Question

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: 23 0 37 35 16 22 14 −20 −11 −15 y: 21 −10 17 21 16 18 17 −3 −9 −4

(a) Compute Σx, Σx^2, Σy, Σy^2.

Σx ( ) Σx^2 ( )

Σy ( ) Σy^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 two decimal places.)

x y

^_x ( ).   ( )

s^2   ( ).   ( )

s ( ). ( )

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

x y

Lower Limit ( ). ( )

Upper Limit   ( ). ( )

Use the intervals to compare the two funds.

( ) 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.

( ) 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.

( ) 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.

( ) 25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

(d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.)

x y  

CV ( ) % ( ) %

Use the coefficients of variation to compare the two funds.

( )For each unit of return, the stock fund has lower risk.

( )For each unit of return, the balanced fund has lower risk.

( )For each unit of return, the funds have equal risk.

If s represents risks and x represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better?  

( ) A smaller CV is better because it indicates a higher risk per unit of expected return.

( ) A smaller CV is better because it indicates a lower risk per unit of expected return.

Answer 1