Question

you have a $16,000 portfolio which is invested in stocks a and B, and a risk-free asset. $8000 is invested in stock a. stock a has a beta of 1.82 and a stock Bhas a beta of 0.61. How much needs to be invested in stocks be if you want a portfolio beta of 1.10?

Answer 1

Let investment in B be $x. Given that investment in A=$8000.

So, investment in risk free asset=$(16000-8000-x)=$(8000-x)

Beta of A=1.82, beta of B=0.61 and obviously risk free asset has no beta.

Required portfolio beta=1.1.

Thus,

8000 + 1.82 + C + 0.61 + (8000 - x) * 01/16000 = 1.1

(14560 + 0.61.c) = 17600

0.61.1 = 3040

I= 4983.60

Thus required investment in stock B=$4983.60.

So, total investment needed for require portfolio beta=$(8000+4983.60)=$12983.60