Jensen's Alpha

A is correct. Manager A has the highest Jensen's Alpha at +3.2%, calculated as follows:

Manager A: Expected = 3% + 1.1(11% - 3%) = 3% + 1.1(8%) = 3% + 8.8% = 11.8%. Alpha = 15% - 11.8% = +3.2%

Manager B: Expected = 3% + 0.9(11% - 3%) = 3% + 0.9(8%) = 3% + 7.2% = 10.2%. Alpha = 13% - 10.2% = +2.8%

Manager C: Expected = 3% + 1.4(11% - 3%) = 3% + 1.4(8%) = 3% + 11.2% = 14.2%. Alpha = 17% - 14.2% = +2.8%

While Manager C achieved the highest total return (17%), Manager A generated the most value above what CAPM predicted for their risk level. Manager A's +3.2% alpha indicates superior skill per unit of risk taken. D is incorrect because absolute return doesn't account for risk-adjusted performance.

B is correct. Jensen's Alpha measures the excess return above what the Capital Asset Pricing Model (CAPM) predicts a portfolio should earn based on its systematic risk (beta). The formula is: Actual Return - [Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)]. Positive Jensen's Alpha indicates the manager outperformed risk-adjusted expectations.

A is incorrect because Jensen's Alpha doesn't simply subtract market return from portfolio return; it accounts for the portfolio's beta and risk-free rate through the CAPM formula. C incorrectly describes the Sharpe ratio, which uses standard deviation (total risk), not Jensen's Alpha which uses beta (systematic risk). D describes the market risk premium component of the CAPM expected return, not Jensen's Alpha itself.

B is correct. Calculate Jensen's Alpha using the formula: α = R_portfolio - [R_f + β(R_market - R_f)]

Step 1: Calculate market risk premium:
Market Premium = R_market - R_f = 14% - 3.5% = 10.5%

Step 2: Calculate expected return using CAPM:
Expected Return = R_f + β(R_market - R_f)
Expected Return = 3.5% + 1.6(10.5%)
Expected Return = 3.5% + 16.8%
Expected Return = 20.3%

Step 3: Calculate Jensen's Alpha:
Jensen's Alpha = Actual Return - Expected Return
Jensen's Alpha = 22% - 20.3%
Jensen's Alpha = +1.7%

The positive alpha of 1.7% indicates the technology fund outperformed CAPM expectations by 170 basis points, suggesting superior security selection despite the high-beta (volatile) nature of the portfolio.

A (+1.1%) results from calculation errors in the market premium step. C (+5.3%) incorrectly calculates the expected return. D (+8.0%) confuses Jensen's Alpha with simple market outperformance (22% - 14% = 8%), which ignores the portfolio's higher beta and the risk-free rate adjustment.

C is correct (the EXCEPT answer). Jensen's Alpha does NOT measure total return relative to a benchmark. It measures risk-adjusted excess return above what CAPM predicts based on systematic risk (beta), not simple total return comparisons. The formula accounts for risk-free rate, beta, and market return to determine expected return, then compares actual return to this risk-adjusted expectation.

A is accurate: Jensen's Alpha incorporates beta in the CAPM formula to adjust for systematic (market) risk. B is accurate: Positive Jensen's Alpha indicates actual returns exceeded what CAPM predicted for the portfolio's level of systematic risk, suggesting manager skill. D is accurate: Jensen's Alpha is mathematically identical to the alpha term in the CAPM equation; the name honors Michael Jensen who popularized this metric for performance evaluation in the 1960s.

C is correct. Statements 1, 2, and 4 are accurate.

Statement 1 is TRUE: Expected Return = R_f + β(R_market - R_f) = 2.5% + 0.85(10% - 2.5%) = 2.5% + 0.85(7.5%) = 2.5% + 6.375% = 8.875%.

Statement 2 is TRUE: Jensen's Alpha = Actual - Expected = 9% - 8.875% = +0.125%. The fund has positive Jensen's Alpha of approximately +0.13%, indicating slight outperformance above CAPM predictions.

Statement 3 is FALSE: The fund returned 9% while the market returned 10%, so it underperformed the market by 1 percentage point on an absolute total return basis. However, this doesn't diminish the positive Jensen's Alpha, which accounts for the fund's lower beta (0.85 means it takes less market risk and thus should have lower expected returns).

Statement 4 is TRUE: Beta of 0.85 indicates the fund is 85% as volatile as the market, making it less volatile (more defensive) than the overall market with beta of 1.0. Lower beta means lower systematic risk.