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Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable...

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Basic Math

Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent returnfor Vanguard Total Stock Index (all stocks). Let y be arandom variable representing annual return for Vanguard BalancedIndex (60% stock and 40% bond). For the past several years, we havethe following data.

x:

29

0

18

35

32

18

24

?23

?16

?9

y:

18

?4

20

17

22

11

28

?2

?8

?6

(a) Compute ?x, ?x2, ?y,?y2.

?x?x2
?y?y2


(b) Use the results of part (a) to compute the sample mean,variance, and standard deviation for x and for y.(Round your answers to two decimal places.)

xy
x
s2
s


(c) Compute a 75% Chebyshev interval around the mean for xvalues and also for y values. (Round your answers to twodecimal places.)

xy
Lower Limit
Upper Limit


Use the intervals to compare the two funds.

75% of the returns for the balanced fund fall within a narrowerrange than those of the stock fund.75% of the returns for the stockfund fall within a narrower range than those of the balancedfund.    25% of the returns for the balancedfund fall within a narrower range than those of the stock fund.25%of the returns for the stock fund fall within a wider range thanthose of the balanced fund.

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