The social utility of hedging

I have been engaged in a stimulating email conversation with Vivek Oberoi on the social utility of hedging. The hedger is clearly better off by hedging and reducing risk, but Vivek’s question was whether society as a whole can be worse off? I found the discussion quite interesting and thought it worthwhile to widen the conversation by sharing it on this blog. Moreover, it is heartening to see people in the financial industry introspect about the social utility of their industry. Perhaps, this will encourage others in the financial industry to look at their own work more critically.

My position is that hedging has powerful redistributive effects but is socially useful so long as (a) the hedging is carried out in liquid derivative markets and (b) hedgers do not suffer too much from the Endowment Effect. Vivek of course is not convinced. Anyway here is the conversation so far

Vivek Oberoi writes:

If I buy tickets to travel for my vacation in December today, I am indifferent to any subsequent change in the price of oil. To be able to sell me the ticket forward, a risk averse airline will hedge their fuel for the sale. It too is now indifferent to the price of oil. The airline and I have made allocational choices based on forward price of oil today. If oil price on the day of the flight is different from what it is today, there will be an allocational loss. Both the airline and I may be better off (we are risk averse). But there will be dampening of the price signal. That will lead to an allocational loss (negative externality?) to society.

My response:

One key question is whether the forward contracts can be sold to a third party or can be unwound with the original party at market related prices. The ticket cannot, but the oil hedge can. Illiquid derivatives can be harmful for allocative efficiency. For example:

1. You may be willing to accept $500 in return for postponing your vacation by a couple of days
2. Somebody who needs to take that flight due to a personal emergency may be willing to pay $1000 premium to get on that flight.

The airline and the government would step in and say that you cannot do the trade. The wrong person gets on the plane and the outcome is inefficient.

But if you were allowed to do the trade then the Coase Theorem implies that allocative efficiency is achieved regardless of the initial allocation of property rights. In other words, it does not matter whether you owned the ticket or the other person owned the ticket in the beginning; after the bargaining and trading, the right person will get on the plane. The initial ownership will only determine who is richer/poorer at the end of the trade. The Coase Theorem requires low transaction costs which would be the case in liquid futures markets and in liquid OTC markets, but not in highly customized and illiquid bilateral forward contracts.

Behavioural finance will of course have a different take on this. The Endowment Effect could imply a loss of allocative efficiency due to derivative contracts. In the corporate context, you need some takeover threats from asset strippers (who would monetize the fuel hedges and then shut down the airline) to prevent the loss of allocative efficiency caused by managers suffering from the Endowment Effect.

Vivek Oberoi continues:

Imagine a risk-averse consumer of oil. He needs 1 unit of oil to drive to office. The price of oil is USD 100/unit. The consumer has USD 100. If the price of oil goes up to, say 150, he will have to take public transport. To keep things simple, assume the public transport ticket will cost 100. If the price goes down to 50 he will use the money saved to see a movie. The consumer is risk-averse. He dislikes the thought of using public transport more than the enjoyment of seeing a movie.

At time t0 the consumer gets into a fixed price contract for the purchase of 1 unit of oil at time t1. Assume oil prices spike to USD 150/bbl. Now the customer has a choice. He can either use the oil to drive to work. Or he can sell the oil for USD 150/unit. Use USD 100 of that for public transport and the remaining USD 50 for the movie. The essence of risk-aversion is that the combination of using public transport and seeing the movie will not be as good as driving to work.

My response:

I would interpret the situation a little differently. First of all, we can avoid expected values and risk aversion by just focusing on the case where the price of oil is 150. We must still take into account the non linearity (concavity) of the utility function which is what leads to risk aversion, but we can avoid probabilities and expectations.

In the $150 price scenario, the choices of the hedger are

1. Spending $100 to drive to work and
2. Spending $50 (net) to take the train leaving $50 surplus for the movie ticket.

The person who did not hedge also has two choices:

1. Spending $150 to drive to work
2. Spending $100 to take the train.

What is the difference? It is as if the hedger won a lottery ticket with a prize of $50. That is all. For the hedger, the car and the train are both cheaper by $50, but the relative cost of car versus train is the same for both hedger and non hedger (150-100=100-50=50).

