process that identifies effi- cient portfolios. It is remarkably robust. For a given time horizon or assuming returns are expressed in continuous units, it delivers the correct result if returns are approximately elliptically distributed, which holds for return distributions that are not skewed, have stable correlations, and comprise asset classes with relatively uniform kurtosis, or if investor preferences are well described by mean and variance.
Chapter 3: The Importance of Asset Allocation
It is commonly assumed that asset allocation explains more than 90% of investment performance.
This belief is based on flawed analysis by Brinson, Hood, and Beebower.
The analysis is flawed because it implicitly assumes that the default portfolio is not invested; it thereby fails to distinguish between the risk driven by asset allocation decisions and the risk driven by the fundamental decision to invest in the first place.
Also, this study, as well as many others, analyzes actual investment choices rather than investment opportunity. By analyzing actual investment choices, these analyses confound the natural importance of an investment activity with an investor's choice to emphasize that activity.
Bootstrap simulation of the potential range of outcomes associated with asset allocation and security selection reveals that security selection has as much or more potential to affect investment performance as asset allocation does.
It does not necessarily follow, though, that investors should devote more resources to security selection than asset allocation, because, as argued by Paul Samuelson, it is easier to be successful at asset allocation than security selection.
Asset allocation is very important, but not for the reasons put forth by Brinson, Hood, and Beebower.
Chapter 4: Time Diversification
It is widely assumed that investing over long horizons is less risky than investing over short horizons, because the likelihood of loss is lower over long horizons.
Paul A. Samuelson showed that time does not diversify risk because, though the probability of loss decreases with time, the magnitude of potential losses increases with time.
It is also true that the probability of loss within an investment horizon never decreases with time.
Finally, the cost of a protective put option increases with time to expira-tion. Therefore, because it costs more to insure against losses over longer periods than shorter periods, it follows that risk does not diminish with time.
Chapter 5: Divergence
Investors commonly assume that standard deviations of asset returns scale with the square root of time and that correlations of returns between assets are invariant to the return interval from which they are estimated.
Both beliefs rest on the same underlying assumption that returns are serially independent from one period to the next.
However, this assumption is empirically false; standard deviations and correlations of longer-interval returns diverge substantially from the standard deviations and correlations estimated from shorter-interval returns.
Investors usually attribute this divergence to non-normality of the returns, but instead it is usually driven by nonzero lagged autocorrelations and cross-correlations.
The divergence of high- and low-frequency estimates of standard deviations and correlations has important implications for portfolio construction, performance measurement, and risk management.
Chapter 6: Correlation Asymmetry
Investors mistakenly believe that diversification is unconditionally beneficial because they implicitly assume that correlations are symmetric.
The evidence shows, however, that correlations differ significantly depending on the size and direction of returns.
Investors should seek diversification when their portfolios' main growth component is performing poorly and unification when their portfolios' main growth component is performing well.
Unfortunately, most asset class pairs exhibit unfavorable correlation profiles characterized by unification on the downside, when it is not wanted, and diversification on the upside, when it is not needed.
Investors can employ full-scale optimization, which is introduced in Chapter 12, to construct portfolios that account implicitly for asymmetric correlations.
Chapter 7: Error Maximization
Some investors believe that optimization is hypersensitive to estimation error because, by construction, optimization overweights asset classes for which expected return is overestimated and risk is underestimated, and it underweights asset classes for which the opposite is true.
We argue that optimization is not hypersensitive to estimation error for reasonably constrained portfolios.
If asset classes are close substitutes for each other, it is true that their weights are likely to change substantially given small input errors, but because they are close substitutes, the correct and incorrect portfolios will have similar expected returns and risk.
If asset classes are dissimilar from each other, small input errors will not cause significant changes to the correct allocations; thus, again the correct and incorrect portfolios will have similar expected returns and risk.
Nevertheless, estimation error is an important challenge to optimization, and investors would be well served to explore ameliorative measures such as Bayesian shrinkage, resampling, and the use of stability-adjusted return distributions.
Chapter 8: Factors
Some investors believe that factors offer greater potential for diversification than asset classes because they appear less correlated than asset classes.
Factors appear less correlated only because the portfolio of assets designed to mimic them includes short positions.
Given the same constraints and the same investable universe, it is mathematically impossible to regroup assets into factors and produce a better efficient frontier.
Some investors also believe that consolidating a large group of securities into a few factors reduces noise more effectively than consolidating them into a few asset classes.
Consolidation reduces noise around means, but no more so by using factors than by using asset classes.
Consolidation does not reduce noise around covariances.
Our results challenge the notion that investors should use factors as portfolio building blocks.
Nevertheless, factors can be useful for other reasons. Factor analysis can help investors understand and manage risk, harvest risk premiums, and enhance returns for investors who are skilled at predicting factor behavior. But we should weigh these potential benefits of factor investing against the incremental noise and trading costs associated with factor replication.
Chapter 9: 1/N
It has been argued that equally weighted portfolios perform better out of sample than optimized portfolios.
The evidence for this result is misleading because it relies on extrapolation of historical means from short samples to estimate expected return. In some samples, the historical means for riskier assets are lower than the historical means for less risky assets, implying, contrary