Long-term investors face economic consequences from short-term regulatory horizons. The authors examine the optimal portfolio wealth and the economic costs of imposed regulation when the regulatory horizon is as long as the investment horizon and when the regulatory horizon is shorter than the investment horizon.

## What’s Inside?

The authors investigate the effects of a misalignment between the 10- to 15-year strategic planning horizon of institutional investors and the standard short-term horizon of regulators who are enforcing prudential standards and practices. Regulators consider nonoverlapping, repeated, short-term subperiods, but these short-term periods will ultimately sum to an equivalent long-term stretch of time. The genesis of the problem is that to satisfy the current period’s regulatory constraint—as well as the necessity of holding the portfolio wealth above the minimum portfolio wealth level to fulfill the next periods’ regulatory hurdle—regulated investors must hold more risk-free and low-risk assets than is ideal, thereby limiting their ability to profit from positive financial performance.

## How Is This Research Useful to Practitioners?

The 2008 financial crisis revealed the unattractive impact of a simultaneous decrease in pension assets as a result of poor stock market performance and increase in pension liabilities as a result of low interest rates. The authors show that the costs of imposing both value at risk (VaR) and expected shortfall (ES) constraints, when imposed dynamically over rolling short-term periods, lead to surprisingly similar optimal portfolios and wealth distributions. Each type of regulatory constraint requires the institutional investor to hold enough wealth to satisfy future regulatory constraints and thus introduces a large opportunity cost by limiting the investor’s ability to invest in risky assets and profit from favorable stock market performance.

The advantages of having frequent short-term VaR or ES constraints include smaller expected portfolio wealth losses, but the economic cost is measured by the equivalent amount of wealth that is lost because of the regulatory constraints. The cost of imposing these constraints can be significant—about 2.5–3.8% of initial wealth over a 15-year horizon. Studies exploring such a misalignment are particularly relevant to those interested in Basel II regulation for banks and the newly proposed Solvency II guidelines for insurance companies, particularly given the strong equity market performance after the widespread acceptance of the errant “new normal” global macro framework, which forecasts muted asset class returns following the 2008 financial crisis.

## How Did the Authors Conduct This Research?

The authors investigate the differences between imposing a VaR constraint and imposing an ES constraint. They then study the optimal portfolio wealth under a single regulatory constraint that matches the investor’s long-term planning horizon and under multiple regulatory planning constraints that are made up of smaller subperiods. In the single-constraint model, the horizon of the regulatory constraint equals the investment horizon, whereas in the two-constraint model, the regulatory constraint is half as long as the investment horizon.

Four assets are assumed to be available: a zero-coupon bond maturing at time
*T*, a cash account, a stock index, and a constant maturity zero-coupon
bond with maturity *M*. The zero-coupon bond maturing at time
*T* has two tasks: It serves to achieve the optimal interest rate exposure
for speculative purposes and hedges the interest rate risk over the long-term investment
horizon. Regulators can impose either a VaR-type or an ES-type regulatory constraint on the
institutional investor. The VaR-type constraint aims to control the probability of having a
portfolio wealth loss greater than the prespecified amount, whereas an ES-type constraint
aims to limit the magnitude of the portfolio wealth loss rather than the probability. The
authors explore an ES constraint as well as an expected discounted shortfall (EDS)
constraint, both of which are relatively small numbers—less than 1% of initial wealth.
The distinction between ES and EDS constraints lies in whether or not the expected portfolio
wealth shortfall is discounted using a pricing kernel, another name for the stochastic
discount factor used in asset pricing.

## Abstractor’s Viewpoint

Various constraints effectively redistribute wealth among the various states of the investment environment. Other researchers have reconfirmed the well-known result that when the regulatory horizon is as long as the investment horizon, different types of regulation result in different optimal portfolio wealth and investment strategies. A key distinction is that for the VaR constraint, there is no punishment for the severity of the loss once it occurs; therefore, it is optimal to accept large losses in bad investment environments. The ES and EDS constraints, however, do weigh the size of the loss and thus force the investor to put more weight on hedging assets as financial market performance deteriorates. The investor under a VaR-type constraint has an incentive to “gamble”; this incentive is still present but much weaker under ES and EDS constraints.