Morningstar Advisor - December 2013/January 2014 - (Page 66)
Gray Matters
Optimal Portfolios for the Long Run
By David Blanchett
Our study shows that equity risk declines as time
horizon expands.
There is surprisingly little agreement among
academics about the existence of time
diversification, which we define as the anomaly
where equities become less risky over
longer investment periods. The primary critique
of time diversification is theoretical and the
primary defense empirical.
Samuelson (1963) and Bodie (1995) pointed
out that if stocks are less risky in the long run
there is a free lunch for long-run equity
investors. Bodie (1995) emphasized the fact
that time diversification violates the
Black-Scholes option pricing model. If time
diversification exists, then options hedging
long-run equity risk should reflect a decreasing
likelihood of loss over longer time periods (they
don't).1 Campbell and Viceira (2003) argued
that empirical evidence shows that stock
returns are not independent and identically
distributed over time (they tend to mean revert),
which implies that long-run stock returns
may be predictable and that long-run investors
should overweight equities.2
1 Black-Scholes could also be inconsistent with time diversification if security returns don't follow a Weiner or Brownian process. 2 Campbell and Viceira (2003) also note that the
mean reverting returns, which are necessary for time diversification, imply that a buy-and-hold strategy is suboptimal. Those who practice time diversification should be aware that
the logic which underlies time diversification is also consistent with valuation-based market timing.
66 Morningstar Advisor December/January 2014
Table of Contents for the Digital Edition of Morningstar Advisor - December 2013/January 2014