Computer Information Systems

Part a: Required Rate of Return on Assets A and B Using CAPM The Capital Asset Pricing Model (CAPM) formula is: E(R_i) =R_F+β_i×(E(R_M) −R_F) Where: E(R_i) = Expected return on asset i R_F = Risk-free rate (5%) Β_i = Beta of asset i E(R_M) = Expected return on the market portfolio (18%) E(R_M)-R_F = Market risk premium For Asset A (β_A=0.2): E(R_A) = 5% + 0.2× (18%−5%) E(R_A) =5%+0.2×13% E(R_A) =5%+2.6% E(R_A) =7.6% For Asset B (β_B=1.1): E(R_B)=5%+1.1×(18%−5%) E(R_B)=5%+1.1×13% E(R_B)=5%+14.3% E(R_B)=19.3% Part b: Finding the Beta of Asset C (β_C) Here, the required rate of return for asset C E(R_C)=15%. We'll rearrange the CAPM formula to solve for β_C : E(RC)=RF+βC×(E(RM)−RF) 15%=5%+βC×(18%−5%) 15%=5%+βC×13% 10%=βC×13% βC=10%/13% βC=0.769 Part c: No Risk-Free Asset and Portfolio P Given: E(Rp) = 4% X'pΣXM = 0 (where X'p is the transpose of portfolio P's weights, Σ is the covariance matrix, and XM is the market portfolio's weights) Note: This condition implies that Portfolio P is uncorrelated with the market portfolio. Without a risk-free asset, the Capital Market Line (CML) becomes the tangent line to the efficient frontier. The expected return on any asset or portfolio is determined by its beta relative to this tangent line. Since Portfolio P is uncorrelated with the market, its beta is zero. Therefore, the required rate of return for Assets A, B, and C remains the same as calculated in Part a, as their betas are relative to the market portfolio, not the risk-free asset. To summarize: E(RA) = 7.6% E(RB) = 19.3% E(RC) = 15% (using βC ≈ 0.77) In the absence of a risk-free asset and with Portfolio P uncorrelated to the market, the required rates of return for Assets A, B, and C remain unchanged. E(Rc) = 15% βC ≈ 0.77 Rf = 5% E(Rm) = 18% Using the CAPM formula: E(Rc) = Rf + βC * (E(Rm) - Rf) Substituting the values: 15% = 5% + 0.77 * (18% - 5%) 15% = 5% + 0.77 * 13% 15% = 5% + 10.01% 15% ≈ 15.01% Final Answers: Part A: Required Return for Asset A: 7.6% Required Return for Asset B: 19.3% Part B: Beta for Asset C: 0.77 Part C: Required Return for Asset A: 7.6% Required Return for Asset B: 19.3% Required Return for Asset C: 15%

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Anu Bhardwaj

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