Question

Q1 - Data of return of the stocks for six years period is given below: Year Stock Y 0.17 0.15 -0.02 -0.04 -0.09 0.18 Stock z 0.03 0,02 -0,05 -0,05 0,01 0,02 a. Compute the arithmetic mean annual rate of return for each stock. Which stock is most desirable by this measure? b. Compute the standard deviation of the annual rate of return for each stock. By this measure, which is the preferable stock? C. Compute the coefficient of variation for each stock. By this relative measure of risk, which stock is most preferable? d. Compute the geometric mean rate of return for each stock. Discuss the difference between the arithmetic mean return and the geometric mean return for each stock. Discuss the differences in the mean returns relative to the standard deviation of the return for each stock.

Answer 1

All the formulas and calculations are shown in the below images:

a) Arithmetic mean of stocks Y and Z:

a) Arithmetic mean = ritrotrz +---+rn Arithmetic mean austor -0.02 -0.04 -0.07 2.09 +0.18 of stock Y, ry = 0.058 0.03+0.02 -0.05 -0.05 +0.01 +0.02 Arithmetic mean of slock z, rz- =-0.003 return than stock a. Therefore, slock y stock eis Ý has more desirable.

B) Standard deviations of stocks Y and Z:

b) I Standard deviation - )+(z-7)+-- + (rm-712 Sn Standard deviation lion 1 (0:11-0.05-8) + (0.15-0.058)+(-0.02 -0.058) rela m ene of stock Y, Gy = 1 I + (-0.04 -0.058) + (-0.09-0.058) + (0.18-0.058) 0.012544+0.008464 + 0.006084 + 0.009604 +0.021904 + 0.014884 :5y = 0.11. Standard deviation slock Z, Gz = 1 10.03 -0.003)2 + (0.02-0.003)2+(-0.05-0.003) +(-0.05 -0.003)+(0.01-0.003)' + 10.02 -0.003) 0.000729 + 0.000289+ 0.002809 + 0.00 2809 +0.000049 + 0.000289 is 52 = 0.034. As standard deviation *o less, stock z ºs of stock z desirable.

c) Coefficient of Variation of stocks Y and Z:

d)

c) Coefficient of variation - 1 Standard Mean deviation coefficient of varicelion of stockh'y Sy - OL1897. tv 0.058 = 1.897. 0.058 Coefficient y vonialion Tz 0.034 .-11.33. of stockez As stock z bas less I preferred. Ten coefficient of vasiation, stock z is

Geometric mean of stocks Y and Z:

Geometric mcan - petro)- (1+r2). (1+r3) ---- (itin Geometric mean of stock Y, ãy (H0-17) *(1 +0-15)x11-0-02)*(1-0.04) x(1-0.09)(010) -1 =918359265864 -1 - 1.05249-1 = 0.052 Geometric mean stock z, gz - %(1+0:03)*(1 +0.02) «ll-o-oglu (1-0-05)x (140-01), (140-02) - 0. 9768 -1 -0.9961-I = -0.0039. Differences between Acthmelic mean and Geomelic mean! 19, 8-Fal = 10082-0.056) =(0.006!. 1qz-Tz) = 1 -0.0039-60.003) - -0.002940003) = 0.0009 Geometric man is considered over calithmetic mean because of is calculated taking Compounding that occues from peried to period into account Coefficient of variation of stock 0.052 Coefficient of vacation of Valia'on OTECCV2 DO 34 stock 2:02 - - -0.0039 - 8.72 Jon stock Y, there exisli difference of 0.223 and for stocks, Their exists difference of 2.61 1.