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Help Topics: Index Arbitrage Program Trading Calculator
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| Help Topic |
Description |
| General Description of the Calculator |
The calculator determines the fair value
premium and related premiums for sell and
buy programs, namely sell threshold, sell
active and buy threshold, buy active. (For
more information about these terms, click
here.) These values are determined from your
input data. The meaning and valid ranges
for the input data are described below.
If input data are entered in all fields,
the resultant premiums and a graph of probability
of program trades vs. premium are displayed.
The premiums described above are shown on
the bottom line of the output area. A grey
line extends from each value to its corresponding
place on the horizontal axis of the graph.
If the output values have unrealistically
small or large values, they are displayed
without the probability graph.
If a data field is missing, contains something
other than a positive number (or, in some
cases, a percentage sign), is outside its
valid range, or has a value that conflicts
with some other field, an error message will
be displayed. The first four data inputs
described below are those needed to determine
fair value and, if they have no errors, the
fair value premium will be displayed along
with any error(s) for the other fields. |
| Distorted Calculator Image |
If the calculator that is displayed on your
screen is distorted, has image breaks or gaps, or is otherwise
impaired, click here for a version of the calculator that has
less demanding image handling requirements.
If that version works better with your browser,
you may wish to save that link to bypass
going to the default graphics version of
the calculator.
This problem arises because some browsers
cannot render the images needed to construct
the calculator. Further, if you have configured
your browser to disable displaying images, you will not be able to use
this calculator because the resulting
output data are shown as an image. |
| Input Data Fields |
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| Index Value |
This is the current, or spot, value of the
index, such as the S&P 500, the Nasdaq
100, the Dow Jones Industrial Average, or
the Nikkei 225.
The valid range is zero to less than ten
billion. This field is constrained to a maximum
of ten characters, all of which must be numbers
with the exception of an optional, single
decimal point character. |
| Time |
This is the time from now to the expiration
of the future that is associated with the
index whose value was entered above. Time
can be expressed as either a number of days
or years. If you would like help on the number
of days to the futures contract expiration
and the index is one of the three covered
by this web site, you may click here and then click on the desired future's link
to obtain its number of remaining days.
The valid range is from zero to 36,500 days
or zero to one hundred years. This field
is constrained to a maximum of five characters,
all of which must be numbers with the exception
of an optional, single decimal point character. |
| Riskfree Interest Rate |
This is the interest rate of an essentially
riskfree debt instrument whose term to maturity
coincides with the time period stipulated
above. It is conventionally based on "zero-coupon,
real" rates derived from Eurodollar
deposit rates and futures or from U. S. Treasury
debt.
The valid range is from zero to 100 percent.
The percent sign is implied and, therefore,
does not have to be entered but its presence
will not cause an error. This field is constrained
to a maximum of eight characters, all of
which must be numbers with the exception
of an optional, single decimal point character
and an optional, single percent sign character. |
| Dividends |
This field specifies the dividends that are
forecasted to be earned on the stocks that
comprise the index during the specified time
period. Dividends can be expressed as either
an amount or a yield.
If expressed as an amount, the dividends
must conform to the index's construction
and its divisor. If the index is capitalization
weighted, the dividend amounts must be capitalization
weighted. For either capitalization-weighted
or price-weighted indexes, the dividends
must be divided by the index's divisor. The
valid range is from zero to less than one
hundred million.
If expressed as a yield, this field should
be expressed as the annual dividend yield
on the underlying stocks in the index on
a percentage basis. The calculator will apply
the annual rate to the specified time period
to determine the relevant dividend amount.
As with the "amount" method, dividend
accounting must conform to the index's construction.
The valid range is from zero to 100 percent.
The percent sign is implied and, therefore,
does not have to be entered but its presence
will not cause an error.
If you would like to see our estimates of
the actual values for dividend amounts and
yields for the three indexes covered by this
web site and their related futures contracts,
click here and then click on the desired future's link.
This field is constrained to a maximum of
eight characters, all of which must be numbers
with the exception of an optional, single
decimal point character and, for the yield
method, an optional, single percent sign
character. |
| Bonus Interest Rate Minimum |
This is the minimum additional yield over
the riskfree rate that would entice an arbitrageur
to execute a buy program. The implication
is that for any smaller bonus interest rate,
no buy programs would be initiated. Hence,
this variable controls the value of the "buy
threshold" premium.
The valid range is from zero to 100 percent.
Typical values are one to fifteen percent
but clearly, the magnitude is proportional
to the riskfree rate. Note the intentionally
overlapped range with bonus interest rate
maximum; clearly, bonus interest minimum
must be less than or equal to bonus interest
rate maximum. The percent sign is implied
and, therefore, does not have to be entered
but its presence will not cause an error.
This field is constrained to a maximum of
eight characters, all of which must be numbers
with the exception of an optional, single
decimal point character and an optional,
single percent sign character. |
| Bonus Interest Rate Maximum |
This is the additional yield over the riskfree
rate at which numerous buy programs would
probably be executed. As the spread between
the futures and the spot index increases,
the bonus interest rate increases for a buy
program. While there is no theoretical maximum
bonus rate, one can hypothesize those values
that would prove irresistible to arbitrageurs
and, hence, the premium levels where buy
programs would probably be prevalent. Hence,
this variable controls the value of the "buy
active" premium.
