# Alpha return

Collette Gallant, CFA, employs the capital asset pricing model (CAPM) to determine the required returns for stocks. Gallant works for Trey-Black Inc. (TBI) which uses the Treynor-Black model for portfolio optimization. Gallant is deciding whether to include stock ABZ in the TBI’s actively managed portfolio. She forecasts that the ABZ stock return will be 15% next year. TBI provides Gallant with the following information.

• Expected return on the S&P500 stock market index = 15%.
• 1-year Treasury bill rate = 5%.
• ABZ stock beta = 1.25.

TBI determines that Gallant’s forecast ability has been very poor. TBI also finds that the average alpha across stocks in their actively managed portfolio equals 1%. Determine if Trey-Black’s allocation to ABZ in its actively managed portfolio should be an above or below average, long or short position.

Magnitude Position A) Below average Long B) Above average Short C) Below average Short

According to the Treynor-Black model, the actively-managed portfolio takes long positions in positive alpha stocks and short positions in negative alpha stocks. The alpha is defined as the difference between the analyst’s forecast return for the stock and its required return. As stated in the question, the required return for stock ABZ is calculated using the CAPM:

E® = RF + _β_m) – RF] = 0.05 + 1.25[0.15 – 0.05] = 0.175 = 17.5%.

Gallant’s forecast return (15%) is less than the required return (17.5%):

alpha = 0.15 – 0.175 = −0.025 = −2.5%.

Therefore, Gallant’s predicted alpha is much higher in absolute magnitude than the average alpha (1%), which would suggest an above-average short position if Gallant’s forecasting ability is reliable. However, TBI has determined that Gallant’s forecast ability is poor. Therefore, her forecast alpha will be adjusted severely toward zero to account for her poor forecast ability. The end result is that only a small short position will be taken in ABZ.

Hi,

This seems very clear to me. The right answer is C.

Think about it logically. You are investing according to analyst X’s recommandation.

They forecast something about a stock. You take their forcaste and you substract what the (instrinsic) return should be…aka what we call here the required return.

If the analyst predicts you are getting less (negative alpha) than what the market says you should get, you want to sell this like a hot potatoe… hence you listen to this guy and you sell what is not yours aka …take a short position that you will cover at a later date!

However, it turns out this guy is an idiot…well would you still want to listen to him and take a short (where in theory you could have unlimited losses)??? No, hopefully!!!

So you adjust his alpha by the squared correlation of this guy’s forecasting error over a period of time and in this case it makes it very small.

So you listen to him to take a short position but because he does not know what he is talking about (proved historically)…you only listen a little…hahahah.

Hope my personal logic helps.

Makes sense.

You wanna short b/c neg alpha but you don’t want to short too much b/c you have poor forecasting ability.

I generally follow. To clarify, I understand that you want your predicted return to at least equal the required return. In this case, it doesn’t…so you short sell.

I’m trying to visualize though, how does short selling help you realize the stocks expected underperformance (assuming the analyst is correct) ??

I agree with the Short but what is the rationale for below-average or above-average?

If you are a portfolio manager and an analysts comes to you and says alpha is 20%, are you going to believe him?

It depends on his forecasting ability.

An analysts forecasting ability is measured by rho.

If rho = 1, then the analyst perfect forecasting ability

If rho = 0, then the analyst is always wrong.

The higher the rho (forecasting ability of the analyst) the more weight you should give.

To calculate rho, you look at the track record of the analyst. Then you do a regression with actual alpha as the independent variable and forecasted alpha as the dependent variable.