# Reading 55: Treynor-Black Model example pp. 468-471

I found the lead-up to this example somewhat difficult, so I went straight to the example.

Early in the example, they calculate a ‘quick’ Sharpe ratio for the DPF portfolio, including the broad market and 3 individual stocks. But there is no weighting applied. I would expect that you must first get the security weights for the portfolio, and then calculate the Sharpe ratio.

They used equation 10, which also has no weights. It seems that this equation would hold only if the security weights are equal.

Am I missing something?

Also, there is a note at the beginning of the chapter saying that candidates are not responsible for deriving or memorizing the formulas in Sections 4 - 6. So, this would probably not be something to worry too much about.

I havent learnt these formulas also as its not mentioned in LOS

There are two LOSs vis-à-vis Treynor-Black:

55b. Describe the steps and the approach of the Treynor-Black model for security selection.

55c. Explain how an analyst’s accuracy in forecasting alphas can be measured and how estimates of forecasting can be incorporated into the Treynor-Black approach.

Neither mentions calculations. Forget about them.

There are two less readings in the PM section this year compared to last year. With precious little material now in PM, I’m not going to take a risk and not know the formulas. They’re tested in the EOCs and that’s enough for me.

Cinderella plz tell a way to remember these formulas

I watched the Elan lecture for it over the weekend. It’s all pretty intuitive and the video does a great job I think.

elan saying to learn formula?

This is an example of material that if you want to study it at all, you basically have to put it into Excel.

EOC #1 is essentially a verbatim of the example in the text, except with 4 securities in the active portfolio instead of 3. #2 you can do by copying #1 and deleting rows from the data table where the portfolio weights are negative. It’s hard for me to see how these are feasible to learn without putting them in Excel.

i think one can do a better job of understanding black-treynor model by trying to know the purpose of the model.

to find out forecast alpha , which is excess returns(of portfolio/assets) over the benchmark . further to arrive at the forecast alpha of the portfolio one has to calculate the weigths of each asset in the portfolio , the weights are computed based on specific risk and returns of each asset .Treynor-Black model says weight of each security in the portfolio to arrive at the forecast alpha should be based on ratio of its mispricing(alpha) to its nonsystematic risk . the formula for weigths is alpha of the ith asset in the numerator divided by the variance of the returns of error term of the ith asset . Why the variance of the error term ? if you regress the returns of the asset against the benchmark the variance of the historical returns explains the overall risk the regression coefficient would be beta(systemic risk) and the unexplained error term would be specific risk .

This becomes more intuitive if one looks in the liner regression framework , where the assumption that specific risk (s(ei^2))are distributed independently . I dont think they will ask question requiring direct application of formula but knowing the purpose of the model would help derive the formula logically .

I was struggling with this concept too this article helped me to clear my concepts