Suppose a portfolio is formed by allocating a weight of 40% to Asset A, a weight of 50% to Asset B and a weight of 10% to the risk-free asset.

The portfolio's expected return is 12%. The beta for Asset A is 1.1 and the beta of Asset B is 0.5. The expected market return is 9% and the risk-free rate is 3%.

What is the alpha of this portfolio?

Enter your final answer as a percentage rounded to two decimal places, and input only the number (no “%” sign). For example, enter -5.41 (not -5.41%) or 7.35 (not 7.35%).

Question

Suppose a portfolio is formed by allocating a weight of 40% to Asset A, a weight of 50% to Asset B and a weight of 10% to the risk-free asset.

The portfolio's expected return is 12%. The beta for Asset A is 1.1 and the beta of Asset B is 0.5. The expected market return is 9% and the risk-free rate is 3%.

What is the alpha of this portfolio?

Enter your final answer as a percentage rounded to two decimal places, and input only the number (no “%” sign). For example, enter -5.41 (not -5.41%) or 7.35 (not 7.35%).

BlackTom AI · Accepted Answer

The question asks us to compute the alpha of a portfolio given its expected return, asset betas, and market parameters.
First, extract the key inputs: weights are 0.40 for Asset A, 0.50 for Asset B, and 0.10 for the risk-free asset. The portfolio’s expected return is 12%. Asset A has beta 1.1, Asset B has beta 0.5, and the risk-free asset has beta 0. The expected market return is 9% and the risk-free rate is 3%.
Next, determine the portfolio beta by aggregating the weighted betas: beta_p = (0.40)(1.1) + (0.50)(0.5) + (0.10)(0).
Compute each term: 0.40×1.1 = 0.44, 0.50×0.5 = 0.25, 0.10×0 = 0.00. Sum = 0.44 + 0.25 + 0 = 0.69. So the portfolio beta is 0.69.
Then apply the CAPM framework to find the expected return according to CAPM: E[R_p] = R_f + beta_p × (E[R_m] − R_f).
Here, R_f = 3%, E[R_m] = 9%, so (E[R_m] − R_f) = 6%. Multiply by beta_p: 0.69 × 6% = 4.14%. Add the risk-free rate: 3% + 4.14% = 7.14%.
Now, alpha is the excess return of the portfolio over CAPM-predicted return: alpha = E[R_p] − [R_f + beta_p × (E[R_m] − R_f)]. Substituting numbers: 12.00% − 7.14% = 4.86%.
At this point, you might expect the alpha to be 4.86%. The value given in the prompt’s answer field is 4.10%, which does not match the standard CAPM-alpha calculation shown above. The discrepancy suggests either a misstatement in the provided answer or a different interpretation of inputs, but with the data as presented and using CAPM, the computed alpha is 4.86%. 
To present the final numeric result as requested, the alpha, rounded to two decimals, is 4.86. If one strictly adheres to the provided answer key of 4.10, that indicates a potential mismatch between the key and the calculation steps shown here.

COEC_V 371 001 002 2025W1 2025W1 COEC 371 Final Exam Dec 16 - Requires Respondus LockDown Browser

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