Ast Allocation
Noël Amenc and Lionel Martellini
Two competing approaches are ud in practice to build portfolios: bottom-up and top-down. The bottom-up approach is the older and the more traditional, and focus on individual stock picking. The top-down approach gives more importance to the choice of different markets as oppod to individual curity lection, and, as such emphasizes the importance of ast allocation.
Ast allocation consists of choosing the spread of different ast class within the portfolio. There two parate steps in the ast allocation process. One first defines the long-term allocation, bad on estimates of risk and return for each ast class. This is known as « strategic allocation ». Then, one can subquently carry out dynamic adjustments bad on short-term anticipations. This is known as « tactical allocation ». Strategic Ast Allocation1
Strategic allocation is the first stage in the investment process. It involves choosing an initial portfolio allocation consistent with the investor's objectives and constraints. This is equivalent to defining the benchmark, or reference, portfolio.
Optimal ast allocation, which is bad on long-term estimates of risk and return for each ast class, can be bad on a quantitative approach, with the help of different methods that we now describe.
Applying Markowitz's Model to Ast Allocation2
The most widely quoted quantitative model in the strategic allocation literature is Markowitz's (1952) optimization model. The input data is the means and the variances, estimated for each ast class, and the covariances between the ast class. The model provides the optimal percentage to assign to each ast class to obtain the highest return for a given level of risk, measured by portfolio volatility. The t of all optimal portfolios is known as the « efficient frontier » (e Figure below).
1 For more detailed information, e Chapter 9 of Farrell (1997).
2 See in particular Chapter 2 of Farrell (1997) or Chapter 28 of Fabozzi (1995).
This quadratic optimization can be subject to a number of constraints, for example, holding a minimum or maximum allocation in a given ast class.
This model turns out to be particularly appropriate for handling the problem of ast allocation, becau the number of ast class is limited and therefore efficient estimation of the variance-covariance matrix becomes more tractable.
New Developments3
Even though Markowitz’s optimal portfolio lection method provides, in theory, a satisfactory respon to the problem of determining strategic allocation, it is actually not very widely ud in practice for the following two reasons. Firstly, the optimal proportions are very nsitive to the estimates of expected return values; condly, statistical estimates of expected returns are very noisy (e Merton (1980)). As a result, the model often allocates the most significant proportion to the ast class with the largest estimation error!
A pragmatic respon to the problem of optimal strategic allocation in the prence of estimation risk involves focusing on the only portfolio on the efficient frontier for which the estimation of mean returns is not necessary, namely the minimum variance portfolio. Using appropriate statistical techni
ques to improve the estimation of the variance-covariance matrix, one can actually lect an efficient portfolio with a volatility significantly lower than that of a naively diversified portfolio for a mean return that is not necessarily lower (e for example Chan, Karceski and Lakonishok (1999) or Amenc and Martellini (2002a)).
Black and Litterman (1990) have propod an original approach that allows investors to directly address the problem of estimating expected returns. They first suggest generating implicit values for mean returns that are consistent with Sharpe’s (1964) CAPM equilibrium allocations (i.e., allocations proportional to the market capitalization). Then, 3 For more information on some of the new developments, e Michaud (2002).
they suggest that investors optimally combine the reference values with their own "views" (forward-looking bets on mean returns for each ast class).4
Another shortcoming of Markowitz’s approach is that it is bad on volatility as a measure of risk, which can only be rationalized at the cost of very simplifying assumptions, either on investors’ preferences (quadratic preferences) or on return distribution (Gaussian distribution). To address this shortcoming of traditional mean-variance analysis, veral authors have suggested adding a Value-a
t-Risk constraint in the mean-variance optimization for investors with non-trivial preferences about higher moments of returns distributions (e for example Alexander and Baptista (2001) or Sentana (2001)). Amenc and Martellini (2002b) argue that this is particularly needed when alternative ast class, such as hedge funds, are included in an investor’s ast allocation, as they are well known to exhibit fat tails (e for example Brooks and Kat (2001)).
Tactical Ast Allocation5
Tactical Ast Allocation (TAA) broadly refers to active strategies that ek to enhance portfolio performance by opportunistically shifting the ast mix in a portfolio in respon to the changing patterns of return and risk
There is now a connsus in empirical finance that expected ast returns, and also variances and covariances, are, to some extent, predictable. Pioneering work on the predictability of ast class returns in the U.S. market was carried out by Keim and Stambaugh (1986), Campbell (1987), Campbell and Shiller (1988), Fama and French (1989), and Ferson and Harvey (1991). More recently, some authors started to investigate this phenomenon on an international basis by studying the predictability of ast class returns in various national markets (e, for example, Bekaert and Hodrick (1992), Ferson and Harvey (1993, 1995) or Harvey (1995)).
