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Dominick,
I think this is what you want to do:
load into Indicator builder and
Insert your base market ( index ) and then change the Periods to your setting.
Then when you open a chart with a mutual fund..you will see the Alpha , beta, and R_squared..
Anthony
//Alpha AND Beta Indicators
//Ver.1.00, 2/10/02
//coded by Anthony Faragasso
//e-mail: ajf1111@xxxxxxxx
//Insert your Stock_index,Composite_index, S&P,etc.
//as the **Base Market**.
MaxGraph=5;
/***Base Market************/
Mkt="^ndx";//Must be enclosed in "....."Quotations.
P=Foreign(Mkt,"C",1);
/**************************/
Periods=14;//Set the period of Observation
//****Beta***********************/
Beta=(( Periods * Sum(ROC( C,1) * ROC(P,1),Periods )) - (Sum(ROC(C,1),Periods) * Sum(ROC( P,1),Periods))) / ((Periods * Sum((ROC(P,1)^2 ),Periods)) - (Sum(ROC(P,1 ),Periods)^2 ));
/******************************************/
//*****Alpha*********************/
Alpha=(Sum(ROC( C,1) ,Periods) - ( Beta ) * Sum( ROC( P,1) ,Periods ) ) / Periods;
/******************************************/
/***R-Squared*****************/
R2=Correlation(P,C,Periods)^2;
/************************************/
Plot(beta,"Beta",colorRed,styleLine);
Plot(Alpha,"Alpha",colorBlue,styleLine);
/**R_squared graphing*****/
Plot(r2,"R2",colorYellow,styleLine);
/*************************/
Title=Name()+" "+"ALPHA "+EncodeColor(colorBlue)+"("+WriteVal(Alpha,format=1.2)+")"+" "+EncodeColor(colorBlack)+" BETA "+EncodeColor(colorRed)+"("+WriteVal(Beta,format=1.2)+")"+"\n "+EncodeColor(colorBlack)+" R_SQUARED "+EncodeColor(colorYellow)+"("+WriteVal(r2,format=1.2)+")";
/**Notes***/
//You've got to start with r-squared, which is an
//indicator of the validity of the beta AND alpha
//measures. Because the r-squared measures just how
//closely the Stock OR fund tracks the
//index with which it is being compared.
//An r-squared of 1.0 indicates
//A perfect match. AND, in that case, you can
//trust that the beta AND alpha measures are
//valid, too. But, the lower the r-squared, the less
//reliable beta AND alpha measures are.
//"[Betas and alphas on] a Stock or fund with an r-squared that's below //0.50 are completely meaningless.
//Assuming the r-squared is, say, 0.75 OR higher, you can move on to the //beta.
-------Original Message-------
From: amibroker@xxxxxxxxxxxxxxx
Date: Saturday, February 15, 2003 10:00:12 AM
To: amibroker@xxxxxxxxxxxxxxx
Subject: Re: [amibroker] r-squared and regression analysis
Hi Anthony:When I used to subscribe to Morningstar which rated mutual funds, themeaing of R2 referred to how much of the mutual fund point movementwas due to its comparative index, usually the S&P 500. If the fundhad an R2 of 80, that meant 80 percent of the funds movement will bedue to the index. The other 20% was attributed to the individualcharacteristics of that fund.You would think the above would have been beta but it's not.Is your R2 and the one above the same? If not could a code be writtento determine the R2 for a set number of periods?TIA,Dominick Post AmiQuote-related messages ONLY to: amiquote@xxxxxxxxxxxxxxx (Web page: http://groups.yahoo.com/group/amiquote/messages/)Check group FAQ at: http://groups.yahoo.com/group/amibroker/files/groupfaq.html Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
____________________________________________________ IncrediMail - Email has finally evolved - Click HereAlpha and Beta:
In security analysis, a lot of focus is given to a stock's beta.
The beta is the stock's coefficient measure of how volitile
it is as compared to the rest of the market (represented by
the S&P 500). Thus a stock with a beta of 1 means it moves
in perfect harmony with the market. The market goes up
10% in one week, that stock will go up 10% in that same week.
