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Streetwise Professor

July 28, 2010

Risk Preferences and Forward Curves

Filed under: Derivatives,Economics,Energy — The Professor @ 3:43 pm

Not long ago I wrote a post about commodity forward curves, focusing on the confusion between “backwardation” as the term is used in the market, and as misused by Keynes, to the confusion of many.  The basic point was that  Keynesian “normal backwardation” stories cannot explain directly observable forward curves.  Normal backwardation is about risk premia–differences between futures prices and expected spot prices–and these risk premia are not observable directly.

For an asset that is always in positive supply, there can be backwardation in the Keynesian sense but the forward curve will always be at full carry.  Arbitrage considerations drive the forward curve, and risk preferences of the marginal speculator affect both spot and futures prices, without affecting the spot-futures spread.  In essence, if the futures price is downward biased, the spot price will be less than the present value of the expected spot price; this price depression causes an appreciation in the spot price that rewards someone holding the asset for the risk, and this upwards drift over and above the risk free rate is exactly the same as the upward drift in the futures price.  Changes in risk preferences affect both spot and futures prices in the same way by the same amount, leaving spreads unchanged.

But commodities are not always in positive net supply.  There are sometimes stockouts.  Indeed, stockouts must occur in an efficient equilibrium, as if not, some units of the commodity would be produced but never consumed, which would be wasteful.

If risk preferences are to affect the forward curve, then, it must be through their effect on stockholding.  I have investigated this using a dynamic structural storage model of the kind that I examine in detail in my forthcoming book.

The technical details in a nutshell:  I utilize a simple model in which there is one random, mean reverting demand shock; that is, the demand shock follows an O-U process.  Production costs are subject to decreasing returns.   I solve the dynamic programming problem giving the optimal storage rule using the standard machinery.

To take risk preferences into account, I take a trick from contingent claim pricing theory.  If the marginal speculator is risk neutral, the forward price is the expected spot price, where expectations are taken with respect to the true (physical) probability measure.  If the demand shock risk is priced, however, due to risk aversion, the forward price is the expected spot price, where the expectations are taken with respect to an equivalent measure.  The demand shock process in the equivalent measure has a “drift” that differs from that of the process under the physical measure.  A negative drift adjustment means that the forward price is downward biased (Keynesian backwardation).  A positive drift adjustment means that the forward price is upward biased.

I solve the dynamic program for the storage problem under three values of the drift: zero, as under the assumed physical measure, plus 5 percent and minus 5 percent.

The results are interesting, and intuitive (I think, anyways).  The drift–and hence risk preferences–have a first order effect on inventories.  With downward bias, inventories are lower than under the physical measure.  Intuitively, downward bias makes it costly to hedge inventories, so inventories are smaller.

I’ve studied the performance of these model economies using long simulations.  Interestingly, even though inventories are smaller in the downward biased economy, the effects on prices are relatively small.  Plots of the spot prices (based on the same sequence of simulated shocks) from the two economies are almost on top of one another, and the average difference in prices across the simulations is about 1 percent.  There is a slight difference in price volatility (about a 5 percent difference).  Volatility is higher in the downward biased economy as demand shock-buffering inventories are smaller in that economy.  Importantly, prices are highly correlated across the two economies.  Demand shocks are the main drivers of price movements in both economies, and for an identical set of demand shocks, price movements are highly correlated.

Spot-forward spreads are affected somewhat.  (I simulate a spot-3 month spread).  Backwardations are more pronounced, and more frequent, in the downward bias economy.  This is because stockouts are more likely in this economy due to the smaller stockholdings.  But overall, the differences in calendar spreads between the two economies are not large (although they are larger than the price differences); the time series plot of the simulated spread for the downward biased economy is a slight displacement of the simulated spread for the risk neutral economy.  Backwardations peak at about the same times in each simulation, and contangoes/full carry periods exhibit large overlaps (though not complete overlaps, because there are times that the downward biased economy exhibits departures from full carry when the risk neutral economy does not).

One key result is that almost never in the simulations does a substantial backwardation exist in the downward biased economy while the risk neutral economy is at full carry.

Results for the upward biased economy are symmetric.  Inventories are larger, price volatility smaller, and prices about the same in the upward biased economy as in the risk neutral one.  Spreads tend to be closer to full carry, and backwardations are not as extreme, although the timing of backwardations is highly coincident in the two economies.

This has implications for the speculation debate.  Changes in market structure that lead to increased integration between a commodity market and the broader financial markets can, in theory, have an impact on the behavior of the commodity market.  In general, if you believe that a commodity market that is, as in the Keynesian treatment, isolated from the broader financial market exhibits “normal backwardation”, then the entry of diversified speculators that results in a dissipation of downward bias will have some effect on prices and spreads, and potentially a big effect on inventories.

The effect on prices and spreads is likely to be very hard to detect.  Even with a relatively big bias like that I assumed in the simulations, the effects on prices and spreads are not large.  Scholars have had a very hard time detecting any risk premium/bias in forward prices going back to the seminal contribution of Telser in 1960.  Certainly, there are no reliable estimates of bias as large as I assumed in my simulations.  This suggests that any effects of increased speculation on price bias/risk premia would be too small to have any effect on prices and spreads that could be identified reliably.

So, I am skeptical that any “financialization” of commodities that has occurred in recent years has had an effect on price levels or forward curves that can be distinguished against the normal noise in prices and spreads.

It should be noted, moreover, that integration of the commodity markets into the broader financial markets leads to consistent pricing of risks across markets.  Indeed, arguably differences in risk prices is a major driver of flows of capital.  If, for instance, a commodity market (say, oil) is not perfectly integrated in the financial system, so the price of oil price risk is higher than the price justified by risk premia on other investment opportunities in the economy, investors have an incentive to take on more oil price risk in order to capture its too high price. This will reduce the bias.

Integrating fragmented markets and equalizing price differences is typically efficiency enhancing.  It leads to a more efficient allocation of risk.  That’s a big part of what capital markets should be about.

In the commodity case, if the isolated commodity market exhibits downward biased forward prices, the entry of speculative capital that reduces this bias makes hedging cheaper, and encourages the holding of larger buffer stocks.  This reduces price volatility.

Phil Verleger has argued that this process has occurred in the energy markets.  That due to greater financialization, inventories are larger.  He points to the specific case of heating oil, and argues that recent stock buildups encouraged by more speculative activity in the market have helped prevent big price spikes during cold snaps.

These conclusions are also diametrically opposed to the scare stories that are repeatedly told about the effects of the entry of financial players into the commodity markets.  People telling those stories–and you know who they are–assume that the good old days when commodities and finance didn’t mix (which was never completely the case) were some sort of golden age, and that the entry of financial players has upset the operation of the market.

The simple model I’ve set out here implies that such entry may indeed change the market, but in a salutary way by leading to a more efficient allocation of risk.  The effects on price levels and spreads are likely small, and certainly not  immense, as the commodity Cassandras have asserted.  The effects on inventories are likely larger, but this effect is salutary, and tends to reduce price disruptions in the market.

The basic moral of the story: be very skeptical about claims that changes in the degree of financial participation in commodity markets have first order effects on prices and spreads.  Don’t try to explain changes in the shape of forward curves based on changes in speculative activity in the markets.  Intertemporal optimization–adjustment of inventories–in response to fundamental shocks is the most important driver of forward curves, and changes in financial participation likely have second or third order effects on prices and spreads.

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