Trade in Risky Assets

The paper develops “a simple but general theory of the determinants of the international pattern of trade in risky assets” (Introduction), observing that while trade theory had extensively studied the pattern of trade in goods, “it seems that there is much less research done on the pattern of trade in explicitly risky assets.” Rather than examining trade equilibria directly (the “direct approach” dominant in contemporary trade and equity-trade literature), Svensson deliberately chooses the older “comparative advantage approach”: first express autarky (no-trade) asset prices in terms of underlying country characteristics, then use the law of comparative advantage to infer the trade pattern from autarky-price differences. He justifies this choice because it lets him “borrow from the general-equilibrium asset-pricing theory developed by Lucas (1978), Breeden (1979), and others” to express autarky prices in a convenient closed form (Section 1).

The theory covers trade in “any arbitrarily specified set of assets, complete or incomplete” (Section 1), where completeness means there are at least as many linearly independent assets as states of the world. Three special cases are carried through the paper: the sure bond, which “pays one unit of the good in each state” (Eq. 2.1a); stocks, defined as claims to home or foreign period-2 output (Eq. 2.1b); and Arrow-Debreu securities, which each pay one unit of the good in exactly one state (Eq. 2.1c). The model does not assume markets are complete – when the state of the world is bivariate normal and the number of assets is finite, the asset market is in fact incomplete “whenever the number of assets is finite” (Section 2).

An asset’s autarky price can always be written as “the present value of the difference between its expected return and its risk measure” (Eq. 4.5): q_j = {E[R_j] − Π_j}/(1+r), where r is the autarky real interest rate (defined from the autarky price of the sure bond, Eq. 4.3) and Π_j ≡ −Cov[U_c(y_2)R_j]/E[U_c(y_2)] is the autarky risk measure, the covariance between the marginal utility of period-2 consumption and the asset’s returns, scaled by expected marginal utility (Eq. 4.4). A positive risk measure means the asset is riskier than the sure bond; a negative risk measure means it is less risky than the sure bond (Section 4b). Differences in r move the autarky price of every asset in the same direction, while differences in Π_j are asset-specific.

The paper’s central formal result is (q − q)·z ≥ 0 (Eq. 3.2): on average the home country imports the assets whose autarky price is higher at home than abroad*, proved (Section 3) from the gains-from-trade theorem exactly as in standard trade theory (Dixit and Norman 1980; Woodland 1982). With only one traded asset this is an exact prediction, but with more than one asset “it does not provide an exact relation for each individual good” – it is a correlation across the vector of assets, not a certainty for any one of them, which is why every substantive claim in the paper is phrased as a “tendency” (Section 3, following Deardorff 1980’s treatment of the same issue for multi-good trade).

A country with relatively more output in period 1 has a lower autarky interest rate and a tendency to be a net lender, exporting goods in period 1 and importing in period 2 – “a standard consumption smoothing result (across countries…not across time)” (Eq. 4.12, Section 4(i)). If period-1 outputs are equal, a sufficient condition for a lower home interest rate is that home period-2 output is first-order stochastically dominated by foreign period-2 output (Eq. 4.14), i.e. home output is on average lower. Under non-increasing absolute risk aversion (so the third derivative of the utility function is positive, Eq. 4.16), a second sufficient condition is that home period-2 output is riskier than foreign output in the second-order-stochastic-dominance sense (Eq. 4.17) – a special case being that home and foreign output have the same mean but home output has higher variance (Eq. 4.18). For risk measures taken asset-by-asset (holding interest rates equal), the paper shows a tendency to import foreign stocks whenever home and foreign period-2 output are “less than perfectly positively correlated” (Eq. 4.24), and to import the Arrow-Debreu security for state s whenever home output in that state is lower than foreign output in that state (Eq. 4.26).

If the home country has a lower rate of time preference (a larger subjective discount factor β), home autarky asset prices are higher for all assets with positive prices, so “there is a tendency for all assets to be imported into the home country, and for the home country to be a net lender” (Eq. 4.27, Section 4(ii)) – this follows directly from the definition of the autarky price (Eq. 4.2), since a more patient country values future-state payoffs more highly in every state.

Because ordinary expected-utility preferences (Eq. 2.2) do not allow risk aversion to be varied independently of intertemporal substitution, the paper switches to Selden’s (1978) “ordinal certainty equivalent” formulation (Eq. 4.28-4.29), under constant absolute risk aversion (Eq. 4.30), so that a country’s risk aversion parameter γ can be changed holding other preferences fixed. Under this formulation, a more risk-averse home country (higher γ) has a lower certainty-equivalent future output and hence a lower autarky interest rate, “contribut[ing] to a tendency for the more risk averse home country to import all assets” (Eq. 4.32-4.34). Holding interest rates equal (by letting discount factors differ), the more risk-averse country has a tendency to import assets whose risk measure is negative – i.e., assets less risky than the sure bond and negatively correlated with period-2 output – and to export stocks, since stocks are positively correlated with output and therefore riskier than the sure bond (Eq. 4.35-4.37, Section 4(iii)).

When countries’ subjective probability distributions over states differ, “it is no longer true that a low autarky interest rate contribute[s] to a tendency for all assets to be imported” – a low home interest rate now only guarantees a tendency to import the sure bond, not other assets, because expected returns themselves differ across countries’ beliefs (Section 4(iv)). The general result is that the home country has a tendency to import an asset “if the home country assigns higher probabilities than the foreign country to the states where the asset pays well” (Eq. 4.44), i.e. where probability-density differences are positively correlated with marginal-utility-weighted returns. For stocks under constant relative risk aversion ρ (Eq. 4.46), the direction flips on whether ρ is above or below 1: with ρ above 1, pessimism or perceived extra riskiness about future output raises the tendency to import stocks (as for the sure bond); with ρ below 1 the opposite holds (Eqs. 4.46-4.48).

The paper stresses that “when asset markets are incomplete, overall capital account deficits or surpluses depend on what assets are available for international trade” (Section 5/Conclusions). For example, if only claims to one country’s own output are tradable, whether that country is a net borrower or lender depends specifically on whose output’s claims are being traded, “since a country has a tendency to export claims to its own output and import claims to other countries’ output.” The paper notes this implies that in a monetary extension of the model with incomplete markets, the currency denomination of available assets would matter for capital flows because of price-level risk.

A central caveat flagged in the conclusion is that the theory, in common with “most of the finance literature,” treats each asset’s gross real returns as an exogenously given vector across states, whereas “most assets…have gross real returns endogenously determined” – equities are claims to profits that depend on endogenous production and price decisions, and even assets with exogenously fixed payoffs in terms of one good have state-contingent “real” returns that depend on endogenous relative prices once there are many goods (Section 5). The paper’s proposed workaround is to take an asset’s equilibrium trade-economy return vector as a fixed hypothetical return, compute what its autarky price would be in each country, and use that hypothetical autarky-price comparison to predict the direction of trade – but this is offered as a methodological fix, not a fully worked-out extension.

The author states plainly that “the analysis has been restricted to a barter model without any money” and that extending it to nominal assets “raises several issues” – in particular that the appropriate real return on a nominal asset depends on price-level risk, which itself depends on the exchange-rate regime and monetary policy, and that the gains-from-trade theorem underlying the whole comparative-advantage argument need not hold if there are domestic distortions in autarky, so “it will be crucial for the analysis how money is modeled” (Section 5). The paper points to companion work – Svensson (1987) on nominal assets and Persson and Svensson (1987) on exchange-rate variability and capital movements – as the natural next steps, and notes the results generalize (with correspondingly weaker, correlation-only predictions) to settings with more than two goods and more than two periods.