How much CO2 does a gas stove add to indoor air?

For fun I got a carbon dioxide (CO₂) meter. Standard atmosphere contains 400ppm of CO₂. Some studies suggest that mental performance begins to degrade when CO₂ concentration exceeds 1000ppm. I was surprised to see that when cooking on my gas stove (in the kitchen) the CO₂ meter in my office began to register levels approaching 2000ppm. I was curious to calculate how much CO₂ a simple gas burner adds to indoor air.

TL;DR: using a gas stove to boil a gallon of water in an airtight 30m³ room adds about 2200ppm of CO₂ to the air.

Detailed calculations:

It takes about 1,300kJ of energy to heat a gallon of water from room temperature (20°C) to just boiling (100°C). (Specific heat of water is 4.2 J/g/°C, a gallon of water weights 3.8kg, so we have 3.8kg * 80°C * 4.2kJ/kg°C = 1,300kJ. Note that this does not actually boil the water because it takes another 2.3 J/g to vaporize liquid water at 100°C.)

A gas stove is around 50% efficient in transferring heat to water in a pot, so we need to burn enough gas to produce 2,600kJ. Natural gas is mostly methane (CH₄), and 1 mole of methane releases 900kJ when burned with oxygen, so we're looking at burning 3 moles of methane. The combustion reaction is CH₄ + 2 O₂ -> CO₂ + 2 H₂O, so we get one mole of CO₂ per mole of methane burned.

At standard temperature and pressure 1 mole of gas occupies 22 liters. If the kitchen is 30 cubic meters = 30,000L then it contains 1,363mol of gas. Adding 3mol of CO₂ would roughly be adding 3/1,366 = 2200ppm CO₂ to the room. So it's easy to see how cooking with gas can markedly raise CO₂ levels throughout a house!

(Notes: For comparison, an average human at rest exhales about 11 moles of CO₂/day. Also, as noted in my previous post, a properly ventilated house exchanges air every 4 hours.)

How much water is in the air?

My skin and sinuses don't like dry air, and nothing dries air like heating it: Heat freezing air at 40%RH to room temperature and the relative humidity drops below 10%, which is as dry as deserts at noon!

So when indoor heat comes on in the winter I break out the humidifiers. If my living space has a central air handler I install an automatic humidifier on that. If not I have to manually fill portable humidifiers. Which led me to wonder: How much water does it take to bring the humidity in dry air back up to comfortable levels?

It turns out that the moisture capacity of air is very non-linear with temperature: For example, air at 100°F holds 10 times as much water as freezing air!

Thanks to data here we can see that air at room temperature (20°C/68°F) holds up to 17g of water per cubic meter. So a 1000ft² living space with 9-foot ceilings holds just over 4kg, or 1 gallon of water, at 100%RH.

Humidity in living spaces should be kept below 50%RH because mold really thrives above that level. So when outdoor air is below freezing we need to add half a gallon of water to the heated indoor air of my hypothetical 1000ft² living space. But healthy living spaces also exchange fresh air – ASHRAE recommends eight air changes per day – so if that living space is properly ventilated then we will have to add four gallons of water per day!

The Bubbly, Runaway Cost of Bitcoin

In my last post I described in microeconomic terms why the prices of popular cryptocurrencies are likely inflated. I glossed over the nuances of different cryptocurrencies, even though I referenced a price history of Bitcoin ("BTC"), which is presently the largest. But not all cryptocurrencies are the same: Some are pegged to assets, and some like BTC have a floating value. The runaway price of BTC in particular has led to some unintended consequences that confirm the hypothesis that it is in a speculative bubble.

The real effect of increasing a floating cryptocurrency’s price is to attract more distributed computing power – a.k.a. “miners” – to its blockchain. At present there are two kinds of blockchains: “Proof of Work” (PoW) and “Proof of Stake” (PoS). A PoW currency is provably secure so long as no single organization can acquire more than half of the miners. PoW is elegant in theory. BTC is essentially a PoW blockchain that happens to pay miners in its associated currency. What seemed good in a whitepaper has turned out to be an inefficient mechanism for regulating the mining power used by the blockchain. It wasn’t until the past few years that we discovered how far unthrottled PoW could spin out of control.

