Hedging a Portfolio: What It Costs, What It Protects

A hedge is a separate position taken to offset an exposure the holdings already carry, so the holdings stay where they are. Hedge half of the Anantara portfolio's Rs 300 crore equity sleeve and all 28 names remain. Carried equity exposure moves from 60.0 per cent of the portfolio to 30.0 per cent. The offset works in both directions, and it is paid for either way.

A hedge is not a shield that sits quietly until trouble arrives. A hedge is an active position with a price, it works while the market rises as well as while it falls, and on the day nothing bad happens it has still been paid for. Everything that follows is arithmetic around those two facts.

The running example is the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for an invented charitable endowment whose investment committee Rukmini Deshpande chairs. Its policy shape is equity 60.0 per cent at Rs 300 crore, fixed income 30.0 per cent at Rs 150 crore and cash 10.0 per cent at Rs 50 crore. Those three sum to Rs 500 crore exactly. The equity sleeveThe part of a portfolio that sits in one asset class, managed as a block. holds 28 names, and the allocation decision fixed it at Rs 300 crore before a single holding was considered.

Every cost below is a supplied rate applied to one stated twelve month period, not a market level. A hedge price quoted without its instrument, its notional and its period cannot be checked by anybody who reads it.

What does a hedge actually do to a portfolio?

When the Anantara Multi-Asset Portfolio buys a name it acquires two things in the same transaction, and almost nobody separates them. The portfolio acquires the asset itself, the entitlement and the position in the register; and it acquires an exposure to whatever moves that asset, largely the equity market plus whatever is particular to the business. The two arrived together, so it is natural to assume they cannot be pulled apart.

A hedgeA position placed to move the opposite way to an exposure already carried. pulls them apart. A hedge is a second position placed alongside the holdings. The hedge is chosen to move the opposite way to the exposure the holdings carry, so adding the two together cancels part of the market movement. The holdings do not move at all: the register is identical the day after the hedge as the day before, and only the exposure of the combination has changed.

The same idea at household scale. A household runs a small shop selling umbrellas, so a wet season is a good season and a dry season is a bad one. The household does not sell the shop. Instead it adds a second small line that pays better in a dry season, cold drinks from the same counter, and now the season matters much less to the total. The shelves are unchanged; what changed is what the household's income depends on. Everything after this is size, price and honesty about what is left over.

Separating the exposure from the holding is also why hedging belongs in implementation rather than selection. Selection asks which names go into the sleeve and how much of each; a hedge asks nothing about names, and takes a position against a chosen slice of the exposure the sleeve carries. A hedge changes what the portfolio is exposed to without revisiting a single thing the portfolio chose, and so it is an implementation decision rather than a selection one.

What is the difference between the exposure a portfolio holds and the one it carries?

Held exposureWhat a portfolio has in an asset class, at what value. is what appears on the holdings statement: what the portfolio actually has, at what value. Carried exposureHow much a portfolio still moves with an asset class after offsets. is how much of that the portfolio still moves with, once any offsetting positions are counted in.

Work it on the Anantara portfolio. Before the hedge the two are the same thing: the portfolio holds Rs 300 crore of equity across 28 names, 60.0 per cent of the Rs 500 crore portfolio, and it moves with all of it. Now hedge half. The notionalThe face amount a hedge is written against. The notional is the size the offset is measured on, and no money is paid out for it. is Rs 150 crore, which is 50.0 per cent of the Rs 300 crore sleeve and 30.0 per cent of the Rs 500 crore portfolio. The same Rs 150 crore is a half and a third depending on which base was meant, so both bases have to be named.

After the hedge, the portfolio still holds Rs 300 crore across 28 names, still 60.0 per cent of the portfolio, and it carries Rs 150 crore of equity exposure, 30.0 per cent of the portfolio. Two sentences are now true about the same portfolio at the same moment and they give different equity weights, and the only thing separating them is which question was asked.

