Answer: 1.112375
Explanation:
Number of stocks = 20
Portfolio beta(Bp) = 1.1
Worth of stock to be sold(Ss) = 100,000
Portfolio worth(Wp) = 4,000,000
Beta of stock to be sold(Bs) = 0.9
Beta of other stock to be purchased(Bo) = 1.4
Therefore, new worth of portfolio (Np) :
(4,000,000 - 100,000) = 3,900,000
Bp = (Ss / Wp)Bs + (Np / Wp)Br
Where Br = Beta of what is left after the sale of the $100,000 stock
1.1 = (100,000 / 4,000,000)0.9 + (3,900,000/4,000,000)Br
1.1 = (0.025 × 0.9) + (0.975)Br
1.1 = 0.0225 + 0.975Br
1.1 - 0.0225 = 0.975Br
Br = 1.0775 / 0.975
Br = 1.105
New beta(Bn) :
(Ratio of sold stock × Bo) + (ratio of stock left × Br)
(100,000/4000000)1.4 + (3900000/4000000)1.105
Bn = (0.025 × 1.4) + (0.975 × 1.105)
Bn = 0.035 + 1.077375
Bn = 1.112375
