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 buggest hurdle in understanding the topic. Here goes.
- 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?
- 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.
- 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.
- 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.
- How do I know how good is my OVERALL PORTFOLIO?
If it’s sharp ratio is higher than the market 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 f 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.
- Is that it?