Tag Archives: finance

Investing time to gain lifetime

Exercising lengthens lifespan, but the return is diminishing in the amount of exercise. From zero physical activity, one extra hour of exercise per week gains about one year of life expectancy (doi:10.1371/journal.pmed.1001335.t003). Thus investing 1/168 of total weekly hours, or about 1% of the waking hours that are not spent on the quickest possible eating or hygiene, adds about 1/80 of lifespan in developed countries. This time investment has a positive return, because the percentage of lifetime spent on sports is less than the percentage gained.

Exercising may be optimal even for someone who intensely dislikes exercise, because one way to think about this investment is as choosing a year of being dead or a year of exercising plus some extra time living and not exercising. If doing sports is weakly preferred to being dead, then the first few hours of exercise per week are a positive-return investment.

One criticism of the above logic is that the lifetime gained is at the end of life, but the time doing sports is spread evenly throughout life. If extra time when old is worth much less than when young, then investing time in one’s youth to gain years of life in retirement may not be optimal. However, the question then becomes why is time less valuable when old. If the reason is lower ability to enjoy life (due to chronic diseases, cognitive decline, decreased libido, etc), then counterarguments are that exercise increases healthspan (quality-adjusted years of life) and the progress of medicine increases the quality of life in old age over time. If technological progress becomes fast enough to lengthen average lifespan by more than one year each year, then life expectancy becomes infinite. Increasing one’s lifespan to survive until that time then has an infinite return.

If life expectancy does not become infinite in the 21st century, then the diminishing return to exercise in terms of lifespan implies that there is a finite optimal amount of exercise per week, unless one’s utility increases in exercise no matter what fraction of time is spent on it. At 10 hours of physical activity per week, one needs to add about 10 more hours to gain one year of life (doi:10.1371/journal.pmed.1001335.t003). Spending 10% more of one’s waking time to gain 1/80 of lifetime is a negative-return investment in pure time terms, but may still be rational for the increase in health and quality of life.

In the research, exercise is defined as moderate- or vigorous-intensity activities: those with an intensity level of at least three metabolic equivalents (METs) according to the Compendium of Physical Activities. In other words, the energy cost of a given activity divided by the resting energy expenditure should be at least three (the approximate intensity of a brisk walk). The relevant weekly hours of moderate- or vigorous-intensity activity and the years of life gained are in the table below.

Physical Activity Level:0 0.1–3.74 3.75–7.4 7.5–14.9 15.0–22.4 22.5+

Years of life gained: 0 1.8 2.5 3.4 4.2 4.5

Firms could short the stock of competitors

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If a firm designs a great new product, a more efficient production process or gains some other privately known competitive advantage, then the firm could financially profit by short selling its competitors’ stock before revealing its advantage. The revelation reduces the expected discounted profits of competitors, thus their stock price. Symmetrically, if a firm loses cheap suppliers, suffers a manufacturing breakdown or otherwise becomes less able to serve its customers, then its competitors will probably benefit and their stock will rise. The firm could mitigate its losses by buying rivals’ stocks, with leverage.

Shorting competitors does not seem to be illegal insider trading, as defined by the US courts: the purchasing or selling a security while in possession of material, non-public information concerning that security, where the information is obtained from a breach of fiduciary duty, or a duty arising from a relationship of trust or confidence. I am not a lawyer, so this is just a guess, but a firm usually does not possess inside information about its competitors and does not owe fiduciary duty or trust to its rivals. Maybe there is some other reason not to trade in competitors’ stock, but a casual web search did not reveal why.

Overbidding incentives in crowdfunding

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Crowdfunding campaigns on Funderbeam and other platforms fix a price for the shares or loan notes and invite investors to submit the quantity they want to buy. If demand exceeds supply, then the financial instruments are rationed pro rata, or investors requesting quantities below a threshold get what they asked and others receive the threshold amount plus a pro rata share in the remaining quantity after the threshold amounts are allocated. Rationing creates the incentive to oversubscribe: an investor who wants n shares and expects being rationed to fraction x of her demanded quantity will rationally put in the order for n/x>n shares to counteract the rationing. For a mechanism not to invite such manipulation, the amount allocated to a given bidder in the event of oversubscription should not depend on that bidder’s bid quantity. For example, everyone gets the minimum of their demanded amount and a threshold quantity, where the threshold is determined so as to equate demand and supply. If there are s shares and all m investors demand more than s/m, then each gets s/m.

