UV garch model forecasts

[TomDoan]

With p=.01, the Poisson approximation to the binomial is MUCH better than the Normal. You can also do an exact calculation using the %BETAINC (incomplete beta) function:

compute p=.01,n=250
do i=0,10
   ?i %poisson(n*p,i) %betainc(1-p,n-i,i+1)
end do i

though there is no practical difference between the Poisson approximation and the exact calculation.

Thanks - Yes, it's a one liner:

report(atrow=5,atcol=6,fillby=cols) %if(ntrigger_1>=10.0,"Red",%if(ntrigger_1<=4.0,"Green","Yellow"))

How to proceed with the ES Traffic Light?

Your 10 and 4 are specific to a particular combination of N and alpha. Why would you restrict yourself that way?

The "ES Traffic Light" is (a) not really about the ES and (b) looks like gibberish (mainly because of (a)). What they are analyzing is not the "expected shortfall" (which would be a $ amount) but the observed percentile. If the distribution is thin-tailed, a loss of 10% over the VaR might give you a .50 value, while in a thick-tailed distribution, a loss of 50% over the VaR might give you a .25 value.

[ac_1]

With p=.01, the Poisson approximation to the binomial is MUCH better than the Normal. You can also do an exact calculation using the %BETAINC (incomplete beta) function:

compute p=.01,n=250
do i=0,10
   ?i %poisson(n*p,i) %betainc(1-p,n-i,i+1)
end do i

though there is no practical difference between the Poisson approximation and the exact calculation.

Thanks - Yes, it's a one liner:

report(atrow=5,atcol=6,fillby=cols) %if(ntrigger_1>=10.0,"Red",%if(ntrigger_1<=4.0,"Green","Yellow"))

How to proceed with the ES Traffic Light?

Your 10 and 4 are specific to a particular combination of N and alpha. Why would you restricted yourself that way?

The "ES Traffic Light" is (a) not really about the ES and (b) looks like gibberish (mainly because of (a)). What they are analyzing is not the "expected shortfall" (which would be a $ amount) but the observed percentile. If the distribution is thin-tailed, a loss of 10% over the VaR might give you a .50 value, while in a thick-tailed distribution, a loss of 50% over the VaR might give you a .25 value.

Yes, I am using a different size window than N=250.

[ac_1]

A few more questions:-

[A] Interpretation:

As coded in the rpf file, dlogdm=log(dm/dm{1}), log returns are time additive; the portfolio value is value=100, and ftrigger=VaR/value.
Now let's say e.g. VaR=2.6, this can be interpreted as 2.6% is at risk on the portfolio value: be it 1,000 USD, 10,000 USD or x USD in value. In otherwords, a probability p=0.01 (say) of losses >= to 2.6% on any USD sized portfolio. Correct?

E.g. For FX, from the point-of-view of a dollar investor, I would model USD/XXX, as that would be XXX per 1 USD, and based on the 100 USD portfolio the 2.6% loss would be in terms of USD. Correct?

Returns to USD/XXX and XXX/USD are signed opposites of each other. USD/XXX would give you USD per xxx (literally---that's what / means), not the other way around. In GARCHUV.RPF, the data are in USD/DM so, as written, that would be analyzing returns in holding DM's.

My analysis is from the point-of-view of a dollar investor, i.e. using dollars to invest in foreign currency.

I want to confirm the wording:
https://estima.com/webhelp/topics/garch ... casts.html : the investment would be a $100 US invested in DM.
https://estima.com/webhelp/topics/egarc ... terpf.html : returns to 100 DM
viewtopic.php?t=3645&start=15 : In GARCHUV.RPF, the data are in USD/DM so, as written, that would be analyzing returns in holding DM's
https://estima.com/webhelp/topics/garchbootrpf.html : returns to 100 yen

So those examples are using dollars to invest in foreign currency and being LONG XXXUSD.
Correct?

(Note the modern way is to quote currency pairs without the forward slash see: https://en.wikipedia.org/wiki/Currency_pair, and as an example click on forex tab https://tradingeconomics.com/)


If I have rawdata on USDJPY (the large number e.g. 145.00) i.e. Yen's per dollar, I would calculate:

set JPYUSD=1.0/USDJPY
set returns = 100.0*log(JPYUSD/JPYUSD{1})

that way round would make it easier to follow the garch examples above, and from them calculate VaR and ES analysis for a LONG position in JPYUSD. Correct?
And as per discussions in this topic for a SHORT [right-tail] position in JPYUSD.


