dark side of the nudge

“Why Does the Law of One Price Fail? An Experiment on Index Mutual Funds” Choi, Laibson & Madrian (2005)

In their decision making process investors give too much weight to past returns, a statistic with little predictive value, and too little weight to costs, a statistic with much predictive value. These issues are exacerbated when choosing between index funds. If past returns vary solely due to different fund start dates, and the two funds track the same index with little error, then only costs should be considered. Another paper covered on this blog showed that high-cost index funds persist in the market despite their guaranteed underperformance. This paper uses an experimental setup to test whether additional information disclosures can help investors make better decisions when choosing index funds.

The experiment had three between-participant conditions. All participants received four S&P500 fund prospectuses and had to allocate $10,000 between them. In one condition participants received additional fee information, including a translation of front-end loads and ongoing fees into their dollar cost. In another condition, participants received historical returns information which was negatively correlated with fee amounts (due to different start dates). Participants were incentivised by the chance of receiving one of their chosen funds’ returns from the next year. Additionally, the experiment removed the impact of fund services – a common justification for high-fee funds.

The experiment showed that clarifying fee information shifted participants’ choices towards low-fee funds compared to the control condition, although allocations to high-fee funds were still substantial. Given the high correlation between these funds this is a situation where diversification does no pay off. And giving additional returns information lead to a shift towards high-fee high-performance funds.

This latter result is perhaps not surprising, and demand effects could be cited for both of these findings, but why is clarifying cost structure having such a weak effect on participants’ behaviour? One thing the authors note, and that I readily agree with, is naïve diversification. When choosing between multiple funds investors tend to allocate their funds fairly uniformly, even if the funds are not different enough to provide any true diversification benefit. Redesigned the experiment, so that investors must allocate their funds to only one fund, or are choosing from only two funds, should increase the size of the effect. Evidence in support of this interpretation comes from the finding that high-fee subjects tend to me more doubtful about their portfolio allocations.


“Systematic Noise” Barber, Odean & Zhu (2003)

The “noise” in the title of this paper refers to fluctuations in assets prices that are not based on information. It originates from a paper by Fischer Black, which states that a certain level of noise is unavoidable, as a level of uninformed investor activity is needed to provide markets with liquidity. This is unlike the famous “no-trade theorem”, where rational traders agree on asset prices without trading against each other. Of course we see a lot of trading in actual stock and currency markets, and it can be argued that this trading provides socially useful liquidity – allowing investors to buy or sell without unduly affecting prices.

Early views of finance assumed that noise would not lead to distortions. Either investor mistakes would be uncorrelated and hence cancel out in aggregate, would diminish over time as these investors lost capital, or rational traders would arbitrage any abnormal profit opportunities away. A paper by De Long and colleagues showed that this need not be the case: “noise” traders create their own risk which arbitrageurs on limited time horizons cannot eliminate. Noise traders might even make above-average returns in the long run due to their overconfidence! My own view is that noise hurts investor returns and negatively affects the economy through the bursting of asset price bubbles.

This paper uses two large datasets to make the following observations. There is a high correlation for individual investor purchases, more so than when it comes to sales. When it comes to stocks that have risen there are two countervailing biases. The disposition effect dominates at short lags (the last three months), where individual investors tend to sell stocks that have risen recently. At slightly longer lags (1year+) return chasing dominates, where individual investors buy stocks that have a more sustained recent history of price rises.

Efforts to moderate the systematic trading decisions of individual investors should therefore focus primarily on their buying decisions. The authors of the current study list two major causes: attention and the representativeness heuristic. Although this is probably the case historically, it’s my view that investors are merely grabbing on to these noisy heuristics because more fundamentally informative information is hard for them to process. Reducing the levels of  noise in our markets would probably do a lot of good. First, professional investors cannot eliminate all pricing distortions on their own. And second, when they do reduce such effects it will always be through a zero-sum transfer away from individual investors. Reducing these mistakes in the first place would be a much more equitable solution.

“Trading is Hazardous to Your Wealth” Barber & Odean (2000)

This paper is the classic reference on the cost to investors of individual stock overtrading. While the last paper covered on this blog showed that these costs are extremely economically meaningful in the aggregate, this paper focuses on the immediate impact that overtrading has on investor returns.

The striking result of this paper is that although the before-cost returns to investors are nearly unaffected by overtrading, the net after-cost returns are incredibly divergent. Before-cost average returns are clustered around 18.5%-18.7%/year. But the investors who trade most frequently in this sample earn an average after-cost return of 11.4%/year, compared to 18.5%/year for those who trade the least (and a return of 17.9%/year for the market).