Both figures are struck against the same Rs 500 crore base, so the base law arrives here in different clothes: what differs is not the denominator but the numerator, one counting what is held and the other what is carried. A reader handed a bare "equity 30 per cent" has been told something true and has no way of knowing which of the two it is.

What does a hedge cost, and when is that cost paid?

Every hedge has a price. The form of that price depends on the instrument used, and instruments are covered separately. Throughout this walkthrough the price is a single rate applied to the notional over a stated period, and the timing of the payment matters more than its form.

A hedge buys the removal of an outcome from the range rather than the outcome itself. The cost is paid whether or not the feared event arrives. A trade is different: a spread and a commission are paid for a transfer that definitely happened, which trading costs work through separately. A hedge pays for a state of affairs that may never be tested, and if equity rises all year the protection costWhat is paid to hold a hedge over a stated period. was still spent.

Take a rate of 1.0 per cent of the notional for the stated year, a supplied figure used as an illustration and not a stated market level. On a notional of Rs 150 crore that is Rs 1,50,00,000/-, or Rs 1.50 crore. Against the Rs 500 crore portfolio that is 0.30 points; against the Rs 300 crore sleeve it is 0.50 points. The figures 0.30 and 0.50 are the same rupee amount, and a reader handed one of them without its base cannot reconstruct the other. The base has to be named every time.

How large is that cost next to the year's own result?

A cost is large or small only against something, and the record gives three somethings for the one stated twelve month period. The portfolio returned 14.2 per cent on Rs 500 crore, or Rs 71 crore, and the composite benchmark returned 12.6 per cent, or Rs 63 crore. The difference is Rs 8 crore, being 1.6 points of gross excess return. A hedge cost of Rs 1.50 crore is 18.75 per cent of the year's entire gross excess in rupees, for something that produced no return of its own.

The record splits that same 1.6 points two ways, for two different questions, and the two have to be kept apart. The attribution split asks where the excess came from: allocation plus 0.35 points and selection plus 1.25 points. On a Rs 500 crore portfolio the selection effect is Rs 6.25 crore, and Rs 1.50 crore is 24.0 per cent of it. The beta split asks how much of the excess was simply carrying more market than the benchmark: 0.488 points of market exposure and 1.112 points left over. The 1.112 points left over is Rs 5.56 crore, and Rs 1.50 crore is 27.0 per cent of it.

The attribution split and the beta split are not competing estimates of one quantity, and no term from one may ever be set beside a term from the other. Both sum to 1.6 points because both are complete answers, each to its own question. Adding 0.35 to 0.488, or calling 1.112 a selection effect, produces a sentence that sounds like analysis and means nothing.

Why does taking off a loss also take off a gain?

Because a straight offset does not know which direction it is offsetting. The hedge is chosen to move opposite to the exposure, and it does that faithfully in both directions. The property is called symmetryA position behaves symmetrically when it gives back on the way up exactly what it takes off on the way down.. The word protection carries a one directional feeling that the arithmetic does not share, and that is where most readers are surprised.

Work it on the sleeve. Equity falls 20 per cent over the stated period. Unhedged, the Rs 300 crore sleeve loses Rs 60 crore, 12.0 points of the Rs 500 crore portfolio. Half hedged and before the cost, the carried Rs 150 crore loses Rs 30 crore and the offset Rs 150 crore loses nothing, so the total is Rs 30 crore, or 6.0 points. Run the same 20 per cent upwards and every one of those figures repeats with its sign flipped, as the four bars below show. The same Rs 30 crore that was taken off the fall is the Rs 30 crore given up on the rise, and the two are equal because they come from the same offset.

Arrangements that keep the upside and take off only the downside do exist, at a different shape and a different price, and they belong to the instrument layer. If somebody offers one at the price of a symmetric hedge, the description is wrong somewhere.

Put the cost back in and the picture stops being symmetric. The Rs 1.50 crore is spent in both branches, so it deepens the fall and shallows the rise by the same amount. Half hedged and after cost, a 20 per cent fall costs the portfolio Rs 31.50 crore, 6.30 points, and a 20 per cent rise earns it Rs 28.50 crore, 5.70 points, either side of the 6.0 points the offset alone would have produced. The offset is symmetric and the cost is not, so a hedged portfolio is slightly worse off in both directions than the offset arithmetic on its own suggests.

