Hedge Ratio: How Much of a Holding to Write Against

The hedge ratio sets how many units of a contract stand against each unit of a holding, and everything after that is arithmetic: the share covered, the exposure covered, the exposure left with the holder, and the margin the contract side has to fund. Effectiveness is a different thing, read out of a period that has already gone by, so the tool below returns none until a period's readings are put into it.

A figure living only inside a calculator cannot be read by anybody who is not running it, so the defaults the calculator opens on are set out here in plain text and worked through below. Twenty units held at Rs 2,000.00/- a unit. A held thing that moved 20.0 per cent over a stated past period, a contract that moved 24.0 per cent over the same period, and a correlation of 0.90 between them. The minimum-variance ratio is 0.90 times 20.0 divided by 24.0, or 0.7500. Then 0.7500 of twenty units is 15.00 units, and at five units a contract that is exactly 3.00 contracts. The rounding leaves nothing over either way. Fifteen units against twenty held is 75.0 per cent coverage, Rs 30,000.00/- written against, Rs 10,000.00/- standing net long, Rs 2,400.00/- of margin at the invented 8.0 per cent, and an effectiveness of 81.0 per cent, the correlation squared.

What does this tool set, and what does it read out of the past?

The sizing side sets a quantity. The hedge ratioHow many units of a contract stand against each unit of a holding. A count, chosen in advance, rather than a reading taken later. is how many units of a contract are written against a holding, and a quantity is chosen before anything has moved. Two counts and a price are all the sizing lines need, so they can be worked on a morning when no price has changed since the previous day.

The other half of the panel is not like that at all. Hedge effectivenessA measure of how much of the movement in one thing was met by the movement in the position written against it, across a stated stretch of time. is a reading taken after the event, out of the movements both sides recorded across a stated stretch of days. The two are different in kind, and they are not two readings of one number. The calculator will not manufacture the second from the first: say no period was stated and every backward-looking line goes blank while the sizing carries on.

A household decides that four of its six monthly bills will go on a fixed arrangement and two will stay on the going rate. Choosing four fixed and two floating is a setting, made in advance at the kitchen table with nothing in front of it except a list. Whether the fixed arrangement ended up close to the going rate is a separate question, unanswerable until several months of going rates exist. Asking the kitchen table to answer it is asking a list to remember a year it has not lived through.

Which numbers have to be brought before anything can run?

Counts and a price carry the sizing. Readings off a period that has already passed carry everything else. The first count is the units heldThe count of the thing the holder actually has. It comes off the holder's own record and from nowhere else., off the holder's own record and not from an estimate or a rounded figure somebody remembers. Then the spot price, then the units inside one contract, then the contracts written. The contracts written are the decision the tool turns into arithmetic. The three readings are how far each side moved over a stated stretch of days and how much of that movement they shared.

The body of this guide counts in units of the reference assetThe invented thing these figures run on. It pays nothing at all while it is held, which is why every number here is built from a price and a count and nothing else. rather than in contracts, and the reason is not a matter of style. The units inside one contract are set by the exchange under the framework of SEBI at sebi.gov.in, differ from one contract to the next, and move, so stating one here as a fact would mean writing a specification from recollection. The calculator carries it as a field with an invented five in it, labelled invented wherever it appears, and the prose runs in units, exact whatever the specification happens to be.

A real holding almost never divides into a whole number of contracts, so a remainderThe units of a holding that do not fit into a whole number of contracts, and which therefore cannot be covered even where the holder would like them covered. is the normal case and not the awkward one. Contracts come in sizes somebody else decided and holdings in sizes the holder arrived at alone, so the two were never going to line up. Move the correlation slider from 0.74 to 0.75 and watch the rounded row jump from two contracts to three: one hundredth of a reading moves the position by five units, and the residual against the target flips from a shortfall of 2.33 units to an excess of 2.50.

The prices are written the same way every time. The spot priceThe price for taking delivery of the thing now, today, rather than on some later date. of the reference asset is Rs 2,000.00/-, and the contract price for the later date is Rs 2,130.00/-, of which Rs 130.00/- is carry at a financing rate of 6.50 per cent a year. Because the reference asset pays nothing while it is held, the carry has nothing subtracted from it. Nothing whatever is paid to open a contract of this kind, so both are prices and neither is a premium.

One coincidence needs naming before it confuses anybody. The spot price of one unit is Rs 2,000.00/-, and the exposure carried by one unit is also Rs 2,000.00/-, for one reason only: a single unit bought at the spot price puts exactly the spot price at risk. Twenty units at Rs 2,000.00/- is Rs 40,000.00/- of exposure, and that multiplication is where the two part company for good.