The average annual portfolio turnover in this sample is 70%, and small account holders tend to have a higher turnover than large account holders. The authors argue that the poor performance of high turnover investors is due to overconfidence. My reading is a little different. If investors were overconfident then shouldn’t this also be reflected in a before-cost deficit? But individual investors actually outperform the market before costs. The clear negative relationship between costs and returns seems to me that investors are simply not accounting for the deleterious effects of costs. Large account holders likely have more appreciation for the total costs of trading and hence turn their portfolios over less frequently.

As I’ve argued in the last blog post, I think this could be because a major cost of trading, the bid-ask spread, is not a cost that is cognitively accessible. Investors have to infer it from looking at the spread. Making the cost of the spread clear, by multiplying the number of units bought or sold on each transaction by half the spread, could be a useful nudge.

This could have a number of beneficial knock-on effects. Investors could begin to trade more patiently, supplying more liquidity to the market instead of demanding it. Furthermore, increased cost-sensitivity would incentivise market-makers to quote more competitive prices. Individual investors’ trades tend to be highly correlated. Could it be that getting them to trade less often would help decrease the formation of financial bubbles?

Consumers are liquidity demanders. Make them demand less and increase their supply. Incentives for market makers to quote more competitively.

“Just How Much Do Individual Investors Lose by Trading?” Barber, Lee, Liu & Odean (2006)

This paper uses a remarkably complete dataset on the Taiwanese stock market from 1995-1999 to examine the magnitude of investors’ losses from overtrading. Barber and Odean are the authors of the seminal paper on overtrading, showing the very clear negative relationship between portfolio turnover and investment returns. The advantage of the dataset in the 2006 paper is that it can be used to precisely measure these losses for individual investors in an entire country, and also show who these losses flow to.

Many of the papers discussed on this blog are about mutual funds. The Taiwanese market is peculiar in that only 1% of individuals’ investments are through mutual funds or other intermediaries; the rest is through direct investment in individual stocks. Additionally, turnover is incredibly high, at around 300%/year (the average stock is held for only around 4 months). These features make the market almost a perfect microcosm of the costs of individual stock overtrading.

The results are truly staggering: individuals lose 2.2% of GDP per year due to their overtrading.

Individual stock trading can be thought of as a zero-sum game. If one investor outperforms  relative to the market, then this must be mirrored by another investor’s underpeformance. So who wins from individual investors’ overtrading? Financial institutions. Much of this flows overseas to large institutional investors. From a social welfare perspective, it seems clear that limiting some of this large wealth transfer would be beneficial.

Investors’ losses are primarily through their most aggressive trades. Demanding immediate liquidity leads to excess returns for liquidity providers (market makers, and large institutional traders). Institutions, on the other hand, gain both with their aggressive and passive trades. The authors state that this is probably because of their superior market knowledge.

How can we reduce individual investors’ losses? My own feeling is that overtrading might partly be caused by the unusual representation of costs in investing. The bid-ask spread is the main cost for individual stock trading. For a round-trip transaction – buying one stock and purchasing another – this can easily amount to 5% of the amount bought and sold. Given that long-term expected stock returns are around 6%/year, this takes out a large chunk. And turning your portfolio over three times a year, as the average Taiwanese did in this study, could easily cost you 15% (before accounting for taxes and the direct cost of transacting).

But the bid-ask spread is not a salient cost. It is paid implicitly through selling your actual holdings for a low price and buying your new stocks at a high price. There are few implicit costs such as this in the real world. Buying and selling on Ebay, for example, leads to direct fees that are easily measured. And another issue with the bid-ask spread is that its constant corroding effects are masked by high stock volatility. A way of making the bid-ask spread salient would be to multiply half the spread by the number of units being bought or sold. If the spread is 5%, and an investor is trying to sell £10,000 of stock, then before confirming the transaction they might be informed that the total implicit cost of this trade is £250 (whereas the direct brokerage cost of this trade might only be £10). It would be fairly trivial to mandate this information disclosure on online trading platforms, and my feeling is that it would greatly reduce the incidence of overtrading – and could go some way towards reducing the massive wealth transfer towards financial institutions.

“Choice Bracketing” Read, Loewenstein & Rabin (1999)

This paper follows up on a paper by the first two authors with a more encompassing theoretical account. The idea is that preferences are susceptible to how broad or narrow the decision context is. People act differently when they consider the sum consequences of a number of decisions, compared to when they consider the merits and weaknesses of only a single decision at a time. For example, the authors say that although the individual decision to smoke each cigarette might seen inconsequential, bracketing over a year’s consumption would make the costs much more salient. When it comes to investing, I think that the common bias of insufficient diversification might be caused by choice brackets that are too narrow.

