Naive Diversification: Spreading Evenly Rather Than Sensibly

Naive diversification is putting the same amount into each option offered. The split is naive not because spreading is wrong but because the menu decides it. Change the number of options and the allocation changes, and nothing about the underlying things has changed at all. The menu is doing work nobody intended it to do.

Naive diversification rests on one question that almost nobody asks out loud. Who chose the denominatorHow many options the total is divided by.? An even split feels like a decision about what to hold, and it is really a decision taken by whoever settled how many boxes to print. The person who settled that number held no view about anything inside the boxes. Somebody was fitting a printed sheet, covering a range, or keeping a list short enough that it would actually get read. A number chosen that way makes the result arbitraryDecided by something that held no view at all about the outcome. rather than merely simple, and merely simple would have been perfectly respectable.

What is the rule, and what makes it naive rather than simply simple?

The rule is one line long and already familiar. The total being placed is divided by the count of options in front of the decider, and the same amount goes into each. Four things listed, a quarter each. Eight things listed, an eighth each. As arithmetic it is the total divided by the number of options, and that count is the only quantity entering it. Nothing about what sits inside any option is used. Nothing about what sits inside any option was ever asked for.

The wedding buffet is the familiar version. Twenty dishes are laid along the table, a spoon of each goes onto the plate, and by the last dish the table has decided the dinner rather than the appetite. The same person at a counter carrying five dishes takes very much bigger spoons. The food never changed. The number of trays did.

So where does the word naive come in? The word describes where the number came from, and it is not an insult aimed at anybody using it. Naive diversificationPutting the same amount into each option offered. took its name from Benartzi and Thaler, writing in the American Economic Review in 2001 in a paper titled Naive Diversification Strategies in Defined Contribution Saving Plans. Benartzi and Thaler examined how people spread contributions across the options a savings plan set in front of them, and the resulting mix tracked the shape of the list. Spreading is not the naive part. The naive part is that the number of things being spread across was handed over by somebody who was not thinking about the person deciding at all.

Hold two ideas apart from here on. An even splitEqual amounts to each option, which is a strong claim rather than a neutral one. describes an outcome: equal amounts, nothing more. Naive diversification describes a process, where the equal amounts arrived because the list happened to have a certain length. The same holding can come out of either, one of them can be defended afterwards and the other cannot, and staring at the amounts will not say which.

Why does the menu decide the split?

Look at the arithmetic once more. The expression is doing something quietly in plain sight. The share going to each option is one hundred divided by the number of options, and there is exactly one quantity in that expression. Change the number of options and the answer moves. Change every fact about every option and the answer does not move at all. A rule with one input hands its whole output to whoever controls that input.

And who controls it? Never the person putting the money in, and that is the whole trouble. A menuThe set of options as presented, which is chosen by somebody other than the person deciding. is set by a plan sponsor, by an adviser trimming a shortlist, by a results screen that shows ten names because ten is what fits, or by a paper form printed with four boxes to suit the sheet. Every one of those people had a reason for the number they chose. Not one of the reasons was about how much of anybody's total belongs anywhere.

Thaler and Sunstein, in Nudge in 2008, gave the general form of this a name. Somebody has to decide how a set of choices is presented, and no arrangement is free of a message: a list has a length, an order and a top. Under an even split the length by itself does the work of a whole allocation. A count of boxes is a printing decision, and under an even split it quietly becomes an allocation decision.

The reason all of this stays invisible is that only one list is ever in view at a time. From inside a single menu the list looks like the world, and the split looks as though it followed from the options rather than from their number. The dependence appears only when the same things are relisted at a different length.

What happens to the same things when the list is printed at a different length?

Offer somebody four options and an even split puts 25.0 per cent into each. Offer the same person eight options covering the same underlying things and it puts 12.5 per cent into each. Recompute both rather than taking them on trust: one hundred divided by four is 25.0, one hundred divided by eight is 12.5. Between those two sentences nothing being held has changed, and the only thing that moved is how many lines the list was printed on.

