Risk Transfer is not a Transfer of Risk

As an actuary risk is my bread and butter. So, I spend a lot of time thinking about it. With a background in philosophy and physics, I try to approach claims critically and realistically.

One of the major ways of discussing actuarial science and insurance contracts involves discussion of “risk transfers.” We use phrases such as “the insurer assumes the risk” or “the insured pays for transferring the risk” and so forth. I am going to dispute the natural reading of those phrases because they are inherently misleading.

Consider a very simple insurance contract, something like property insurance. When the insured purchases the policy he receives a contract containing information about the various claims he has against the insurance company. If his property is damaged or destroyed, he can make a claim and receive certain benefits.

Now the way that we talk is that the insurer is receiving premiums because he assumes the risk. The risk can be given a price and the insurer charges him for taking it off his hands. While this is a typical way that it is explained, it is obviously wrong.

Supposed that the insured’s property is utterly destroyed and he makes a claim. The insurance company after review of the claim writes him a check and settles the contractual obligations.

The first thing to note is that the insured still suffered a real financial loss. His property was really destroyed. This means that he still “possessed” the risk he was insuring. Moreover, if the company was insolvent, the insured may not have even received any benefits in spite of the “risk transfer.”

What is really going on is that the insured owns some property. As the owner there are certain risks associated with maintaining it on his personal balance sheet. Should it be destroyed or damaged that is going to have a financial impact on his net worth. This is the reality of ownership.

When he enters into an insurance contract with another party, the insurer sells him a claim against his balance sheet. This enters on the liability side. The insurer charges him for this claim against the insurer’s assets, similar to how you might charge someone to rent your house. The insured has a claim to make use of the insurer’s assets under certain contingent circumstances.

Now, there are risks associated with this insurance contracts for the insurer. He may end up having to pay out a claim, when he would prefer to maintain his capital. However, this risk is not identical to or coextensive with the risk that the owner of the insured property possesses.

There is no transfer of risk in an insurance agreement. There is a risky circumstance which if realized allows a claim to be initiated against the insurer. Insurance is fundamentally about selling a claim against the insurer’s assets that produces an obligation for him to pay the claimant under certain circumstances.

Bitcoin’s Chinese Room

Cross-posted here

In 1980 John Searle proposed a thought experiment in the realm of computer science concerning artificial intelligence. He asked people to consider a man in a closed room with an opening for papers coming in and another for papers going out. The papers he would receive were in Chinese and he was not able to read Chinese but had a well-defined rule book for translating the Chinese inputs into outputs. The thought experiment was meant to show that a computer could follow clearly defined rules for translating inputs into outputs without actually understanding anything about the meaning of the inputs or outputs, something Searle took as a property of a real mind. I would like to propose a similar thought experiment, but this time in the realm of finance and economics concerning Bitcoins.

Consider a large group of accountants in a closed room. Each accountant has a copy of the same ledger. This ledger is used to track the ownership and exchange of a set of assets. These assets are located in a secure room to which no one has access.

At random an accountant will receive an anonymous phone call proposing a transaction of the secured assets. The accountant will verify that the proposed transaction is legitimate by a clearly defined set of rules and if it is legitimate, he will enter it on his ledger. He then proposes the update to the other accountants and once 51% agree that the transaction is valid, they all enter it into their copy of the ledger. Those outside the room have a read access to the agreed version of the ledger. This process goes on and on.

Now consider that the assets in the secured room are destroyed. However, since no one has access to the room, no one knows that the assets no longer exist. Consequently, the accountants continue to receive calls, update their ledgers, verify transaction and share the agreed version with the outside. At this point there is no property being exchanged. There is nothing of value be transacted between the parties making phone calls. All that is happening is that units of account or numbers on the ledger are being moved between accounts. The ledger is now a closed system that references nothing outside of itself. The efforts of the accountant have become a waste of time and resources.

Next, consider the same situation except that there is no secure room of assets at the start. There are only the accountants receiving calls and updating the ledgers. With each call an agreed upon amount is added to a relevant account and thus the accounts continue to grow over time to an agreed limit. However, as with the situation above after the assets were destroyed, there is no property, nothing being exchanged. There are simply units of account being moved and added to the ledger. Again the ledger is a closed system referencing no real property.

Finally, turn to Bitcoin. A Bitcoin is called the “unspent output of transactions.” It is what is left over after transactions take place plus the little extra that a miner receives from solving the cryptographic puzzle. The Bitcoin is the unit of account on this distributed ledger. However, as with the above examples, the entries on the ledger reference no real assets and no real property is being exchanged in a transaction. The Bitcoin blockchain as a distributed ledger is a closed system that references no real property as in the situations above.

As in the case of Searle where there is no real understanding simply because there is a well-defined formalism for translating inputs into outputs, there is no real value or exchange of property simply because there is a well-defined formalism for securely updating a ledger.

Musing: No Arbitrage Theorem

No Arbitrage and Linear Algebra

The No Arbitrage Theorem is extremely simply, but there is the hint of something from linear algebra in it. I suspect that the conditions state in the theorem come from theorems in linear algebra for sets of equations that take the form defined.

I suspect in terms of linear algebra the existence of the positive vector ψ guarantees the existence and uniqueness of the asset price vector. This seems like it is nothing special about finance in particular, but is a theorem of linear algebra that we can put the financial situation into.

No Arbitrage and Reality

It seems like the No Arbitrage Theorem must be wrong and perhaps it is never correct. The theorem holds that there is a unique price for every asset given all of the possible future states of payoffs of those assets. However, the price is driven, more or less, by subjective valuations which may be more or less objective.

There are also manifestly arbitrage opportunities in reality. So then, what is the usefulness of a theorem that is mathematical, but not real? So far, it appears that it is practical, even if it is not reflective of reality.

As a matter of modeling, it is only useful as a way of determining approximations of asset prices. We are not trying to determine fundamental mechanisms driving these forces as we might in physics, but we are attempting to determine a way to arrive at a reasonable guess. This seems a bit of Ptolemy, but it works to the desired approximation even if we need to add another epicycle later on.