26. Information about mutual funds provided by Morningstar Investment Research i

Question

26. Information about mutual funds provided by Morningstar Investment Research includes the type of mutual fund (Domestic Equity, International Equity, or Fixed Income) and ge Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208 pter 4 Introduction to Probability the Morningstar rating for the fund. The rating is expressed from 1-star (lowest rating) to 5-star (highesating). A sample of 25 mutual funds was selected from Morningstar Funds 500. The following counts were obtained .Sixteen mutual funds were Domestic Equity funds. .Thirteen mutual funds were rated 3-star or less. Seven of the Domestic Equity funds were rated 4-star .Two of the Domestic Equity funds were rated 5-star. Assume that one of these 25 mutual funds will be randomly selected in order to learn more about the mutual fund and its investment strategy a. What is the probability of selecting a Domestic Equity fund? b. What is the probability of selecting a fund with a 4-star or 5-star rating? c. What is the probability of selecting a fund that is both a Domestic Equity fund and a fund with a 4-star or 5-star rating? What is the probability of selecting a fund that is a Domestic Equity fund or a fund with a 4-star or 5-star rating? d.

Explanation / Answer

Since it was given that in the 16 domestic funds, 7 of them had 4 stars and 2 had 5 stars, therefore 16-7-2 = 7 had 1 or 2 or 3 stars.

It was also given that 13 had 1 or 2 or 3 stars, of which we know 7 were in domestic fund, therefore the remaining 13-7 = 6 belonged to international or fixed income category.

All we can say is that for international and Fixed income, the no. of funds having 4 and 5 stars = 3

Remember, P(Event) = No. of favourable outcomes/Total No. of outcomes

(a) Probability of selecting a domestic equity fund: Favourable = 16 and Total = 25, Therefore P = 16/25 = 0.64

(b) Probability of selecting a fund with a 4 star or 5 star rating.

Favourable = all funds having 4star + 5 star rating = 9 funds of domestic + 3 funds of international and Fixed = 12

Total Outcomes = 25. Therefore P = 12/25 = 0.48

(c) Probability of selecting a fund which is both Domestic Equity and is a 4 star or 5 star Fund.

Favourable = 9 Funds. Total = 25. Therefore P = 9/25 = 0.36

(d) Probability of selecting a domestic equity fund or a fund with a 4 or 5 star rating.

Favourable = Domestic equity funds + Funds with 4 or 5 star rating - Domestic equity funds having 4 or 5 star rating (since these will have been counted in both cases)

= 16 + 12 - 9 = 19

Total = 25. Therefore P = 19/25 = 0.76

Domestic International and Fixed Total 1+2+3 stars 7 6 13 4 stars 7 Cannot determine 5 stars 2 Cannot determine Total 16 9 25

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