How Risk and Return Work Together, and Why Neither Is a Promise
Risk and return are related by price. Something whose outcome is less certain has to be offered cheaper before anybody will hold it, and being cheaper is what produces a higher return if it works. A price falling until somebody is willing to hold is a description of how prices get set, not a promise made to anybody. Taking more risk does not deliver more return. Taking more risk delivers a wider range of outcomes.
The relationship is usually handed over as though it were a law of nature, as though the world pays people for being brave. The relationship is not a law, and nothing pays anybody for anything. A great many people putting prices on things they are unsure about is what produces it. Reading it as an outcome of pricing rather than as a rule of nature is the whole of what stops it being heard as a promise.
Where does the relationship between risk and return actually come from?
Start away from money entirely, in a lane where two second-hand two-wheelers are for sale. Same model, same year, same afternoon. The first comes with its service record and the previous rider standing beside it answering questions. The second comes with no papers at all and a seller who says it ran fine.
Everybody already knows what happens to the two prices, and nobody needed a theory to know it. The second machine goes for less. Not because anybody decided it should, and not because bravery is being rewarded. At the first machine's asking price nobody was willing to take the second, so the number had to keep falling until somebody was.
A lane with no market and no jargon anywhere in it holds the entire origin of the relationship between risk and return. The seller wants to sell. The buyer has an alternative. The price is wherever those two meet, and where one side cannot answer the questions, the meeting point moves down.
Now the part that gets skipped every single time. The person who bought the machine with no papers did not get a better machine. The buyer got the same machine at a lower price, and alongside it a set of things that might turn out to be true about it. If the engine is sound, the lower price is what makes their purchase the better one. If it has been ridden into the ground, the lower price was not enough. The discount arrived on the day and is theirs for certain; what it might turn into arrives later or not at all.
Translate the lane into the language people actually meet. A business whose earnings nobody can predict, a piece of property in a part of town nobody can read, a holding whose worth turns on a court date: in each the buyer offers less because the buyer cannot be told what will happen. Nothing in that sequence is a reward, and nobody in it has promised anybody anything.
Why is something with an uncertain outcome priced lower than something with a settled one?
Why does an uncertain outcome have to be cheaper before anybody will hold it?
Because nobody is obliged to hold anything. The answer sounds too simple to be the mechanism, and it is the mechanism.
Put two things beside each other that could come to the same place later. One will get there. The other might. At the same price everybody takes the first, so the second does not sell, and the seller lowers the number until one person looks at the gap and says, at that number I will take my chances. The discount exists because at the old price there was no buyer, and for no other reason.
The discount has a plain name once its work is visible. The name is compensationA lower price offered because an outcome is uncertain. The seller hands it over when the sale is made, not later., in the narrow sense of something offered up front to make an uncomfortable arrangement acceptable. A household knows the shape from ordinary life: the flat above the noisy junction lets for less, and the shift nobody wants pays a little more. Neither promises the taker a good outcome.
The ordinary reading goes wrong at exactly this point, so notice what is being compensated. Nobody is compensated for the bad outcome, and nobody is compensated for having been brave. The payment is for not knowing, and not knowing is a different thing altogether. The money changes hands on the day, before anybody knows anything. The compensation is handed over in advance and the outcome it was offered against arrives later, if it arrives.
Why is being cheaper what produces a higher return, if it works?
A returnWhat a holding produces, or what it is worth when it is finally turned back into money, measured against what went in. has two ingredients and only two. The two are what arrives, and what went in. Almost every conversation on the subject looks only at the first. The second is the one already settled, and the second is the one worth watching.
The amount that went in is fixed on the day. A receipt records it, and it never moves again for as long as the holding is held. The amount that arrives is unknown until realisationThe point at which an outcome actually occurs, usually when a holding is sold or a payment finally lands., and may be more than what went in, about the same, or a good deal less.
Put those two facts together and the whole relationship falls out without any theory being needed. If what went in is smaller, a smaller number sits underneath the same arriving amount, so the return is bigger. The lower price is not a prediction that more will arrive. A smaller amount sits underneath whatever does arrive, and a smaller number underneath is arithmetic rather than a claim about the future.
