ST113 Worksheet 3

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Bentley University *

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113

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Business

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May 7, 2024

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pdf

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3

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Dr. Jackson Lautier Bentley University ST113 Business Statistics Name: Worksheet 3 The file JanusFunds.xlsx posted on Brightspace has the yearly returns (%) for the 17 years 2000- 2016 for two Janus mutual funds: The Janus Balanced Fund : This “core” fund consists of stocks and bonds and its goal is diversification. It has historically produced solid long-term returns through different market cycles. The Janus Overseas Fund : This fund invests in overseas companies based on their individual merits instead of their geography or industry sector. 1. (a) Use Excel to compute descriptive statistics for the two funds, including the mean, median, variance, and standard deviation. Mean Median Variance Standard Deviation Balanced Fund 5.99 7.83 96.17 9.81 Overseas Fund 6.14 12.10 1093.59 33.07 (b) Which fund has the higher return? (c) Using the standard deviation, which fund is riskier? 2. (a) Compute the coefficient of variation for each investment. (b) By that measure, which fund is more volatile relative to the average return? 3. (a) Compute the Sharpe Ratio for each fund. (Assume a risk-free return of 2% for the 10 year period.) (b) By that measure, which fund is a better investment?
Dr. Jackson Lautier Bentley University ST113 Business Statistics 4. (a) Compute the correlation coefficient for the two funds. (Use Excel.) (b) Based on the correlation coefficient, would investing in these two funds help to diversify a portfolio? 5. Empirical Rule: Assume the distribution of returns for each fund follow roughly a bell-shaped distribution. (a) For the Balanced Fund, between what two returns are the middle 68% of all returns? (b) For the Overseas Fund, between what two returns are the middle 95% of all returns? 6. The following table shows the annual returns (in percent) for Fidelity’s Electronic and Utilities funds. Enter the data in Excel or your calculator and do the following calculations. Year Electronic Utilities 2005 13.23 9.36 2006 1.97 32.33 2007 2.77 21.03 2008 50.00 35.21 2009 81.65 14.71 (a) Calculate the sample mean, the sample standard deviation, and coefficient of variation for each fund. Mean Standard Deviation Coefficient of Variation Electronic 9.92 42.07 4.24 Utilities 8.44 25.86 3.06 (b) Which fund had the higher average return? (c) Which fund was riskier over this time period? Use both the standard deviation and the coefficient of variation in your explanation.
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