Tracking Error Fund Benchmark Active Dev from Squared Period Return Return Retur

Question

Tracking Error Fund Benchmark Active Dev from Squared Period Return Return Return Mean Deviation 9.5010.00 4.50 5.00 -5.00-125-1 4 9.50 10.00-0. 4.50 5.00 6 -2.50 5.00 2.5 Sum Mean o. Variance 2 STDEV 2. a.) What is the tracking error for this portfolio? b.) Interpret your answer c.) Suppose there is another portfolio with an alpha (mean active return) of 0.75 and a tracking error of 1.75.. How might you choose between the two? Assume that the only relevant data are the alpha and the tracking error.

Explanation / Answer

(i) Period Fund Return Benchmark Return Active return Dev. From mean Squared Deviation (rp) (rb) AR =Rp- Rb Dev =AR - Mean AR DEV^2 1 9.5 10 -0.5 -1 1 2 4.5 5 -0.5 -1 1 3 -2.5 -5 2.5 2 4 4 9.5 10 -0.5 -1 1 5 4.5 5 -0.5 -1 1 6 -2.5 -5 2.5 2 4 3 12 Mean AR = SUM AR/n = =3/6 0.5 Tracking error = Sq root of (SUM DEV^2/n)         = Sq root of 2         = 1.414214 (ii) The lower is the tracking error, the better it is as it shows risk involved with active return. Here the tracking error is lower therefore it is good. (iii) Other portfolio - Mean 0.75 Tracking error 1.75 Calculating Information ratio - This shows how much return we will get for one unit of risk (Higher the better) - IR = Mean/Tracking error IR (existing portfolio) = 0.5/1.4142 = 0.353553 IR (New portfolio) = 0.75/1.75 = 0.428571 New portfolio will provide better returns as IR is higher then the other. Please provide feedback…. Thanks in advance…. :-)

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