What are the words if it works actually doing in that sentence?
Read the full sentence once, slowly. Something less certain is priced lower, and the lower price produces a higher return if it works.
Now delete three words and read it again. Something less certain is priced lower, and the lower price produces a higher return.
The second sentence is not a shortened version of the first one; it is a different and false claim, and three words is all it took. They are not a hedge somebody added at the end for legal reasons. The three words are the word uncertain doing its job inside the sentence, and if they could be safely removed then the thing being described was never uncertain in the first place.
What does the word expected actually mean here?
Here is where more households are misled than anywhere else on this subject, and nobody has to lie for it to happen. One word is carrying two meanings, and the meanings are not close.
In ordinary speech, expected means what will probably happen. A person expects the bus at seven, or expects that she will be at the wedding. One result is pictured, and the rest of the evening is arranged around it.
In the sentence about risk and return, expectedThe average across a whole range of possible results. An average is not what is likely, and not what anyone has promised. means the average across a whole range of possible results. Averaging is arithmetic performed on a list, and averaging has a property that catches people every time: the average can be a result that cannot actually occur.
A hall that books wedding dinners knows this in its bones. The kitchen can run two sittings and no others, so the hall takes bookings of two hundred plates or four hundred and nothing else. The average of the two is three hundred, correctly calculated, and no evening in the history of that hall has ever served it. The average across a range is a fact about the range, not a description of any evening.
So when somebody says the expected outcome on this is such and such, two things happen in the same breath and only one is heard. The word does its technical job, naming an average across a range that may be very wide. The listener hears the everyday job instead. The everyday job is this is roughly what will happen. The word cannot settle which of the two it was carrying, so ask how wide the range runs.
Somebody uses the word expected about an outcome that is not settled. What does the word mean in that sentence?
Does taking more risk deliver more return?
No. Every gentler version of that answer has been used to sell something to somebody, so the short answer deserves to stay short.
The reason it cannot be so is not a technicality, so look at it closely. If taking more risk reliably delivered more return, the thing being taken on would not be uncertain in the part that matters, and it would stop being priced as though it were. A dependable extra is not a risk, and a risk is not a dependable extra, and the sentence people repeat quietly assumes it can be both.
The relationship actually says, in full, that things whose outcomes are uncertain tend to be priced lower because of that uncertainty, and that where they do work out, the lower price produces a higher return. The sentence rewards a second reading. There is a tendency in pricing and a conditional about outcomes, and neither is a thing anybody can hand over.
What does more risk actually deliver, then?
A wider range of outcomesThe set of results that could occur. Having a range at all is what uncertainty means.. A wider range is the whole of the delivery. A wider range sounds like a disappointment and is really the answer, which is why it is worth saying out loud.
The word for the width of that range is dispersionHow widely spread the possible results are. A wide spread means the good and the bad ends are both further from the middle., and dispersion moves both edges. The top of the range moves up. The bottom moves down. Most people, asked to picture what happens when risk increases, picture the top edge climbing while the bottom stays put, and no such picture has ever been true of anything.
Two households on the same lane make the point without any finance in it. One has a salary that lands on the same date every month, the same amount. The other runs a stall whose takings depend on whether the road is dug up. The second is not richer and not poorer; it has a range, and the range means good months the first never sees and bad ones it never sees either.
The answer is worth settling before the control below is touched. An outcome becomes more uncertain. What happens to the range of results?
Make an outcome more uncertain. Watch what the drawing does, and watch what it refuses to do.
One thing changes here: how uncertain the outcome is, from settled at the left of the control to as unsettled as this drawing goes at the right. One thing is deliberately held still: the middle of the band. The middle sits on the same level at every setting and never rises. At the widest setting the band reaches exactly as far below where it started as above it. Nothing on this drawing is a return, an amount of money or a likelihood.
Because a reading inside a panel cannot be quoted by anybody who has not moved the control, here are its corners. At the settled end the band has no width at all: one result, drawn as a single point. At the middle setting it reaches five steps above the starting level and five below, and at the widest, ten above and ten below. At all eleven settings the middle sits at exactly the height it started at: widening is not rising.
So does taking more risk deliver more return?
Why does a wider range matter most where a date cannot move?
