A Half Century of Returns on Levered and Unlevered Portfolios of Stocks, Bonds, and Bills, with and without Small Stocks

Abstract

In two earlier papers (Grauer and Hakansson 1982; Grauer and Hakansson 1984), we applied the multiperiod portfolio theory of Mossin (1968), Hakansson (1971, 1974), Leland (1972), Ross (1974), and Huberman and Ross (1983) to the construction and rebalancing of portfolios composed of U.S. stocks, corporate bonds, government bonds, and a risk-free asset. Borrowing was ruled out in the first article, while margin purchases were permitted in the second. The probability distributions used were naively estimated from past realized returns in Ibbotson This paper applies multiperiod portfolio theory to the construction and rebalancing of portfolios composed of U.S. stocks, corporate bonds, government bonds, and a risk-free asset, with small stocks included as a separate investment vehicle. Probability assessments are based on the past, joint empirical distribution. Our principal findings are (1) small stocks, while totally ignored at times, entered even the most riskaverse portfolios most of the time and (2) small stocks, when chosen, tended to replace common stocks, except in the 1970s and early 1980s, when they were primarily held in lieu of the risk-free asset. * Presented at the Australian Graduate School of Management and at Macquarie University, both in Sydney, Southern Methodist University, Duke University, the University of Southern California, the London Graduate School of Business, and the annual meeting of the Western Financo Association in Scottsdale, Arizona. The authors thank the participants of these seminars, especially Michael Brennan and Ehud Ronn, for helpful comments. Financial support from the Social Sciences and Humanities Research Council of Canada and the Financial Research Foundation of Canada is gratefully acknowledged. The authors also wish to thank Changwoo Lee for research assistance and are greatly indebted to Frederick Shen for computational assistance.