Three essays on the efficiency of selected financial markets

Abstract

The aim of this paper is to address risk in carry-based currency portfolios. I take the interest differentials of currencies as the return forecast, assuming that currency movements follow a random walk. The historical volatility serves as basis to forecast the variance. Traditional carry trades tend to be profitable, but contain a high crash risk. The approach presented herein is a mean-variance optimization of a currency portfolio in order to obtain the best return-to-risk ratio. The crash risk can be diver- sified away with a mean-variance optimized portfolio, as mean-variance outperforms an equal weighted 1/n portfolio on a risk-adjusted basis. The diversified carry trade turns out to have been a surprisingly low-risk strategy over the last 20 years, with Sharpe ratios between 0.8 and 1.6 depending on the design of the strategy and the time period. This means the uncovered interest rate parity can be rejected. The results are robust over the investment horizon, the currency universe, and the opti- mization methodology. The failure of uncovered interest rate parity to explain short-term exchange rate movements is well documented. The return of a long-term bond should be equal to the risk-free rate under the expectation theory of interest rates. Given this theory, the uncovered interest rate parity should be equal for short- and long-term interest rates. However, I will show that the uncovered interest rate parity fails for short- term interest rates but holds for long-term interest rates, even over short horizons. Furthermore, controlling for a time-varying risk of the exchange rate improves the relationship with the long-term interest rates. These ambiguous results are caused by the failure of the expectation theory for the term structure of interest rates, as long-term interest rates are a bad predictor for future short-term interest rates. The significance increased over the last decade, as the liquidity of the exchange rate and the interest rate market increased. The results are robust for interest-rate maturities of between 12 months and 30 years. The first equity futures was launched in 1982 on the S&P 500 Index. The futures market has grown enormously since then, and is more liquid than is the cash market in many countries. The analysis here proves that the futures market is highly effi- cient from many perspectives. Transaction costs in futures are on average one third of those in the cash market. Arbitrage is hardly ever possible. As futures contain information about future dividends, they can be used to analyze the market estima- tion for dividends. Even this proves to be quite efficient, with an exception in 2008, when the market either underestimated the subsequent dividends, or the increased risk aversion caused market values of future dividends that were too low. Withhold- ing taxes caused a split between the futures and the cash markets. For investors who cannot reclaim foreign withholding taxes, it is beneficial for them to invest only in futures, as dividend earnings implied in the futures price are not taxed.