Can a cryptocurrency waste computing power? BTC evangelists argue that there’s no such thing as too many miners: More miners means more security. That’s sort of true, but at some point it loses meaning because hijacking the blockchain requires a single entity to run more computing power than all of the other miners combined – and likely to continuously fend off the counterattacks of all of the blockchain stakeholders. And how much computing power are we talking about? In 2017, when the price of BTC surpassed $1,000, the cost of electricity required to mine one dollar of BTC exceeded the cost of mining precious metals. And here’s the problem: The resources devoted to mining grow linearly with the price of BTC. Double the price of BTC and miners will profitably spend roughly twice as much working its blockchain. When BTC traded over $25,000 it was estimated that the energy devoted to running its blockchain exceeded the energy used by many developed countries. The demand for mining hardware has created such shortages of GPUs that NVidia tried more than once to cripple its high-end graphics cards so that they couldn’t be used for mining. With BTC trading over $50,000, miners are burning on the order of $50MM per day working its blockchain.

What is the right level of mining to secure a blockchain? No matter the answer, it’s almost certain that BTC is exceeding that level: Nobody is bidding up the price of BTC because they think, “I need to pay more to ensure the BTC blockchain is secure!” On the contrary, it is speculation in BTC that is driving the resources devoted to mining. BTC bulls argue that the increase in mining (and hence security) is increasing the value of BTC. So who’s to say BTC mining is “too high?” The BTC specification itself gives us this result: Presently BTC miners are paid with a combination of transaction fees and new BTC. By design, the creation of new BTC is limited and will phase out, so transaction fees are what will sustain the blockchain in the long run. In the short run, with BTC priced over $50,000 the new BTC created by mining pays miners more than 10 times as much as does the transaction fee. But this source of compensation will go away! Transaction fees alone will determine the long-term level of mining. Will BTC users pay $50MM or more per day in fees to miners? If not then the current level of mining is higher than necessary to secure the blockchain.

Bitcoin "investors" are not buying BTC at this price with the goal of increasing the amount of mining. Rather, miners are devoting these excessive levels of resources to mining because BTC is presently priced so high. Nobody has calibrated the BTC price to the cost of work, and in the long run there is no necessary relationship between the two because mining will not be compensated with BTC. This fits the definition of a bubble. It could be a bubble in consumption of mining power, a bubble in the price of BTC, or both.

On Bubbles: Cryptocurrency

Cryptocurrencies are experiencing a bubble reminiscent of the 17th-century Dutch Tulip mania. Here is a log-scale chart of the U.S. Dollar price of Bitcoin (presently the largest cryptocurrency) from 2012 to the present, showing a roughly 200% annualized increase in price over that period:

Popular cryptocurrencies like Bitcoin and Ethereum are not backed by any real assets. So what drives this appreciation in price?

These pure blockchain cryptocurrencies do have intrinsic value, but that intrinsic value is nothing more than the computing power and infrastructure of their associated blockchains. Any value that people attribute to a cryptocurrency above the value of its blockchain is based solely on the expectation that other people will do likewise. In other words: The cryptocurrency bubble is being driven by the Greater Fool phenomenon.

Demand for a currency can certainly exceed its intrinsic value. Currency is a medium for exchanging value, and there is clearly demand for a decentralized, anonymous, secure means of exchanging value that is satisfied by cryptocurrency. (Blockchains themselves also have value as a service for validating the date and authenticity of data, such as contracts.) But that demand can be satisfied by any cryptocurrency: if the market price of one cryptocurrency inflates significantly above its intrinsic value then people who are buying cryptocurrency in order to exchange value with others (and people paying to place data in a blockchain) can use a currency that is cheaper – i.e., priced closer to its intrinsic value. Therefore the market equilibrium value of any cryptocurrency is limited by the barriers to entry of establishing a new cryptocurrency.

