We provide the first systematic study of liquidity in the foreign exchange market.
We find significant variation in liquidity across exchange rates, substantial
illiquidity costs, and strong commonality in liquidity across currencies and with
equity and bond markets. We analyze the impact of liquidity risk on carry trades,
a popular trading strategy that borrows in low-yielding currencies and invests in
high-yielding currencies. Results show that funding (investment) currencies offer
insurance against (exposure to) liquidity risk. A liquidity risk factor has a strong
impact on carry trade returns from 2007 to 2009, suggesting that liquidity risk
is priced. We present evidence that liquidity spirals may trigger these findings.
Using a novel and comprehensive dataset, we provide the first systematic study of liquidity in the foreign exchange (FX) market. Contrary to common perceptions, we find significant variation in liquidity across exchange rates, substantial costs due to FX illiquidity, and strong commonality in the liquidities of different currencies. We analyze the impact of liquidity risk on the carry trade, which is a popular trading strategy that borrows in low interest rate currencies and invests in high interest rate currencies. We find that low (high) interest rate currencies tend to offer insurance against (exposure to) liquidity risk. A liquidity risk factor has a strong impact on daily carry trade returns from January 2007 to December 2009, suggesting that liquidity risk is priced in currency returns. Finally, we provide evidence that liquidity spirals may trigger these findings.
We present a geometric approach to discrete time multiperiod mean variance portfolio optimization that largely simplifies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decomposed in an orthogonal set of basis strategies, each having a clear economic interpretation. This implies that the corresponding multiperiod mean variance frontiers are spanned by an orthogonal basis of dynamic returns. Specifically, in a k-period model the optimal strategy is a linear combination of a single k-period global minimum second moment strategy and a sequence of k local excess return strategies which expose the dynamic portfolio optimally to each single-period asset excess return. This decomposition is a multi period version of Hansen and Richard (Econometrica (1987)) orthogonal representation of single-period mean variance frontiers and naturally extends the basic economic intuition of the static Markowitz model to the multiperiod context. Using the geometric approach to dynamic mean variance optimization we obtain closed form solutions in the i.i.d. setting for portfolios consisting of both assets and liabilities (AL), each modelled by a distinct state variable. As a special case, the solution of the mean variance problem for the asset only case in Li and Ng (Mathematical Finance 10 (2000)) follows directly and can be represented in terms of simple products of some single period orthogonal returns. We illustrate the usefulness of our geometric representation of multiperiods optimal policies and mean variance frontiers by discussing specific issues related to AL portfolios: The impact of taking liabilities into account on the implied mean variance frontiers, the quantification of the impact of the rebalancing frequency and the determination of the optimal initial funding ratio.
