A Portfolio Manager (PM) has the following four stocks in his portfolio: Security No. of Shares Market Price Per Share (₹) Beta Dahlia Ltd. 10,000 50 0.9 Rose Ltd. 5,000 20 1.0 Cauliflower Ltd. 8,000 25 1.5 Apples Ltd. 2

Adjusting Portfolio Beta to 1.2 with Risk-Free Investment/Borrowing Given: Current Portfolio Beta (β P ) = 1.1084 (from part (i)) Desired Portfolio Beta (β Target ) = 1.2 Total Value of Current Portfolio = ₹12,00,000 Beta of Risk-Free Securities (β RF ) = 0 Let W 1 be the proportion of the portfolio invested in the risky assets (current portfolio). Let W 2 be the proportion of the portfolio invested in risk-free assets (or borrowed at risk-free rate). The formula for the target portfolio beta is: β Target = (β P × W 1 ) + (β RF × W 2 ) Since β RF = 0: β Target = β P × W 1 Substituting the values: 1.2 = 1.1084 × W 1 W 1 = 1.2 / 1.1084 W 1 ≈ 1.0826 This means the proportion of the portfolio invested in risky assets (W 1 ) needs to be greater than 1 (108.26%). This implies that the PM needs to invest more than the current portfolio value in risky assets, which can only be achieved by borrowing at the risk-free rate. The proportion of risk-free investment (W 2 ) required is: W 2 = 1 - W 1 = 1 - 1.0826 = -0.0826 A negative W 2 indicates that the PM needs to borrow at the risk-free rate, rather than invest in risk-free assets. Amount to borrow at risk-free rate = Total Current Portfolio Value × |W 2 | Amount to borrow = ₹12,00,000 × 0.0826 Amount to borrow ≈ ₹99,120 The PM should borrow approximately ₹99,120 at the risk-free rate and invest this amount, along with the existing ₹12,00,000, into the four aforementioned securities (risky assets). This would increase the total investment in risky assets to ₹12,00,000 + ₹99,120 = ₹12,99,120, thereby increasing the portfolio beta to 1.2.