The valid range is from zero to 100 percent.
Typical values are four to twenty percent
but clearly, the magnitude is proportional
to the riskfree rate. Note the intentionally
overlapped range with bonus interest rate
minimum; clearly, bonus interest minimum
must be less than or equal to bonus interest
rate maximum. The percent sign is implied
and, therefore, does not have to be entered
but its presence will not cause an error.
This field is constrained to a maximum of
eight characters, all of which must be numbers
with the exception of an optional, single
decimal point character and an optional,
single percent sign character. |
| Short Interest Rebate Minimum |
Short interest rebate, or SIR, is the percentage
of interest earned on the short sale proceeds
in a sell program that is rebated to the
arbitrageur. When a sell program is executed,
the index future is bought and the stocks
in the index are sold short. The short seller
of the stocks in the underlying index borrows
those stocks from some organization and sells
them. The proceeds are retained by the stock
lender as collateral and are invested in
essentially riskfree interest bearing instruments.
A portion of the earned interest on these
investments is rebated to the short seller (who
is also the index arbitrageur or program
trader). Short interest rebates are quoted
either on each individual stock in the program
trade or on the basket of stocks as a whole.
This input to the calculator reflects the
percentage of the total amount of interest
on the proceeds that the arbitrageur receives.
As the difference of the future minus the
spot index declines, two things happen: first, sell programs become
increasingly attractive, eventually reaching
profitability, and second, sell programs can occur with decreasing
values in the short interest rebate (SIR).
By way of contrast, as the
future - spot index difference increases, sell
programs can only become profitable with
correspondingly larger values of the short
interest rebate (SIR). As the spread approaches
fair value, the SIR required for a profitable
sell program would approach 100% or more
and, hence, would be unobtainable and unrealistic.
The SIR minimum value determines the
"sell active" level of program
trading. When sell programs are profitable
at the lower SIR levels, some arbitrageurs
will be able to obtain higher SIRs from their
institutions and, hence, achieve even greater
trading profits. Hence, sell programs would
probably be prevalent.
The SIR that an arbitrageur can obtain in the marketplace
theoretically ranges from zero to 100 percent but typical values
for SIR minimum range from zero to seventy percent.
(Note the intentionally overlapped range with SIR maximum; clearly,
SIR minimum must be less than or equal to SIR maximum.)
Despite the above theoretical limits,
sell programs occasionally occur only at premium levels that
correspond to negative SIR levels. This deviation from the
theoretical range can perhaps be explained by the difficulty
in obtaining sufficient quantities of stocks to sell short
in order to undertake a sell program.
This field in the calculator is constrained to a maximum of
eight characters, all of which must be numbers
with the exception of a possible (leading) minus sign,
a possible single decimal point character, and an optional,
single (trailing) percent sign character. (The percent sign is
implied and, therefore, does not have to be entered
but its presence will not cause an error.)
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| Short Interest Rebate Maximum |
Short interest rebate, or SIR, is the percentage
of interest earned on the short sale proceeds
in a sell program that is rebated to the
arbitrageur. When a sell program is executed,
the index future is bought and the stocks
in the index are sold short. The short seller
of the stocks in the underlying index borrows
those stocks from some organization and sells
them. The proceeds are retained by the stock
lender as collateral and are invested in
essentially riskfree interest bearing instruments.
A portion of the earned interest on these
investments is rebated to the short seller (who
is also the index arbitrageur or program
trader). Short interest rebates are quoted
either on each individual stock in the program
trade or on the basket of stocks as a whole.
This input to the calculator reflects the
percentage of the total amount of interest
on the proceeds that the arbitrageur receives.
As the difference of the future minus the
spot index declines, two things happen: first, sell programs become
increasingly attractive, eventually reaching
profitability, and second, sell programs can occur with decreasing
values in the short interest rebate (SIR).
By way of contrast, as the
future - spot index difference increases, sell
programs can only become profitable with
correspondingly larger values of the short
interest rebate (SIR). As the spread approaches
fair value, the SIR required for a profitable
sell program would approach 100% or more
and, hence, would be unobtainable and unrealistic.
The SIR maximum value determines the
"sell threshold" level of program
trading, namely the spread between futures
and the spot index at which sell programs
would commence, albeit in a limited way.
The SIR that an arbitrageur can obtain in the marketplace
theoretically ranges from zero to 100 percent but typical values
for SIR maximum range from twenty to ninety percent.
(Note the intentionally overlapped range with SIR minimum; clearly,
SIR minimum must be less than or equal to SIR maximum.)
Despite the above theoretical limits,
sell programs occasionally occur only at premium levels that
correspond to negative SIR levels. This deviation from the
theoretical range can perhaps be explained by the difficulty
in obtaining sufficient quantities of stocks to sell short
in order to undertake a sell program.
This field in the calculator is constrained to a maximum of
eight characters, all of which must be numbers
with the exception of a possible (leading) minus sign,
a possible single decimal point character, and an optional,
single (trailing) percent sign character. (The percent sign is
implied and, therefore, does not have to be entered
but its presence will not cause an error.)
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