Suppose that you bought GE 6 years ago at a price of $128 per share. The price h

Question

Suppose that you bought GE 6 years ago at a price of $128 per share. The price has decreased to $75...

a.) What is Standard Return for GE's Stock over the entire 6 year period assuming that GE paid no

dividends over the 6 years?

b.) What is the Log Return for GE's stock over the entire 6 year period assuming that GE paid no

dividends over the 6 years?

c.) What is Standard Return for GE's Stock over the entire 6 year period assuming that GE paid $2.50 in

dividends in each of the 6 years?

d.) What is the Log Return for GE's stock over the entire 6 year period assuming that GE paid $2.50 in

dividends in each of the 6 years?

e.) What impact did dividends have on GE's calculated returns?

f.) Find the annually-compounded year-by-year return for parts a-d

Explanation / Answer

Standard return r = (Vf-Vi)/Vi

Where Vf=Final value of stock including dividends interests

Vi= Initial value

Here Vi=128

Vf=75

No dividend .

So , Standard return= (75-128)/128=-41.40%

So standard return over six years is      -41.40%

Log return = R= ln (Vf/Vi)

=ln(75/128)

=ln(0.586)

=-0.534=-53.4%

So log return over 6 years is -53.4%

Here Vf = $75 + dividends= $75+$6*2.5=$90

Vi=$128

So standard return = (90-128)/128

=-29.68%

So std return in this situation is -29.68% over 6 years.

Log return in this case is R=ln(90/128)

=ln(0.703)=-0.3524

So log return over six years is -35.24%

Dividends are increasing the total benefits received from the stock and improving the standard return by around 12% and log return by around 18%

Annually compounded return for standard return = r= (1+R)1/t -1

Where r =annually compounded return , t = no of periods, R= return over a period of t

Here R= -41.40%

So, r=(1-0.4140)1/6-1

r=0.9146-1=-0.0854= -8.54%

So annualized compounded return for situation a is -8.54%

For log return annualized log return is r=R/t , where R=log return over period t.

So , r= -53.4/6=-8.9%

So annualized log return in situation b is -8.9%

Here R=-29.68%

So, r= (1-0.2968)1/6-1

= -0.0571

=-5.71%

So , annualized compounded return for situation c is -5.71%

Here R=-35.24%

So r= -35.24/6=-5.87%

So annualized log return in situation d is -5.87%

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