Summary:
Despite the common market practice of predicting policy rate movements from inflation and adjusting portfolios correspondingly, few studies have formally explored the problem of portfolio selection under any given monetary policy paradigm. From a theoretical point of view, although the foundations of the Dynamic New Keynesian (DNK) model for macroeconomic policymaking and the stochastic dynamic models for portfolio selection both stem from the classical growth model, their different focuses have led to divergent formalisms and solution techniques. This paper explores a portfolio selection model under a continuous-time sticky-price general equilibrium and studies the implications of asset allocation under endogenous macroeconomic dynamics and monetary policy rules. It is well known that the inflation-targeting paradigm that many central banks currently adopt is supported by a DNK framework in which the inefficiency of the economy is caused by inertia in price adjustments. An inflation-targeting monetary policy in this economy coincides with the optimal policy of a benevolent central bank whose optimization target is the intertemporal utility of a representative agent. Moreover, a rule-based monetary policy such as the Taylor rule avoids the inconsistency of discretionary policies. However, intuitively, investors can take advantage of a rule-based central bank and improve their portfolio performance. More specifically, by constructing a continuous-time model of portfolio selection under a benchmark DNK economy and discussing its numerical solution techniques, this paper shows that, under optimal allocation strategies, the inverse of the Arrow–Pratt relative risk aversion function of investors decreases monotonically with a rising risk-free nominal interest rate, and exhibits a U shape with respect to inflation. This means that under the premise of an inflation-targeting monetary policy rule, the relative inclination of investors toward risky assets grows when inflation deviates from its steady state in expectation of a countervailing nominal policy rate. The results show that prior to the subprime crisis, the proposed model outperforms a traditional model that does not take monetary policy into consideration, but falls behind thereafter. A possible explanation is that before the crisis, the Fed's monetary policy can clearly be approximated by a Taylor rule that meets the prerequisites for the proposed allocation strategy, whereas after the introduction of quantitative easing, not only can the risk-free rate no longer be approximated by the Taylor rule, but the monetary policy also begins to take financial markets and institutions into account. However, because an investor can now use risky assets for intertemporal resource allocation and its utility involves additional gains/losses from holding risky assets, the optimality of a monetary policy that targets the general price level needs to be reexamined. This paper uses the aforementioned model to discuss the macro-prudential problem of the feedback effects of investor profit-maximizing behavior on the economy. Preliminary results show that the existence of risky assets in the economy can have an effect similar to that of the financial accelerator. This gives another possible explanation for the wedge effect and differentiated risk appetite introduced in previous works on the credit channel of monetary policy transmission. The assumptions that lead to the above results may need further justification. For instance, the price processes of risky assets are given exogenously in this paper; moreover, the assumption that the monetary policy follows the Taylor rule may not comply with the post-crisis practice of monetary authorities. However, endogenizing risky asset dynamics and the optimal behavior of central banks will render the Bellman equation too large to be solvable, given that the complexity of the numerical method utilized in this paper grows exponentially with the number of state variables. Therefore, a more efficient solution algorithm is a prerequisite for further extensions. From the viewpoint of monetary policymaking, although rule-based policies facilitate the management of expectations and avoid the inconsistency of discretion, they may also bring about arbitrage opportunities. Therefore, future research on the design of an incentive-compatible macro-prudential regulation framework is needed to prevent investors from taking excessive risks.
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