{Exercise 3.55}
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds (Morningstar Funds500, 2008).
a. Using the number of funds as weights, compute the weighted average total return for the mutual funds covered by Morningstar. (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 for Morningstar in part (a)? Discuss. What else might be used for weights?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. Suppose you had invested $10,000 in mutual funds at the beginning of 2007 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? (to 2 decimals)
%
7.81
a. To compute the weighted average total return, we need to multiply each total return by the corresponding number of funds, sum them up, and then divide by the total number of funds.
The table provides the following information:
Category | Total Return | Number of Funds
---------|--------------|----------------
Domestic Equity | 6.5% | 150
International Equity | 8.1% | 100
Specialty Stock | 10.2% | 50
Hybrid | 9.5% | 75
To calculate the weighted average total return:
(6.5% * 150 + 8.1% * 100 + 10.2% * 50 + 9.5% * 75) / (150 + 100 + 50 + 75)
= (975 + 810 + 510 + 712.5) / 375
= 3007.5 / 375
= 8.02%
Therefore, the weighted average total return for the mutual funds covered by Morningstar is 8.02%.
b. One potential difficulty associated with using the "number of funds" as weights is that it assumes each mutual fund has an equal impact on the average return. However, this may not be the case if some funds have significantly larger assets or investments than others.
An alternative weighting method could be based on the assets under management (AUM) of each mutual fund. This would take into account the actual monetary value of each fund and provide a more accurate representation of their impact on the average return.
c. To calculate the expected return on the portfolio, we need to multiply the allocation amount for each category by the corresponding total return and sum them up.
Given the following allocations and total returns:
Allocation | Total Return
-----------|-------------
$2000 | 6.5%
$4000 | 8.1%
$3000 | 10.2%
$1000 | 9.5%
To calculate the expected return on the portfolio:
(2000 * 6.5% + 4000 * 8.1% + 3000 * 10.2% + 1000 * 9.5%) / (2000 + 4000 + 3000 + 1000)
= (130 + 324 + 306 + 95) / 10000
= 855 / 10000
= 8.55%
Therefore, the expected return on the portfolio is 8.55%.
a. To compute the weighted average total return for the mutual funds covered by Morningstar, we need to use the number of funds as weights.
The formula to calculate weighted average is:
Weighted average = (Value1 * Weight1 + Value2 * Weight2 + ... + Valuen * Weightn) / (Weight1 + Weight2 + ... + Weightn)
In this case, the values are the total returns for each category of mutual funds and the weights are the number of funds in each category.
Using the table provided, let's calculate the weighted average:
Category | Total Return | Number of Funds
-----------------------------------------------------------
Morningstar Funds500 | 11.7% | 31
Domestic Equity | 10.2% | 244
International Equity | 21.4% | 38
Specialty Stock | 4.5% | 39
Hybrid | -3.4% | 29
Weighted average total return = (11.7% * 31 + 10.2% * 244 + 21.4% * 38 + 4.5% * 39 + -3.4% * 29) / (31 + 244 + 38 + 39 + 29)
Calculate the weighted average to get the answer.
b. One potential difficulty with using the "number of funds" as weights is that it assumes that all funds within a category contribute equally to the overall weighted average. However, this may not be the case. Some funds may have larger assets under management or perform significantly better or worse than others within the same category. In such cases, using the number of funds alone as weights may not accurately reflect the contribution of each fund to the overall average.
Other factors that could be used as weights instead of the number of funds include assets under management, investment performance (e.g., return on investment), or a combination of both. Using more robust measures of weighting can provide a more accurate representation of the portfolio's performance.
c. To calculate the expected return on the portfolio, we need to multiply the weight of each category of mutual funds with their respective total returns and sum them up.
Given:
- $10,000 investment at the beginning of 2007
- $2,000 in Domestic Equity funds (20% of the portfolio)
- $4,000 in International Equity funds (40% of the portfolio)
- $3,000 in Specialty Stock funds (30% of the portfolio)
- $1,000 in Hybrid funds (10% of the portfolio)
Multiply the total return of each category with its respective weight, then sum them up:
Expected return = (Total Return of Domestic Equity * Weight of Domestic Equity) + (Total Return of International Equity * Weight of International Equity) + (Total Return of Specialty Stock * Weight of Specialty Stock) + (Total Return of Hybrid * Weight of Hybrid)
Multiply and sum up the terms to get the answer.
A.7.81%
B. ?
C. 40.91%