Scenario Analysis and Forecast: What Separates Them

Scenario analysis prints what a position owes at each of a set of prices, and every cell in it is exact arithmetic that says nothing about which of those prices turns up. A forecast says which one turns up, or ranks them by likelihood. A likelihood attached to prices is the single input one object needs and the other never touches.

The boundary between the two kinds of writing is easier to walk across on figures a reader can check than to describe in the abstract. Every price, premium, payoff, profit, rate and party below therefore belongs to an invented record built for that walk, with no exchange behind it, no contract specification and no observed price.

Here is the situation. Somebody hands a reader a sheet with four prices down the left and four amounts down the right. Every amount is correct. Two of them check out when tested. And then, without any notice being taken of it, the reader leaves the room believing something about which of those four prices is going to turn up. Not one sentence on the sheet said so. A table can send a reader away holding a belief it never printed, and it does that through its shape rather than through its sentences.

So the question to settle is not whether a piece of writing is careful. Careful writing walks across this boundary all the time, usually in a heading rather than in a paragraph. The question is which of two objects is in front of the reader, and one input answers it every time.

What is scenario analysis, and what makes every cell in it exact?

Scenario analysisA statement of what a position owes or receives at each of a set of stated prices, worked out one price at a time. states what a position owes or receives at each of a set of prices. The definition holds nothing more. The position goes in, a list of prices goes in, and the arithmetic supplies one amount for each price on the list. Nothing else goes in, and nothing else comes out.

Two properties give it its value, and it is worth being exact about both because most readers hold only the first. The first is that it is exact. The amount owed at a stated price is not an estimate and not a range: the obligation was written into the contract, so the amount at a price is a subtraction that can be done twice for the same answer. The second is that it is complete in one narrow sense. Every price named on the list gets an answer, and no price on the list is quietly skipped because it was awkward. Complete about the list, exact on each line.

A reader who meets the two virtues alone will supply a third one unprompted, so the property scenario analysis does not have belongs here rather than three sections later. A scenario table contains nothing whatsoever about which of its prices turns up. Not a hint of it, not a lean towards one end of the list, not a quiet ranking. The arithmetic that fills the cells never had a likelihood as one of its inputs, so no amount of staring at the cells will recover one.

The everyday version is a fare chart at a bus stand. The chart prints a fare against every distance, it is exact for each one, and it is silent about where anybody standing in front of it is going. A chart that gave the fare for eleven kilometres and also said that most people travel eleven kilometres would be doing two different jobs, and only one of them is the chart.

The same split holds all the way down. The fare table is arithmetic on a distance. Where anybody is going is a statement about people, and no amount of fare arithmetic produces one.

What is a forecast, and how wide does that word have to be?

A forecastA statement of which price arrives, or of how the possible prices rank by how likely each one is. states which price arrives. Everybody already holds that half of the definition, and holding only that half is why most forecasts get through unnoticed. Here is the other half, and it is the working half. A statement that ranks prices by how likely each one is, without naming a single price as the one that arrives, is still a forecast.

Widen it once more. The word is wider than a document. A clause saying that one price is worth planning around while another is remote has ranked two prices, and one clause is enough. There is no minimum length. There is no requirement that the ranking be numeric. A likelihoodA statement of how probable something is, whether written as a number, as a word such as remote, or as an ordering between two possibilities. written in words is the same object as one written as a number, and the words are harder to catch precisely because nobody thinks of them as arithmetic.

Now what a forecast is not. The distinction is not one of quality. A forecast is not a worse kind of writing, and neither object outranks the other. The two are different objects with different inputs. Somebody who has genuinely studied how a price behaves, and who says so plainly, has produced a forecast, and has produced something a scenario table cannot produce at any length.

Producing a forecast needs a likelihood attached to prices, and no likelihood is attached to any price below. The shape of a forecast follows, stated carefully enough that the object can be recognised when somebody else hands it over. Being handed one by somebody else is the situation a reader is actually in.

What is the single input that separates the two?

A forecast needs a likelihood attached to prices. Scenario analysis never uses one, at any point in its construction. A likelihood is the separator. Everything else within reach, tone, length, how technical it sounds, how confident the writer seems, sorts nothing at all.

