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Abstract: More than two decades ago, James Tobin suggested imposing a tax on all foreign exchange transactions (Tobin, 1978). Similar proposals for imposing transaction tax on trading of other securities (see Schwert and Seguin, 1993 for a review) are also often made by eminent economists (Stiglitz, 1989, Summers and Summers, 1989). One of the putative benefits of a transaction tax is that this may decrease the volatility of prices. The intuitive rationale behind this, believed to be first articulated by Keynes in 1936, is that a transaction tax would hurt the speculators disproportionately more because they tend to trade much more frequently. An implicit assumption in this argument is that speculative trading is on average destabilizing which in turn causes prices to be more volatile. A contrasting view is offered by Milton Friedman who argued (Friedman, 1953) that rational speculators may in fact help stabilize prices. The relative merits of these opposing views can only be judged by analyzing this issue empirically. The empirical evidence on the effect of transactions taxes on volatility of prices is rare. Umlauf (1993), using Swedish stock market data from the 1980s, shows that the introduction of, or an increase in Swedish tax, led to an increase in volatility of stock prices; Jones and Seguin (1997) show that the reduction in the commission portion of the transactions costs in 1975 led to a decrease in volatility (and increase in volume) of stock prices. However, there appears to be no empirical evidence in the extant literature on the effect of a transaction tax in the foreign exchange market on the volatility of exchange rates. In this paper, we provide some evidence. Our results, suggest that a Tobin tax on foreign exchange transactions may, in fact, lead to an increase in the volatility of exchange rates which is exactly the opposite to the claim made by Tobin and proponents of his suggestion such as Jeffrey Frankel who recently resurrected Tobin's argument (see Frankel, 1996). We estimate the effective transactions costs in the foreign exchange market for the period 1977 to 1999 using foreign currency futures data. Our approach in estimating the transactions costs in the foreign exchange market makes a contribution in two ways. First, we show that previous approaches for estimating the transactions costs in the foreign exchange market (Frenkel and Levich, 1975, 1977, 1979 and McCormick, 1979) had some methodological problems arising from the incorrect use of bid and ask price data and from the use of non-synchronous data in the spot and forward markets. Second, we measure transactions costs faced by the marginal investors that set prices in the foreign exchange markets which is unlike the previous approaches which, if implemented correctly, would measure transactions costs in foreign exchange market that are faced by commercial customers of banks. While the estimates of transactions costs useful for judgements about the impacts of alternative exchange rate regimes on the levels of trade, might be those incurred by commercial firms, the estimates of cost relevant for determining prices, in contrast, are the smaller costs incurred by large commercial banks who are likely to be marginal investors determining prices in the foreign exchange market. We estimate that transactions costs over the last two decades on average were no more than one-twentieth of one percent, and in the last decade may have fallen to as low as one-fiftieth of one percent. We then, using our approach, construct time series of monthly estimates of effective transactions costs for four currencies, the British Pound, the Deutsche Mark, the Japanese Yen and the Swiss Franc. We also construct time series of monthly volatility (i.e., standard deviation) of foreign currency futures returns and monthly volume (i.e., number of futures contracts traded) for the four currencies. Using regression analysis, we document that volatility is positively associated with the level of transactions costs and that volume is negatively associated with the level of transactions costs. Thus our results are consistent with the notion that an increase in transactions costs does indeed lead to a reduction in volume of trading as one might expect, but its effect on volatility is exactly opposite of what proponents of Tobin tax would have liked to see.
Abstract: We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex-ante risk assessed by investors. We find that both components of risk vary substantially over time, are quite persistent, and correlate with each other and with the stock index. Using a simple general equilibrium model with a representative investor, we translate the filtered measures of ex-ante risk into an ex-ante risk premium. We find that the average premium that compensates the investor for the risks implicit in option prices, 10.1 percent, is about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex-ante equity premium that we uncover is highly volatile, with values between 2 and 32 percent. The component of the premium that corresponds to the jump risk varies between 0 and 12 percent.
Abstract: In this paper, we propose a unifying class of affine-quadratic term structure models (AQTSMs) in the general jump-diffusion framework. Extending existing term structure models, the AQTSMs incorporate random jumps of stochastic intensity in the short rate process. Using information from the Treasury futures market, we propose a GMM approach for the estimation of the risk-neutral process. A distinguishing feature of the approach is that the time series estimates of stochastic volatility and jump intensity are obtained, together with model parameter estimates. Our empirical results suggest that stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a stochastic jump intensity process that is negatively correlated with interest rate changes. Overall, negative jumps tend to have a larger size than positive ones. Our empirical results also suggest that, at monthly frequency, while stochastic volatility has certain predictive power of inflation, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with informational shocks in the financial market.
Term Structure, Affine, Quadratic, Jumps, GMM
Abstract: The issue of estimation risk is of particular interest to the decision-making processes of portfolio managers who use long-short investment strategies. Accordingly, our paper explores the question of whether a VaR constraint reduces estimation risk when short sales are allowed. We find that such a constraint notably decreases errors in estimates of the expected return, standard deviation, and VaR of optimal portfolios. Furthermore, optimal portfolios in the presence of the constraint are substantially closer to the 'true' efficient frontier than those in its absence. Finally, we provide VaR bounds and confidence levels for the constraint that lead to the best out-of-sample performance.
Estimation Risk, Portfolio Selection, Short Sales, VaR, Risk Management
Abstract: We examine the impact of adding either a VaR or a CVaR constraint to the mean-variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bound. Second, portfolios on the CVaR-constrained boundary exhibit (K 3)-fund separation, where K is the number of states for which the portfolios suffer losses equal to their VaRs. Third, an example illustrates that while the VaR of the CVaR-constrained optimal portfolio is close to that of the VaR-constrained optimal portfolio, the CVaR of the former is notably smaller than that of the latter. This result suggests that a CVaR constraint is more effective than a VaR constraint to curtail large losses in the mean-variance model.
Value-at-risk, Conditional value-at-risk, Portfolio selection, Discrete distributions
Abstract: Existing literature reports an empirical puzzle about the foreign exchange forward premium, the spread between the forward rate and the concurrently-observed spot exchange rate. The premium is often negatively correlated with subsequent changes in the spot rate. This defies economic intuition and possibly violates market efficiency. Various explanations have been offered, ranging from non-stationary risk premia through econometric mis-specifications. Some researchers have accepted the puzzle as a fact of inefficient foreign exchange markets, a phenomenon that provides profitable trading opportunities. We suggest there is really no puzzle at all. The simplest conceivable model adequately fits the data; forward exchange rates are unbiased predictors of subsequent spot rates. The puzzle has arisen because (a) the forward rate, the spot rate, and the forward premium all follow non-stationary (or nearly so) time series processes, and (b) the forward rate is a noisy predictor. We document these features with an extended sample and show how they can give the delusion of a puzzle.
Foreign Exchange, Anomalies, Non-stationary Time Series
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