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The following data is given for a particular sample period:

Portfolio P Market M
Average return 35 % 28 %
Beta 1.2 1.0
Standard deviation 42 % 30 %
Calculate the following performance measures for portfolio P and the market: Sharpe, Jensen (alpha) and Treynor. The Treasury bill rate during the period was 6 %. By which measures did portfolio P outperform the market? What do these measures mean or imply? Explain

User Anita
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Final answer:

The question revolves around calculating the Sharpe, Jensen's Alpha, and Treynor ratios for a portfolio and comparing them with the market to determine outperformance. These measures assess different aspects of performance, including return per unit of risk (Sharpe), performance against expected risk-adjusted returns (Jensen), and returns relative to systematic risk (Treynor).

Step-by-step explanation:

The student has provided data and is asking to calculate performance measures for a portfolio and the market, specifically the Sharpe, Jensen's Alpha (Jensen), and Treynor ratios, using a given Treasury bill rate. Then, to assess by which measures the portfolio P outperformed the market and to explain what these measures imply.

To calculate the Sharpe ratio, we use the formula: (Portfolio Return - Risk-Free Rate) / Standard Deviation of Portfolio. For Portfolio P, it would be (0.35 - 0.06) / 0.42, and for Market M, it would be (0.28 - 0.06) / 0.30.

For Jensen's Alpha, the formula is: Portfolio Return - (Risk-Free Rate + Portfolio's Beta * (Market Return - Risk-Free Rate)). For Portfolio P, this would be 0.35 - (0.06 + 1.2 * (0.28 - 0.06)).

The Treynor ratio is calculated using: (Portfolio Return - Risk-Free Rate) / Portfolio's Beta. For Portfolio P, it's (0.35 - 0.06) / 1.2.

After calculating these values, we compare them between Portfolio P and Market M to determine which outperformed the other. Each performance measure indicates different aspects of investment performance: the Sharpe ratio measures excess return per unit of risk, Jensen's Alpha measures the portfolio's performance relative to the expected risk-adjusted return, and the Treynor ratio gauges return relative to systematic risk.

User Stpn
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