In the market, the Yen dollar currency pair is typically traded having being quoted as USDJPY (the large number e.g. 145.00). So the analysis for JPYUSD would have reverse interpretations from the point-of-view of a dollar investor having traded USDJPY i.e.
- VaR and ES for LONG position in JPYUSD would be the same dollar amount for SHORT position in USDJPY
- VaR and ES for SHORT [right-tail] position in JPYUSD would be the same dollar amount for LONG position in USDJPY
Correct?

[TomDoan]

The g10xrate file has all currencies quoted as USD value of a foreign currency unit whether that is the standard quotation or not.

set x = -100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of $100 US.

set x = +100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of 100 yen.

However, it doesn't really matter, does it? GARCHBOOT.RPF shows how to bootstrap returns to a long position of A in terms of B. As long as you understand what your data mean, you don't need to understand what the data in the example mean.

[ac_1]

The g10xrate file has all currencies quoted as USD value of a foreign currency unit whether that is the standard quotation or not.

set x = -100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of $100 US.

set x = +100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of 100 yen.

However, it doesn't really matter, does it? GARCHBOOT.RPF shows how to bootstrap returns to a long position of A in terms of B. As long as you understand what your data mean, you don't need to understand what the data in the example mean.

And for a SHORT position using right-tail analysis:

set x = -100.0*log( (1.0/usxjpn) / (1.0/usxjpn{1}) )

would give the return to a SHORT position of $100 US.

set x = +100.0*log( (1.0/usxjpn) / (1.0/usxjpn{1}) )

would give the return to a SHORT position of 100 yen.

Correct?

[TomDoan]

log(1/x)=-log(x)

[ac_1]

Sorry, I am unclear as to what x I use for the corresponding SHORT [right-tail] positions of $100 US and of 100 yen, respectively.

[TomDoan]

Isn't a short on USD/JPY identical to a long on JPY/USD?

[TomDoan]

G10XRATE is one of the data files used in Pritsker, Matthew (2006), "The hidden dangers of historical simulation," Journal of Banking & Finance, vol. 30, no. 2, pp 561-582 which might be helpful for you, since it looks at calculations of VaR.

[ac_1]

The g10xrate file has all currencies quoted as USD value of a foreign currency unit whether that is the standard quotation or not.

set x = -100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of $100 US.

set x = +100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of 100 yen.

An interpretation question, based on the formulae.

Definition: if JPYUSD rate is 0.0075, means that 1 Japanese yen is equivalent to 0.0075 US dollars.

Thus, I can calculate the following:

1) JPYUSD for a dollar investor, LONG and SHORT.

usxjpn = JPYUSD

set x = -100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of $100 US.

because log(1/x)=-log(x)

And all calculations are for JPYUSD from the perspective of a dollar investor, and say I calculate VaR for LONG = 1.74 and for SHORT = 1.49 throughout the analysis, then 2), 3) and 4) follow from 1). Correct?

2) JPYUSD for a yen investor, SHORT and LONG i.e. OPPOSITE

set x = +100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of 100 yen i.e. SHORT


3) USDJPY for a dollar investor, SHORT and LONG i.e. OPPOSITE

4) USDJPY for a yen investor, LONG and SHORT


A: as a dollar investor:

If the JPYUSD rate is falling, it means the Japanese yen is weakening against the US dollar.

Long JPYUSD: I am betting that the Japanese yen will strengthen against the US dollar. If the JPYUSD rate is falling, the yen is weakening, means my position is losing value. My VaR would be HIGHER because the market is moving against my position.

Short JPYUSD: I am betting that the Japanese yen will weaken against the US dollar. If the JPYUSD rate is falling, the yen is weakening, means my position is gaining value. My VaR would be LOWER because the market is moving in favor.

The numbers I get: If I am long JPYUSD and the rate is falling, are my VaR is HIGHER (VaR = 1.74). Conversely, if I am short JPYUSD, your value at risk is LOWER (VaR = 1.49)

That makes sense to me.


B: as a yen investor:

If the JPYUSD rate is falling, it means the Japanese yen is weakening against the US dollar, i.e. same logic but opposite numbers.