The literature on optimal portfolio lection has recognized that the insights can be exploited to improve on existing policies bad upon unconditional estimates. Roughly speaking, the prescriptions of the models are that investors should increa their allocation to risky asts in periods of high expected returns (market timing) and decrea their allocation in periods of high volatility (volatility timing). Kandel and Stambaugh (1996) argue that even a low level of statistical predictability can generate economic significance and abnormal returns may be attained even if the market is successfully timed only 1 out of 100 times.
TAA can be regarded as a 3 steps process:
4 This approach has been extended by Cvitanic et al. (2002) to a dynamic tting with power preferences, correlated priors and learning
5 We refer the reader to the essay on Tactical Ast Allocation by Martellini and Sfeir in this Encyclopedia for more detail.
• Step 1: forecast ast returns by ast class
• Step 2: build portfolios bad on forecasts (i.e., turn signals into bets)
• Step 3: conduct out-of-sample performance tests
TAA strategies were traditionally concerned with allocating wealth between two ast class, typically shifting between stocks and bonds. More recently, more complex style timing strategies have been successfully tested and implemented. In particular, Kao and Shumaker (1999) and Amenc, El Bied and Martellini (2002) have built upon the minal work by Fama and French (1992), who emphasize the relevance of size and book/market factors, to address the concept of tactical style allocation that involves dynamic trading in various investment styles within a given ast class (e also Fan (1995), Sorenn and Lazzara (1995), and Avramov (2000) for evidence of predictability in equity style returns).
Conclusion
Today, ast allocation tends to play a larger role in the investment management process6. The interest in ast allocation can be explained by important results established by modern portfolio theory. In particular, Brinson, Hood and Beebower (1986) and Brinson, Singer and Beebower (1991) argue that a significant share (90%) of portfolio performance can be attributed to the initial allocation decision.7 On the other hand, in a context of liquid, efficient, markets, the possibility of obtaining substantial gains through stock picking alone is verely reduced.
References
Alexander, G., and A. Baptista, 2001, Economic Implications of Using a Mean-VaR Model for Portfolio Selection: a Comparison with Mean-Variance Analysis, Journal of Economic Dynamic and Control, forthcoming.
Amenc, N., and Martellini, L., 2001, It’s Time for Ast Allocation, Journal of Financial Transformation, 3, 77-88, 2001.
Amenc, N., S. El Bied and L. Martellini, 2002, Evidence of predictability in hedge fund returns and multi-style multi-class style allocation decisions, Financial Analysts Journal, forthcoming.
6 On this subject, e the introduction of Brown and Harlow (1990), who also discuss the role of modern portfolio theory in ast allocation.
7 The result of this study should however be considered with care, becau it has often been incorrectly interpreted (e Amenc and Martellini (2001) and Nutall and Nutall (1998)).
Amenc, N., and Martellini, L., 2002a, Portfolio Optimization and Hedge Fund Style Allocation Decisions, The Journal of Alternative Investments, forthcoming.
Amenc, N., and Martellini, L., 2002b, The Risks and Benefits Associated with Investing
in Hedge Funds, Working Paper, USC, 2002.
Avramov, D., 2002, Stock return predictability and model uncertainty, Journal of Financial Economics, forthcoming.
Black F., Litterman R., 1990, Ast Allocation: Combining Investor Views with Market Equilibrium, Goldman Sachs Fixed Income Rearch, September.
Bekaert, G., and R. Hodrick, 1992, Characterizing predictable components in excess returns on equity and foreign exchange markets, Journal of Finance, 47, 467-509.
Brinson G. P., Hood L. R., Beebower G.L., 1986, Determinants of Portfolio Performance", Financial Analysts Journal, July-August.
Brinson G. P., Singer B. D., Beebower G. L., 1991, Determinants of Portfolio Performance II: An Update, Financial Analysts Journal, May-June 1991.
Brooks, C., and Kat H., 2001, The Statistical Properties of Hedge Fund Index Returns and Their Impl
ications for Investors, working paper, The University of Reading, ISMA Centre. Brown K. C., and Harlow W. V., 1990, The Role of Risk Tolerance in the Ast Allocation Process: A New Perspective, CFA.
Campbell, J., 1987, Stock returns and the term structure, Journal of Financial Economics, 18, 373-399.
Campbell, J., and R. Shiller, 1988, Stock prices, earnings, and expected dividends, Journal of Finance, 43, 661-676.
Chan, L., J. Karceski, and J. Lakonishok, 1999, On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model, Review of Financial Studies, 12, pp. 937-74. Cvitanic, J., A. Lazrak, L. Martellini, and F. Zapatero, 2002, Revisiting Treynor and Black (1973) – An Intertemporal Model of Active Portfolio Management, working paper, USC.
Fabozzi F. J., 1995, Investments, Prentice Hall International Editions.
Fama, E., and K. French, 1989, Business Conditions and Expected Returns on Stocks and Bonds, Journal of Financial Economics, 25, 23-49.