But for this post I’m going to stray slightly off-topic and talk about how choice bracketing might affect self-control issues surrounding potential addictions. My view is that in many cases not only are we unable to voluntarily choose our own brackets, but that outside forces prevent us from using brackets that are beneficially narrow.

The authors discuss how Alcohol Anonymous advises alcoholics to hand their problem “one day at a time”. The implication being that because a lifetime’s non-drinking might seem inconceivable, and hence doomed to fail, that a narrower and more achievable bracket might be helpful. Interestingly this deviates from the recommendations of hyperbolic discounting models, which recommend broad brackets for addictive substances.

My personal take is that with many addictive substances we are unable to choose our own brackets; instead, they are set by the product’s seller. It seems fairly common-sense to me that for many self-control issues we might lack the cognitive power to choose our own bracket size. Take smoking as an example. Cigarettes are most commonly purchased in packs of 10 or 20 (at least in the UK, some friends tell me that 10-packs are not sold in their country). The size of a purchased product then becomes the inevitable bracket. If I’ve bought 20 cigarettes then I’m not going to “waste” half of my purchase by throwing them away: I’m going to smoke them all (even if the last 10 cigarettes provide me a negative marginal utility).

Now consider the dilemma of a smoker trying to quit. We can think of their problem as lots of small decisions, spread out through time, not to smoke. If they at any time fail, then the number of cigarettes that they purchase will be bracketed together and inevitably smoked. Therefore, their decision problem is made much harder if cigarettes are sold in large default packets. They only have to fail on one occasion before they embark on a protracted bout of smoking. Now consider a hypothetical world where cigarettes can only be bought individually: now their resolve has to fail on 20 separate occasions before an equal amount of damage is done.

There are many instances when sellers of addictive products adopt large brackets. The brackets they push then become the consumer’s inevitable bracket and exacerbate self-control issues. Junk food sellers use sell large portions at a discount. My personal bracket problem is with Domino’s pizza: they offer “any-size” pizzas for a given price such as £9.99. Ordering a medium-size pizza at this price seems like a waste, but buying a large-size pizza leads to me eating far too much. Bulk-buying of alcohol at supermarkets seems like a great saving but leads to excessive drunkenness (OK – this is no longer about me). Gambling companies use incentive schemes to bracket many individual gambles together. And cigarettes are of course sold in fairly wide brackets.

My opinion is that many self-control issues could be helped if narrower brackets were encouraged by regulators, either with the price system, outright limitations on purchases, or hurdles to bulk-buying (such as the filling out of tedious forms). Some of these actions might seem a bit too interventionist for hardcore libertarian paternalists. But, given that sellers of these products are intentionally adopting broad brackets – my favourite “dark nudges” – I think such action would be justified.

“On Persistence in Mutual Fund Performance” Carhart (1997)

“Past performance is not indicative of future returns” is a familiar tag-line to investors, but is it true? Other papers covered in this blog have shown that past returns are given a high weight in investors’ decision making processes, and that past returns moderate diversification bias. This paper shows that good past performance does in fact not indicate high future returns, but that the opposite can in fact be the case (if the performance is based on loading up on specific risk factors).

As with any good finance study (and hence my gripe with Borges et al., 1999), returns have to be compared to the expected returns from an asset pricing model. Taking more risk than the market is an easy way to outperform without necessarily displaying any skill. This paper uses a four factor model, which includes the Fama French value and size factors, as well as a momentum factor. Depending on your view of finance these factors can either be rationally priced risk factors or behavioural anomalies, but they do help to explain and predict performance better than the CAPM. Returns on these additional factors tend to wax and wane. The value premium might be very negative for many years, such as in the dot com bubble, and then suddenly reappear. This is why investing based purely on high raw returns is a bad idea, as it might have been from loading up on asset classes with specific risk factor sensitivities which will then mean-revert.

This paper shows that after correcting for these risk factors, that there is very little persistence in fund performance. For example, a fund could outperform the market by overweighting small-cap value stocks, but this does not reflect skill since it can be mimicked by a passive strategy. And in fact the only real unexplainable persistence in returns in this study is that of the worst mutual funds. Now, obviously there is such a thing as investment skill. Perfectly efficient markets are not possible. But can your average retail access obtain access to skilled managers, and can they obtain their services for less than the cost differential? Investing with a manager who can produce 1% of alpha a year is no use if their marginal cost is 1.5% a year. My intuition, and the fact that high-performing hedge funds such as Renaissance Technologies do not accept any investor capital at all, suggests otherwise. Retail investors are much more likely to end up with the managers that are persistently bad.

