Do bonds reduce the overall risk of an investment portfolio.pdf

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Bonds may reduce overall investment risk. The document analyzes annual return data from 2000-2009 for a total stock index fund (x) and a balanced index fund with 60% stocks and 40% bonds (y). It computes sample statistics like the mean, variance, and standard deviation for both funds and uses them to calculate 75% Chebyshev intervals around the means to estimate the range of future returns.

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Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable
representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random
variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For
the past several years, we have the following data. x: 37 0 18 33 13 17 12 23 12 12 y: 11 11 24 21
20 23 26 8 11 9
(a) Compute x, x
2
, y, y
2
.
(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 four decimal places.)
(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values.
(Round your answers to two decimal places.) (find lower and upper limits for x and y)

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