Now put money against it. The Palash decision log is an invented record of decisions taken by sixty investors across eight quarters, and it opens Meera Sundaram's holding on 4 January at Rs 12,00,000/- in four positions of Rs 3,00,000/- each: the Vindhya index scheme, the Nilgiri mid-cap scheme, Suvarna Chemicals Limited and Kesari Logistics Limited. Check it in both directions. Rs 12,00,000/- divided by four is Rs 3,00,000/-, four positions of Rs 3,00,000/- add back to Rs 12,00,000/-, and four shares of 25.0 per cent add to one hundred.

Now suppose the same four things had been set in front of her as eight lines. Nothing real would have to change for that: each scheme listed as two share classes, or each holding shown as two tranches bought a fortnight apart. An even split across eight of the same Rs 12,00,000/- puts Rs 1,50,000/- into each line, and eight times that comes back to Rs 12,00,000/-. The holding would be identical in substance and different in every single line, and no view about any of it would have been formed either way.

The ladder below runs the same Rs 12,00,000/- from a list of two to a list of twenty. Read the last column. The last column carries the argument, and it says the same thing at every row.

The boundary of the claim matters as much. Whether four lines were too few, whether eight would have been better, whether Rs 3,00,000/- was the right amount for any of the four: each of those is a claim about how a holding ought to be arranged, and each belongs to portfolio construction. Naive diversification says something narrower. The number in the allocation came from the length of the list, and that length was somebody else's decision.

How steeply does the share fall as the list gets longer?

The control below moves one thing: how many options the list carries. Everything underneath the control is stipulated identical at every setting. A visible difference while nothing real has moved is the cleanest evidence there is. An answer is worth settling on before the control moves.

Now look at the shape the readings trace. From a list of two to a list of four the share halves, falling 25.0 points from 50.0 to 25.0. From ten to twenty it halves again, and this time the fall is only 5.0 points. So the length matters most where lists are shortest. Short lists are exactly where most people meet them: a shortlist of four names, a form with five boxes. The curve below is a picture of the menu, and there is nothing in it about anything being held.

Read the marked point at four. The point sits there because the list had four lines, and not one fact about the Vindhya index scheme or Kesari Logistics Limited would change anywhere along the curve.

What does an even split silently assume?

Here is the part that surprises people. An even split looks like the most modest thing anybody could do with a list, and it is in fact the loudest claim on offer. Equal amounts say that every option deserves exactly the same weight. Saying that is an assertion rather than a shrug. Three claims are packed inside it, and each can fail on its own.

The first is that the options are interchangeableAlike in every respect that would justify giving one a different weight from another.. Nothing about what they hold, what they cost or how large they are makes any of them deserve more room than another. Interchangeability can be perfectly true, and often is. The value of saying it out loud is that it can then be heard as a claim.

The second is that the list is complete enough to be worth splitting across. An even split can only put money into boxes that somebody printed, so whatever was left off gets nothing at all, and nothing is an allocation too, reached by omission rather than by decision. A list is a claim about what is worth listing, made silently.

The third is that no two boxes hold the same thing, and this one bites in practice. The eight-line version of the same Rs 12,00,000/- runs at Rs 1,50,000/- a line. If two of those lines hold the same underlying thing, that thing collects Rs 3,00,000/- while each of the remaining six collects Rs 1,50,000/-, and the total is still Rs 12,00,000/- across seven real things rather than eight. The split looks even on the list and is not even underneath. Nobody decided to double up. The list did. An even split is not the absence of a view. An even split is the view that every option deserves exactly the same weight, and that view may well be right.

How is a naive split different from a deliberate equal weighting?

Two people each put a quarter into each of four things. Same list, same amounts, same total. One looked at what else was possible, worked out that nothing available separated the four, and chose equal weight on purpose. The other saw four boxes and filled them. The holdings are indistinguishable from outside. The decisions have almost nothing in common.