So what are the barriers to creating a new cryptocurrency? A blockchain has no value until it has attracted enough investors with enough of a stake to pay for its maintenance. The "currency" associated with a blockchain gets another bump in value once it is listed on a currency exchange where it can be easily exchanged for other items of value. But these barriers are negligible: Adding another blockchain to the mining marketplace and adding its associated currency to the thousands presently listed on the CoinBase exchange is virtually as easy as thinking up a new name.

If one day all the speculators wake up and decide they don’t value Bitcoin then its value will drop to whatever miners charge for continuing the Bitcoin blockchain. Could this happen? Students of the history of speculative bubbles will see it as a virtual certainty.

Comment on fiat currencies

Some speculators draw a false sense of security from comparing cryptocurrency to fiat currency. Those are not the same: Fiat currencies have value because they are backed by governments. For example, if everyone wakes up tomorrow and decides they don’t value U.S. dollars, dollars are still legal tender for debts. The U.S. government will still demand taxes in dollars, pay interest in dollars, and dispense benefits in dollars. A government's ability to support its currency is not unlimited, but it is still tethered by the government's control of power and resources.

On Bubbles – Part I

Are financial markets in a bubble?

The global economy was running along when out of nowhere a pandemic pushed global markets into unprecedented crisis. Does the following stock market index reflect the impact of the COVID pandemic?

Put in the context of the past decade of market returns, the crash associated with the pandemic is just a blip: Less than a year later the stock market has recovered and resumed its upward trend at an annualized rate of 12% per year.

Stock markets are fundamentally forward-looking: Investors pay for future returns on stocks.  Unexpected losses attributable to one-time events that don't disrupt the long-term profitability of a company shouldn't alter a stock's value or long-term price.  Is the pandemic just a blip in the economic value that these companies can generate?

Is it possible for the world to just take a long vacation and then get back to work like nothing happened?  Before and beginning the pandemic plenty of people thought not.  People who have lost jobs and businesses sure feel like the pandemic turned their financial world upside down.  But governments stepped in with massive financial interventions – e.g., the U.S. CARES Act – and those sorts of one-time loans arguably could smooth over a one-time virtual economic holiday.

Stock markets aren't the same as the economy.  (But they're related.)  Yes, economies overall took major blows.  Some industrial sectors were devastated and probably won't recover.  But others grew enormously.  The pandemic could have catalyzed and accelerated "creative destruction" that was already underway – e.g., telework and virtual retail.  Companies in the decimated sectors are now underrepresented in the market, while those that serve the new economy have had their valuations appropriately boosted.

To be continued...

The Strange Behavior of Closed End Funds (CEFs)

Closed End Funds (CEFs) are entities that invest money and trade on stock exchanges. In contrast to “open-ended” funds (OEFs) like mutual funds and conventional exchange-traded funds (ETFs), CEFs are formed and sold with a fixed pool of initial investment capital. I.e., they are designed to not accept further capital after their IPO, and it is nearly impossible for shareholders to redeem shares by asking the CEF to liquidate holdings and buy the shares back. The advantage of this structure is that a CEF can enter long-term contracts and investments that open-ended funds either should not or cannot, because an open-ended fund has to be able to liquidate its positions whenever investors ask for their money back (i.e., when a shareholder “redeems” shares).

One of the curious results of CEFs being “closed” is that they can trade at values significantly different from their NAV. NAV, or Net Asset Value, is the intrinsic/market value of an investment fund’s assets. If a fund sold everything it owned at the current market price, it could redeem its shares at the NAV. As a result, except during extreme market crises when securities can’t be sold in large quantities, open-ended funds always trade very close to their NAV.