If some investors demand less than s/m, then the allocation process is recursive as follows. The i1 investors who asked for less than s/m each get what they requested. Their total t1 is subtracted from s to get s1 and the number of remaining investors reduced to m1=m-i1. Then the i2 investors asking for less than s1/m1 get what they demanded (t2 in total), and the new remaining amount s2=s1-t2 and number of investors m2=m1-i2 determined. Repeat until the number of investors asking for less than sj/mj is zero. Divide the remaining amount equally between the remaining investors.

An alternative is to let the market work by allowing the price to adjust, instead of fixing it in advance. Everyone should then submit demand curves: for each price, how many shares are they willing to buy. This may be too complicated for the unsophisticated crowdfunding investors.

However, complexity is probably not the main reason for the inefficient allocation mechanism that invites overbidding. The crowdfunding platform wants to appear popular among investors to attract companies to raise funds on it, so wants to increase the number of oversubscribed campaigns. Rationing is a way to achieve such manipulation if the fundraisers ignore the investors’ incentives to overbid and do not compare the platform to competing ones with similar allocation mechanisms. If fundraisers are irrational in this way, then they do not choose competing platforms without overbidding incentives, because funding campaigns there seem to attract less investor interest. Competing platforms with more efficient allocation mechanisms then go out of business, which eliminates comparison possibilities.

Platform providers fake being popular

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Crowdfunding platforms, stock exchanges and other providers of two-sided markets want to appear popular, because having more buyers attracts more sellers and vice versa. The platform’s revenue is usually proportional to the number of users, because it charges a commission fee on trades or advertisers pay it to show ads to users. The exchange’s marginal cost of a user is close to zero, giving it an incentive to fake a high volume of trades, a large limit order book and a small bid-ask spread.

The platform’s cost of posting a great volume of outstanding buy and sell orders at a small spread is that many investors try to trade at these favourable bid and ask prices. Either the market maker has to take the other side of these attempted transactions or is found fraudulent. Taking the other side results in a large loss if some investors are better informed than the exchange.

The platform could falsely display a large trading volume, but keep the order book honestly small by adding fake trades at prices between the bid and the ask only, so no investor’s real limit order is ignored. This seems difficult to detect, unless one side of the limit order book is empty (e.g. no buyers) and at least one at-market order on the other side (e.g. a sell) is outstanding. In this case, any trades occurring would have to satisfy the at-market order. However, the platform or real investors can then take the other side of the at-market order at a very favourable price to themselves, which discourages at-market orders. A large trading volume with a thin order book is still slightly suspicious, because it requires that crossing buy and sell orders between the bid and ask prices arrive almost simultaneously, in order to be matched without appearing on the order book for long, and without triggering the real limit orders. Displaying the fake buys and sells on the order book risks attracting actual matching trades, which the platform would have to honour (at a cost).

Without automated quote matching, there are no at-market orders, for example on the Funderbeam crowdfunding platform. Instead, everyone either posts a limit order or picks an order from the other side to trade with, e.g. a buyer chooses a sell. Investors can pick an order with a worse price (higher sell or lower buy) on the other side, which frequently occurs on Funderbeam. Choosing a worse price is irrational, unless the traders in question are colluding, so the asset is effectively not changing ownership. Reasons to carry out such seemingly irrational trades are to manipulate price and volume, e.g. price can be raised or reduced by targeted trades outside the bid-ask interval. Volume can only increase after added trades, rational or not, but such seemingly greater activity is exactly what benefits the stakeholders of the platform. The employees of the market maker have a natural motive to fake-trade between themselves to make their firm look good, even without any inappropriate pressure from their boss.

Another way to attract issuers and investors is to demonstrate successful initial public offerings, meaning that the funds are raised quickly (good for issuers) and the price of the newly listed stock (or other asset) goes up, which benefits investors. Adding fake capital-raisers is difficult, because potential investors will check the background of the supposed issuer. Inserting spoof investors into an actual funding campaign is costly, because real money would have to be invested. One way to manipulate popularity upward is to simultaneously add a fake issuer and fake investors who satisfy its funding need. The idea is to not leave time for real investors to participate in the campaign, by pretending that the capital-raiser achieved its target funding level before most investors could react. This is easier in markets with a small number of real investors and without an auto-invest feature. However, the real investors who were supposedly pre-empted may still research the supposedly very popular issuer.

A costless way to briefly boost the popularity of a real fundraising campaign is to add fake investors after the target funding is achieved, and forbid issuers from increasing the target or accepting funds from those who subscribed after the goal was reached. Any campaign meeting its target can then be made to look heavily oversubscribed. However, if the issuers are informed in advance of the restriction not to increase the target, then they may find an alternative unrestricted platform to raise funds. On the other hand, if the restriction is not mentioned beforehand, then it will likely anger the issuers who will then create negative publicity for the platform. Competition between exchanges thus curtails their manipulation incentives.

