Consider the following and show work Stock A Stock B Beta 0.8 1.4 Share price, $
ID: 2707902 • Letter: C
Question
Consider the following and show work
Stock A
Stock B
Beta
0.8
1.4
Share price, $
20
40
Standard deviation
25%
50%
Correlation between A and B
0.25
Treasury bills currently yield 2%, and the market risk premium is 6%.
(a) Compute the expected return and standard deviation of a portfolio of 100 shares of Stock A and 100 shares of Stock B.
(b) Gordon has $10,000 to invest. He plans to invest $4,000 in Stock B. He will allocate the rest of his money to Treasury bills and Stock A. His goal is to construct a portfolio with a beta of 1.0. Compute the investment amounts (in dollars) in Treasury bills and Stock A required to achieve the goal.
Stock A
Stock B
Beta
0.8
1.4
Share price, $
20
40
Standard deviation
25%
50%
Correlation between A and B
0.25
Explanation / Answer
a) expected return = risk free rate + beta ( market return - risk free rate )
= 2% + 0.8 (6%-2%) = 5.2% return on 100 shares A = 100*$20*0.052 = $104
expected return on stock B = 2% + 1.4(6%-2%) = 7.6%
return on 100 shares of stock B = 100*$40*0.076 = $304
$4000 is invested in stodk B = 40%
% invested in stock A = x
40%*0.8 + x*1.4 = 1, calculating for x , x= 48.57% or $4857 in stock A
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