Up to here a range has been an abstraction, a shape on a drawing. A date is what makes the low end of it real, and until a date is involved the whole subject stays comfortably theoretical.
Think about what a household actually has in its calendar. A school fee due in the first week of June. A deposit that has to be handed over before the keys are. A wedding in November that people have already been told about. None of those dates negotiates.
Now put a range next to a date. If nothing has to be paid on any particular day, the low end of the range is a number on a piece of paper and a bad feeling. If something has to be paid on a particular day, whatever the range is sitting at on that day is what the household has. A date converts the low end of a range from a possibility into the amount a household is actually holding.
People mean exactly this when they say a longer horizon carries less risk, and the usual explanation of it is wrong. The range does not narrow over time. The range gets wider the further out the horizon runs, and a longer horizon gives the freedom not to be standing at the low end of it on the one day that mattered.
Which is why the honest version of the question is never how much risk should be taken. The honest version asks what dates this household cannot move, and what has to be sitting there when they arrive. Risk is not a quantity of bravery; it is the relationship between a range and a calendar.
A household has a date it cannot move and something with a wide range of outcomes attached to it. What does the width actually do?
What do the Bhosale household's own two positions look like through this?
A treatment of risk and return that quietly assumes a reader has holdings assumes too much, so the position is worth stating plainly first. At the end of year two the Bhosale household holds no shares, no fund and no monthly investment plan. The household holds instead two things that sit at the two ends of everything above, and neither was bought as a holding at all.
The first is the credit card balance. At 31 March of year two the Bhosale household owed Rs 48,594/- on it, out of Rs 71,594/- owed in all. The card's own term sets that cost at 3.5 per cent a month once the balance is not cleared in full, and the household pays the cost rather than earning anything. Here is the property that matters: there is no range around it at all. It is a certain outcomeA result that occurs regardless of how anything turns out, such as a cost somebody owes under a contract., and it occurs unless the balance is cleared.
Work it through so the shape is visible. Rs 48,594/- growing at 3.5 per cent a month, compounding, reaches Rs 73,429/- after twelve months if nothing is paid against it, so the cost across that year is Rs 24,835/-. The Rs 24,835/- is not an estimate and not an expectation in either sense of the word. The figure is arithmetic performed on a contract the household has already signed.
The second is the gold. Rs 1,40,000/- at the Bhosale household's own estimate: two bangles and a chain, received at a wedding. Nobody chose it as a holding and no rate is attached to it. Could anybody say what the gold will come to in ten years? Nobody can bound it. The honest summary of the gold is not that it will do better than the card costs; it is that nobody can say, and any number attached to it is a claim rather than a fact.
Set the two side by side and the difference is not which one is bigger. The difference is that they are different kinds of number: one settled by a contract, the other settled by nobody. Comparing a certain cost with an uncertain outcome as though the two were the same sort of measurement is the most common arithmetic mistake a household is invited to make.
The card's cost has no range around it at all. What does that make it?
The failure: hearing the relationship as a promise, and then reading outcomes backwards
The version almost everybody carries is four words long. More risk, more return. The four words are short, they sound like common sense, and they invert the claim they came from. The relationship says that uncertain outcomes tend to be priced lower because of that uncertainty. The compensation is offered in advance and delivered only sometimes, and only sometimes is what uncertain means.
A household carrying the four-word version does two specific and expensive things, and the second one is the half nobody warns about.
The first is that a fall gets read as evidence that something went wrong. Somebody erred. The thing was bad. I was cheated. Sometimes one of those is true. But a fall on its own is not evidence of any of them. A fall is the range doing exactly what the word range meant when the arrangement was entered into, and a range that only ever went upward was never a range.
The second is that a rise gets read as evidence of a good decision. A rise read as proof of judgement is the comfortable error, and a comfortable error is rarely called one. Daniel Kahneman and Amos Tversky spent their working lives on how badly people reason about uncertain outcomes, and one of the plainest findings in that work is how quickly a mind rewrites its own judgement once it knows how things turned out. A sound decisionOne that was reasonable on what was actually known at the time, whatever happened afterwards. is one that was reasonable on what was known then, and a good outcome does not certify it.
