Question

a portfolio consist of $35,000 in stock and $50,000 i cash. the beta of the portfolio is currently 1.20 and the target beta should be 1.30

what would be the ne weight of cash after required rebalancing to achieve the target beta?

Answer 1

Beta of a portfolio = Weigted average Beta of all stocks in the Portfolio

Beta of Current Portfolio = Weighted Average Beta of Stock + Weighted Average Beta of Cash

Beta of Cash = 0

Let Beta of Stock Be Y

Substituting Values :

1.2 = (35,000/ 85000) Y + (50000/85000) x 0

1.2 = (35/85) Y

Y = 2.9143, That is Beta of Stock is 2.9143

Required Beta =1.3

We are Required to determine the Net weight of Cash after required Rebalancing

Lets Assume the Cash in the portfolio after rebalancing is W

so,

1.3 = [35000/(35000+W)] x 2.9143 + [W/(35000+W)] x 0

1.3 ={102000.5 /(35000+W)]

W = 43462 is the required Cash Balance

Weight of Cash in the Portfolio is 43462/78462 = 0.554