What does the sizing return once the counts are in?

Three lines and a check, every one worked here rather than quoted, on twenty units held with fifteen units of contract written against them on the short sideThe side of a contract that is bound to sell at the agreed price on the later date, whatever the price happens to be by then..

Run it. CoverageThe share of a holding that has a contract written against it, always quoted with the base it is struck on. first: fifteen over twenty is 75.0 per cent of the units held, and the base is said in the same breath because a share without its base is not a figure. Then exposure coveredThe part of the holding a contract has been written against, measured in rupees at the spot price of the day., fifteen units at Rs 2,000.00/-, and that is Rs 30,000.00/-. Then exposure leftThe part of the holding still carrying its original risk, because no contract has been written against it., five units at Rs 2,000.00/-, and that is Rs 10,000.00/- and 25.0 per cent of the units held.

Here is the check to run every single time: Rs 30,000.00/- and Rs 10,000.00/- of exposure add to the Rs 40,000.00/- the whole holding carries at the spot price. Not approximately, and not after a rounding. Exactly. If those two lines do not add back to the third, either a count is wrong or the two lines are using different prices. The calculator prints that check as a sentence and rewrites it at every setting.

The holding did not get smaller. Twenty units went in and twenty units came out, and Rs 40,000.00/- of exposure went in and Rs 40,000.00/- came out. A boundary appeared inside the holding, with Rs 30,000.00/- on one side and Rs 10,000.00/- on the other, and the two sides now carry completely different things.

Five settings at once make the shape obvious. Read the rows downwards: the boundary slides right, the margin bar beside it grows, and the outer edge of the holding does not move in any row.

What does a move in the price do to each part of the holding?

Take a 4.0 per cent move in the price of the reference asset, struck on the Rs 2,000.00/- spot price and worth Rs 80.00/- on one unit, and take it on the final date. The moment matters more than anything else in this block, so say it plainly. On the final date the contract price and the spot price are the same price, so a unit held and a unit written against it meet each other to the rupee. On any earlier day they do not. The financing cost applies to the new price as well as the old, so the contract price for the later date shifts by more than the price today did.

Now spread the Rs 80.00/- across the holding. Twenty units at Rs 80.00/- is Rs 1,600.00/- of movement across the whole holding. Fifteen of those units have a contract standing against them, so Rs 1,200.00/- of that movement is met on the contract side. Five of them do not, so Rs 400.00/- of it is not met by anything. Add the two back: Rs 1,200.00/- and Rs 400.00/- make Rs 1,600.00/-, and that check works at every setting, not only this one.

Say plainly what the Rs 400.00/- is. The whole tool exists to put that number in front of somebody. It is the exposure the holder still has, in exactly the form they had it before. No contract stands against those five units, so when the price moves that Rs 400.00/- arrives with no other side to it. The Rs 400.00/- is the honest number to plan around, and it is quieter than the Rs 1,600.00/- the newspapers would print.

Now say what the Rs 1,200.00/- is not. Readers go wrong exactly here. It is not risk that stopped existing. The Rs 1,200.00/- is met by a position which itself has to be carried, funded and honoured. The covered part changed shape. The risk did not leave.

What margin does the contract side have to fund, and does sizing change that?

The contract side is not carried for nothing. Initial marginWhat is posted before a position is carried at all. The percentage worked here is invented for teaching and is not a requirement. is posted before the position is carried, and here it is worked at 8.0 per cent of the Rs 2,000.00/- spot price, or Rs 160.00/- on one unit. The 8.0 per cent worked here is an invented teaching figure and not a requirement of any kind. The requirement is set by the clearing corporation under the framework of SEBI at sebi.gov.in, differs by contract, and changes daily.

Fifteen units at Rs 160.00/- a unit is Rs 2,400.00/- of margin posted, cash the contract side has to find before the position exists at all. Margin is not a payment for anything: it sits against the position and comes back or gets used, according to where the price goes. The Rs 1,200.00/- that a 4.0 per cent move puts on the contract side is 50.0 per cent of that Rs 2,400.00/-, exactly the ratio one single unit produces, where Rs 80.00/- is 50.0 per cent of Rs 160.00/-.

Here is the fact a reader is least likely to guess: the sizing changes how much of the holding is covered, and changes nothing whatever about how hard a move hits what was put down. Moving from five units to fifteen triples the exposure covered and triples the margin posted, and leaves the relationship between a move and that margin exactly where it was.

