برآورد نرخ نهایی مورد انتظار از جانشینی: استثمار سیستماتیک از ریسک ویژه

We develop a methodology to estimate the shadow risk free rate or expected intertemporal marginal rate of substitution, “EMRS”. Our technique relies upon exploiting idiosyncratic risk, since theory dictates that idiosyncratic shocks earn the EMRS. We apply our methodology to recent monthly and daily data sets for the New York and Toronto Stock Exchanges. We estimate EMRS with precision and considerable time-series volatility, subject to an identification assumption. Both markets seem to be internally integrated; different assets traded on a given market share the same EMRS. We reject integration between the stock markets, and between stock and money markets.

In this paper, we develop and apply a simple methodology to estimate the shadow risk-free rate or expected intertemporal marginal rate of substitution (hereafter “EMRS”). We do this for two reasons. First, it is of intrinsic interest. Second, when different series for the EMRS are estimated for different markets, comparing these estimates provides a natural test for integration between markets. Our method is novel in that it exploits information in asset-idiosyncratic shocks. While the primary objective of this paper is methodological, we illustrate our technique by applying it to monthly and daily data covering firms from large American and Canadian stock exchanges. Our method delivers EMRS estimates with precision and striking volatility. Estimates from different markets can be distinguished from each other and from the Treasury bill equivalent. Section 2 motivates our measurement by providing a number of macroeconomic applications. We then present our methodology; implementation details are discussed in the following section. Our empirical results are presented in Section 5, while the paper ends with a brief conclusion.

In this paper, we have developed a methodology for estimating the expected intertemporal marginal rate of substitution (EMRS). Our technique relies on exploiting the general fact that idiosyncratic risk, which does not alter any risk premia, should deliver a return equal to the market's expectation of the marginal rate of substitution. This enables us to estimate the expected risk-free rate from equity price data, an object that is intrinsically interesting. Comparing the rates estimated from different markets also provides a natural test for market integration, since integrated markets should share a common expected MRS. We apply our methodology to a decade of monthly data and a year of daily data, including data on stocks traded on the New York and Toronto Stock Exchanges. For both data sets, we find estimates of the expected marginal rate of substitution with reasonable means but time-series volatility which is high enough to be puzzling. We cannot generally reject the hypothesis that markets are internally integrated in the sense that different assets traded on a given market seem to have the same expected marginal rate of substitution. However, we find it easy to reject the hypothesis of equal EMRS across markets. This is both of direct interest, and indicates that our technique has statistical power. Still, we do not wish to claim too much for our technique. When we estimate period constants, they are typically jointly insignificant; accordingly, allowing for them does not substantially alter our results. Including them reduces the precision of the estimates of EMRS substantially, but ruling them out a priori seems implausible. There are many possible ways to extend our work. One could add a covariance model to Eq. (14). A well-specified covariance model should result in more efficient estimates of the EMRS. One could sort stocks into portfolios in some systematic way (e.g., size, industry, or beta), and use portfolios instead of individual equities. Our analysis could be extended to other assets, such as long bonds or commodities. We could imagine more extensive tests for internal and cross-market integration. More or different factors could be added to the first stage regression, Eq. (15). While our use of the View the MathML sourcep˜tj normalization has advantages, others might be used instead. One could test for excess returns that should be possible if EMRS diverges across markets, and if the EMRS is not equal to the T-bill rate. Most importantly, while we have been able to reject the hypothesis of integration in the sense of equal expected marginal rates of substitution across markets, we have not explained the reasons for this finding of apparent market segmentation. If our result stands up to scrutiny, this important task remains.