How to calculate the following questions in excel? Suppose the standard deviatio

Question

How to calculate the following questions in excel?

Suppose the standard deviation of the market return is 20%.

a. What is the standard deviation of returns on a well-diversified portfolio with a beta of 1.3?

b. What is the standard deviation of returns on a well-diversified portfolio with a beta of 0?

c. A well-diversified portfolio has a standard deviation of 15%. What is its beta?

d. A poorly diversified portfolio has a standard deviation of 20%. What can you say about its beta?


Answers:

A.

B.

C.

D.

Explanation / Answer

a. The formula for covariance is covar = r *sigma m *sigma p where r = coefficient of correlation between returns of market and portfolio sigma = standard deviation of returns for market and portfolio respectively Now r can be assumed to be 1 for a well diverrsified portfolio. formula for beta is beta = covar / (sigma m)^2 this evaluates to beta = r *(sigma p/sigma m) substituting gives the value of two unknown variables sigma p = beta* sigma m/r = 1.3*20% = 26% .............Ans (a) b. beta = 0 So Sigma p = beta* sigma m/r = 0 ...........Ans (b) c. beta = r *(sigma p/sigma m) = 1*15%/20% = 0.75 ....Ans (c) d. beta = r *(sigma p/sigma m) = r*(20%/20%) = r. Value of r can vary between -1 to 0 for a poorly diverifed portfolio

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