Either limb alone misleads, so the other belongs beside it. Rs 2,000.00/- of exposure on Rs 160.00/- of margin is 12.50 times, and that does not move with the count either: fifteen units gives Rs 30,000.00/- on Rs 2,400.00/-, the same 12.50 times. The contract side stands on a small fraction of what it references, and a modest move takes a large share of that fraction. Quote either without the other and the picture is wrong in a predictable direction.

Why does a cover that reaches every unit still miss?

Everything above holds the contract and the holding to one reference asset, so a unit written meets a unit held to the rupee on the final date. Loosen that and coverage does not change at all while what the cover meets falls away underneath it. The gap between the two has a name, basis riskWhat is left when the thing covered and the thing the contract is written on do not move together, so an offset arrives short, long or not at all., and the calculator produces it rather than describing it.

Press the button marked cover every unit at a correlation of 0.60 and read the two outputs against each other. Coverage reads 100.0 per cent of the units held and the exposure standing net against the holding is Rs 0.00/-, so in contract terms nothing is left. Effectiveness over the same stated period is 0.0 per cent. The contract moved 24.0 per cent against the held thing's 20.0 per cent, and only 0.60 of that movement was shared, so every unit is covered and none of the movement is met. A cover written unit for unit on something that moves further and only partly together adds as much movement as it removes.

Hold the coverage at 75.0 per cent instead and walk the correlation down. At 0.90 the effectiveness is 81.0 per cent, comfortably above the coverage figure. At 0.60 it is 27.0 per cent, a third of what coverage says. At 0.40 it is minus 9.0 per cent. The position with three quarters of its units covered met less than nothing. The coverage line never moved through any of that. Coverage counts units and knows nothing about how the two sides behaved, so the coverage line cannot move.

Where does every number here actually come from?

The units held come off the holder's own record, and the spot price from the market for the thing itself on the day, here an invented figure standing in for one. The contracts written are the decision, and there is nowhere to look that up because nobody has made it yet. The three readings come off a record of a stated past period and out of no other source.

Then there is the second group, and every entry in it belongs to an authority. The six rows are set out below. Every one is SEBI at sebi.gov.in, every one moves, and not one appears here with a real value.

Here is the working rule for anybody putting this arithmetic against something real: every figure that comes from an authority is looked up on the day it is needed, and none is ever carried in the head. Not a contract size remembered from last year, not a margin percentage somebody quoted at a desk. Contract sizes and margin percentages change without announcement in the places most people read, and a sizing built on a remembered specification is wrong in a way that will not show up until it matters. The five in the calculator field and the 8.0 per cent beside it exist so the arithmetic can run, and on a real job both boxes start empty.

Why does effectiveness need a period that has already passed?

Because two things have to exist before it can be read, and the reader who has just landed on a setting is exactly the person who most wants to skip them.

The first is a period, with a start and an end. Nothing can be measured across no time, and until somebody says which stretch of days, the question has no subject. Ask how much of the movement was met and the honest reply is another question: met over what?

The second is the movements that actually happened inside that period, on both the holding and the position written against it. Not what might happen and not what the sizing implies at a 4.0 per cent move. The movements that occurred: two recorded runs of change, one on each side, lined up day against day. The three reading fields are those runs boiled down to three numbers, how much each side moved and how much of that movement they shared.

So the calculator will not invent them. Set the period field to say no period was stated and every backward-looking line prints a refusal. The coverage, the exposure and the margin need only a count and a price, so those three carry on. A confident-looking score could be returned whatever the reader supplied, but that figure would come out of the tool's own assumptions rather than out of anything that occurred. A blank sends the reader off to find something and a number says to stop looking, so a number with no visible parentage is worse than a blank.

What would have to be known before anybody could choose a setting?

The arithmetic cannot say what setting anybody should be on. A slider invites a reader to believe there is a right position for it. The minimum-variance ratio is not that: it is what one stated period's readings imply, and a different period gives a different number.

Here is what the choice turns on, and notice that not one item is arithmetic. How much of the holding the holder needs to be certain about. How much cash can be found on the day the position moves against them. Whether the holding will still be there on the day the contract ends, a question about intentions the arithmetic cannot see. Which thing the contract is actually written on, and how closely that thing matches the holding. And what the authority requires before a position counts as a hedge, set by SEBI at sebi.gov.in and named here without a value.

Notice what is not on the list. Whether a covered position did better than an uncovered one. No such outcome exists in these figures. And whether covering something is the careful or the responsible course, a judgement dressed up as a fact. The word hedge carries enough of that sense already. Being able to work the arithmetic of a setting is not a reason to make one.

The reference asset, the holder, every price and every unit count in this guide are invented.
Educational material. Not advice on any investment, tax, budget or market position.