Please post formula sheet / direct me to other relevant post. Thank you.
Do we need to know the formula for BR?
BR is BR^0.5 and is # of independent forcasts.
There’s a way longer formula for Br
BR = n/(1+(n-1)x(correlation coefficient))
PM formulas? There are bunch depending what you are looking at…
Basic Fundamenal Law : Return Active = Information Coefieicent * Sqrt(Breadth) * Standard Deviation of Active Return
Full: Return Active = Transfer Coeffieicnet * Intformation Coeffiencet * Sqrt(Breadth) * Standard Deviation of Active Return
If we divided by active return we can ge t the information ratio.
Return active = Return on Portfolio - Return on Benchmark
Sharp ratio for a active portfolio = SRp^2 = Sharpe Ratio ^2 + Information Ratio ^2, then take the square root to get Sharpe Ratio of the portfolio.
A big one for me is the value added broken down by Asset Allocation and Security selection.
Letting wi = Weight Port - Weight Bench
Sum (Wi*RBj) + Sum (Weight P * RP) gives us the value added.
The first term is return from Asset allocation, where Rbj is the Return on the bench for asset j.
The second term is the value from Security selection.
The Optimal level of risk for a portfolio =
STD(RA) = (Information ratio/Sharp Ratio Bench)*Standard Deviaton Benchmark
That is a big one because we can build portfolios that way by going long and short Active vs Bench.
Here is a really crappy example of this
· Example: Active port = IR = .3, active risk = .08, bench sharpe = .4, and total risl = .16 then
· Solve Optimal level of risk = (.3/.4)*.16 = 12%
· If constructed with this level of risk, then the Active managed portfolio sharpe ratio (From abovel ) = (.4^2 + .3^2)^(1/2)
· Active manager would either need to increase active risk and preserve IR, or short the benchmark.
· Solve Amount to go long and Short: 12/8 (opitmal level/current active) = 1.5 times invested in active fund. Short .5 of the Benhcmark.
thank you
yes, do we need to memorise this formula ?
c state and interpret the fundamental law of active portfolio management including its component terms—transfer coefficient, information coefficient, breadth, and active risk (aggressiveness);
It doesn’t say calculate breadth. Just knowing that breadth is the amount of independent decisons made, that breadth can be overstated either through making the same investment decisons every month (they are no independent) or decisions correlated with each other such as credit risk with bonds.