Q 23 I do not not understand this statement:
Filbert describes a returns-based benchmark. To create a returns-based benchmark using Sharpe style analysis, an optimization procedure is used in which the portfolio’s sensitivities are forced to be non-negative and sum to 1.
??
weights on the portfolio are > 0 (between 0 and 1) total sum of all the weights = 1.
normal thing in MVO with no short sales.
Hi Cpk,
That I understand. I am confused about -'Sharpe style analysis, an optimization procedure"-
All somewhere in the depths of the text book
The first technique of style identification was Sharpe’s (1988, 1992) returns- based style analysis (RBSA). This technique focuses on characteristics of the overall portfolio as revealed by a portfolio’s realized returns. It involves regressing portfolio returns (generally monthly returns) on return series of a set of securities indices. In principle, these indices are: ■ ■ ■ mutually exclusive; exhaustive with respect to the manager’s investment universe; and distinct sources of risk (ideally they should not be highly correlated).41 Returns-based style analysis involves a constraint that the coefficients or betas on the indices are nonnegative and sum to 1.42 That constraint permits us to interpret a beta as the portfolio’s proportional exposure to the particular style (or asset class) represented by the index.43 For example, if a portfolio had a beta of 0.75 on a large-cap value index, a beta of 0 on a large-cap growth index, a beta of 0.25 on a small-stock value index, and a beta of 0 on a small-stock growth index, we would infer that the portfolio was run as a value portfolio with some exposure to small stocks. The factor weights on large-cap value, large-cap growth, small-cap value, and small-cap growth indices are 75 percent, 0, 25 percent, and 0, respectively. (The factor weights are also known as style weights or Sharpe style weights.)
And look at the footnotes at the bottom of the page: (too)
41 Sharpe (1992), examining U.S. mutual funds, used 12 indices representing U.S. Treasury bills, intermediate-term government bonds, long-term government bonds, corporate bonds, mortgage-related securities, large-cap value stocks, large-cap growth stocks, mid-cap stocks, small-cap stocks, non-U.S. bonds, European stocks, and Japanese stocks. 42 With this constraint,the model must be solved using quadratic programming(e.g.,Solver in Microsoft Excel). It is possible to do a returns-based style analysis constraining the coefficients to sum to 1 but not constraining the coefficients to be nonnegative; that approach could capture elements such as the use of leverage (a negative coefficient on T-bills, included as an index). 43 Furthermore,Lobosco and Di Bartolomeo(1997)have shown how to calculate approximate confidence intervals for the weights.
I think the context is devising a benchmark for a terminated plan. Why rbsa based optimization is preferred to liability based 1
im so confused…