Diversification Across Time
Yale University - Yale Law School; Yale University - Yale School of Management
Barry J. Nalebuff
Yale University - Yale School of Management
October 4, 2010
Yale Law & Economics Research Paper No. 413
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.
Number of Pages in PDF File: 34
Keywords: Diversification, Leverage, Retirement, Investment Strategy
JEL Classification: D31, G1, G11, G18, H5
Date posted: October 5, 2010 ; Last revised: November 5, 2010
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