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Measures of performance

Tracking Error


Information Ratio

 


Sortino Ratio

 

 

 

Where MAR is the Minimum Acceptable Return
 

Example

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
 

Solution

Ans. D.

 

  • Tracking Error (TE):  (Std. dev. of portfolio’s excess return over Benchmark index) 
    • Where Ep = RP – RB
    • RP = portfolio return, RB = benchmark return
    • Lower the tracking error lesser the risk differential between portfolio and the benchmark index 
  • Information Ratio (IR):
    • 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 Rp<MAR
  • Higher the Sortino Ratio, lower is the risk of large losses
Example

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
 

Solution

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%
 

Solution

B. 
 
Semi Standard Deviation = SSD = 0.3658%
Semi Variance = SSD2 = 0.1338%
 

 

Example

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
 

Solution

C. 
 

 

Example
 
  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
 
Correlation ρPB = 0.961
Solution
  • Sharpe ratio for Portfolio
 
 
Absolute performance is poor
 
  • Sharpe ratio for benchmark
 
 
Absolute performance is even poorer than portfolio
 
  • Information ratio
Absolute performance is even poorer than portfolio
 

 

 





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