Treynor Black Quickie its, determine, active, Black, index

joehogue

The Treynor-Black (T-B) model uses two portfolios – the passive index portfolio and the active portfolio to determine the optimal risky portfolio. Each stock’s weight in the active portfolio is determined on the basis of its alpha, beta, and

Valores

to calculate alpha…

ShooterMcCFA

CPK always the man!! thanks

tikfed

You’re a little confused, and it’s tricky. Beta is not used to calculate the weight of the stock in the active portfolio, beta in this context refers to the Beta of the active portfolio as a whole.
TB model assumes that you have found a collection of securities that are expected to have alpha. If you take all of these securities and put them into a portfolio, you have the “active portfolio”. The weight of these securities in this portfolio will be determined through mean variance and risk appetite. Once you have this established, you need to determine the Beta and SD of this portfolio as a whole in order to  determine the optimal weight of the portfolio.
Why do you need the Beta to determine the weight? Because you need to know the exposure to the systematic risk. If the portfolio has a high beta, all else being equal, you want to hold more of it relative to the market portfolio

economicz

This is just a little help with Treynor-Black, overly simplistic just to get the overall idea…I believe that someties not seeing the overall picture is the biggest hurdle in understanding the topic. Here goes.
1) What are we trying to do with TB?
You believe that the market is not 100% efficient, there are a few stocks that are mispriced, so why not use them to improve return?
2) How do I do that?
Well, check CAPM for example and see what it says the minmum required rate on some selected stocks, A, B, and C. Then do your own forecasting and see what return you expect. The difference (yours - CAPM return) is called alpha. You also need to know what each stock’s unsystematic risk is, not too hard…if you are using CAPM, it is the error term in the equation: R = Rf + Beta(Rm-Rf) + e. You need that because you know that you are getting a return above market for a reason, i.e., you are assuming some additional risk. You need the variance of that extra return, Variance(error term). Don’t panic yet, most of these numbers will be given to you on the exam.
3) What’s next?
Back to the overall picture, you want to put these stocks A, B, and C in a portfolio and call it, the ACTIVE PORTFOLIO. The other portfolio you need is called the MARKET PORTFOLIO. You want to put some money in the ACTIVE PORTFOLIO and some in the MARKET PORTFOLIO so that your overall return beats the market.
4) Fair enough, how much should I put in the ACTIVE PORTFOLIO and how much in the MARKET PORTFOLIO?
You will be given the weights, they will not ask you to use the formula for that. Then you will know the weight of each, Wa and Wm. So now your OVERALL PORTFOLIO is Wa + Wm.
5) How do I know how good is my OVERALL PORTFOLIO?
If its sharp ratio is higher than the market’s then you are good to go, but there is a litte trick here. Because the risk between your portfolio and that of the market are different, you need to use M^2, which is M^2 = SHRPE_p * STDDEV_m - Rm - Rf, or: (Rp-Rf)/Sigma_p * Sigma_m- (Rm-Rf). It’s the sharpe ratio of your portfolio times the std deviation of the market minus the market risk premium. This will tell you how much extra return you are getting for assuming the *same* risk as the market, that’s what matters in the end.
6) Is that it?
Mostly, yes.