than characterizing returns as coming from a single, stable regime, it might be more realistic to assume they are generated by disparate regimes such as a calm regime and a turbulent regime.
Investors may wish to build portfolios that are more resilient to turbulent regimes by employing stability-adjusted optimization, which relies more on relatively stable covariances than on unstable covariances, or by blending the covariances from calm and turbulent subsamples in a way that places greater emphasis on covariances that prevailed during turbulent regimes.
These approaches produce static portfolios, which still display unstable risk profiles.
Investors may instead prefer to manage a portfolio's asset mix dynam- ically, by switching to defensive asset classes during turbulent periods and to aggressive asset classes during calm periods.
It has been shown that hidden Markov models are effective at distin-guishing between calm and turbulent regimes by accounting for the level, volatility, and persistence of the regime characteristics.
Chapter 23: Scenario Analysis
Scenario analysis requires investors to define prospective economic scenarios, assign probabilities to them, translate the scenarios into expected asset class returns, and identify the most suitable portfolio given all these inputs.
The greatest challenge to scenario analysis is determining each scenario's probability.
We can estimate a scenario's probability by measuring its statistical similarity to current economic conditions or normal economic conditions using a statistic called the Mahalanobis distance.
This framework also allows us to identify the smallest changes in the scenario descriptions that would be required to equate the empirical probabilities with our subjective views.
We can further enhance scenario analysis by describing scenarios as paths rather than as single-period average outcomes.
Chapter 24: Stress Testing
Investors typically evaluate exposure to loss based on a portfolio's full- sample distribution of returns at the end of their investment horizon.
However, investors care about what happens throughout their investment horizon and not just at its conclusion.
They also recognize that losses are more common when markets are turbulent than when they are calm.
First passage time probabilities enable investors to estimate probability of loss and value at risk throughout their investment horizon.
The Mahalanobis distance allows investors to distinguish between calm and turbulent markets.
Investors can assess risk more realistically by applying first passage time probabilities to the returns that prevailed during turbulent subsamples.
CHAPTER 1 What Is an Asset Class?
Investors have access to a vast array of assets with which to form portfolios, ranging from individual securities to broadly diversified funds. The first order of business is to organize this massive opportunity set into a manageable set of choices. If investors stratify their opportunity set at too granular a level, they will struggle to process the mass of information required to make informed decisions. If, instead, they stratify their opportunity set at a level that is too coarse, they will be unable to diversify risk efficiently. Asset classes serve to balance this trade-off between unwieldy granularity and inefficient aggregation.
In light of this trade-off and other considerations, we propose the following definition of an asset class.
An asset class is a stable aggregation of investable units that is internally homogeneous and externally heterogeneous, that when added to a portfolio raises its expected utility without requiring selection skill, and which can be accessed cost-effectively in size.
This definition captures seven essential characteristics of an asset class. Let us consider each one in detail.
STABLE AGGREGATION
The composition of an asset class should be relatively stable. Otherwise, ascertaining its appropriate composition would require continual monitoring and analysis, and maintaining the appropriate composition would necessitate frequent rebalancing. Both efforts could be prohibitively expensive.
Asset classes whose constituents are weighted according to their relative capitalizations are stable, because when their prices change, their relative capitalizations change proportionately. By contrast, a proposed asset class whose constituents are weighted according to attributes that shift through time, such as momentum, value, or size, may not have a sufficiently stable composition to qualify as an asset class. Sufficiency, of course, is an empirical issue. Momentum is less stable than value, which is less stable than size. Therefore, a group of momentum stocks would likely fail to qualify as an asset class, while stocks within a certain capitalization range might warrant status as an asset class. Value stocks reside somewhere near the center of the stability spectrum and may or may not qualify as an asset class.
Investable
The underlying components of an asset class should be directly investable. If they are not directly investable, such as economic variables, then the investor would need to identify a set of replicating securities that tracks the economic variable. Replication poses two challenges. First, in addition to the uncertainty surrounding the out-of-sample behavior of the economic variable itself, the investor is exposed to the uncertainty of the mapping coefficients that define the association between the economic variable and the replicating securities. Second, because the optimal composition of the replicating securities changes through time, the investor is exposed to additional rebalancing costs.
INTERNALLY HOMOGENEOUS
The components within an asset class should be similar to each other. If they are not, the investor imposes an implicit constraint that two or more distinct groupings within the proposed asset class must be held according to their weights within the asset class. There is nothing to ensure that the weights of distinct groupings within a larger group are efficient. If the proposed asset class is disaggregated into distinct groupings, the investor is free to weight them for maximum efficiency.
Consider, for example, global equities. Domestic equities may behave very differently from foreign equities, and developed market foreign equities may behave differently from emerging market equities. Investors may be able to form a more efficient portfolio by disentangling these equity markets and weighting them based on their respective contributions to a portfolio's expected utility, as opposed to fixing their weights as they appear in a broad global index. Not only might the optimal weights of these components shift relative to each other, but the optimal allocation to equities as a whole might shift up or down relative to the allocation that would occur if they were treated as a unified asset class.
EXTERNALLY HETEROGENEOUS
Each asset class should be sufficiently dissimilar from the other asset classes in a portfolio as well as linear combinations of other asset classes. If the asset classes are too similar to each other, their redundancy will force the investor to expend unnecessary resources analyzing their expected return and risk properties and searching for the most effective way to invest in them.
In Chapter 2, we build portfolios from seven asset classes: US equities, foreign developed market equities, emerging market equities, Treasury bonds, corporate bonds, commodities, and cash equivalents. We considered including intermediate-term bonds as well. However, the lowest possible