Abstract
I investigate the question of how to construct a benchmark replicating portfolio consisting of a subset of the benchmark’s components. I consider two approaches: a sequential stepwise regression and another method based on factor models of security returns’ first and second moments. The first approach produces the standard hedge portfolio that has the maximum feasible correlation with the benchmark. The second approach produces weights that are proportional to a “signal-to-noise” ratio of factor beta to idiosyncratic volatility. Using a factor model of securities returns allows the use of a larger number of securities than the number of time periods used to estimate the parameters of the factor model. I also consider a second objective that maximizes expected returns subject to a target tracking error variance. The security selection criterion naturally extends to the product of the information ratio and the signal-to-noise ratio. The optimal tracking portfolio is either a one-fund or a two-fund portfolio rule consisting of the optimal hedging portfolio, the tangent portfolio or the global minimum variance portfolio, depending on what constraints are imposed on the objective function. I construct buy-and-hold replicating portfolios using the algorithms presented in the paper to track a widely followed stock index with very good results both in-sample and out-of-sample.
Highlights
A frequent question that arises in portfolio management is how on can construct a portfolio of securities that will best mimic the performance of a benchmark index
This table reports the in-s√ample and out-of-sample correlation of the tracking portfolio return with the index return ρpy, daily tracking error v and cumulative out-of-sample return differential between the tracking portfolio and the index RAR, and the intercept αp and the slope βp of a simple linear regression of the portfolio excess return on the benchmark index excess return
The results are quite intuitive and suggest that the securities that make it into the tracking portfolio have the highest ratios of factor beta to residual error variance
Summary
A frequent question that arises in portfolio management is how on can construct a portfolio of securities that will best mimic the performance of a benchmark index. Glabadanidis (2014) applied an approximate factor structure to the mean and variance of security returns, thereby providing more straightforward optimal portfolio weight solutions. In the context of replicating hedge fund returns, Hasanhodzic and Lo (2007) apply linear multi-factor regressions of hedge fund returns on the returns of several asset classes encompassing a broad spectrum of risk exposures They offer a good way of scaling the replicating portfolio weights to match the volatility of the target in sample. I show that in the context of minimizing the tracking error variance, the replicating portfolio weights are proportional to the tangent portfolio weights scaled by the benchmark beta This approach allows for a number of securities that can be much larger than the number of periods used to estimate the factor model parameters.
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