Katy is a private wealth management consultant for the Webster Family Trust, whi

Question

Katy is a private wealth management consultant for the Webster Family Trust, which is valued at $800M. The family patriarch has instructed her to keep the overall trust Beta at 1.20. The trust currently has $100M invested in Apple Computer (stock A) which has a beta of 1.4 and $300M invested in Berkshire Hathaway (stock B) with a beta of 0.6. Katy needs to invest the remaining $400M and wants to divide the money between an asset with a beta of 1.6 and risk free asset. How much should Katy invest in the risk free asset?

Explanation / Answer

Target beta =1.2 is nothing but weighted average beta of all the stocks in the portfolio

Let X be the amount of funds invested in stock with beta of 1.6

Amount invested in stcok with a beta of 1.6 =400M-X

1.2 = 1.4*(100M/800M)+0.6* (300M/800M)+1.6(x/800)+(400-x)/800 * 0

1.2 = 1.4*0.125+0.6*0.375+1.6(x/800)

0.8=1.6x/800

0.8*800 = 1.6x

1.6x=640

x=640/1.6

x=400M

Therefore no investment is made in risk free asset. Substituting X in funds to be invested in risk free asset =400-400=0

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