Suppose that the monthly return for two bond managers is as follows:

Month

Manager I

Manager II

$1$

$9\%$

$25\%$

$2$

$13\%$

$13\%$

$3$

$22\%$

$22\%$

$4$

$18\%$

$24\%$

a$.$What is the arithmetic average monthly rate of return for the two managers?

b$.$What is the time$-$weighted average monthly rate of return for the two managers?

c$.$Why does the arithmetic average monthly rate of return diverge more from the time$-$weighted monthly rate of return for manager II than for manager I?