The point cuts both ways. A loss on its own does not settle whether the choice behind it was a bad one. A gain does not settle it either, and the gain is the harder of the two to hear. An outcome is not a verdict on a decision, in either direction.
The cost is not only emotional. A household that reads a fall as a fault tends to unwind an arrangement at the point where the range is at its low end, turning a position into a settled loss to make an uncomfortable feeling stop. The two errors are the same error, and a household can make both inside the same year.
Something a household holds falls in worth. What does that fall, on its own, tell anybody about the decision to hold it?
Where does this relationship break down altogether?
Everything above rests on one thing: that somebody is pricing something, weighing an outcome they are unsure about against a number they are willing to pay. Take that away and the relationship does not weaken, it simply is not there. Two cases do exactly that, and neither announces itself.
The first case is that nobody is pricing at all. Where nobody has offered or refused anything, no number ever fell to attract a buyer, so there is no discount and nothing for a higher return to come out of. Nobody has bid for the Bhosale household's bangles. An estimate nobody has tested with an offer is not a price, and the relationship described here has nothing to say about it.
The second case is that a price exists but came from somewhere other than a view about the outcome. A figure set by a rule. A number produced by a forced sale, where the price says more about the seller's calendar than anything else. A price somebody simply asserted. In each the number did not come from anybody weighing uncertainty, so nothing about a return follows from it.
There is a third qualification that is not quite a breakdown. Even where pricing works perfectly well, the relationship describes what tends to come out of a great many prices, and people price things wrongly all the time. A tendency across many prices is not a property of the single price in front of a household.
Name a situation where the relationship between risk and return simply does not hold.
How do people who work with this every day actually use it?
Three people use the same idea in three ways, and none of them uses it the way the four-word version suggests.
A lender uses it as a pricing instrument and never thinks of it as taking risk for reward. Where repayment is less certain the lender charges more, and the extra arrives from the first month regardless of how repayment eventually goes. The Bhosale household's card is that move at its most visible. The lender's uncertainty became the household's certainty. Pricing does that to a risk when it changes hands.
An analyst uses it as a sorting question asked before anything else. Given a number attached to something, is this a fact or a claim? A contracted rate sits in a document and will occur, so a contracted rate is a fact. A figure describing what something might come to later is a claim, and the next move is to ask what would have to be true for it to hold.
A household uses it in the smallest and most valuable way of the three. When a number is put in front of a household, one question comes first: does the thing it describes have one outcome or a range? If a range, the number sits somewhere inside it and the next question is who is standing under the low end. The question turns a sales conversation into an ordinary one, and somebody holding nothing at all can ask it.
Why does none of this tell a household what to do?
Because a mechanism and a decision are different objects. A decision needs what a household holds, what it owes, which dates cannot move, and what it could survive, and none of that is contained in a mechanism.
There is a second reason, and it is why figures about outcomes are better kept away from a mechanism. The moment a number appears beside a mechanism like this one, the number is what gets remembered and the mechanism is what gets dropped. Returns, historical figures and likelihoods sit outside the mechanism rather than inside it.
The mechanism is a shape rather than an instruction. Uncertainty is priced, and the price is where the compensation lives. The compensation turns into a range rather than a result. A range is only a problem where a date makes its low end real. And an outcome does not settle whether the decision behind it was sound.
References
| Source | Document | Where |
|---|---|---|
| Securities and Exchange Board of India | Investor education material on market conduct and disclosure | sebi.gov.in |
| Reserve Bank of India | Material on deposits, whose outcome is settled by contract, and on exposures that carry a range instead | rbi.org.in |
| Association of Mutual Funds in India | Published material on mutual funds as a category of regulated market exposure | amfiindia.com |
| Daniel Kahneman and Amos Tversky | Work on judgement under uncertainty, source of the finding that a mind rewrites its own judgement once it knows how things turned out | Published research literature |
The Bhosale household, Meghna Bhosale, Ashok Bhosale and Ira Bhosale are invented, and so are the wedding hall, the Rs 48,594/- card balance at 3.5 per cent a month and the Rs 1,40,000/- estimate on the gold.
Educational material. Not advice on any investment, tax, budget or market position.