The efficiency of target-date funds

Abstract

To evaluate the efficiency of target-date funds (TDFs), one of the fastest growing lines of mutual funds, we take 36 TDF series offered in the market and calculate investors’ welfare loss from TDF investment. We divide welfare loss into two categories: loss from suboptimal risky portfolio and loss from inappropriate glide path. We find that inappropriate glide path constitutes the major source of TDF performance inefficiency. This inefficiency could reduce an investor’s annual consumption by up to 17 per cent. We also find that the substantial heterogeneity in TDF performance is primarily caused by variation in glide paths. The heterogeneity contradicts the notion that one TDF fits everyone and it confirms the urgency to match TDF selection to investors’ risk profiles. In this spirit, we advocate a risk-based selection strategy as a remedy for TDF inefficiency. We estimate that this strategy could reduce approximately half of the welfare loss suffered from other commonly used strategies.

Appendices

Appendix A

Appendix A Numerical solution method

Our dynamic programming model was solved using backward induction. The state variables in each period (age) include the cash-on-hand at the beginning of each period and the transitory shock. In the last period, the agent simply consumes all cash-on-hand and generates the value function from that consumption. This value function is then used to compute the policy rules, and the corresponding value function, for the previous period. This process is carried out from the last period to the first period.

We obtained the optimal decision variables (consumption and portfolio allocation) in an unconstrained problem using Nelder-Mead method. When the unconstrained solution generated by Nelder-Mead method is infeasible, we applied a standard grid search to the constrained problem. We also applied standard grid search in several fund family and confirmed that Nelder-Mead method generates global optimal. Then Nelder-Mead is used throughout all of the remaining fund families for computational efficiency. The state-space was discretized using power grid in which the ratio of two adjacent state variables equals to a chosen power parameter. The upper and lower bounds for state-space were chosen to be non-binding in all periods. Gauss–Hermite quadrature method is used to approximate the density functions for innovation to excess stock returns, labor income shock and transitory shocks to perform numerical integrations. In evaluating the value function that corresponds to state variables that do not lie in the chosen grid points, we used a cubic spline interpolation in the log of the state variables.

Appendix B

Estimating TDF risky portfolio return moments

To compute return moments of risky portfolios under each TDF, we adopt the CAPM asset pricing model and regress the excess return of each equity asset under the TDFs on market portfolio – S&P 500 index:

where R _i,t is the excess return for equity asset i at time t; MKT is the excess return for S&P 500. The time period for regression is 1997/1–2010/7(or less if not available for some equities). Using the estimated risk loading from the regression above, we can estimate moments for each equity asset as: where is the vector of estimated mean excess return over all equity assets; is the estimated variance-covariance matrix of excess returns over all equity assets; and are the mean excess return and variance of market portfolio (S&P 500); and is the idiosyncratic risk estimated from the variance-covariance matrix of regression residuals ɛ _i,t .

Now, based on the estimated mean and variance of returns over all equity assets, we estimate moments of risky portfolio in each TDF:

where ω is the weight vector over individual equity assets in the risky portfolio of a particular TDF fund. The risky portfolio return is adjusted for TDF expense e _p . Last, the average risky portfolio returns and standard deviations across all TDFs in one series is used as the return-risk measures for risky portfolio in that TDF series.