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CA Final · Integrated Business Solutions (Multidisciplinary Case Study with Strategic Management) · Advanced Financial Management

Case: Aarav Wealth manages a Rs 10 crore portfolio with a beta of 1.2. The risk-free rate is 6%. The portfolio returned 15% with a standard deviation of 18%. The market returned 11% with a standard deviation of 12%. Which statement correctly compares the portfolio with the market using Sharpe and Treynor measures?

The portfolio's Sharpe ratio is 9 divided by 18, or 0.50, against the market's 0.4167. Its Treynor ratio is 9 divided by 1.2, or 7.5, against 5 for the market. It therefore outperforms the market on both risk-adjusted measures.

  1. ASharpe 0.50 vs market 0.4167 and Treynor 7.5 vs market 5; portfolio outperforms on bothCorrect
  2. BSharpe 0.50 vs market 0.4167 and Treynor 7.5 vs market 5; portfolio underperforms on Treynor
  3. CSharpe 0.833 vs market 0.4167 and Treynor 7.5 vs market 5; portfolio outperforms on both
  4. DSharpe 0.50 vs market 0.4167 and Treynor 9.0 vs market 5; portfolio outperforms on both

Explanation

Sharpe portfolio = (15-6)/18 = 0.50; market = (11-6)/12 = 0.4167. Treynor portfolio = (15-6)/1.2 = 7.5; market = (11-6)/1 = 5. The portfolio is higher on both, so it outperforms. Using 15/18 = 0.833 forgets to subtract the risk-free rate.

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