An input cannot be seen. Only an output can. So here is the test, and it is something to do rather than something to be careful about. Point at any figure in the writing and ask whether it would change if every price on the list became equally likely. If nothing moves, no likelihood was ever used, and the object is a scenario table. If something moves, a likelihood was in there, and the object is a forecast whether or not the writer would call it one.

Run it once on a fare chart to feel it working. Make every destination equally likely and the fare for eleven kilometres does not budge. Now run it on a sentence about which bus is worth waiting for. Make every destination equally likely and that sentence has nothing left to stand on. Two objects, one question, and the question does the sorting in about four seconds.

The test is more reliable than reading the prose, and the reason is worth sitting with. A likelihood gets into a table through emphasis, through ordering and through naming, and none of those three is a sentence. A checker who reads for claims reads sentences. The claim is not in a sentence. The claim sits in the bold row, in the top row, and in the row carrying a name the other rows do not carry. All three are invisible to somebody looking for something to disagree with.

What does a complete scenario table look like on one position?

One position, with every cell filled in. The position is a long forward on the invented reference asset, and the price written into it is Rs 2,130.00/-. Writing that hands over a struck price without showing where it came from has taught the reader to accept numbers, so the figure is multiplied out below rather than quoted.

The invented reference asset is quoted at Rs 2,000.00/- today. Financing costs 6.50 per cent a year. The asset hands over nothing at all while it is held, and that sentence is load bearing: if it paid something out during the year, the payout would come off the carryThe cost of holding the underlying from today until the agreed date, which here is one year of financing and nothing else. and every number below would move. So one year of financing on Rs 2,000.00/- is Rs 130.00/-, and Rs 2,000.00/- plus Rs 130.00/- is Rs 2,130.00/-.

Now the four rows. The long side has agreed to pay Rs 2,130.00/- on the agreed date whatever the price then is, so each row is one subtraction: the price on the date, less the Rs 2,130.00/- promised.

Four things about that table, and the fourth is the one that matters most. Every cell is exact rather than estimated. Each one is a subtraction between two figures that were fixed in advance. Every row is in price order, lowest first, and price order is an ordering nobody has to defend. No row carries a name that the other rows do not carry. And the four prices were chosen to show the arithmetic working across a wide span: they are not levels, they are not forecasts, and no likelihood is attached to any of them.

One row surprises almost everybody, and it is the second one. A price that has not moved at all costs the long side Rs 130.00/-, to the rupee. There is no trick in it. The long side did not agree to pay yesterday's price. The long side agreed to pay Rs 2,130.00/-, and Rs 2,130.00/- was made of Rs 2,000.00/- plus a year of financing. Standing still for a year does not give the financing back. The carry of Rs 130.00/- is being looked at from the other end: a cost to the side paying it, and the same Rs 130.00/- when the price fails to cover it.

A habit has quietly been overturned in the course of that. Most people carry a rule that says an unchanged price means an unchanged position. The rule is true of something bought and held, and untrue of something agreed to be bought later. The scenario table catches that quietly, by printing the row and letting the subtraction speak.

Why is a forward price arithmetic rather than a forecast?

The forward price is the same boundary one level up, and it is the single most useful case of it. A reader meets Rs 2,130.00/- against a spot price of Rs 2,000.00/- and concludes that somebody, somewhere, expects a rise of 6.50 per cent over the year. The figure says nothing of the kind, and it never did.

Rather than assert that, walk it. Four steps, each of which is something a person could actually do, and none of which involves an opinion about where a price is going.

1. Borrow Rs 2,000.00/-The money is taken at 6.50 per cent a year, the financing rate used throughout.
2. Buy one unit of the invented reference assetIt is quoted at Rs 2,000.00/- today, so the borrowing covers it exactly.
3. Hold it for one yearIt hands over nothing at any point during the year. Nothing arrives to reduce what is owed.
4. Repay Rs 2,130.00/-The Rs 2,000.00/- borrowed plus Rs 130.00/- of financing. The total is the forward price.

So Rs 2,130.00/- is what the year of holding costs, worked out in advance. A buyer could purchase today with borrowed cash, hold, deliver, and pocket the difference without ever having a view about the price. So anybody willing to sell forward for less than Rs 2,130.00/- is offering to hand over money. The forward price is a cost, and a cost is not an opinion.

