Portfolio optimisation in the foreign exchange market
Introduction: The mean-variance optimal portfolio performs particularly poorly in practice as a result of measurement error in the expected return vector and the variance-covariance matrix. Indeed it has been shown that a naïve equally weighted portfolio generally yields a superior risk-return trade-off. However, the empirical evidence to date is largely confined to the equity market.
Question: What is the optimal portfolio of currencies? Can one improve upon the mean-variance optimal portfolio?
Framework: Compare the performance of the following portfolios, inter alia, for a sample of foreign exchange rates (perhaps the G10 currencies, or a broader set of currencies including emerging markets, or including commodities)
• The theoretically optimal tangency portfolio based on estimated expected return vector and variance-covariance matrix
• The equally weighted portfolio
• The risk-balanced portfolio (with weights that yield equal risk contributions among the constituent currencies)
• The ‘market’ portfolio with weights proportional to GDP, international trade or some other measure of market size
Supplementary analysis could include incorporating time-varying expected returns and volatility, active portfolios that employ the Black-Litterman framework, and an analysis of currency overlay strategies.
Requirements: Data collection, optimisation and matrix calculations using Excel and VBA.
Introductory reading:
DeMiguel, V. Garlappi, L. and Uppal, R., 2009, “Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?” Review of Financial Studies 22, 1915-1953.
Levy, H., 1981, “Optimal Portfolio of Foreign Currencies with Borrowing and Lending”, Journal of Money, Credit and Banking 13, 325-341.
Foreign exchange risk and firm value (Jane Shen)
There is a large body of literature that measures FX exposure of individual firms and attempts to explain its determinants. It is generally found that a large fraction of multinational corporations have significant FX exposure, which is related to their level of foreign activity. The measured FX exposure tends to be reduced by hedging. Empirical evidence suggests that FX exposure varies considerably over time. The existence of FX exposure presents two questions: first, is FX exposure priced in domestic equity markets? i.e. are investors compensated for investing in firms whose equity returns are correlated with currency changes; secondly, can firms increase their value by hedging FX exposure?
The limits to dynamic mean-variance portfolios (Evarist Stoja)
• Static mean-variance portfolio generates a higher Sharpe ratio relative to the undiversified asset.
• Dynamic mean-variance portfolios generate somewhat higher SR relative to static portfolio. However accounting for transaction costs, the benefits of frequent rebalancing of the portfolio (in terms of performance fees) appear to be only marginally higher than the costs (Fleming et al, 2001,2003, Della Corte et al, 2008) and often smaller than them (De Miguel et al, 2008).
• This leads to the following question:
(a) What is the maximum possible benefit from dynamic portfolio rebalancing?
(b) Why don’t dynamic portfolio rebalancing models achieve this maximum?
• To address this question, focus on two frameworks: statistical and economic along the lines of Harris et al. (2010). Calculate the statistic and economic performance measures using
1. Static portfolio constructed using the VCV matrix from the estimation sample Multivariate GARCH VCV
2. Multivariate EWMA VCV
3. ARMA(p,q) model in realized weights
4. Realized weights constructed with the ex-post realized VCV matrix.
References:
Corte, P. D., L. Sarno, and I. Tsiakas, 2008, “An Economic Evaluation of Empirical Exchange Rate Models,” Review of Financial Studies.
DeMiguel, V. Garlappi, L. and Uppal, R. 2007 “Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?” Review of Financial Studies.
Long run forecasts of the covariance matrix (Evarist Stoja)
• The literature generally suggests that predicting volatility is possible only for short horizons (e.g. West and Cho, 1995; Christoffersen and Diebold, 2000).
• Brand and Jones (2006) find that there is substantial substantial forecastability of volatility as far as one year from the end of the estimation period. However, their approach is computationally challenging which detracts from its usefulness.
• Harris et al. (2011) provide an alternative approach to forecast long run (univariate) volatility which is simpler and performs at least as well as Brand and Jones’ model.
• Question:
(c) Is it possible to extend this framework to the multivariate context?
• To address this question, focus on two frameworks: Harris et al. (2011) and Harris and Yilmaz (2009).
• The performance can be evaluated statistically and economically against the main competing M-GARCH models.
References:
Brandt, M., Jones, C., 2006. ‘Volatility forecasting with range-based EGARCH models’, Journal of Business and Economic Statistics 79, 61–74.
Harris, R.D.F. Stoja, E. and Yilmaz, F. (2011) ‘A Cyclical Model of Exchange Rate Volatility’, Journal of Banking and Finance, 35, 3055-3064.
Harris, R.D.F. and Yilmaz, F. (2009) ‘Estimation of the Conditional Variance-Covariance Matrix of Returns using the Intraday Range’, International Journal of Forecasting.