Long JPYUSD: I am betting that the Japanese yen will strengthen against the US dollar. If the JPYUSD rate is falling, the yen is weakening, means my position is losing value. My VaR would be HIGHER because the market is moving against my position.

Short JPYUSD: You are betting that the Japanese yen will weaken against the US dollar. If the JPYUSD rate is falling, the yen is weakening, means my position is gaining value. My VaR would be LOWER because the market is moving in my favor.

However, JPYUSD for a yen investor is SHORT and LONG i.e. OPPOSITE of a dollar investor. So B does not make sense as I would have for LONG (VaR = 1.49) and for SHORT (VaR = 1.74).

How do I explain that?

[TomDoan]

I'm lost, but from what I can tell, you are again confused about VaR analyzed for a short position. For a short position, the risk is in the right tail, not the left one. If the distribution of returns isn't symmetrical (and by assumption yours isn't since you're assuming the yen is weakening), those numbers will be different. It might help you to draw some pictures of asymmetrical distributions and see how that works.

[ac_1]

I'm lost, but from what I can tell, you are again confused about VaR analyzed for a short position. For a short position, the risk is in the right tail, not the left one. If the distribution of returns isn't symmetrical (and by assumption yours isn't since you're assuming the yen is weakening), those numbers will be different. It might help you to draw some pictures of asymmetrical distributions and see how that works.

The best thing is to remove the distinction between a dollar investor and yen investor, and just have my interpretation as I have done the calculations:

1) JPYUSD for a dollar investor, LONG and SHORT.

usxjpn = JPYUSD

set x = -100.0*log(usxjpn/usxjpn{1})

would give you the return to a long position of $100 US.

because log(1/x)=-log(x)

Obviously, as it's an asymmetrical distribution the VaR's are different, the LONG (VaR = 1.74) and SHORT[right-tail] (VaR = 1.49).


And would that be OPPOSITE VaR's for

3) USDJPY for a dollar investor, SHORT[right-tail] (VaR = 1.74) and LONG (VaR = 1.49) ?

[TomDoan]

There are, in effect, two possibilities (whether actually done or only done in theory):

1. sell dollars to buy yen now and reverse next period
2. sell yen to buy dollars now and reverse that next period

The rate of return is the same whether you are a dollar investor (so in #1 you would be going long yen) or a yen investor (so in #1 you would be going short dollars). If you continue to be confused about this, you need to go to someone who can teach you about it.

[ac_1]

A question about JULIAN dates:

Reading in Data as

Code: Select all

OPEN DATA "filename.csv"
DATA(FORMAT=PRN,ORG=COLUMNS) / Close

In RATS
View -> Series Window

	Obs  F Dates
CLOSE 	4377 U 1 4377
P	4377 U 1 4377
LP	4377 U 1 4377
DLP	4376 U 2 4377
Y	4376 U 2 4377
U	4376 U 2 4377
H	4376 U 2 4377
SES_1	3377 U 1002 4378

SES_1 are the backtest forecasts. That's correct!

But reading in data (JULIAN dates commands are required to plot diagrams with dates) as:

Code: Select all

OPEN DATA "filename.csv"
DATA(FORMAT=PRN,ORG=COLUMNS,DATEFORMAT="dd/mm/yyyy",JULIAN=INDEX) / Close
CALENDAR(JULIAN=INDEX)

In RATS
View -> Series Window

	Obs  F Dates
INDEX	4377 i start end
CLOSE 	4377 i start end
P	4377 i start end
LP	4377 i start end
DLP	4376 i start end-1
Y	4376 i start end-1
U	4376 i start end-1
H	4376 i start end-1
SES_1	3377 i start end-WIN

where
start is a date
end is a date

SES_1 looks wrong w.r.t. the dates! Similarly: DLP Y U H.


Both no dates and JULIAN dates give the same forecasts - so calculations are correct - and importantly mapping back the dates are correct when I print or graph, having

SET sES_1 WIN+1+1 %allocend()+1 = hat_1(t)

With JULIAN dates why does the View -> Series Window -> List of Series give SES_1 with those dates, having used the SET instruction?

And how to fix, if I really need to, It's just how they are stored when View -> Series Window -> List of Series.

However, why is this happening

[ac_1]

I'd appreciate a response as this should not be happening with the dates, the dates should be start end as with no dates View -> Series Window -> List of Series.

And whilst we're here, is there an opposite function to %datelabel(e), i.e. dates back to entry e?