Diversification Across Time

34 Pages Posted: 5 Oct 2010 Last revised: 5 Nov 2010

See all articles by Ian Ayres

Ian Ayres

Yale University - Yale Law School; Yale University - Yale School of Management

Barry J. Nalebuff

Yale University - Yale School of Management; Yale University - Cowles Foundation

Date Written: October 4, 2010


By employing leverage to gain more exposure to stocks when young, individuals can achieve better diversification across time. Using stock data going back to 1871, we show that early leverage combined with reduced equity exposure when older can reduce lifetime portfolio risk. For example, an initially-leveraged portfolio can produce the same mean accumulation as a constant 75% stock allocation with a 21% smaller standard deviation. Since the mean accumulation is the same, the reduction in volatility does not depend on the equity premium. A leveraged lifecycle strategy can also allow investors to come closer to their utility-maximizing allocation. If risk preferences would lead an investor to allocate 50% of his discounted retirement savings to stocks, that would require a young investor to put well more than 50% of his liquid savings into stocks. We employ leverage (limited to 2:1) to help the investor overcome a limited ability to borrow against human capital. Based on historical returns, we find a 37% improvement in the certainty equivalent (for CRRA=4). Monte Carlo simulations show that these gains continue even with equity premia well below the historical average.

Keywords: Diversification, Leverage, Retirement, Investment Strategy

JEL Classification: D31, G1, G11, G18, H5

Suggested Citation

Ayres, Ian and Nalebuff, Barry, Diversification Across Time (October 4, 2010). Yale Law & Economics Research Paper No. 413, Available at SSRN: https://ssrn.com/abstract=1687272 or http://dx.doi.org/10.2139/ssrn.1687272

Ian Ayres (Contact Author)

Yale University - Yale Law School ( email )

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Yale University - Yale School of Management

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Barry Nalebuff

Yale University - Yale School of Management ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States
203-432-5968 (Phone)
203-432-6974 (Fax)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-5968 (Phone)

HOME PAGE: http://barrynalebuff.com

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