By Dominic J. Brewer
Offers an summary of section I (2001-2004) of Qatar's daring K-12 schooling reform initiative, schooling for a brand new period, in line with RAND's stories during this formidable, multi-participant attempt. RAND tested Qatar's present schooling approach, urged recommendations for development a world-class approach, and supported implementation of the selected choice, that is in line with across the world benchmarked curriculum criteria and parental collection of colleges.
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Returns are measured in percent per quarter. The Sharpe ratio is defined as the mean excess return divided by the standard deviation of return. Figs. 1, 2, and 3 contain plots of the constrained (short sales precluded) frontiers and the unconstrained (short sales permitted) frontiers based on the dividend yield riskfree rate, historic, and CAPM means in panels A, B, and C, respectively. 41 Extreme Mean-Variance Solutions 8 Unconstrained Frontier (No Riskfree Asset) Expected Return (% per quarter) 6 4 RB RL 2 0 Constrained Frontier (No Riskfree Asset) -2 0 2 4 6 8 10 12 14 Standard Deviation (% per quarter) Fig.
The n-vector of historic means at the beginning of period t is denoted as lHt ¼ ðr1t ; . . ; rnt Þ0 PtÀ1 (8) where rit ¼ 1=kð t¼tÀk rit Þ and k ¼ 32. The choice of 32 quarters for the ‘‘moving’’ window follows the discrete-time power-utility literature. ) This historical approach estimates the means one at a time, relying exclusively on information contained in each of the time series. 26 ROBERT R. GRAUER Stein’s (1955) suggestion that the efficiency of the estimate of the means could be improved by pooling the information across series led to an alternative set of so-called shrinkage estimators that shrink the historical means to some grand mean.
10 4. FOUR ESTIMATORS OF THE MEANS Historical estimators of the means were the first to be employed in the literature. The n-vector of historic means at the beginning of period t is denoted as lHt ¼ ðr1t ; . . ; rnt Þ0 PtÀ1 (8) where rit ¼ 1=kð t¼tÀk rit Þ and k ¼ 32. The choice of 32 quarters for the ‘‘moving’’ window follows the discrete-time power-utility literature. ) This historical approach estimates the means one at a time, relying exclusively on information contained in each of the time series.