Long Term Bonds, Risk Neutral Pricing, and How Small Shocks get Magnified

If I knew for certain that the German 10 year bond would trade at a 3% yield in a year, I would be fantastically bullish on Eurozone stocks. Imagine what that world would look like. Because long term bond yields are driven a large amount by inflation expectations, a 3% yield would suggest that inflation is returning to the Eurozone. Aggregate demand would be restored, a European “lost decade” averted.

In short, an unconditional forecast of high long term bond yields should be paired with a conditional forecast of economic strength. This connection between joint forecasts of long term bond yields and economic conditions allows me to apply the theory of risk neutral pricing, and explain why

  1. Term premiums should be in a secular decline
  2. How a temporary oil shock can have such an effect on long term bond yields

In the canonical theory of asset pricing, current prices should be the discounted value of expected future scenarios under the risk neutral measure (See chapter 1 of “Asset Pricing”, for example). What this concretely means is that payoffs in future states that “hurt” a lot get weighted more relative to their true physical probability, and that scenarios that hurt less are down-weighted.

What does it mean to “hurt”? The classic theory is based off of consumption pricing. If the economy is doing poorly, then marginal utilities are high, and therefore any payoffs in these states of the world have magnified effects on utility. If assets do well in these states of the world, they should earn less return because they insure people against the worst in these bad states of the world.

But fund managers set prices, you might say, and they certainly don’t rely on their performance fees for consumption. But even though fund managers don’t “consume” out of their returns, it should be clear that their levered positions, as an aggregate, perform better when the global economy is strong. And if things go too poorly, margin calls and other liquidity stresses can be very costly. Hence fund managers too should be expected to worry more about how assets pay off in bad economic times.

In this model, a risk premium for long term bonds arises when the painful economic scenarios are also scenarios in which interest rates are high. This can happen, for example, if the central bank loses control of inflation and causes interest rates to skyrocket, as in the 1970's in the United States.

But as the thought experiment at the beginning of this post reminds us, these high interest rate states of the world are looking less painful relative to low interest rate states of the world. High rates mean things are getting back to normal. Low rates mean continued stagnation.

Concretely, this is a reason for a secular decline in long term bond yields. Term premia fall because these bonds are even more negatively correlated with bad economic outcomes.

On a closing note, how does this risk neutral pricing explanation interact with the oil price shock? One explanation for the global fall in bond yields is the global fall in oil prices. Lower oil prices, hence lower inflation expectations and hence lower long term bond yields.

I cannot reject this explanation. But the magnitudes don’t seem to make enough sense. If we attribute the 60 basis point drop in the 10 year breakeven since June to oil prices, that implies the 10 year price level is forecasted to be 12 percent lower than what people thought in June.

The value of the risk neutral pricing story is that it can explain why a temporary change in the oil price can have an outsize effect on the 10 year bond yield. If a glut of oil rules out negative supply shocks that drive inflation and long term bond yields higher, then that strengthens the claim that high long term bond yields will be associated with stronger economic conditions. As such factors affecting oil prices today can have large effects on the yield curve.