If the market goes down 10%, expect that stock to do the
same. Stocks with a beta greater than 1 means that the stock
will move greater than the market. For example if the market
moves up 10% in one week and the beta for a certain stock is
2, that stock will move up 20% or twice the market. A beta of
less than 1 means that the stock will move less than the
market. If a stock has a beta of 0.5 and the market goes up
10%, the stock will go up only 5%. You can also assume the
reverse to be true as well.
But a beta only gives you part of the picture. To get a better
sense of the nature of a stock, one should look at the alpha. A
stock's alpha is a coefficient that measures return from
nonmarket risk. Basically alpha is saying "Hey, ignoring the
effects of the market, what would this company's return be?"
An alpha of say 1.15 tells us that ignoring all other factors, we
should expect this stock to appreciate 15% per year. Now I
know what you are going to say, "Is it realistic to ignore how the
market effects the price of a stock?" If alpha is just used alone
then no, it would not be. But when used it tandem with beta
and a few other factors, it can give you a clearer picture. A
simple hypothetical example of this would be:
Company XYZ @ $45 per share
Alpha - 1.19
Beta - 1.50
If the projected gain in the S&P 500 was 11% for the year, the
beta is telling us that XYZ will appreciate 16.50%. Adding on
alpha, it wouldn't surprise if XYZ came out ahead 19%. But
what if the market goes flat for the year with only minimal gain
or a small loss? Factoring in alpha you can have a range from
a 2.50% gain (alpha of 19% minus 16.50%) to a 19% gain (the
basic alpha). Now lets say the projected loss of the S&P 500
was -11%. Beta tells us that XYZ would go down 16.50%. But
once again factoring in alpha, it would be possible that XYZ
could ink out a gain of 2.50%. As you can see, alpha can give
you the ability to run different senario returns for a
stock. Just another tool in your analysis box to make more
informed investment decisions.
QUESTION: Can you explain how to use the
alpha and beta measurements for evaluating
mutual fund performance? If the beta of a
mutual fund is +1.17 and the alpha is -9.58,
what exactly does that mean?
— Anita Bowser
ANSWER: Alpha, beta and their companion,
r-squared, are statistics related to Modern
Portfolio Theory. They are derived by comparing
a fund or security's returns and volatility to an
index. Here's how to use them when evaluating
mutual funds.
You've got to start with r-squared, which is an
indicator of the validity of the beta and alpha
measures. That's because the r-squared
measures just how closely the fund tracks the
index with which it is being compared.
(Generally, equity funds are measured relative
to the S&P 500 and fixed-income funds relative
to Treasury bills.) An r-squared of 1.0 indicates
a perfect match. And, in that case, you can
trust that the beta and alpha measures are
valid, too. But, the lower the r-squared, the less
reliable beta and alpha measures are. The
Fidelity Japan Small Companies (FJSCX)
fund, for instance, has an r-squared of 0.11, indicating little correlation with the
S&P 500. "[Betas and alphas on] a fund with an r-squared that's below 0.50 are
completely meaningless," explains Dr. John Markese, president of the American
Association of Individual Investors.
Assuming the r-squared is, say, 0.75 or higher, you can move on to the beta. This
figure measures the fund's volatility relative to the benchmark index. The beta of
the benchmark, or index, is 1.00. So a fund with a beta coefficient of 1.00 has
experienced up and down movements of roughly the same magnitude as the
benchmark. Generally, a fund with a beta of 1.25 is expected to do 25% better
than its benchmark in an up market and 25% worse in a down market.
Conversely, a fund with a beta of 0.75 is expected to do 25% worse than its
benchmark in a rising market and 25% better in a falling market. A low beta,
however, does not necessarily mean lower volatility -- just that the fund does not
have a high correlation with its benchmark.
Now comes alpha. This is the most controversial of the three figures, since it is
viewed by many as an indicator of just how effective a fund's management is,
explains Markese. It does this by comparing the fund's performance to the
expected performance based on the fund's beta. A positive alpha means that the
fund has performed better than expected, given its beta. But a fund with an alpha
of -9.58 (like the one you mentioned) suggests that the fund has performed 9.58%
below its expected returns. Of course, the validity of the alpha depends upon a
close relationship with the benchmark index. Which brings us back to the
Attachment:
Description: " r-squared. "
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