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A portion of a data set containing information for 45 mutual funds that are part of the Morningstar Funds 500 for 2008 follows. The complete data set is available i...

Question

A portion of a data set containing information for 45 mutual funds that are part of the Morningstar Funds 500 for 2008 follows. The complete data set is available in the file named MutualFunds. The data set includes the following five variables: Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income). Net Asset Value (\$): The closing price per share on December 31, 2007. 5-Year Average Return (\%): The average annual return for the fund over the p

A portion of a data set containing information for 45 mutual funds that are part of the Morningstar Funds 500 for 2008 follows. The complete data set is available in the file named MutualFunds. The data set includes the following five variables: Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income). Net Asset Value (\$): The closing price per share on December 31, 2007. 5-Year Average Return (\%): The average annual return for the fund over the past 5 years. Expense Ratio (\%): The percentage of assets deducted each fiscal year for fund expenses. Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of $1-$ Star to a high of 5 -Stars. a. Develop an estimated regression equation that can be used to predict the 5 -year average return given fund type. At the .05 level of significance, test for a significant relationship. b. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain. c. Develop the estimated regression equation that can be used to predict the 5 -year average return given the type of fund, the net asset value, and the expense ratio. At the .05 level of significance, test for a significant relationship. Do you think any variables should be deleted from the estimated regression equation? Explain. d. Morningstar Rank is a categorical variable. Because the data set contains only funds with four ranks (2-Star through 5-Star), use the following dummy variables: 3StarRank $=1$ for a 3 -Star fund, 0 otherwise; 4 StarRank $=1$ for a 4 -Star fund, 0 otherwise; and 5 StarRank $=1$ for a 5 -Star fund, 0 otherwise. Develop an estimated regression equation that can be used to predict the 5 -year average return given the type of fund, the expense ratio, and the Morningstar Rank. Using $\alpha=.05,$ remove any independent variables that are not significant. e. Use the estimated regression equation developed in part (d) to estimate the 5 -year average return for a domestic equity fund with an expense ratio of $1.05 \%$ and a $3-$ Star Morningstar Rank.



Answers

Growing Annuities For some annuities encountered in busi-
ness finance, called growing annuities, the amount of the peri-
odic payment is not constant but grows at a constant periodic
rate. Leases with escalation clauses can be examples of growing
annuities. The present value of a growing annuity takes the form
$$P=\frac{R}{i-g}\left[1-\left(\frac{1+g}{1+i}\right)^{n}\right]$$
where
$$\begin{aligned} R &=\text { amount of the next annuity payment, } \\ g &=\text { expected constant annuity growth rate, } \\ i &=\text { required periodic return at the time the annuity is } \\ & \text { evaluated, } \\ n &=\text { number of periodic payments. } \end{aligned}$$
A corporation's common stock may be thought of as a claim on
a growing annuity where the annuity is the company's annual
dividend. However, in the case of common stock, these payments
have no contractual end but theoretically continue forever. Com-
pute the limit of the expression above as $n$ approaches infinity
to derive the Gordon-Shapiro Dividend Model popularly used
to estimate the value of common stock. Make the reasonable
assumption that $i>g .$ Hint: What happens to $a^{n}$ as $n \rightarrow \infty$ if
$0<a<1 ?$ Source: Robert $D .$ Campbell.


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