ex post risk constraints include the loss of the investment manager’s personal compensation and reputation when the portfolio wealth turns out to be low. They found that ex ante risk constraints tend to decrease gains from dynamic investment while ex post risk constraints can be welfare improving.

Basak and Shapiro (2001) compare the impact of VaR-type and Expected Shortfall-type regulation on the institutional investors’ portfolio wealth and trading strategies. Their results show that these two types of regulatory constraints lead to different portfolio wealth distributions. The VaR constraint keeps the portfolio value above or at the threshold value, e.g., the value of a pension fund’s liability, when the investment environment (state of the world) is favorable but generates a sizeable loss in unfavorable states of the world. The favorable (unfavorable) states are the ones in which it is cheap (expensive) for the investor to raise his portfolio wealth to the level of the threshold value. Thus, ironically, the loss under a VaR constraint is even larger than the one without a VaR constraint in unfavorable states. The unfavorable states of the world occur with probability α. This probability is set by the regulator. The explanation is as follows. The VaR constrained investor is only concerned about the probability but neither the magnitude of the loss, nor in which (cheap or expensive) states this loss occurs. Therefore, it is optimal for him to incur losses in unfavorable states where it is most expensive to raise his portfolio wealth. An Expected Shortfall-type constraint, on the contrary, limits the expected magnitude of a loss given default, and thus, does not allow an institutional investor under regulation to incur excessive loss in all market circumstances.

In Basak and Shapiro (2001), the regulatory horizon equals the investment horizon and interest rates are deterministic. We extend the Basak and Shapiro (2001) setting by embedding a number of subsequent and non-overlapping short-term regulatory constraints in the portfolio optimization problem and allowing for a stochastic interest rate. We show that (1) more frequent regulation can prevent the investor from generating losses in unfavorable states due to the fact that there is a minimum amount of portfolio wealth required to fulfill future regulatory constraints and (2) both types of regulation result in a similar portfolio wealth distribution and economic costs if the regulatory constraint is imposed repeatedly.

Cuoco et al. (2008) consider the optimal trading strategy of institutional investors under short-horizon VaR constraints assuming that the portfolio allocation over the VaR horizon is constant and the interest rate is deterministic. We extend Cuoco et al. (2008) by allowing for optimal and time-varying portfolio allocations over the regulatory horizon, having a stochastic interest rate and analyzing the impacts of imposing Expected Shortfall-type regulatory constraints. The extensions enables us to (1) quantify the costs and benefits of both VaR-type and Expected Shortfall-type regulatory constraints given that institutional investors behave optimally, (2) study the hedge strategies of investors under both types of constraints and (3) investigate the difference of imposing these two types of constraints.

This paper is also related to the literature about dynamic trading strategies of pension funds. Sundaresan and Zapatero (1997) consider an optimal asset allocation with a power utility function in final surplus. Boulier et al. (1995) assume a constant investment opportunity set with a risky and a risk-free asset. In their paper, the pension plan sponsor aims to minimize the expected discounted value of future contributions over a given horizon. Inkmann and Blake (2011) propose a new approach to the valuation of pension obligations taking into account the asset allocation strategy and the underfunding risk of a pension fund. This paper focuses on the optimal portfolio wealth of a pension fund when the regulatory horizon is shorter than its investment horizon and evaluates the economic costs of such a regulation. Advantages of having frequent short-term VaR or Expected Shortfall constraints include, among others, smaller expected portfolio wealth losses.

The rest of this paper is organized as follows. Section 2 describes the investment environment our institutional investor operates in. Subsequently, Section 3 introduces the various regulatory constraints and studies the optimal portfolio wealth and trading strategies under a single-regulatory constraint and multiple regulatory constraints respectively. Section 4 discusses the costs of imposing 15 short-term regulatory constraints. Section 5 concludes.

Section snippets

The investment environment

We consider a stochastically complete continuous-time financial market with a finite horizon [0, T]. In this market, four assets are available: a zero-coupon bond maturing at time T, a cash account, a stock index, and a constant maturity zero-coupon bond fund with maturity M. The stock index (with reinvested dividends) is assumed to follow:dSt=(rt+ΦS)Stdt+σSStdZS,t,where rt denotes the short-term interest rate, ΦS is the stock risk premium, σS is the instantaneous stock price volatility and ZS,t

Optimal portfolio wealth and trading strategies

We consider the problem of an institutional investor who starts with an endowment W0 and must dynamically select a portfolio π  Π so as to maximize the expected utility E[u(WT)] of the terminal value of the trading portfolio. We assume that the institutional investor has a power utility function with constant relative risk aversion (CRRA) parameter γ and an investment horizon of T years.

The regulator imposes regulatory constraints, of either a VaR or an Expected Shortfall type, on the

Certainty equivalent loss

In this section, we consider a pension fund with 15-year investment horizon as an example to analyze the cost and the benefit of both the VaR-type and the Expected Shortfall-type prudential regulation. The regulatory horizon considered here is 1 year, meaning that in the 15-year investment horizon, there are 15 non-overlapping regulatory constraints.

To avoid agency conflicts between a pension fund’s participants and the pension fund’s managers, regulatory constraints are needed to protect the

Conclusions

Value-at-Risk and Expected Shortfall constraints are often adopted by regulators to limit the portfolio risk of institutional investors. However, the regulatory horizon is usually much shorter than the institutional investors’ investment horizon. In this paper, we compare the optimal portfolio wealth, optimal portfolio allocation and the overall economic costs when VaR and Expected Shortfall constraints are imposed repeatedly over an institutional investor’s investment horizon. We find, e.g.,

Acknowledgements

We thank the editor, the anonymous referee, Christine Brown, Frank De Jong, Hans Degryse, Paul Kofman, Theo Nijman, Peter Schotman, Hans Schumacher, Jenke Ter Horst, and seminar participants at the IBF annual conference 2012, the third annual Deakin Finance Colloquium, The University of Melbourne, Netspar Pension Day, the Systemic Risk, Basel III, Financial Stability and Regulation conference in Sydney and Tilburg University for helpful comments and suggestions. We kindly acknowledge support

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