Computing optimal rebalance frequency for log-optimal portfolios

Log-optimal investment portfolio is deemed to be impractical and cost-prohibitive due to inherent need for continuous rebalancing and significant overhead of trading cost. We study the question of how often a log-optimal portfolio should be rebalanced for any given finite investment horizon. We develop an analytical framework to compute the expected log of portfolio growth when a given discrete-time periodic rebalance frequency is used. For a certain class of portfolio assets, we compute the optimal rebalance frequency. We show that it is possible to improve investor log utility using this quasi-passive or hybrid rebalancing strategy. Simulation studies show that an investor shall gain significantly by rebalancing periodically in discrete time, overcoming the limitations of continuous rebalancing.     

Positive forward rates in the maximum smoothenss framework

In this paper we present a nonlinerar dynamic programming algorithm for the computation of forward rates within the maximum smoothness framework. The algorithm implements the forward rate positivity constraint for a one-parametric family of smoothness measures and it handles price spreads in the constraining data set. We investigate the outcome of the algorithm using thw Swedish Bond market showing examples where the absence of the positive constraint leads to negative interest rates. Furthermore we investigate the predictive accuracy of the algorithm as we move along the family of smoothness measures. Amon other things we onserve that the inclusion of spreads not only improves the smoothness of forward curves but also significantly reduces the predictive error.     

Reduction of estimation risk in optimal portfolio choice using redundant constraints

It is well known that when the moments of the distribution governing returns are estimated from sample data, the out-of-sample performance of the optimal solution of a mean–variance (MV) portfolio problem deteriorates as a consequence of the so-called “estimation risk”. In this document we provide a theoretical analysis of the effects caused by redundant constraints on the out-of-sample performance of optimal MV portfolios. In particular, we show that the out-of-sample performance of the plug-in estimator of the optimal MV portfolio can be improved by adding any set of redundant linear constraints. We also illustrate our findings when risky assets are equally correlated and identically distributed. In this specific case, we report an emerging trade-off between diversification and estimation risk and that the allocation of estimation risk across portfolios forming the optimal solution changes dramatically in terms of number of assets and correlations.     

Do commodities add value in multi-asset portfolios? An out-of-sample analysis for different investment strategies

An essential motive for investing in commodities is to enhance the performance of portfolios traditionally including only stocks and bonds. We analyze the in-sample and out-of-sample portfolio effects resulting from adding commodities to a stock-bond portfolio for commonly implemented asset allocation strategies such as equally- and strategically-weighted portfolios, risk-parity, minimum-variance as well as reward-to-risk timing, mean-variance and Black–Litterman. We analyze different commodity groups such as agricultural and livestock commodities that currently are critically discussed. The out-of-sample portfolio analysis indicates that the attainable benefits of commodities are much smaller than suggested by previous in-sample studies. Hence, in-sample analyses, such as spanning tests, might exaggerate the advantages of commodities. Moreover, the portfolio gains greatly vary between different types of commodities and sub-periods. While aggregate commodity indices, industrial and precious metals as well as energy improve the performance of a stock-bond portfolio for most asset allocation strategies, we hardly find positive portfolio effects for agriculture and livestock. Consequently, investments in food commodities are not essential for efficient asset allocation.