A deliberate equal weightingThe same allocation arrived at by examining the alternatives and rejecting them. is equal weight reached by examining alternatives and putting them down. Its distinguishing feature is not the number. The number is identical either way. The distinguishing feature is that the alternatives existed in the decider's head at the moment of deciding, so asking why not a third here and a sixth there gets an answer.

The naive version has no answer, and not because anybody was lazy. The answer is missing because the question never came up: from inside a single list the split feels as though it came out of the options themselves, so nothing presents itself as needing justification. The allocation cannot say which of the two happened; only a record of what was considered can.

Two students both answer C. One worked the problem through; the other guessed. Same mark, same tick. Ask the second what would change if a number in the question moved and there is silence, and that silence is the entire difference.

Which single question separates them?

No audit of anybody's thinking is needed. One question does the whole job, and it is a counterfactual, meaning it asks about a world that did not happen. Would the answer have been different if the same things had been listed differently?

Run it on the opening in the log. Four things, Rs 3,00,000/- into each. Relist the identical four as eight lines and ask whether the answer would then have been Rs 1,50,000/- across eight. If it would, the count was in charge. If a quarter would still have gone to each of the four real things however many lines they were printed on, something other than the count produced the split, and that something can be written down and argued with.

Most people find a second form of it easier to answer honestly. Which alternatives were looked at and put down? If the answer to either question is nothing, the count was in charge, and that is a description rather than an accusation. Neither question needs a method, a model or a spreadsheet.

Where is spreading evenly exactly the right answer?

Everything above could be misread as a warning against even splits, and it is not one. Spreading evenly is the correct answer whenever the options really are alike on the information actually obtainable. Not on information that exists somewhere. On what can be checked before the decision has to be made.

Three sealed envelopes sit on a table, identical from the outside, and one of them is known to hold more than the others without which one being said. Putting a third on each is not a failure to decide. An equal third is the only statement available that matches what is known, and any uneven split would assert a distinction that cannot be named.

Equal weight has three things going for it there. It states what is known accurately. Equal weight carries no quantity that can be estimated wrongly, and there is nothing in it to estimate. And anybody can check it in a second. When nothing available separates the options, equal weight is the honest expression of having nothing to say, and it is the right answer rather than a lazy one.

So the difference between the naive version and the correct version never lives in the numbers. The difference lives in whether the equality was claimed or inherited. Claimed equality can be stated, dated and later found wrong. Inherited equality cannot, and no later fact could contradict it.

How does an adviser, or somebody deciding alone, actually use this?

Devika Rao, the adviser at the invented Palash Advisory Services Private Limited, prints shortlists for a living. The moment she settles on a length, she has settled the allocation for every client who then spreads evenly, whether or not she meant to. So the practice she runs records why a list had the length it had, next to what the list contained. A reason for a list's length is a note about the menu rather than about the holdings, and most decision records never carry it.

For somebody deciding with no adviser and no committee, the same discipline is one line in a notebook: where the list came from, how long it was, and who chose that length. Write it before allocating rather than afterwards. Afterwards the number already feels as though it came from the options.

Now take the third reader, looking in from outside. An analyst, a lender weighing a borrower's position or a compliance reviewer cannot tell a naive split from a deliberate one. A statement carries amounts and no process at all. So they ask for the note. If there is none, the right conclusion is not that the split was poor but that nothing about it can be verified in either direction.

The log carries a measurement on exactly this. Twenty of the sixty investors adopted a written checklist on 4 November. Across quarters five to eight those twenty recorded a written reason on 34 of 41 decisions, being 82.9 per cent, against 19 of 63, being 30.2 per cent, for the other forty. No return difference is claimed, measured or implied by any of that, and eight quarters across sixty people could not support such a claim. The share of decisions that left something behind to read is what changed. Nothing about an even split can be checked from the amounts alone, so the only thing worth adding to it is a note saying where the list came from.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Palash 100 index, the Vindhya index scheme, the Nilgiri mid-cap scheme, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.