What is basis risk, and why does a hedge never quite cancel?

Everything above assumed the offset was exact. The offset is rarely exact, for a structural reason rather than a lapse of care. The Anantara sleeve is 28 particular names; whatever the hedge is written against is something else, a broad market measure or an index of many more names. The two are related, and that relation is why the hedge works at all. The two are not identical, and that difference is why it does not work perfectly.

Basis riskThe chance that a hedge and the thing it offsets do not move by the same amount, leaving a difference behind. is the name for that leftover. Suppose the hedged Rs 150 crore of holdings falls 8.0 per cent over a period while whatever the hedge is written against falls 7.0 per cent. The offset gives back the 7.0 and the holdings lost 8.0. A one point difference on a Rs 150 crore notional is left, and that difference is Rs 1,50,00,000/-. A gap of that size is not knowable when the hedge is placed; it can only be measured after both the holdings and the hedge have moved.

A hedge exchanges a large exposure everybody understands for a smaller exposure almost nobody looks at, and that is a real improvement and is not the same thing as reaching zero. The honest sentence for a committee is that equity exposure fell from Rs 300 crore to Rs 150 crore, and a smaller, less familiar exposure to the difference between the holdings and the hedge appeared where there was none. Anybody who says the exposure is now zero has stopped measuring one step too early.

How much has to be hedged before the exposure actually moves?

More than people expect, and one line settles it. The sleeve is Rs 300 crore of a Rs 500 crore portfolio, so anything done inside the sleeve reaches the portfolio at 0.60 of its size. Hedge a tenth of the sleeve, a notional of Rs 30 crore, and carried equity falls from Rs 300 crore to Rs 270 crore, so the carried weight goes from 60.0 per cent to 54.0 per cent. A tenth of the sleeve buys six points of carried exposure, and it is paid for at the full rate on the full notional whether or not six points was what anybody wanted to move.

The general rule for this portfolio follows from that ratio: hedging a share of the sleeve moves the carried equity weight by sixty times that share. One sixth of the sleeve, Rs 50 crore of notional, moves it exactly ten points, and all of the sleeve moves it to zero carried equity, at which the portfolio still holds every one of its 28 names.

Two things fall out of that table. The first is that a small hedge on a large sleeve is a rounding difference with a full price attached: hedging a tenth moves the carried weight six points and costs Rs 30,00,000/- for the stated year, and if six points was not what anybody set out to move, the exercise bought a number nobody asked for. The size of a hedge is settled by the exposure it is meant to move, computed in advance, rather than by what felt substantial in the room.

The second is a break-even. If the hedged part falls by less than the cost rate over the period, the portfolio spent more on the hedge than the hedge took off; if it falls by more, the reverse. At a supplied rate of 1.0 per cent of the notional, the break-even fall is 1.0 per cent. Both the cost and the amount taken off scale with the same notional, so the notional cancels out. The break-even does not depend at all on how much was hedged. A larger hedge does not move the break-even; it moves what is at stake on either side of it.

Does the equity band constrain the holdings or the exposure?

The Anantara mandate carries an equity bandA stated range the equity share of a portfolio must stay inside. Here it runs from 50 to 70 per cent. of 50 to 70 per cent, written before anybody had asked whether a hedge might be placed, so nobody at that moment had to decide what the words equity share meant. Now the hedge is on, and the question cannot be avoided.

Read the band against holdings and the portfolio holds Rs 300 crore of equity, 60.0 per cent, comfortably inside 50 to 70. Read it against exposure and it carries Rs 150 crore, 30.0 per cent, twenty points below the floor of 50. Same portfolio, same day, same band, and one reading has it well inside while the other has it twenty points outside. The wording of the band settles which reading governs, and every individual mandate has a real answer. The arithmetic holds on both readings.

