Portfolio Management-Active Returns

To calculate Active Returns, 2 formulas are given in the curriculum- (pg 473)

  1. Value added is the sum product of the active weights and asset returns: ie summation (ΔwiRi) and

  2. Value added as the sum product of active weights and active security returns: ie summation ΔwiRAi. Now RAi is Ri-RB. I am not able to understand this part.

Can someone pls help.

What exactly have u nt understood, if I may ask

How can Ra(i) = Ri - RB ie. Active Return of security = Return on Security - Return on Benchmark.

Return on benchmark is calculated as the weighted average return. And here we are subtracting return on benchmark from the return on one security…I did not understand the part in bold. Active Return is 1.2%, thats being calculated in 2 ways.

Example-

Benchmark = 60/40 weighted composite portfolio of stocks/bonds but investor holds a portfolio that is weighted 70% stocks and 30% bonds

The return on the stock market turned out to be 14.0% and the return on the bond market turned out to be just 2.0%.

As a result, the return on the managed portfolio is 0.70(14.0) + 0.30(2.0) = 10.4% and the return on the benchmark is 0.60(14.0) + 0.40(2.0) = 9.2%. From these final numbers, one could directly calculate the value added as 10.4 – 9.2 = 1.2%.

But a more informative calculation of value added showing the contributions from each segment is RA = 0.10(14.0 – 9.2) – 0.10(2.0 – 9.2) = 0.5 + 0.7 = 1.2%. This breakout suggests that a 0.5% return relative to the benchmark was generated by being overweight stocks and a 0.7% return was generated by being underweight bonds, for a total of 1.2%.

  1. Why does active portfolio with the highest (squared) information ratio will also have the highest (squared) Sharpe ratio?

  2. According to mean–variance theory, the expected information ratio is the single best criterion for assessing active performance among various actively managed funds with the same benchmark. (Why expected? Why not realized?)

Can someone help me understand? Pls…

Hi

I had this doubt. We have a portfolio of two composites, Stocks and Bonds, for which we get the Active returns as below.

(Pls see in edit mode, because the table gets distorted.)

Returns WB WP Active Return Stock 14% 60% 70% Bonds 2% 40% 30% 9.2% 10.4% 1.2%

Now, in the curriculum, there is a way to find out whether the underweights and overweights, did actually help. So, my doubt is that we are taking the total return on the stock portfolio and subtracting the benchmark returns (same for bond portfolio). How is this an apple to apple comparision?

Active Weights Return - Benchmark Return Active Return 10% 5% (ie 14%-9.2%) 0.5% (10%*5%) -10% -7% (2%-9.2%) 0.7% (-10%*-7%) 1.2%

Any help will be appreciated. I am just stuck here.