Question

Supposed San Jose portfolio consisting of a $10,000 investment in each of H different common stocks the portfolios beta is 1.25 now supposed Stan decided to sell one of the Stocks that has a beta of 1.0 0 NT use the proceeds to buy a replacement stock with a beta of 0.66 what was the portfolios new beta be

Answer 1

Answer-

As investment of $ 10000 each  is used to purchase each H different stocks

The overall beta = 1.25
The beta of stock 1.0 is replaced with a stock of beta of 0.66

As the amount invested in each stock is same of $10000 the beta of the portfolio is the average of the beta of two stocks

initially

1.25 = (1.0 + X) / 2

1.0 + X = 2 x 1.25
1.0 + X = 2.50
X = 2.50 - 1.0
X = 1.50

The beta of 1.0 stock is replaced by beta of 0.66 stock

Therefore the new beta of the portfolio = (1.50 + 0.66 ) / 2 = 2.16 / 2 = 1.08 [ As beta of 1.0 stock is replaced by beta of 0.66 and beta of X stock is 1.50 remains in portfolio ]

Therefore new beta of portfolio after replacement is equal to 1.08