CEFs routinely trade at significant discounts and premiums to their NAV. (When the trading price is below the NAV we say the fund is trading at a discount. When the price is above the NAV we say the fund is trading at a premium.) Trading fluctuations away from NAV are not hard to understand: All securities trade away from their fair market value due to liquidity demands. For example, when an owner wants to sell a large amount of shares he is “demanding liquidity.” If he wants to sell more shares more quickly than the market is prepared to purchase, then he will have to reduce the price he asks for the shares to drum up more buyers. I.e., he sells shares at a discount. (This is the same as when stores put things “on sale” or “clearance:” there are always people looking for a bargain.) Conversely, if someone wants to own more of a security than is for sale at the current price, he will have to offer to buy them at a higher price to entice more people to sell. I.e., he buys shares at a premium. Both of these scenarios are characterized as “liquidity demand,” and they both cause changes in the market price of the stock.

Many stocks also fluctuate in price because investors take different or changing views on the true present value of the underlying company. But in the case of CEFs the true present value is not in dispute: CEFs are just collections of securities, all of which have a public market price. So every day we can look at both the value of what the CEF owns (its NAV) and the price at which the CEF itself is trading. We can also look at the ratio of those two numbers to see the premium or discount the market has assigned to the CEF. For example, here is a chart of the daily price and NAV for a CEF from 2017 to the end of 2019. (EOS is the symbol for the trading price, and XEOSX is the NAV. The charts are from CEFconnect.com.)

From this we can see that sometimes this fund trades at a discount to NAV, and sometimes at a premium. But over this period it almost always traded within 6% of its NAV.

Again, we know that such fluctuations in a stock’s premium and discount can be attributed to liquidity demand.

But there is a phenomenon seen in many CEFs that is very strange: CEFs that trade at persistent and large premiums or discounts. Here is a typical example of a fund that trades at a large and persistent discount (ticker AGD):

Over this six-year period this fund traded at an average discount of more than 10%, and never less than 6%. And there are examples that go the other way. The CEF with ticker RCS trades at a large and persistent premium:

Why would a CEF trade at a large and persistent discount to its NAV over a long period of time? That can’t be explained by liquidity demand. After all, if it were liquidated then shareholders would receive NAV. But in the case of this CEF market participants are always buying and selling the fund’s shares at prices that appear to be significantly less than the present value of the thing they are trading. This shouldn’t happen in an efficient market.

Interactive Brokers vs Fidelity for active trading

For the last two months I have been hand-trading an algorithmic stock strategy in two retail brokerage accounts: One at Interactive Brokers, one at Fidelity.

I didn't anticipate this would be the most exciting two market months since the 2008 Financial Crisis.  But for the purposes of my work the timing was fortuitous: I was able to acquire detailed data and exceptional experience during a live "stress test."  Following are some observations and comparisons of these two online brokers for purposes of trading U.S.-listed stocks:

User Interface (Windows 10): Fidelity offers a platform called Active Trader Pro (ATP).  Interactive Brokers calls its platform Trader Workstation (TWS).  The same functionality is available on both, but for active stock trading I personally prefer the interface of ATP.  (For other securities I suspect TWS would beat ATP hands-down, because Fidelity does not offer access to anywhere near the breadth of markets as does Interactive Brokers.)

Stability: TWS was rock-solid.  ATP suffered one operational failure: On the first day of record-breaking volume in February, during the last ~20 minutes of the regular market, it stopped processing orders and instead returned an ambiguous error message on every attempt.  I discovered I could still manage orders through Fidelity's website, but that is poorly suited to active trading.  Fortunately that was only a one-time hiccup for ATP.

Execution: The positive performance of market orders through Fidelity defies explanation: A significant number of my market orders to buy and are filled at the bid for the stock (and sales filled at the offer).  Otherwise a majority are filled at good prices around the mid of the NBBO.  Fidelity summarizes these "price improvements" for market orders.  I do more limit orders than market orders, and there's no "price improvement" possible on a normal limit order, but even with that dilution I realized an average of 9bp of price improvement across all of my trades at Fidelity.

