Financial Decisions - Document Index

Multi-period Efficient Frontiers and Sharpe Ratios under the Buy and Hold and the Rebalancing Strategies

Marlena Akhbari

Nicolas Gressis

Wright State University

Abstract

We analyze and compare multi-period efficient frontiers and Sharpe Ratios under Buy and Hold and Rebalancing strategies. We show that the single-period capital market line preserves its linearity in the multi-period case under Buy and Hold, whereas it becomes a concave curve under Rebalancing. This finding makes it clear that benchmarks used as measures of performance could likely be inappropriate if the underlying theory is not accounted for in their selection. Further, we show that the multi-period efficient frontier is a hybrid of the Rebalancing frontier for riskless lending/risky equity combinations and of the Buy and Hold frontier for riskless borrowing/risky equity combinations. This finding suggests that more risk tolerant investors can justify their selection of the Buy and Hold Strategy for multi-period investing. Moreover, we show that multi-period Sharpe Ratios are unaffected by the riskiness of the portfolio under Buy and Hold, but inversely related to portfolio risk under Rebalancing. Our analysis indicates that an understanding of the form of the multi-period efficient frontier is important to portfolio performance measurement.