Mutual funds performance. Mutual funds often compare their performance with a benchmark provided by an "index" that describes the performance of the class of assets in which the fund invests. For example, the Vanguard International Growth Fund benchmarks its performance against the Spliced International Index. Table 20.3 gives annual returns (percent) for the fund and the index. Does the fund's performance differ significantly from that of its benchmark? (a) Explain clearly why the matched pairs t test is the proper choice to answer this question. (b) Do a complete analysis that answers the question posed. TABLE 20.3 A mutual fund versus its benchmark index Year Fund Return (%) Index Return (%) Year Fund Return (%) Index Return (%) Year Fund Return (%) Index Return (%) Year Fund Return (%) Index Return (%) 1984 -1.02 7.38 1992 -5.79 -12.17 2000 -8.60 -14.17 2008 -44.94 -43.38 1985 56.94 56.16 1993 44.74 32.56 2001 -18.92 -21.44 2009 41.63 31.78 1986 56.71 69.44 1994 0.76 7.78 2002 -17.79 -15.94 2010 15.66 8.13 1987 12.48 24.63 1995 14.89 11.21 2003 34.45 38.59 2011 -13.68 -13.71 1988 11.61 28.27 1996 14.65 6.05 2004 18.95 20.25 2012 20.01 16.83 1989 24.76 10.54 1997 4.12 1.78 2005 15.00 13.54 2013 22.95 15.29 1990 -12.05 -23.45 1998 16.93 20.00 2006 25.92 26.34 2014 -5.63 -3.87 1991 4.74 12.13 1999 26.34 26.96 2007 15.98 11.17 2015 -0.67 -5.66
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Then, we will perform a matched pairs t-test to determine if there is a significant difference between the fund's performance and its benchmark index. Show more…
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Comparing Risk of Mutual Funds. Investors commonly use the standard deviation of the monthly percentage returns for a mutual fund as a measure of risk for the fund; in such cases, a fund with a higher standard deviation is considered riskier than a fund with a lower standard deviation. It has also been frequently stated that if an investor wishes to earn a higher average rate of return, they must also be willing to accept greater risk. You have been given data containing the monthly returns for two mutual funds: American Century Equity Growth Fund and Fidelity Growth Discovery Fund. a) Provide a table of descriptive statistics and include your preliminary observations. b) Provide confidence intervals for the average monthly return of the two mutual funds. Be sure to interpret their meaning. c) Formulate a hypothesis test to determine if the Fidelity Growth Discovery fund is riskier than the American Century Equity Growth Fund. Be sure to include an explanation of why your test formulation is correct (). d) State your results (test statistic and p-value only), your conclusion and your interpretation. e) Formulate a second hypothesis test, this time to determine if the statement regarding the average return and the amount of risk applies to these two funds. Be sure to include an explanation of why your test formulation is correct (). f) State your results (test statistic and p-value only), your conclusion and your interpretation. g) Based on your findings, briefly explain which of these two mutual funds would be preferred and why?
Shyam P.
Much is made of the fact that certain mutual funds outperform the market year after year (that is, the return from holding shares in the mutual fund is higher than the return from holding a portfolio such as the S&P 500). For concreteness, consider a 10-year period and let the population be the 4,170 mutual funds reported in The Wall Street Journal on January 1, 1995. By saying that performance relative to the market is random, we mean that each fund has a 50-50 chance of outperforming the market in any year and that performance is independent from year to year. (i) If performance relative to the market is truly random, what is the probability that any particular fund outperforms the market in all 10 years? (ii) Of the 4,170 mutual funds, what is the expected number of funds that will outperform the market in all 10 years? (iii) Find the probability that at least one fund out of 4,170 funds outperforms the market in all 10 years. What do you make of your answer? (iv) If you have a statistical package that computes binomial probabilities, find the probability that at least five funds outperform the market in all 10 years.
Manasvee S.
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