ASSET PRICING MODEL: The yield curve 2


The yield curve is most commonly upward sloping, although it may occasionally be hump-shaped or inverted or even have an inverted-hump-shape (see, Campbell et al., 1996, Campbell, 1995, and Stigum, 1990). The substantially higher yield on 6 month- than on 1 month-T bills has been labelled a “term premium puzzle.”20 It is often argued that an upward-sloping yield curve reflects the riskiness of longer maturities. Investors, so the story goes, demand a discount as compensation for price risk (which presumably is correlated with consumption if the standard model applies). This argument is based on an analogy with С АРМ.
It would be worthwhile, though, to provide a precise definition of the notion of “price risk.” CAPM is about the coupon risk of assets. Coupon risk relates to uncertainty about dividends, or, more generally (to encompass uncertainty about preferences and endowments), to uncertainty about the marginal utility of dividends.

Price risk may stem from coupon risk, but it need not. Consider an intertemporal Arrow-Debreu endowment economy (as in Lucas 1978). In this economy, early release of information about future endowments is irrelevant in that it affects neither the real allocation nor the date-0 price of claims on future endowments. On the other hand, release of information affects asset prices, inducing price risk. In an Arrow-Debreu economy, the date-0 price of claims on date-2 endowments can be entirely unrelated to the variance of their date-1 price (or to the covariance of price and some measure of aggregate uncertainty). Price risk per se is not an aggregate risk and thus need not affect asset prices.

Returning to the yield curve, Treasury bonds are basically default-free. Uncertainty about the rate of inflation, however, creates a coupon risk (for nominal bonds), which in turn affects prices. Inflation uncertainty clearly plays an important part in explaining the price risk of long-term bonds. But for short-term bonds the connection is less obvious. A bond that matures in less than a year is quite insensitive to inflation, at least directly. Indirectly, swings in the price of long-term bonds will of course influence short-term prices as long as maturities are partially substitutable. Even so, inflation-induced price risk can hardly explain the term premium puzzle.

Our point is to caution against drawing hasty conclusions about the link between price risk and the slope of the yield curve. A theoretical justification based on the standard CAPM logic cannot be provided, because in a complete market, price risk stemming from early information release will not carry any risk premium. This opens the door for alternative theoretical approaches to analyzing the yield curve. Our liquidity-based asset pricing model offers one possibility.

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