# Measures of performance

**Tracking Error**

**Information Ratio**

Sortino Ratio

**Where MAR is the Minimum Acceptable Return**

For a given portfolio, the expected return is 10% with a standard deviation of 15%. The beta of the portfolio is 0.75. The expected return of the market is 11% with a standard deviation of 18%.

The risk-free rate is 4%. The portfolio's Treynor measure is:

0.060

0.012

0.040

0.080

Solution

Ans. D.

- Tracking Error (TE): (Std. dev. of portfolio’s excess return over Benchmark index)
- Where E
_{p}= R_{P}– R_{B} - R
_{P}= portfolio return, R_{B}= benchmark return - Lower the tracking error lesser the risk differential between portfolio and the benchmark index

- Where E
- Information Ratio (IR):
- Measure of risk-adjusted return for a portfolio, defined as expected active return per unit of tracking error

- Measure of risk-adjusted return for a portfolio, defined as expected active return per unit of tracking error

- Higher IR indicates higher active return of portfolio at a given risk level
- Sortino Ratio (SR):

- MAR is Minimum Accepted Return. SSD is standard deviation of returns below MAR. (Or) SSD is the Semi Standard Deviation from MAR where R
_{p}<MAR - Higher the Sortino Ratio, lower is the risk of large losses

For the past four years, the returns on a portfolio were 6%, 9%, 4%, and 12%. The corresponding returns of the benchmark were 7%, 10%, 4%, and 10%. The minimum acceptable return is 7%.

The portfolio's Sortino ratio is:

0.4743

0.2143

0.5303

0.6700

A.

Average Return

**Example: **

An analyst has compiled the following information on a portfolio:

Sortino Ratio: 0.82

Beta: 1.15

Portfolio return: 12.2%

Standard deviation: 16.4%

Benchmark return: 11.9%

Risk-free rate: 4.75%

Calculate the semi-standard deviation of the portfolio

0.4000%

0.3658%

0.1338%

0.9080%

B.

Semi Standard Deviation = SSD = 0.3658%

Semi Variance = SSD2 = 0.1338%

A portfolio has an average return over the last year of 13.2%. Its benchmark has provided an average return over the same period of 12.3%. The portfolio’s standard deviation is 15.3%, its beta is 1.15, its tracking error volatility is 6.5% and its semi-standard deviation is 9.4%. Lastly the risk free rate is 4.5%. Calculate the portfolio’s Information Ratio (IR)

0.569

0.076

0.138

0.096

C.

Average | Volatility | Performance | |

Risk free | 3% | 0% | |

Portfolio | -6% | 25% | Calculate SR of Portfolio |

Benchmark | -10% | 20% | Calculate SR of Benchmark |

Tracking error | 4% | 8% | Calculate IR of Portfolio |

- Sharpe ratio for Portfolio

- Sharpe ratio for benchmark

- Information ratio