The following table shows the total return and the number of funds for four categories of mutual funds.

Excel File: data$03-17.$xlsx

Type of Fund

Domestic Equity

International Equity

Specialty Stock

Hybrid

Total Return $(\%)$

$4\mathrm{.}65$

$18\mathrm{.}15$

$11\mathrm{.}36$

$6\mathrm{.}75$

$7\mathrm{.}81$

Number of Funds

$9,191$

$2,621$

$1,419$

$2,900$

a$.$ Using the number of funds as weights, compute the weighted average total return for these mutual funds. $($to $2$ decimals$)$

$\%$

b$.$ Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part $($a$)?$ Discuss. What

else might be used for weights?

$($i$)$ Using "number of funds" as weights will only be a good approximation if the amount invested in various funds is approximately equal. The amount invested

in each fund could be used for weights.

$($ii$)$ Using "number of funds" as weights results in a good approximation regardless of the amount invested in various funds. There is no need to use a different

weight.

$($iii$)$ Using "number of funds" as weights will only be a good approximation if the amount invested in various funds is approximately equal. There is no other

option that could be used for weights.

$($iv$)$ Using "number of funds" as weights results in a good approximation regardless of the amount invested in various funds. The total amount invested in all

funds could be used for weights.

Choose the correct option.

$-$ Select your answer $-$ v

c$.$ Suppose you invested $$10,000$ in this group of mutual funds and diversified the investment by placing $$2,000$ in Domestic Equity funds, $$4,000$ in

International Equity funds, $$3,000$ in Specialty Stock funds, and $$1,000$ in Hybrid funds. What is the expected return on the portfolio? $($to $2$ decimals$)$

$\%$