A hedge of this kind offsets what is held rather than adding to it, so it only ever moves carried exposure downwards. On the exposure reading it can take the portfolio through the 50 per cent floor and can never push it through the 70 per cent ceiling. The two edges of the same band are not equally exposed to this question, and a mandate that has thought about it usually says so in a sentence.

What does a hedge leave completely unchanged?

What a hedge leaves alone is the half that gets skipped, and skipping it is how a committee ends up believing a hedge did more than it did. On the holdings statement the morning after, all 28 names are there and the largest holding is still Rs 23 crore. The largest holding is 4.6 per cent of the Rs 500 crore portfolio and 7.67 per cent of the Rs 300 crore sleeve, and it sits inside the 5 per cent per name cap exactly as it did before.

A hedge acts on one shared exposure and touches nothing that belongs to an individual holding, so every concentration figure, every per name limit and every liquidity question survives the hedge exactly as it was. If the largest holding was uncomfortably large on Monday it is exactly as large on Tuesday. And if the sleeve was concentrated in one shared condition, the broad market is not what the concentration was about, so hedging the broad market exposure may leave that condition untouched. An exposure nobody named is one of the three things a hedge cannot act on, and all three come below.

What would the hedge have done to the stated year's result?

The gross excess for the stated year was 1.6 points, or Rs 8 crore. Subtract a hedge cost of Rs 1.50 crore, being 0.30 points, and the same excess arrives net of that cost at 1.30 points. The subtraction is exact, and it is also incomplete.

The subtraction is incomplete because the offset is symmetric. If equity rose during that year, hedging half the sleeve would also have given up the gain on the hedged half. The gain given up would show in the portfolio's own return before any benchmark comparison begins. The record locks the portfolio's total return for the stated year but does not lock the equity sleeve's own return, so the gain that would have been given up is a quantity the record does not supply. The right answer to what the hedge would have done is a third quantity alongside the other two, and the honest label on it is NOT SUPPLIED.

A sleeve return supplied from nowhere would produce a tidy net figure that reads as a finding and is a guess with two arithmetic steps in front of it. The net effect of a hedge on any year cannot be computed until the hedged holdings' own return is known.

What can a hedge not do?

Three things, and almost every complaint about hedging turns out to be one of them rather than a failure of anything the position did. A hedge cannot improve a holding, cannot recover a cost already spent, and cannot act on an exposure nobody identified in advance.

A hedge cannot improve a holding: if one of the 28 names is a poor business bought at a poor price, a hedge on the market exposure leaves it alone, and treating a hedge as a substitute for a selling decision usually means the decision was postponed. A hedge cannot recover a cost. Once the Rs 1.50 crore is spent no later movement gives it back, so sizing happens before the position is placed. And a hedge cannot act on an exposure nobody identified. A hedge does exactly what the person placing it aimed at, so an exposure that was never named goes on being carried in full, and the comfortable feeling of being hedged attaches to a portfolio that is not hedged against whatever eventually moves.

How does anybody use this in a committee room, on a Tuesday?

By writing six lines down before the position exists, and by refusing to approve it until all six are filled in. Writing the six lines is the part a practitioner actually does, and it is duller and more useful than any of the arithmetic above.

An investment committee like Rukmini Deshpande's asks for all six: the notional, both bases, the cost rate and its source, the cost in rupees and in points, the stated period, and one sentence naming which exposure is offset and what is given up in exchange. A lender wants two of those six above all: how much carried exposure is left, and whether the cost recurs each year. A recurring charge changes what the portfolio has to earn to stand still. A hedged portfolio and an unhedged one cannot be laid side by side on a single equity weight, so an analyst comparing two portfolios wants the notional and the period.

The household version is the same six lines with smaller numbers: what the arrangement covers, what it costs each year, what it gives up in exchange, and over what period. The discipline is identical at every size: a position that changes an exposure is written down with its size, its price, its period and what it surrenders, or it will be remembered later as whichever of those four is most convenient.