This study also suggests that high-fee funds actually underperform by more than their cost differential. Increasing fees by 1% tends to decrease returns by 1.54%. Funds that charge a load (a sales charge to invest in the fund) also perform worse, even before accounting for the higher fees.

So why are investors so fixated on a piece of noisy information, while ignoring information – investment costs – which provide a true signal? It might be that the current presentation of fees is simply too abstract and too far removed from most investors’ experience of consumer decision making. Given that it is hard to evaluate fees, investors heuristically give up on evaluating them and “take the best” by focusing on past returns. My hypothesis is that changing the presentation of fees, by making them more salient, might help investors incorporate them into their decision making. Past returns are, after all, not indicative of future returns, so reducing this bias could do a lot of good.

“Reflections on the Efficient Markets Hypothesis: 30 Years Later” Malkiel (2005)

This paper is by the author of the most famous popular book in favour of the efficient markets hypothesis. Put briefly, this hypothesis states that it is very hard to outperform average market returns on a risk-adjusted basis. The only way to reliably outperform the market over time is by taking more risk (either via leverage or by buying stocks with above-average levels of undiversifiable risk). The efficient markets strategy is then to invest in index funds which provide risk exposure and diversification at a very low cost. It’s a controversial argument which is rejected by many practitioners and behavioural finance scholars. For example, Grossman/Stiglitz show that it can never be strictly true, since active investors need an incentive to collect and process costly information. The market cannot be efficient with nobody processing information to be reflected in stock prices.

When looking at the nudge/behaviour change argument central to this blog, however, this debate is not entirely relevant. All that we require is for naïve investors to make enough errors when picking high-cost actively managed funds, and individual stocks, that they’d perform better if nudged towards low-cost index funds. Malkiel gives us some firm data on actively managed mutual funds in support of this hypothesis.

First, past returns are not indicative of future returns. Funds with high past returns do not persist. In fact, there tends to be mean-reversion, where high performing mutual funds then underperform their benchmarks. And this is made worse by the pattern of money flows to these funds. Most high performing funds achieve their best returns when relatively small. The funds massively swell in size, and then tend to underperform. Although these funds overperform their benchmarks on a time-weighted basis, they often underperform on a money-weighted basis, because their low returns come when there is so much more invested in the fund. These funds, which are the best actively managed funds, actually underperform their average investor.

Second, Malkiel shows the average actively managed fund underperforming the S&P 500 by over 2% a year for both 10- and 20-year samples up to 2003. This is approximately equal to their average cost levels, indicating that choosing low-cost funds is the most important part of making good mutual fund choices (and not looking at past returns). Other papers examined on this blog show that expense ratios are given little weight in investors’ decision making process. I think this is an artifact of the way costs are disclosed, however, and I think this behaviour can be changed.

“Bargain Hunting or Star Gazing? Investors’ Preferences for Stock Mutual Funds” Wilcox (2002)

This paper compares the importance of management fees to other information that is important in fund choice, including company brand names and past returns. Somewhat unusually for a behavioural finance study this paper uses an experimental design (instead of being based on empirical data). It replicates two findings from the previous paper: that investors are responsive to front-end load fees (paid on purchase of the fund), but that ongoing management expenses are given little weight in the fund selection process.

Past returns are given the highest weight in this study, with their effect steadily increasing from one year to ten-years of data. An earlier study showed that diversification bias was much more prevalent when well-known assets have performed well. Could it be that a focus on past returns is driving the other biases? Diversification bias might be occurring when the first investment considered happens to have a high enough return that investors decide to “take the best” and make their decision based purely on that factor. Funds with especially high past returns are likely to also have high fees. This could be because of fund incubation, where fund families artificially inflate the average returns of their funds on offer by selectively picking funds that a high return before they were open for public investment. It could also be that actively managed funds have both higher average fees and a greater dispersion of returns than index funds. In that case a focus purely on past returns would move investors to high-fee funds.

Looking at front-end loads and ongoing management expenses, Wilcox finds that front-end loads are weighted with around twice the importance of ongoing fees. This is interesting, as from a rational perspective this would only make sense if investors’ expected holding periods are under two years! Although many investors do change their portfolios frequently, this is an extremely short period. The more likely explanation is that front-end loads are simply given far too high a weight, perhaps because they are more salient. Another explanation could of course be that investors place too much weight on the present relative to the future, as for example shown in hyperbolic discounting. The fact that ongoing expenses are underweighted in this controlled experimental study does at least suggest that this might be a separate bias to the chasing of high past returns.

