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No one really knows how to estimate future expected rates of return well.You must use your own judgment when the result is reasonable.
Industry hires macro/IO guys as strategists/analysts
Risk is a different concept for different person and organization. Measured using different method, different time horizonThat is why funds are so diverseTheoretically there is a globally efficient frontier. But it is unrealistic to construct it, too costly.
The optimization technique requires very large number of estimate inputs. and is very sensitive to any estimation errors.
e.g., to find tangency portfolio from 3000 stocks, need 4,504,500 estimate, including expected return, variance and covariance. a big trouble before 1970sIndustry came up “factor model” to address this trouble (our next lecture)
What’s the main drawback of Markowitz technique?Concentrated position; Sensitive to estimate error; Subjective view not allowed
The Black-Litterman Bayesian asset allocation model is one of the most sophisticated and widely used tools in asset management. It was developed in Goldman Sachs in early 1990s.
BL assumes that the initial expected returns should be equal to what is implied by market equilibrium choices (CAPM or APT). The user is only required to state how her views about expected returns differ from the market's and to state her degree of confidence in the alternative views.
estimate the covariance matrix from historical data (more stable)determine a baseline (prior) forecastintegrate the manager’s private views and confidencedevelop revised (posterior) forecast and apply portfolio optimization
Chapter 27 gives the formula. You can also refer to recommended books.
Why should we care?Theoretical consideration: test if the theory is validPractical consideration: use theory to determine cost of capital, to discover money-making opportunity, to design investment strategies, etc
The basic prediction of the CAPM is that market portfolio is mean-variance efficient (no matter whether risk-free rate exists or not). This requirement can provide a direct test of CAPM.
Complication: market portfolio will almost always be ex-post mean-variance-inefficient, even if it is ex-ante efficient.Hence cannot be tested directly
The security market line (SML) is then a further set of predictions based on the efficiency of the market portfolio. This constitutes a secondary form of test.
Two versions of CAPM: the Sharpe-Lintner form and the Black form
Sharpe-Lintner recognize the empirical proxy for risk-free rate could be stochastic
The CAPM implies relationships between expected (ex ante) returns, whereas we can observe are actual or realized (ex post) returns,
The empirical counterpart is the security characteristic line (SCL) :
Residual terms are assumed uncorrected across time and assetsActually they are correlated!Test would be more precise if it is run on beta-grouped portfolios rather than on individual stocks as residual terms diversified away.
Two-pass regression, first get beta from SCL estimation, then test SML.See textbook p.411-415.
In this form, borrowing rate is higher than lending rate
The test form, note here we use realized return, not excess return
If the Black model is true it implies, in time-series regression,
So α could be positive or negative, depending the value of β.
Further implications, in cross-sectional regression:The estimated market risk premium should be positive;The estimated intercept should be , positive too (hard to know exact value); Beta captures all cross-sectional variation.
[ ]0 0( ) ( ) ( ) ( )i M iM M ME r E r E r E rβ= + −
Black, Jensen, and Scholes (1972): Portfolio Construction
Note that in Jensen (1968) the residuals are correlated which invalidates the simple test.
overcome by using portfolios, but this reduce sample size in second-pass.choose to group assets to obtain maximum dispersion in betas of the portfoliosRandomly formed, betas for most portfolio are close to one (recall lecture 7).
Data from 1926- 1965 (data up to Mar 1966)First rank stocks on basis of betas estimated on the basis of the 5 years of data from 1926 to 1930 (using equally-weighted NYSE stocks as the market portfolioConstruct 10 portfolios with highest beta stock in portfolio 1, and so on downwards until portfolio 10. Compute return on each portfolio for the 12 months of 1931. Next repeat the step for stock from 1927 to 1931. Reform 10 portfolios. Compute their monthly returns in 1932Repeat this process through to 1965. (then calculate return up to Mar 1966 )
For each portfolio, [12 (month) × 35 (year)=420] number of returns 13
This test saves CAPM by using more sophisticated techniqueThe key idea is to assign beta values (estimated from next five year data) to portfolios which are sorted by betas estimated from previous five year data.To bypass the “error-in-variable” problem. Even today, their technique is still the standard. The technique is worthy of US$200,000/year (demand >> supply).
Here I only show the main results:
where the * denotes significance at the 10% level (i.e. 90% sure that the coefficient is different from 0).
Results are broadly consistent with the theory. Especially the third equation.
But CAPM encountered big troubles since 1980. Even Fama recognizes CAPM is a failure. “Beta is dead”