Drag it to the bottom and the point settles itself. At nil financing the forward price is Rs 2,000.00/-, exactly the spot price, and nobody on earth would read that as a prediction that the price will not move. The shaded block collapses because there is nothing left to carry. No view was ever in the number, so nothing about anybody's view has changed on the way down.

Now drag it to the top. At 13.00 per cent a year the forward price is Rs 2,260.00/-, a carry of Rs 260.00/-, and again nothing about what anybody expects has moved by a hair. One input moved, and it was the cost of money. A figure that swings from Rs 2,000.00/- to Rs 2,260.00/- while every opinion in the world stays exactly where it was cannot have been reporting an opinion.

The absence doing the work should be named. No probability and no distribution appears anywhere above. Not one sentence says how likely any price is, and the forward price of Rs 2,130.00/- never needed such a sentence in order to be computed. The computation only ever needed a spot price, a rate and a period.

How does a scenario table become a forecast with no word added?

Here is the failure the whole distinction is built around, and its cleanest feature is that nothing gets written. There are three routes in, all of them typographic rather than verbal, and every one of them survives a careful edit because an editor reads sentences.

The first is naming. Give one row a name the other rows do not have, most commonly by calling it the base caseA row named as the one expected to obtain. The name itself is a claim about likelihood, which is why it does not belong on a table that contains none., and the table now contains a likelihood it did not contain a moment earlier. A base case is a case expected to obtain. The words mean exactly that, and the label therefore works on a reader without their consent.

The second is ordering. Print the rows in any order other than price order and whichever row lands first reads as the one to plan around. Reading position is a ranking, and a reader absorbs it before deciding whether to accept it. A name can at least be pointed at, so ordering is the quieter of the two routes.

The third is emphasis, and it is the fastest of the three. Set one row in heavier type, or in a different colour, or give it a shaded background, and the eye has ranked the rows before the reader has read a word of them. Emphasis takes one attribute in a stylesheet, and nobody signs off on stylesheets.

Not one of the three adds a sentence that a reader could disagree with, and that is exactly why they get through. There is nothing to dispute. There is nothing to fact check. Every figure is still correct. A correctness review is therefore useless against all three.

Which figure in a scenario table is most often the wrong one?

The one that does not know what was paid. A scenario table for an option is where a payoffWhat a contract delivers at expiry, ignoring altogether what was paid to get into it. and a profitThe payoff net of what was paid for the position, which is a different number and often a different sign. get mixed more often than anywhere else, and the reason is structural rather than careless. On a drawing, the two lines sit visibly apart and the gap between them is the premium. In a table there is no shape at all, so nothing warns a reader which of the two kinds of number is in front of them.

Work it on the record's own option pair. A call struck at Rs 2,000.00/- was bought for a premium of Rs 180.00/-. Both figures are given rather than derived, and that matters: no measure of how much the referenced price moves about appears anywhere above, so an option cannot be priced from these figures, and no premium changes when the control above moves.

At a price of Rs 2,130.00/- on the agreed date, the payoff is Rs 2,130.00/- less the strike of Rs 2,000.00/-, or Rs 130.00/-. The profit at that same price is Rs 130.00/- less the premium of Rs 180.00/-, or minus Rs 50.00/-. One position, one price, one date, and two correct figures with opposite signs. The profit does not reach nil until the price is Rs 2,180.00/-, which is the strike of Rs 2,000.00/- plus the premium of Rs 180.00/-, and that price is the breakeven priceThe price at which the profit on a position reaches nil, which for this call sits a full premium above the strike..

A question travels to places a rule never reaches, so carry the check as a question rather than as a rule: does this number know what was paid? The question goes to every figure on every table and every drawing. A number that does not know what was paid is a payoff, and writing a payoff into a profit column records a gain on a losing position.

Then there is the table discipline that follows from it, and it is one line. Label the column, every single time. A drawing can get away with an unlabelled line because the shape carries some of the meaning. A table carries none, so the column heading is the only place in the whole object where the difference between a payoff and a profit can live.

What does somebody who never publishes a table do with this?

Most people who need this distinction will never write a scenario table in their lives. Most readers are on the receiving end, the harder side of it, and the separator earns its keep there rather than at a writing desk.