The last curious relationship in this paper is an inverse relationship between financial experience and the weighting of these factors. More experienced investors in this experiment tend to place a greater weight on past returns relative to fees. This is interesting as it runs counter to the findings of a very large empirical study. One potential explanation is that the current study was fairly small, using only 50 participants. If that is the case, then it may fail to cover a full range of financial sophistication. A plausible hypothesis is that investors with a little bit, but not a great amount, of financial experience are the most likely to overweight past returns in their investment calculus. Of course the empirical study does have its own potential failings with the ever-present possibility of omitted variable bias. My tendency, however, would be to be in favour of those findings at least until the current study has been replicated.

“Out of Sight, Out of Mind: The Effects of Expenses on Mutual Fund Flows” Barber, Odean & Zheng (2003)

This paper presents some evidence toward my hypotheses for why investors overpay for mutual funds. Briefly, investors might be so prone to overpaying because fund charges are described in percentages – e.g. 1% of assets per year – and are subtracted from the fund’s gross return, so they are only indirectly “paid” for. These costs are not salient, unlike other fund expenses which this paper shows investors are sensitive towards . . .

The authors split fund fees into yearly management fees and front-end loads – paid at the point of purchase, and also described in a percentage of assets. The authors hypothesise that front-end loads are a more salient cost than the yearly fee, since their cost can be deduced on the first brokerage statement, while the yearly fee’s impact is swamped by fund volatility. Front-end fees are easier to mentally represent in terms of their actual costs.

Their results should that although investors are cost-sensitive to front-end loads, there is actually a positive relationship between the yearly fee and fund flows. It turns out that this relationship is driven by funds increasing their fees to finance marketing campaigns, with the net result being an increase of net flows to the fund. New investors attracted by the marketing campaign outweigh investors who leave because of the higher fee (and people not joining because the fee is now bigger). Furthermore, experienced investors are less likely to purchase funds with a front-end load but this does not translate to yearly fees.

An additional study on fund supermarkets, which offer a range of mutual funds from different companies, confirms the results on the differential impact of up-front and yearly fees. The funds without an up-front fee tend to have a higher yearly fee, and actually grow faster than the funds with an up-front fee. These fees are usually fairly small, so rational investors with long time horizons should place a much greater weight on the percentage fee, but they don’t.

A worrying conclusion from the paper’s conclusion is that mutual funds have gradually shifted away from using front-end loads and towards using higher yearly fees. They seem to be learning the way to frame their expenses that their customers will be least cost-sensitive to. A dark nudge if ever I’ve seen one.

“Diversification Bias: Explaining the Discrepancy in Variety Seeking Between Combined and Separated Choices” Read and Loewenstein (1995)

Although this is not a behavioural finance paper, I believe it can help explain the anomaly of investors underdiversifying their portfolios. The key finding is that participants seek a lot more variety while making simultaneous than sequential decisions. In the context of consumer decision making sequential choice actually leads to a bias. People seek more diversity than their consuming self at future points would actually desire.

From standard microeconomic theory, diminishing marginal utility is the reason to diversify consumption bundles. You might prefer 1 chocolates to 1 orange, but after consuming 5 chocolates you might now prefer an orange. Your marginal utility – the utility from consuming an extra unit – of chocolate has decreased. Diminishing marginal utility is a big factor over short timescales, but over longer timescales it’s impact is much less. If I’ve just eaten a chocolate I might prefer an orange, but if I last ate chocolate yesterday I might still prefer chocolate today.

In consumer decision making diversification bias arises when people have to make multiple purchases at one instant when the consumption is spread out over time – they go for more diversity than their future selves would prefer. The corollary of diversification bias in investing – where investors place their portfolios in too few assets – might be driven by the opposite mechanism: when investors make multiple asset allocation decisions at different time points. Framing individual investing decisions as part of a greater plan might ameliorate this bias. Two quotes from the paper point to this:

“the discrepancy in variety seeking occurs because simultaneous choices are presented together and are thus framed as a type of portfolio choice, whereas sequential choices are considered in isolation.”

“Simultaneous choices are presented to subjects in the form of a package, and perhaps the most straightforward choice heuristic applicable to such packages is diversification.”

The final experiment of this paper suggests that such a simple reframing can have an influence on choice. During Halloween children were asked to choose 2 chocolates from a tray of 3 alternatives. The manipulation was that some children made this choice simultaneously, while the others chose sequentially between two houses. All of the 13 children in the combined condition chose two different chocolates, while only half of the children in the separate condition did.