According to the expectations hypothesis, a building block of the efficient market hypothesis, forward interest rates should reflect expectations of future spot rates. However, forward rates have on average been higher than realised spot interest rates. There are two possible explanations for this longstanding empirical puzzle. Is the efficient market hypothesis failing in the bond market or are the risk-neutral probabilities weighted more heavily whenever the spot interest rates are relatively higher? The early literature emphasised the importance of liquidity on the term structure of interest rates. Hicks (1946) suggested that risk-averse investors would prefer to hold short rather than long-term bonds because of the price risk they bear in the intermediate dates. Thus, they would request a liquidity premium for holding longer term debt that, in turn, would introduce an upward slope to the yield curve. The same argument was put forward by Lutz (1940) who claimed that longer term securities are relatively less liquid than short-term ones. Finally, Modigliani and Sutch (1966) proposed the preferred habitat hypothesis, arguing that agents prefer to trade bonds to match their asset and liability maturities. Hence, the markets for long-term and short-term bonds would be segmented, and consequently the link between long and short-term interest rates would break down.
According to the expectations hypothesis, a building block of the efficient market hypothesis, forward interest rates should reflect expectations of future spot rates. However, forward rates have on average been higher than realised spot interest rates. There are two possible explanations for this longstanding empirical puzzle. Is the efficient market hypothesis failing in the bond market or are the risk-neutral probabilities weighted more heavily whenever the spot interest rates are relatively higher? The early literature emphasised the importance of liquidity on the term structure of interest rates. Hicks (1946) suggested that risk-averse investors would prefer to hold short rather than long-term bonds because of the price risk they bear in the intermediate dates. Thus, they would request a liquidity premium for holding longer term debt that, in turn, would introduce an upward slope to the yield curve. The same argument was put forward by Lutz (1940) who claimed that longer term securities are relatively less liquid than short-term ones. Finally, Modigliani and Sutch (1966) proposed the preferred habitat hypothesis, arguing that agents prefer to trade bonds to match their asset and liability maturities. Hence, the markets for long-term and short-term bonds would be segmented, and consequently the link between long and short-term interest rates would break down.
In the present paper, we argue that aggregate consumption risk is not the only source of risk-premia in asset prices. An additional risk-premium exists because of the effect of financing costs. Financing costs generate a “wedge” between selling and buying prices and therefore affect marginal utilities and consequently equilibrium prices. Unlike what happens in a representative agent model, this premium exists even in absence of aggregate uncertainty (i.e., when endowments and aggregate consumption are constant), whenever the volume of trade is positive.
model, with cash-in-advance constraints built along the lines of Dubey and Geanakoplos (1992, 2003, 2006), Geanakoplos and Tsomocos (2002), Good hart et al. (2006) and Tsomocos (2003, 2007). We need a general equilibrium model because we want to endogenise all demands for money in order to construct the risk-neutral probabilities and the yield curve. Given the existence of outside money, which produces positive interest rates, these models generate demand for liquidity and locally unique positive nominal interest rates. We price nominal Arrow-Debreu securities (AD securities). The assumption of complete markets is needed here because we want to solve for all AD securities’ prices. If the prices of AD securities were constant through all states of nature, then the historical average of spot interest rates that would proxy rational expectations without a risk-premium Et[rt,t+s] would be equal to the expected interest rate Eˆ?[rt,t+s] using risk-neutral probabilities ˆ?. However, we will show that this is not the case in our model, even when there is no real uncertainty.
The main result of the paper is that, provided that agents’ relative risk aversion is greater than one, states with higher interest rates (lower liquidity supplied by the Central Bank) have higher state prices. The model goes beyond representative agent models in several ways. First, we model trade activity so that it is endogenous - in fact, trade activity is determined by liquidity. Recall that representative agent models can be thought of as “sell all’ models thereby determining trade a priori. These models have been extended, adding money in a cash-in-advance framework (Lucas and Stokey, 1983 and 1987), but money plays a role only through income and expectations, not through trade. Second, because in our model trade is constrained by liquidity, security prices - and in particular bond prices - are determined by liquidity as well. Thus, we are able to calculate explicitly the “liquidity premium”. Finally, even when aggregate endowment and consumption are constant across all states, equilibrium prices manifest a risk-premium. However, the necessary conditions for its existence are, in that case, a positive volume of trade and financing costs.
The lesson of the model is that uncertainty in aggregate production, or in aggregate consumption, is only one part of uncertainty in agents’ marginal utilities. Bansal and Coleman II (1996) produce a representative agent general equilibrium model with transaction costs that capture partly their effect on bond prices. However, in their model, trade is forced, since the representative agent sells all of his endowment and subsequently buys it back, and, in addition, the transaction technology is exogenously specified. In particular, transaction services are generated only from bond holdings and not from asset holdings. Therefore, any model of risk-premium that attempts to proxy welfare solely by production or consumption will underestimate risk-premium. This is especially important for the term structure risk premium since the spot interest rate has both an effect on the asset price and on transaction costs. In that case, the correlation between the marginal utilities and the asset price is likely to be high. Consequently, the error will be an under-estimation of the risk-premium.
Many authors (e.g. Kirman, 1992) have argued that representative agent models are inadequate for welfare analysis ; however, their pricing results are quite robust. According to representative agent models, for any price vector, there exists a representative agent utility that justifies this price vector. But what happens if policy changes the price vector? There is nothing that guarantees that the same representative agent’s utility function is still valid, particularly when the volume of trade is affected by the new price vector (i.e., the classical dichotomy does not hold). The critique hence relies on welfare implications and the impossibility of conducting comparative statics.
Thus, the importance of heterogeneity is sometimes underlined. Fan (2006), for instance, models the time-varying risk premium of the term structure using heterogeneous beliefs. Our paper can be understood as an example of the effects of financing costs on the volume of trade and in turn on prices and allocations. For a given riskless endowment vector, no representative agent model specification would replicate an upward sloping term-structure in our paper. The two-agent general equilibrium model with cash-in-advance constraint that we construct is, on the contrary, able to do so because transaction costs affect marginal utilities, even though they do not affect aggregate consumption.
We model an exchange economy with cash-in-advance constraints where a larger money supply has the effect of only lowering transaction costs and has no other effect on production or endowments. More money supply allows for more efficient trade since transaction costs are lower. The model is derived first with one commodity only, and then extended to multiple commodities, but the intuition is not affected by this extension. In any case, it is intertemporal trade that matters since this is what drive asset prices. The Friedman rule of the optimum quantity of money obtains when the money supply is infinite and, therefore, nominal interest rates are equal to zero. These cash-in-advance models have several drawbacks; in particular the money supply is exogenously given, and the positive value of the interest rate depends on the existence of “outside money” (i.e. agents’ monetary endowments free and clear of any liability), a somewhat controversial assumption. However, the advantage of the cash-in-advance constraint model in our case is that it allows us to incorporate markets for money where money has positive value, even in a finite horizon model. More fundamentally, the cash-in-advance constraint allows money to be non-neutral, although money does not enter agents’ utility function.
Download
Asset Prices in an Exchange Economy with Money and Trade
