Various Actives defined

[Kavita.bhangdia]

HI David,

we have definitiions of various actives..

1. Active return : Portfolio return - benchmark return
2. Active risk : Standard deviation of Active risk??
3. Active weight.. No idea

Please can you help..

Thanks,
Kavita

 

[QuantMan2318]

I do not know about the first two ( I have to check my references ), the third one is logical enough. It all has to do with the portfolio manager who does broadly two major functions
1. Selection of securities (Asset choice)
2. Proportion of his money invested in these two securities (Asset Quantity/Allocation)

The best measure of a portfolio manager's performance is to split how much he/she gained from the Asset choice and how much they gained from the Asset Quantity. Therefore, enter Active Weights. It is a measure that is used to measure portfolio manager performance based on Asset Quantity.

Take a Benchmark portfolio, we can call it a Bogey, suppose it has 50% in Bonds, 40% in Equity and 10% in Cash, however the manager changes that to 20% Bonds, 70% Equity and 10% Cash, we may find out the excess/deficit Asset Allocation, which are called as Active weights (here -30%, +30% and 0) and multiply it by the benchmark return and add our results to get the Gains as a result of our Asset Quantity alone.

Hope this helps

 

[David Harper CFA FRM]

Hi @Kavita.bhangdia

Re (1) and (2), you should have:

• Active risk = σ(active return), just as residual risk = σ(residual return). This is relevant because the FRM's information ratio can be defined as either IR = active_return/σ(active_return) or IR = residual_return/σ(residual_return). Residual return is alpha. To illustrate with the (really simple) single-factor CAPM, assume Rf = 2%, ERP = 4%, and the portfolio's beta is 1.50. Say the benchmark is S&P 1500 with beta = 1.0. If portfolio return is 9.0%, then active return = 9.0% - (4%+2%) = 3.0%, but residual return attributes the beta (i.e., does not give the portfolio credit for returns due to beta exposures) so residual return is here the jensen's alpha = 1.0% = 9.0% - (2% + 4%*1.5)
• Re active weight, I agree with @QuantMan2318 . See, for example our question P2.T8.405 (screen below) at https://forum.bionicturtle.com/threads/p2-t8-405-style-analysis-and-market-timing.7754/ In this question (which merely queries Bodie's examples), the portfolio's active return is +0.90% (active return is called "excess return" in Bodie, which is quite conventional. I don't like it because excess return also implies return above the risk-free rate, I prefer active return). And the question in 405.2 is "... what is the contribution to the excess return from asset allocation?" ... this is the same thing as asking "what is the contribution to the excess return due to active weight" or "... due to over- and/or under-weight relative to the benchmark portoflio?" Just as QuantMan says, this +0.09% active return breaks into two pieces: the contribution from asset allocation (active weights) versus the remainder is the contribution due to security selection. I hope that's helpful!