4 - lecture 3 Descriptive Statistics for Quantitative Data II 1/32 Mean ctd Geometric Mean Return Measures of Variation Range Interquartile Range

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Unformatted text preview: lecture 3, Descriptive Statistics for Quantitative Data II 1/32 Mean ( ctd) Geometric Mean Return Measures of Variation Range Interquartile Range Box-and-whiskers plot Variance, Standard Deviation Empirical Rule for Normals z-scores lecture 3, Descriptive Statistics for Quantitative Data II Outline 1 Mean ( ctd) Geometric Mean Return 2 Measures of Variation Range Interquartile Range Box-and-whiskers plot Variance, Standard Deviation 3 Empirical Rule for Normals z-scores lecture 3, Descriptive Statistics for Quantitative Data II 2/32 Mean ( ctd) Geometric Mean Return Measures of Variation Range Interquartile Range Box-and-whiskers plot Variance, Standard Deviation Empirical Rule for Normals z-scores lecture 3, Descriptive Statistics for Quantitative Data II Mean ( ctd) Geometric Mean Return Rate of Return • In finance, a quantity of big interest is the so-called rate of return (ROR) , or return on investment (ROI); or sometimes just return • The ratio of money gained or lost on an investment relative to the amount of money invested: ROR = final value - initial value initial value • The higher the ROR, the better. lecture 3, Descriptive Statistics for Quantitative Data II 3/32 Mean ( ctd) Geometric Mean Return Measures of Variation Range Interquartile Range Box-and-whiskers plot Variance, Standard Deviation Empirical Rule for Normals z-scores lecture 3, Descriptive Statistics for Quantitative Data II Mean ( ctd) Geometric Mean Return Example 1, ROR An investment of $100,000 declined to $50,000 at the end of Year 1 and rebounded to $100,000 at the end of Year 2. • What is the ROR for each year? • For the first year, ROR R 1 is R 1 = 50 , 000- 100 , 000 100 , 000 =- . 5 =- 50 % • For the second year, R 2 is R 2 = 100 , 000- 50 , 000 50 , 000 = 1 = 100 % • The overall two-year return is , since it started and ended at the same level. lecture 3, Descriptive Statistics for Quantitative Data II 4/32 Mean ( ctd) Geometric Mean Return Measures of Variation Range Interquartile Range Box-and-whiskers plot Variance, Standard Deviation Empirical Rule for Normals z-scores lecture 3, Descriptive Statistics for Quantitative Data II Mean ( ctd) Geometric Mean Return Arithmetic / Geometric Mean ROR • The (arithmetic) mean ROR over Year 1 and Year 2 is- 50 %+ 100 % 2 = 25 % . Misleading! • Geometric mean ROR : the constant return that yields the same wealth at the end of the whole investment period as do the actual return: ¯ R G = (( 1 + R 1 ) × ... ( 1 + R n )) 1 / n- 1 ; where R i is the ROR in time period i . • For Example 1, the geometric mean ROR over the two years is ¯ R G = (( 1 + R 1 ) × ( 1 + R 2 )) 1 / 2- 1 = (( 1- . 5 ) × ( 1 + 1 )) 1 / 2- 1 = ....
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This note was uploaded on 12/04/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.

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4 - lecture 3 Descriptive Statistics for Quantitative Data II 1/32 Mean ctd Geometric Mean Return Measures of Variation Range Interquartile Range

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