DYNAMIC ASSET ALLOCATION FOR TARGET DATE FUNDS UNDER THE BENCHMARK APPROACH

ABSTRACT Target date funds (TDFs) are becoming increasingly popular investment choices among investors with long-term prospects. Examples include members of superannuation funds seeking to save for retirement at a given age. TDFs provide efficient risk exposures to a diversified range of asset classes that dynamically match the risk profile of the investment payoff as the investors age. This is often achieved by making increasingly conservative asset allocations over time as the retirement date approaches. Such dynamically evolving allocation strategies for TDFs are often referred to as glide paths. We propose a systematic approach to the design of optimal TDF glide paths implied by retirement dates and risk preferences and construct the corresponding dynamic asset allocation strategy that delivers the optimal payoffs at minimal costs. The TDF strategies we propose are dynamic portfolios consisting of units of the growth-optimal portfolio (GP) and the risk-free asset. Here, the GP is often approximated by a well-diversified index of multiple risky assets. We backtest the TDF strategies with the historical returns of the S&P500 total return index serving as the GP approximation.

APPROXIMATING THE GROWTH OPTIMAL PORTFOLIO AND STOCK PRICE BUBBLES

In practice, optimal portfolio construction for large stock markets has never been conclusively resolved because estimating the required means of returns with sufficient accuracy is a highly intractable task. By avoiding estimation, this paper approximates closely the growth optimal portfolio (GP) for the stocks of developed markets with a well-diversified, hierarchically weighted index (HWI). For stocks denominated in units of the HWI, their current value turns out to be strictly greater than their future expected values, which indicates the existence of stock price bubbles that could be systematically exploited for long-term asset management. It is shown that the HWI does not leave much room for significant performance improvements as proxy for the GP.

Optimal Risk Budgeting under a Finite Investment Horizon

The Growth-Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize long-term wealth. This multi-horizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz’s mean-variance or risk parity. The GOP literature typically considers risk-neutral investors with an infinite investment horizon. In this paper, we compute the optimal bet sizes in the more realistic setting of risk-averse investors with finite investment horizons. We find that, under this more realistic setting, the optimal bet sizes are considerably smaller than previously suggested by the GOP literature. We also develop quantitative methods for determining the risk-adjusted growth allocations (or risk budgeting) for a given finite investment horizon.

The Kelly Growth Optimal Portfolio with Ensemble Learning

As a competitive alternative to the Markowitz mean-variance portfolio, the Kelly growth optimal portfolio has drawn sufficient attention in investment science. While the growth optimal portfolio is theoretically guaranteed to dominate any other portfolio with probability 1 in the long run, it practically tends to be highly risky in the short term. Moreover, empirical analysis and performance enhancement studies under practical settings are surprisingly short. In particular, how to handle the challenging but realistic condition with insufficient training data has barely been investigated. In order to fill voids, especially grappling with the difficulty from small samples, in this paper, we propose a growth optimal portfolio strategy equipped with ensemble learning. We synergically leverage the bootstrap aggregating algorithm and the random subspace method into portfolio construction to mitigate estimation error. We analyze the behavior and hyperparameter selection of the proposed strategy by simulation, and then corroborate its effectiveness by comparing its out-of-sample performance with those of 10 competing strategies on four datasets. Experimental results lucidly confirm that the new strategy has superiority in extensive evaluation criteria.

Continuous-Time Portfolio Choice and Pricing

The Euler equation is defined. The static approach can be used to derive an optimal portfolio in a complete market and when the investment opportunity set is constant. In the latter case, the optimal portfolio is proportional to the growth‐optimal portfolio and two‐fund separation holds. Dynamic programming and the Hamilton‐Jacobi‐Bellman equation are explained. An optimal portfolio consists of myopic and hedging demands. The envelope condition is explained. CRRA utility implies a CRRA value function. The CCAPM and ICAPM are derived.

A tractable model for indices approximating the growth optimal portfolio

The growth optimal portfolio (GOP) plays an important role in finance, where it serves as the numéraire portfolio, with respect to which contingent claims can be priced under the real world probability measure. This paper models the GOP using a time dependent constant elasticity of variance (TCEV) model. The TCEV model has high tractability for a range of derivative prices and fits well the dynamics of a global diversified world equity index. This is confirmed when pricing and hedging various derivatives using this index.