Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike states that optimal final payo ffs and...

This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded cadlag (right-continuous, left-limited) processes. The Robust No Free Lunch with Vanishing Risk (RNFLVR) condition for simple strategies is equivalent to the...

This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model, for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete. Investment opportunities are driven by, and partially...

A growing literature suggests that even in the absence of any ability to predict returns, holding options on the benchmarks or trading frequently can generate positive alpha. The ratio of alpha to its tracking error appraises a fund's performance. This paper derives the performance-maximizing...

We derive the process followed by trading volume, in a market with finite depth and constant investment opportunities, where a representative investor, with a long horizon and constant relative risk aversion, trades a safe and a risky asset. Trading volume approximately follows a Gaussian,...

A fund manager invests both the fund's assets and own private wealth in separate but potentially correlated risky assets, aiming to maximize expected utility from private wealth in the long run. If relative risk aversion and investment opportunities are constant, we find that the fund's...

Ratios that indicate the statistical significance of a fund's alpha typically appraise its performance. A growing literature suggests that even in the absence of any ability to predict returns, holding options positions on the benchmark assets or trading frequently can significantly enhance...

In this paper we discuss the tractability of stochastic volatility models for pricing and hedging options with the mean-variance hedging approach. We characterize the variance-optimal measure as the solution of an equation between Doleans exponentials; explicit examples include both models...

Leveraged and inverse exchange-traded funds seek daily returns equal to fixed multiples of indexes' returns. Trading costs implied by frequent adjustments of funds' portfolios create a tension between tracking error, reflecting short-term correlation with the index, and excess return, the...

Most institutional investors gain access to commodities through diversified index funds, even though mean-reverting prices and low correlation among commodities returns indicate that two-fund separation does not hold for commodities. In contrast to demand for stocks and bonds, we find that, on...