You are right in saying that at the higher level of wealth induced by winning the lottery ticket, the consumer may be willing to pay $150 to drive to work and so he will not sell the forward contract while at the lower level of wealth, he would take the train. That is the result of the concavity of the utility function (risk aversion). Yet, allocative efficiency is achieved in both cases. The hedger taking the car is not allocative inefficiency – it is simply the redistributive effect of the lottery ticket. Exactly as the Coase theorem would say, the initial allocation of property rights (whether or not there is a forward contract) gives rise to windfall gains and losses (lottery prizes), but there is no loss of allocative efficiency.

Vivek Oberoi continues:

A similar case can be built for a risk-averse producer. Imagine a USD 50/unit drop in oil price will lead to a shutdown of his fields. He hedges to avoid that eventuality. An outcome in which he gets USD 50 in cash and shuts down his field is worse than him producing 1 unit.

My response:

Absolutely correct. The consumer wants to buy a lottery ticket that gives a $50 prize when oil is at $150. The producer wants to buy a lottery ticket that gives a $50 prize when oil is at $50. Each is willing to sell the lottery ticket that the other wants in order to pay for the lottery ticket that he wants. Risk aversion (concave utility functions) is what makes this trade possible. More generally, one party is a put buyer and the other is a call buyer. The combination of these two lotteries (options) is a forward contract. Again the Coase theorem says that the trade that they agree to do is allocatively efficient.

Your arguments do of course bring out some counter intuitive aspects of derivative markets:

• Not all hedgers who cancel their hedges opportunistically are evil. In fact, this behaviour is sometimes necessary to preserve allocative efficiency.
• Not all asset stripping corporate raiders are evil. Sometimes they are necessary to overcome the Endowment Effect and restore allocative efficiency by monetizing derivatives and real options.

Vivek Oberoi responds to my response:

1. As you say, the redistributive effect of the lottery and the concavity of utility function ensures that the consumer of oil drives to work. That decision is allocationally inefficient. The consumer has no incentive to reduce his consumption of oil by taking public transport when the price of oil goes up to USD 150/bbl. Similarly the producer has no incentive (and no surplus funds with which) to increase his production of oil. The price signal is being damped.
2. This transaction results in a net welfare gain for both the consumer and the producer. They are risk averse after all. But for society (i.e everyone besides the two principals) as a whole there is a welfare loss (negative externality). The price at which the derivative contract was struck and the ultimate price of oil are contractually unarbitragable. This reverses the gains from trade. The economic effect of the transaction *on society* is identical to that of price fixing by a government.

My response to his response to my response:

I do not agree that there is any inefficiency for the following reasons:

• Because the demand of the hedgers has become inelastic, the price of oil will rise more than it otherwise would. For example, with no hedging oil may go to say 120 to force everybody to cut consumption by 10%. With hedging suppose half the consumers do not cut consumption at all. Then oil may rise to 150 to force the remaining half of the consumers to cut consumption by 20% so that demand still equals supply. The cost of adjusting to a shortage of oil has been shifted from one set of consumers to another set. This is redistribution and not inefficiency.
• Probably the oil field got developed only because of hedging. If there is a risk that oil may go to $50, the oil company may be reluctant to invest in the wells and pipelines and so on.
• This illustrates why hedging is needed: decisions today depend on the oil price five years from now. Futures markets lead to efficient outcomes in this case. Similar issue arises with the consumer's decision to buy a car – the risk that oil may go to $150 may make him reluctant to buy the car in the first place.
• You are focusing on the price signal from the spot markets. The more powerful price signals come from the futures market. This signal drives oil exploration, purchase of cars, power plants and so on. The long run supply and demand responses are much stronger because of the futures markets.

I think you are underestimating the power of the Coase theorem when markets are deep and liquid.

Posted at 6:09 pm IST on Wed, 11 Apr 2012         permanent link

Categories: derivatives, risk management

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