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The following table shows the total return and the number of funds for four categories of mutual funds. Type of Fund Number of Funds Total Return (%) Domestic Equity 9191 4.65 International Equity 2621 18.15 Specialty Stock 1419 11.36 Hybrid 2900 6.75 a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. 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? c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 3.1, Problem 17E
Textbook Problem
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The following table shows the total return and the number of funds for four categories of mutual funds.

Type of Fund Number of Funds Total Return (%)
Domestic Equity 9191 4.65
International Equity 2621 18.15
Specialty Stock 1419 11.36
Hybrid 2900 6.75
  1. a. Using the number of funds as weights, compute the weighted average total return for these mutual funds.
  2. 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?
  3. c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio?

a.

To determine

Find the weighted average total return for the mutual funds using the number of funds as weights.

Explanation of Solution

Calculation:

The total return and the number of funds for four categories of mutual funds are given.

The weighted mean of the data set can be obtained as follows:

The formula for the weighted mean is given below:

x¯=wixiwi

Here, xi indicate the observations and wi indicate the corresponding weights.

Substitute the values of xi and wi in the above formula.

x¯=9,191(4

b.

To determine

Check whether there is any difficulty associated with using the “number of funds” as the weights in computing the weighted average total return in part (a), and identify the requirements that might be used for weights.

c.

To determine

Find the expected return on the portfolio.

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