The closing value of a Stock Market Index for the month of October, 2007 is given below: Date Closing Index Value 1.10.07 2800 3.10.07 2780 4.10.07…

Date Closing Index Sign of Price Charge 1.10.07 2800 3.10.07 2780 - 4.10.07 2795 + 5.10.07 2830 + 8.10.07 2760 - 9.10.07 2790 + 10.10.07 2880 + 11.10.07 2960 + 12.10.07 2990 + 15.10.07 3200 + 16.10.07 3300 + 17.10.07 3450 + 19.10.07 3360 - 22.10.07 3290 - 23.10.07 3360 + 24.10.07 3340 - 25.10.07 3290 - 29.10.07 3240 - 30.10.07 3140 - 31.10.07 3260 + Total of sign of price changes (r) = 8 No of Positive changes = n₁ = 11 No. of Negative changes = n₂ = 8 μᵣ = (2n₁n₂ / (n₁ + n₂)) + 1 = (2 × 11 × 8 / (11 + 8)) + 1 = 176/19 + 1 = 10.26 σᵣ = √((2n₁n₂(2n₁n₂ – n₁ - n₂)) / ((n₁ + n₂)² (n₁ + n₂ - 1))) = √((2 × 11 × 8) (2 × 11 × 8 - 11 - 8)) / ((11 + 8)² (11 + 8 - 1)) = √(176 × 157) / (19)² (18) = √4.252 = 2.06 Since too few runs in the case would indicate that the movement of prices is not random. We employ a two- tailed test the randomness of prices. Test at 5% level of significance at 18 degrees of freedom using t- table The lower limit = μᵣ − t × σᵣ = 10.26 – 2.101 × 2.06 = 5.932 Upper limit = μᵣ + t × σᵣ = 10.26 + 2.101 × 2.06 = 14.588 At 10% level of significance at 18 degrees of freedom Lower limit = 10.26 - 1.734 × 2.06 = 6.688 Upper limit = 10.26 + 1.734 × 2.06 = 13.832 As seen r lies between these limits. Hence, the market exhibits weak form of efficiency. *For a sample of size n, the t distribution will have n-1 degrees of freedom.