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 0.8 with Risk-Free Investment Given: Current Portfolio Beta (β P ) = 1.1084 (from part (i)) Desired Portfolio Beta (β Target ) = 0.8 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. The formula for the target portfolio beta is: β Target = (β P × W 1 ) + (β RF × W 2 ) Since W 2 = (1 - W 1 ) and β RF = 0: β Target = (β P × W 1 ) + (0 × (1 - W 1 )) β Target = β P × W 1 Substituting the values: 0.8 = 1.1084 × W 1 W 1 = 0.8 / 1.1084 W 1 ≈ 0.72176 So, the proportion of the portfolio that should remain in risky assets is approximately 72.18%. The proportion of risk-free investment (W 2 ) required is: W 2 = 1 - W 1 = 1 - 0.72176 ≈ 0.27824 Amount of risk-free investment = Total Portfolio Value × W 2 Amount of risk-free investment = ₹12,00,000 × 0.27824 Amount of risk-free investment ≈ ₹3,33,888 The PM should bring in approximately ₹3,33,888 in risk-free investment to reduce the portfolio beta to 0.8. This would mean the total portfolio value increases to ₹12,00,000 + ₹3,33,888 = ₹15,33,888, with ₹12,00,000 in risky assets and ₹3,33,888 in risk-free assets. Alternatively, if the question implies reducing the existing risky portfolio by selling some assets and investing the proceeds in risk-free assets, the calculation would be slightly different. However, the phrasing "bring in" suggests adding risk-free assets to the existing portfolio. Following the solution's interpretation: The PM should have (₹12,00,000 × 27.82%) = ₹3,33,840 in the risk-free securities. And (₹12,00,000 × 72.18%) = ₹8,66,160 in the risky securities. This implies that the total portfolio value remains ₹12,00,000, and the PM reallocates the existing funds. If this is the case, the PM would sell ₹3,33,840 worth of risky assets and invest that amount in risk-free securities.