The platform can motivate real investors to raise their bids when the campaign reaches its target by rationing demand: bidders in an oversubscribed share issue get only a fraction of what they wanted to buy. Anticipating this, buyers will increase their requested quantities so that the fraction of their new bid equals their actual demand. This makes the campaign look oversubscribed and creates a feedback loop: if other investors increase their quantities, then rationing reduces the fraction of a given investor’s demand that will be satisfied, so this investor raises her or his requested amount, which in turn makes others increase theirs.

If investors know of the bid rationing in advance, then they may select a rival market provider without this restriction, but if rationing takes them by surprise, then they may leave and publicly criticise the platform. Capital-raisers compare exchanges, so if many market providers inflate demand and the issuers pay attention to the level of oversubscription (instead of the fraction of campaigns reaching the target, which is what should matter to the capital-raiser), then the biggest inflator wins. Of course, platforms may not want to reveal unsuccessful campaigns (e.g. Funderbeam does not), so public data on the fraction of issuers who achieved their funding goal is unlikely to exist.

Theoretically, the feedback from bid rationing to increased quantity demanded could lead to infinite amounts requested. A countervailing incentive is that with positive probability, other investors do not honour their commitment to buy, in which case a given investor may be required to buy the amount (s)he demanded, instead of the lower amount (s)he actually wanted. If there is no commitment to buy (for example, on Funderbeam the bids are only non-binding indications of interest), then the danger of overcommitting is absent, so the rational choice seems to be requesting an infinite amount. Investors do not indicate infinite interest, so either they are irrational or some other penalty exists for outbidding one’s capability to pay.

Fund management fee paid explicitly to nudge consumers to choose better funds

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Mutual funds with lower management fees have higher future before-fee returns (Gil-Bazo and Ruiz-Verdu 2009). Nonetheless, the high-fee funds have not gone out of business, so there must exist a sizable number of silly customers who accept low returns without switching to competitors. When asked explicitly, all fund investors prefer more money to less. Their hourly wage is not large enough to explain their non-switching with the time and hassle costs of comparing fund returns and choosing a new one. Similarly, many Estonians keep their retirement savings in badly performing high-fee pension funds despite the availability of dominating options (Tuleva and LHV index tracking funds). This is costing the customers over one percent of their retirement wealth per year.

By contrast, people with chronic or expensive diseases in the US often pick the health insurance plan that maximises their wealth (coverage minus premiums). This dynamic optimisation involves switching to a different plan when their illness changes. People without costly medical conditions tend not to switch their insurance even when cheaper plans with higher coverage are available.

Both the pension and the insurance plan decisions are complex, but matter greatly for wealth. Why do people pay attention to the financial consequences of their insurance choice when sick, but ignore better options among pension funds (and when healthy, also among insurance plans)? One possibility is that insurance is more salient to the sick, and the greater attention leads to better decisions. Specifically, the premiums and out of pocket payments for medical procedures frequently remind patients of the financial consequences of their insurance, but the missing returns on one’s retirement assets are not observed without explicit comparison to the stock market or competing funds. Most people do not compare their pension plan to the market, so even in retirement may not know what their (counterfactual) wealth would have been had they chosen a better fund .

If it is lack of attention that causes the bad choice of mutual and pension funds, then one solution (proposed by my friend Hongyu Zhang) is to make the management fees more salient by requiring their explicit payment. For example, every month the customer has to transfer the amount of the management fee from their bank account to the fund. Financially, this is equivalent to the fee being deducted from the retirement assets like now (assuming these assets are eventually taxed the same as income, otherwise the transferred fee can be adjusted to make it financially equivalent to the deduction). The attention required is however greater for an explicit payment than for doing nothing following a lack of capital gains. Similarly, requiring customers to pay the difference between the return of their fund and the market return into the fund every two weeks would nudge them towards greater attention to their retirement account.

In practice, such a nudge is unfortunately politically infeasible. Not only would the fund industry lobby against it, but voters would irrationally perceive the required explicit payments as increased taxes. This would make the transition to transferring fees to funds from customers’ bank accounts very unpopular. If people understood the equivalence between low returns on their assets and explicit payments required of them, then they would be financially literate enough to choose low-fee, high-return index funds in the first place. Thus the problem of low-performing pension funds would be absent. To sum up, the fool and his money are soon separated, and it is difficult to protect people from their own bad decisions.