Question

investment

An investor purchases a share of a stock at T0 for $110. At the end of the year. At T1 the investor buys three other shares of the same stock for a total amount of $306. At T2, the investor buys two other shares of the same stock for $88.5 each. At T3 the investor sells all the shares for $145.5 each. The stock paid: $1.75, $0.55, and $2.75 dividends per share at the end of years 1, 2, and 3 respectively. What is the geometric mean of the returns?

Roddy Richards invested $1000 in Wolverine Meat Distributors (W.M.D.) five years ago. The investment had yearly arithmetic returns of -9.7%, -8.1%, 15%, 7.2%, and 15.4%. What is his total compounded return over the 5 years period?

Answer #1

NOTE: NO ROUNDINGS ARE BEING DONE HERE SINCE YOU HAVENT MENTIONED.

PART A ANSWER BELOW

P0=110, P1=306. ,P2=88.5 ,P3=145.5

**RETURN= (CURRENT PRICE-PREVIOUS PRICE+DIVIDEND) /
PREVIOUS PRICE**

R1= (306-110+1.75)/110= 1.79772727273

R2= (88.5-306+0.55)/306= -0.7089869281

R3= (145.5-88.5+2.75)/88.5= 0.67514124293

**GEOMETRIC MEAN RETURN =[(1+R1) * (1+R2) * (1+R3)]^(1/n)
-1**

=((1+1.79772727273 ) * (1+(-0.7089869281)) * (1+ 0.67514124293)) ^(1/3)-1

**= 0.10897843675 OR 10.897843675%**

if rounding to two decimals them GM= 10.90%

PART B ANSEWER BELOW

**GEOMETRIC MEAN RETURN =[(1+R1) * (1+R2) * (1+R3) *
(1+R4) * (1+R5)]^(1/n) -1**

R1=-9.7%, R2=-8.1%, R3=15%,R4= 7.2%, R5=15.4%

=((1 + (-0.097)) * (1 + (-0.081)) * (1 + 0.15) * (1 + 0.072) * (1 + 0.154))^(1/5)-1

**GEOMETRIC MEAN or COMPOUNDED RETURN =0.33761465 or
3.38%(rounded to two
decimals)**

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