Jack Haddad's  Instablog

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durenam Comments (5)
 
So this may be the completely wrong place to ask this question, but it is concerning the risk statistic Alpha. I understand the calculation and everything, but I am getting a negative Alpha, and I'm not sure why? The portfolio I am looking at is measured against the S&P 500, and both the S&P 500 and the portfolio I am viewing have had negative returns through the period I am looking at. My portfolio has higher returns (though they are still negative) and a lower standard deviation than the S&P 500.... shouldn't I have a better alpha? The alpha is better than the S&P500, but it is still negative... My overall question is; Because I have negative returns for the period, is that what is causing my negative Alpha? I hope this makes sense, and I appreciate any help!
29 May 2009, 11:43 AM Reply Like

Jack Haddad Comments (96)
 
You lost me completely... Not sure what you are trying to convey. Be advised that alpha is measured in many different ways, depending on your risk catagory.
29 May 2009, 12:43 PM Reply Like

durenam Comments (5)
 
This is the formula I am using to find the Alpha of a portfolio using the S&P500 as the benchmark:

Returns of portfolio - (TBill returns + Portfolio Beta*(returns of S&P-Tbill returns))

Portfolio has higher returns (though they are still negative) & a lower Standard Deviation than the S&P. S&P also has negative returns. It is my understanding that higher returns & a lower standard deviation results in a greater alpha. Is this true? Is the formula above thrown off because if have negative returns for the time frame?

I understand that there are other things that go into the analysis, but I am trying to figure out why I am getting a negative alpha for the formula above. Apologies if my question is wrongly directed. Any advice on where to find information on this? Many thanks.

29 May 2009, 02:57 PM Reply Like

Jack Haddad Comments (96)
 
Wrong! :) But don't worry... you gave it your best shot.

Okay, as strange as it sounds, the formula doesn't work well in real life, and negative returns are still applicable in that formula. I know CAPM model got a nobel prize, but it doesn't hold true in real life... Alpha is basically the return in access of the CAPM model. If your alpha is less than predicted, it means that youre doing worse than what the suppossed CAPM return is. Alpha takes the volatility (price risk) of a mutual fund and compares its risk-adjusted performance to a benchmark index. The excess return of the fund relative to the return of the benchmark index is a fund's alpha.

I hope i have expressed myself correctly. If a CAPM analysis estimates that a portfolio should earn 10% based on the risk of the portfolio but the portfolio actually earns 15%, the portfolio's alpha would be 5%. This 5% is the excess return over what was predicted in the CAPM model
29 May 2009, 04:46 PM Reply Like

durenam Comments (5)
 
So are you saying that I shouldn't rely on the formula for Alpha? Do you suggest another way of determining the Alpha of a portfolio? Many thanks for the information.
29 May 2009, 05:37 PM Reply Like

tradewind Comment (1)
 
What Jack is saying is that the formula you are using is CAPM and that it gives you the theoretical return based on your portfolio's risk level and it does not give you alpha. To get alpha, you must take the difference between this theoretical return and the actual return of your portfolio. Do not compare it to the Benchmark return because this will not give the correct answer. The Benchmark return is already included in the CAPM formula so there is no need to use it again in the final calculation of alpha.

For example, lets assume the T-bill return is 4%, portfolio beta is 1.5 and the SP500 return is 12%. Using your formula (ie CAPM), theoretical return= 4+(1.5)(12-4) = 16%. Now lets say your actual portfolio return was 20%. Alpha = 20-16 = 4%. This works for negative returns also. Lets say SP500 return is -10%, then theoretical return = 4+(1.5)(-10-4) = -17%. Lets say your actual portfolio return was -13%. Alpha = -13-(-17) = 4%.

I hope this was helpful.
31 May 2009, 05:16 AM Reply Like

Jack Haddad Comments (96)
 
Very good...point well taken.


On May 31 05:16 AM tradewind wrote:

> What Jack is saying is that the formula you are using is CAPM and
> that it gives you the theoretical return based on your portfolio's
> risk level and it does not give you alpha. To get alpha, you must
> take the difference between this theoretical return and the actual
> return of your portfolio. Do not compare it to the Benchmark return
> because this will not give the correct answer. The Benchmark return
> is already included in the CAPM formula so there is no need to use
> it again in the final calculation of alpha.
>
> For example, lets assume the T-bill return is 4%, portfolio beta
> is 1.5 and the SP500 return is 12%. Using your formula (ie CAPM),
> theoretical return= 4+(1.5)(12-4) = 16%. Now lets say your actual
> portfolio return was 20%. Alpha = 20-16 = 4%. This works for negative
> returns also. Lets say SP500 return is -10%, then theoretical return
> = 4+(1.5)(-10-4) = -17%. Lets say your actual portfolio return was
> -13%. Alpha = -13-(-17) = 4%.
>
> I hope this was helpful.
31 May 2009, 05:34 PM Reply Like

durenam Comments (5)
 
Thank you. That was helpful, and I understand the formula and the process now. What would you say about the following scenarios comparing a portfolio to 2 different indices:

scenario 1:
TBills= 3.05%
S&P= -2.19%
Actual Portfolio Returns= -0.45%
Beta= 0.46

Thus:
Theoretical return= 3.05+(0.46)(-2.19-3.05) = 0.64%
Alpha= (-0.45)-(0.64) = -0.0109

Now consider scenario 2:
TBills= 3.05%
Barclays AGG= 4.44%
Actual Porfolio Returns= -0.45%
Beta=0.16

Thus:
Theoretical Returns= 3.05+(0.16)(4.44-3.05) = 3.27%
Aplha = (-0.45)-(3.27)= -0.0372

So would you say that both portfolios return a negative alpha because they performed less than expected, considering their beta?

Also, barclays has a lower standard deviation that the S&P and higher returns than the S&P, is there any reason to believe that this should cause Barclay's Alpha to be higher?


I know this is a lot to take in, but thanks for any comments.


On May 31 05:16 AM tradewind wrote:

> What Jack is saying is that the formula you are using is CAPM and
> that it gives you the theoretical return based on your portfolio's
> risk level and it does not give you alpha. To get alpha, you must
> take the difference between this theoretical return and the actual
> return of your portfolio. Do not compare it to the Benchmark return
> because this will not give the correct answer. The Benchmark return
> is already included in the CAPM formula so there is no need to use
> it again in the final calculation of alpha.
>
> For example, lets assume the T-bill return is 4%, portfolio beta
> is 1.5 and the SP500 return is 12%. Using your formula (ie CAPM),
> theoretical return= 4+(1.5)(12-4) = 16%. Now lets say your actual
> portfolio return was 20%. Alpha = 20-16 = 4%. This works for negative
> returns also. Lets say SP500 return is -10%, then theoretical return
> = 4+(1.5)(-10-4) = -17%. Lets say your actual portfolio return was
> -13%. Alpha = -13-(-17) = 4%.
>
> I hope this was helpful.
2 Jun 2009, 11:25 AM Reply Like