At Interactive Brokers market orders almost always fill at the NBBO (i.e., you buy at the offer and sell at the bid).  If you are skilled at working hidden orders you might be able to do better, but Interactive Brokers only exposes advanced order types to accounts willing to pay commissions on all trades, and commissions presently run about 3.4bp.

Margin Rates: The interest cost of margin at Fidelity (and most other retail brokers) is absurd: Presently it can run over 8%.  Interactive Brokers is charging no more than 1.55%.

Performance Analysis: Fidelity's historical account and performance analysis has glaring shortcomings.  Want to know your historical daily account value?  Unavailable!  Want to analyze trade history?  Fidelity doesn't show order data, only fills!  Interactive Brokers doesn't exactly make it easy, but if you wade into their Custom Statement tools it is possible to get all the data needed for any performance analysis.

Why Markets Are Efficient ... and what you should do about it

It may seem odd for me to declare that "markets are efficient" given that I have spent my career working (successfully) on investment strategies and businesses that "beat the market."

When I say that markets are efficient, I don't mean that I subscribe without qualification to the Efficient Market Hypothesis. Rather, I mean that the average investor should not expect to beat the market.

Financial markets are in fact riddled with inefficiencies.  But the average investor can't exploit those inefficiencies to make money.

Average (Retail) Investors

Almost everyone is an Average Investor.  For the purposes of an Average Investor markets are efficient.  Average Investors can't expect to pick stocks that will outperform the market on a risk-adjusted basis.  They can't expect to outperform markets by timing when they are in or out.

The key word here is expectation.  Simply due to chance it is certainly the case that a particular stock picker or market timer will get lucky and outperform the market.  But for every lucky pick there is an unlucky pick made by another Average Investor.*  So taken as a whole any particular Average Investor will do no better than the average of all investors.  We have a name for the average of all investors: The Market.

Even most professional money managers, including mutual fund managers and investment advisors, are Average Investors.  This fact is so well documented that it bewilders me that there are still money managers charging disproportionate fees for "active management."

So what should you, as an Average Investor, do?  As I have written before: Know your risk tolerance.  Then buy and hold a diversified portfolio of low-cost market index funds that matches your risk tolerance.  Don't try to beat the market.  Just hope to keep up with it.

* There is a broad perception that it is possible to beat the market because the lucky investors tend to loudly advertise their luck – even delusionally attributing their luck to some repeatable skill – whereas unlucky investors are not so prone to tout their misfortune.  Further confusing the perception is the fact that there are businesses that beat the market, which brings us to the next section.

Specialists and Alpha

So what about those inefficiencies I mentioned earlier?  Who gets to take advantage of those to actually "beat the market?"

In the finance industry we refer to investment returns that "beat the market average" as "alpha."  There are all sorts and sources of alpha.  But especially in modern markets they all have one thing in common: They are not accessible to Average Investors.  It takes work to find and harvest alpha.  Alpha capture is a business.  Sometimes alpha businesses are wildly profitable.  (But so are businesses in every other industry.)  In rare cases an individual may stumble onto an overlooked source of alpha and make a vast fortune from it.  (But so do rare tycoons in every other industry.)  For most of us in the alpha business it takes a lot of work to find alpha and build a business to harvest it.

Many sources of alpha fall under the broad term "arbitrage."  In the financial markets arbitrage is strictly the domain of businesses like hedge funds and bank proprietary trading desks, which can bring to bear substantial resources to access and exploit fleeting and statistical inefficiencies.

