Stock Return Averages

EXERCISE #$1$: ABC stock price and dividend history are as follows. Fill in

the returns $($to $4$ decimal places$).$

Month Price Dividend Discrete Return Continuous

Return At Month End Paid at Month End $($end$+$div$-$beg$)/$beg ln$($end$+$div$)-$ln$($beg$)$

Dec $$55\mathrm{.}10$

Jan $$56\mathrm{.}14$ none...................... $\%...............................\%$

Feb $$54\mathrm{.}760\mathrm{.}50......................\%...............................\%$EXERCISE #$1$: ABC stock price and dividend history are as follows. Fill in

the returns $($to $4$ decimal places$).$

EXERCISE #$2$: The average returns in #$1$ are:

Arith:

$\%$ Geom $=$

$\%$ Cont$=.$

$\%$

The st deviation of the returns in #$1$ are $($divisor N $)$:

Discrete$=$

$\%$ Cont$=$

$\%$

EXERCISE #$3$: ABC stock price and dividend history are as follows. Fill in

the returns $($to $4$ decimal places$).$

Mar $$56\mathrm{.}45$ none $......................\%...............................\%$

EXERCISE #$2$: The average returns in #$1$ are:

Arith$=...................\%$ Geom$=...................\%$ Cont$=.................\%$

The st deviation of the returns in #$1$ are $($divisor N$)$:

Discrete$=...................\%$ Cont$=..................\%$

EXERCISE #$3$: ABC stock price and dividend history are as follows. Fill in

the returns $($to $4$ decimal places$).$

Month Price Dividend Discrete Return Continuous Return

At Month End Paid at Month End

Dec $$53\mathrm{.}07$

Jan $$54\mathrm{.}15$ none $...............................\%...............................\%$

Feb $$53\mathrm{.}39$ none $...............................\%...............................\%$

Mar $$55\mathrm{.}08$ none $...............................\%...............................\%$

$$Copyright by Robert Dubil, Revised $2022$

EXERCISE #$4$: The average returns in #$3$ are:

Arith$=.....................\%$ Geom$=.......................\%$ Cont$=.........................\%$

EXERCISE #$5$: Multiply the starting price by the right term that uses the

compound average to show that the arithmetic mean does not recover the

final price while the geometric and continuous means do$.$ Convert the

percent averages to fractions.

$$53.07$ x $(1+$ arith mean$)3=53\mathrm{.}07$ x $(1+..........)3=$ $ $..................................$

$$53.07$ x $(1+$ geom mean$)3=53\mathrm{.}07$ x $(1+........)3=$ $ $...................................$

$$53.07$ x e cont mean x $3=53\mathrm{.}07$ x e $................$ x $3=$ $ $.............................................$

Remember that you will not get the terminal value $55\mathrm{.}08$ right with the arithmetic average.

#$5).$ For example, for $5\mathrm{.}2345\%,$ enter $5\mathrm{.}2345$; $0\mathrm{.}0523$ will be$.$