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I ripped this code out of my Custom Backtest Metrics afl, that is why
the reference to Eq. I also use multiple benchmarks, hence the 1
after the B.
EqCAR = Compound Ann Ret of Equity line (or security)
B1CAR = Compound Ann Ret of Benchmark
n = number of periods
When comparing to Morningstar results, remember that they use monthly
data for trailing three years (36 periods).
A good sanity check for Alpha calculation is to use S&P Total Ret as
security and S&P Price as benchmark. The correlation is 1, so Alpha
should be apprx equal to dividend yield.
--- In amibroker@xxxxxxxxxxxxxxx, Ken Close <ken45140@xxx> wrote:
>
> Thanks Ron:
>
> Before I get further into comparisons, please confirm EqCAR formula
for me.
> I realize it is the Compound Annual Return for Eq, but please
confirm
> formula.
> Further assume B1CAR is annual return of benchmark.
> I assume n = lookback period
>
> Ken
> -----Original Message-----
> From: amibroker@xxxxxxxxxxxxxxx [mailto:amibroker@xxxxxxxxxxxxxxx]
On Behalf
> Of Ron Rowland
> Sent: Sunday, August 31, 2008 12:50 PM
> To: amibroker@xxxxxxxxxxxxxxx
> Subject: [amibroker] Re: Alpha/Beta for Daily and Monthly Data
>
> Ken,
> I did not study your code in detail, but here is what I have been
using. I
> did not compare the results directly to MorningStar since I was
using daily
> data instead of monthly. However, I did some rough comparisons and
> everything seemed to be in the right neighborhood.
> (be careful of line wraps below).
>
> One thing to remember is that alpha calculation is for whatever
interval you
> are using and needs to be annualized.
>
> // Correlation
> B1Cor = Correlation(EqROC, B1ROC, n-1);
> // Correlation Coef (r) to Benchmark 1
> B1Corr = B1Cor * B1Cor;
> // Coef of Deter(r-sqrd) to Benchmark
> 1
>
> // Beta
> B1Beta = (n * Sum(EqROC * B1ROC , n) - Sum(EqROC, n)
* Sum
> (B1ROC, n) )
> / (n * Sum(B1ROC ^ 2 , n) - Sum(B1ROC, n) ^ 2 );
>
> // MPT Alpha (traditional)
> B1Alphad = (MA(EqROC, n-1) - B1Beta * MA(B1ROC, n-1)); //
> Daily Alpha
> B1AlphaA = 100*((1+B1Alphad/100)^252 -1);
> // Annualized Daily Alpha
> B1Alpha = EqCAR - B1Beta*B1CAR;
> // Alpha from Annualized data
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Ken Close" <ken45140@> wrote:
> >
> > Can someone help on this question:
> >
> > I need to calculate Alpha and Beta for two sets of symbols for
> equity, one
> > having daily data, and another set having monthly data.
> >
> > 1. I am using these formulas for Alpha and Beta, yet the units
for
> Alpha do
> > not match those I can find on various web sites.
> >
> > Formulas:
> >
> > Beta = (( Periods * Sum(ROC( C,1) * ROC(Mkt,1),Periods )) -
> >
> > (Sum(ROC(C,1),Periods) * Sum(ROC( Mkt,1),Periods))) /
> >
> > ((Periods * Sum((ROC(Mkt,1)^2 ),Periods)) - (Sum(ROC
> (Mkt,1 ),Periods)^2 ));
> >
> > Alpha = (Sum(ROC( C,1) ,Periods) - ( Beta ) * Sum( ROC(
> Mkt,1) ,Periods ) )
> > / Periods;
> >
> > One article states that Alphas, according to Morningstar, range
> from -11 to
> > 45 with an average of all funds around 2. One such fund is listed
> having an
> > Alpha of 11.5, and my calculation is 0.36.
> >
> > So, do the formulas look right and does anyone have a
> representative measure
> > of Alpha?
> >
> > 2. I am having fits making the formulas calculate daily vs
monthly
> data.
> > My attempts to use inMonthly timeframes does not work (values
> either blank
> > or incorrect when compared to other sources. Thus, I would like
to
> have a
> > single formula run and then manually select Monthly or Daily
> periodicity in
> > the Settings box. Is there a Status command that tells the code
> whether the
> > periodicity is set on Monthly or Daily?
> >
> > 3. Further, I would like the "Periods" in the above formula to
be
> > determined from the date range, and I can calculate a "Periods"
> value when I
> > am in Daily periodicity. But, try as I might, I get Periods equal
> to zero
> > unless I put in a manual setting for periods, say Periods = 12;.
> > This works for Daily, what would I use for a Periodicity of
Monthly?
> > Index1 = ValueWhen( DateNum()== StartDate ,BarIndex(), 1);
> >
> > Index2 = ValueWhen( DateNum()== EndDate ,BarIndex(), 1);
> >
> > Enddate = ValueWhen(DateNum()==Enddate,DateTime(),1);
> >
> > Periods = LastValue(Index2 - Index1);
> >
> >
> > Thanks for any suggestions,
> > Ken
> >
>
>
>
> ------------------------------------
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