Mr. X is of the opinion that market has recently shown the Weak Form of Market Efficiency. To test the validity of his impression he has collected…

CA Final · Advanced Financial Management · MTP · May 2026
Mr. X is of the opinion that market has recently shown the Weak Form of Market Efficiency. To test the validity of his impression he has collected the following data relating to the movement of the SENSEX for the last 20 days. Days Open High Low Close 1 33470.94 33513.79 33438.03 33453.99 2 33453.64 33478.11 33427.82 33434.83 3 33414.06 33440.29 33397.65 33431.93 4 33434.94 33446.18 33377.78 33383.41 5 33372.92 33380.27 33352.12 33370.93 6 33375.85 33389.49 33331.42 33340.75 7 33340.89 33340.89 33310.95 33330.98 8 33326.84 33340.91 33306.17 33335.08 9 33307.16 33328.22 33296.43 33301.97 10 33298.64 33318.60 33254.28 33259.03 11 33260.04 33228.85 33241.66 33251.53 12 33255.92 33289.46 33249.46 33285.89 13 33288.86 33535.67 33255.98 33329.28 14 33335.00 33346.21 33276.72 33284.17 15 33293.83 33310.86 33278.54 33298.78 16 33300.02 33337.79 33300.02 33325.38 17 33323.36 33356.34 33322.44 33329.95 18 33322.81 33345.98 33317.44 33319.67 19 33317.51 33321.18 33294.19 33302.32 20 33290.86 33324.96 33279.62 33319.61 You are required to test the Weak Form of Market Efficiency using Auto-Correlation test, taking time lag of 10 days. Note: Round off all calculations upto 2 decimal points.

Suggested Answer and Working Notes:

Period 1 Closing Prices Change Period 2 Closing Prices Change 1 33453.99 11 33251.53 2 33434.83 -19.16 12 33285.89 34.36 3 33431.93 -2.90 13 33329.28 43.39 4 33383.41 -48.52 14 33284.17 -45.11 5 33370.93 -12.48 15 33298.78 14.61 6 33340.75 -30.18 16 33325.38 26.6 7 33330.98 -9.77 17 33329.95 4.57 8 33335.08 4.1 18 33319.67 -10.28 9 33301.97 -33.11 19 33302.32 -17.35 10 33259.03 -42.94 20 33319.61 17.29 X Y X² Y² XY -19.16 34.36 367.11 1180.61 -658.34 -2.90 43.39 8.41 1882.69 -125.83 -48.52 -45.11 2354.19 2034.91 2188.74 -12.48 14.61 155.75 213.45 -182.33 -30.18 26.6 910.83 707.56 -802.79 -9.77 4.57 95.45 20.88 -44.65 4.1 -10.28 16.81 105.68 -42.15 -33.11 -17.35 1096.27 301.02 574.46 -42.94 17.29 1843.84 298.94 -742.43 ΣX = -194.96 ΣY = 68.08 ΣX² = 6848.66 ΣY² = 6745.74 ΣXY = -164.68 X = -21.66 Y = 7.56 b = (ΣXY - nXY) / (ΣX² - n(X)²) = (-164.68 - 9(-21.66)(7.56)) / (6848.66 - 9(-21.66)²) = 0.62 a = Y - bX = 7.56 – 0.62(-21.66) = 20.99 r² = (aΣY + bΣXY - n(Y)²) / (ΣY² - n(Y)²) = (20.99(68.08) + 0.62(-164.68) - 9(7.56)²) / (6745.74 - 9(7.56)²) = 0.16 r = 0.40 There is moderate degree of correlation between the returns of two periods hence it can be concluded that the market does not show the weak form of efficiency.

Topics: Interest Rate Risk Management

Open in Interactive Practice Hub · Full Practice Hub · Chapter Weightage · More in this subject

Related Questions in this Topic