Take the household case first. It matters most and gets written about least. A message arrives with a neat little grid: four prices, four amounts, one of them shaded. Nobody in the household has to become an analyst to handle it. One thing has to be done: read the shaded row out loud and ask who decided it should be shaded, and on what basis. If the answer is a written reason, weigh it. If the answer is that it came out of the template, then the grid contains exactly what the plain rows contain, and the shading was somebody's furniture rather than somebody's argument.

An analyst reading a note uses it as a filter on the writing rather than on the position. Run the equal-likelihood test on one figure. If nothing in the note moves, the note is a table and can be checked cell by cell. If something moves, there is a view inside it, and the useful question becomes whose view it is and what it rests on. Neither answer makes the note better or worse. The answer changes only what kind of scrutiny the note is owed.

A lender does something narrower and more demanding. A lender who is told what a borrower's position owes at four prices will ask for the price nobody put on the sheet. The missing price is usually the lowest one anybody was willing to type. Leaving a price off the list is the strongest way of ranking it, so the absent row is a claim as loud as a shaded one. Completeness is about the list, and somebody chose the list.

And a person reading a note about a two legged arrangement uses the same reflex on the quantities. A headline of Rs 1,000 crore is a notional, which is a multiplier: the sum that actually moved in the first period was Rs 12.00 crore, which is 1.2 per cent of it, making the headline 83.33 times the cash flow it produced. A notional is covered separately, and the instinct is the same: ask what a number is made of before letting it say how big something is.

What does holding this distinction not do?

Having read all of the above, a reader is better placed, at one thing exactly: reading. Being precise about what has and has not changed is worth the trouble.

A scenario table that is scrupulously free of any likelihood still tells nobody which price arrives. The table leaves every obligation exactly where it was. The table offers no protection of any kind against any price on its own list. Running the equal-likelihood test on a note does not alter what a position owes at Rs 1,600.00/-: the long side is still at minus Rs 530.00/-, before the test and after it. A check catches a misreading. A misreading was never part of what the contract obliged.

One more thing belongs here, and it belongs nowhere else. Somebody who read a shaded row as the one to plan around was reading a table exactly the way tables are almost always built, and the reading was reasonable. A guide that treats that as carelessness has taught blame rather than reading. The whole difficulty of this subject is that the claim arrives in a form nobody was taught to inspect, and the person who missed it did not fail at anything.

Which figures can only come from an authority, and who sets them?

Two requirements are touched by everything above. The name of the authority for each is carried here and the value for neither, and both boxes are drawn visibly empty.

Both boxes are drawn empty for a reason that sits in the reader's interest. Each of those values is set by the authority printed inside the row. Each of them moves. Writing one of them out would hand the reader something wrong rather than something merely old, and wrong is worse. A stale figure invites a check, and a confident figure discourages one.

The same discipline covers the figures printed above that did not come from anybody. Nothing above states a contract specification, a lot size, an expiry, a position limit, an exposure limit or a margin percentage as a requirement. The spot price, the financing rate, the premium and the four scenario prices carry no authority behind them, and each one is labelled for teaching where it is used.

Should a reader who can build a scenario table enter into one of these contracts?

The question arrives right here, so it gets answered here rather than in small type at the foot. A complete table feels like an answer to it. A complete table is not one. Teaching how these instruments work is a different job from telling any particular person whether they belong inside one, and the second job is not taken on above.

Naming what somebody would have to know first is the useful part, and the list shows why the limit is structural. Four things: the position the reader already holds, given that a contract offsetting an existing holding is a different object from the same contract standing alone; the sum whose loss would actually matter to that reader, a fact about a household and not about the contract; a likelihood against every price on the list rather than merely a list of prices that are possible; and what the Securities and Exchange Board of India (SEBI) at sebi.gov.in permits this particular reader to do.

Scenario arithmetic supplies none of the four. Two of them are facts about the reader that no reference work could hold. One of them is the exact input this record does not contain anywhere. And the fourth belongs to an authority named here and not quoted.

The thought worth keeping is this. Exactness about every price and silence about which one arrives are not a virtue and a defect sitting side by side. The two are one property seen from two directions. The table can be exact precisely because it never took in the likelihood that would have let it say which price is coming.

The reference asset, the forward, the option pair and the two legged arrangement are invented.
Educational material. Not advice on any investment, tax, budget or market position.