In broad strokes: alpha businesses make their money exactly because they remove market inefficiencies.  And this is why Average Investors can't beat the financial markets.  Any more than they can hope to make money buying products on Amazon and reselling them from home.  Anyone who wants to make money as a merchant has to invest real time and money into doing so.  If they make a full-time job of it they might be able to earn a living.  But they will do so picking up the crumbs dropped by huge companies (like Amazon) that have more capital, better market access, and vastly cheaper logistical chains than anyone else

There are two noteworthy exceptions to this generalization:

1. The investor with Special Information.  For example: You may work in healthcare, or construction, or some other industry where occasionally a relatively unknown product or company is coming to market.  If you have special information that is better than what the Average Investor can glean – better even than what the investment bank analysts that cover your industry can see – that some company is going to be a breakout success, and you can buy into that company before everyone else can see that; and if your assessment based on your special information is correct, then you can earn excess returns (i.e., alpha) by investing on that.
2. The investor with Special Access.  There are investment opportunities that are just not accessible to the market overall.  For example, only lawyers can own equity in a law firm.  (And only lawyers that are invited by the firm to do so!)  If legal or regulatory restrictions put a general bar on an investment, but you are exempt from that bar, then you can potentially earn better risk-adjusted returns on that investment than you could in the public financial markets.

Retail Investing

A "retail investor" is anyone who is not a professional investor or money manager.  If you have money that you can afford to leave invested for a time in assets that are more risky than a bank savings account, then you can expect for that money to earn more for you than it would at an FDIC insured bank's risk-free interest rate.

A generation ago market investing and portfolio construction was considered a skilled art best left to professionals.

1. There was an erroneous (and now thoroughly debunked) belief that professional "active" mutual fund managers could deliver better performance than one could get by "passively" tracking the market overall.  Active fund managers still charge annual fees ranging from 1-3% (and even more!).  On average, investors in their funds end up under-performing the associated market by exactly the amount of those fees.
2. The theory behind optimal portfolio construction was not well developed, so most individual investors paid an investment advisor to allocate their money to try to match their risk tolerance and personal financial goals.

Market investing today is easier, more transparent, or more efficient than ever.

1. A number of large investment companies, led by Vanguard,* offer low- or zero-cost "passive" funds that allow investors to assemble a diverse portfolio that matches the returns of market indices.
2. The fundamentals of portfolio construction are also mainstream.  Plenty of companies and websites offer questionnaires and calculators to help individuals find a mix of asset classes that are appropriate for their particular risk tolerance.

Using retail investment tools any individual can, with minimal expense, put together a diverse portfolio of financial securities that performs as well as portfolios compiled by professionals.  

Lamentably, the investment advisory industry has been slow adapt to these changes.  I find many individual investors still paying financial advisors or asset management companies anywhere from .5% to 1.5% per year of investable money to compile an efficient and diversified portfolio.  I disapprove of such businesses for several reasons:

1. Advisory expenses do not significantly increase with the amount of assets under management, so they should not charge a fee that is a function of assets under management.
2. Money managers cannot reliably increase risk-adjusted returns through active allocation, so they should not charge a fee that is a function of assets under management. (You will, of course, continue to see managers who advertise their record of “beating the market.” The problem is that nobody can predict ahead of time which managers will outperform their benchmark. Just because someone did it for ten years doesn’t mean they’ll do it for an eleventh. There is ample evidence that, on average, active managers underperform their benchmarks — by an amount roughly equal to the average they charge in fees. Cut out the middleman and keep the fees for yourself!)

* Why I prefer mutual funds from Vanguard: Vanguard is a true mutual company, meaning that it is owned by its customers.  This means that it faces no conflicts of interest with the investors in its funds.  For example, Vanguard funds have been known to turn away large institutional investors with characteristics that could negatively impact the profit of its existing retail investors.  The eminent professional investor David Swensen, who managed Yale's endowment for a number of years, aptly elaborated:

[T]here’s an irreconcilable conflict in the mutual fund industry between the profit motive and fiduciary responsibility. There are two major organizations, Vanguard and TIAA-CREF, which operate on a not-for-profit basis. That conflict between profit and fiduciary duty disappears. Vanguard and TIAA-CREF are dedicated to serving their investors. They are shining beacons in this otherwise ugly morass.