Understanding Carry Trade Risks using Bayesian Methods: A Comparison with Other Portfolio Risks from Currency, Commodity and Stock Markets
Faculty Advisor: Michael Johannes
The purpose of this dissertation is to understand the risks embedded in Carry Trades. For this, we use a broad range of stochastic volatility (SV) models, estimate them using Bayesian techniques via Markov chain Monte Carlo methods, and analyze various risk measures using these estimation results. Many researchers have tried to explain the risk factors deriving Carry returns with standard risk models (factor models, Sharp ratios etc.). However, the high negative conditional skewness of Carry Trades hints the existence of jumps and shows that they have non normal returns, suggesting looking only at first two moments such as sharp ratios or using standard risk models are not enough to understand their risks. Therefore, we investigate Carry risks by delving into its SV and jump components and separate out their effects for a more thorough analysis. We also compare these results with other market portfolios (S&P 500, Fama HML, Momentum, Gold, AUD/USD, Euro/USD, USD/JPY, DXY, Long Rate Carry and Delta Short Rate Carry) to be able to judge the riskiness of Carry relative to other investment alternatives.
We then introduce a new model diagnostic method, which overcomes the flaws of the previous methods used in the literature. This is important since model selection is a central question in SV literature, and although various methods were suggested earlier, they do not provide a reliable measure of fit. Using this new diagnostic method, we select the best-fitted SV model for each portfolio and use their estimation results to carry out the risk analysis. We find that the extremes of volatility, direct negative impact of volatilities on returns, percent of overall risk due to jumps considering both returns and vols, and negative skewness are all more pronounced for Carry Trades than for other portfolios. This shows that Carry risks are more complicated than other portfolios. Hence, we are able to remove a layer from the Carry risks by analyzing its jump and SV components in more depth.
We also present the rolling correlations of these portfolio returns, vols, and jumps to understand if they co-move and how these co-movements change over time. We find that despite being dollar-neutral, Carry is still prone to dollar risk. DXY-S&P appear to be negatively correlated after 2003, when dollar becomes a safe-haven investment. S&P-AUD are very positively correlated since both are risky assets, except during currency specific events such as central bank interventions. MOM becomes negatively correlated with Carry during crisis and recovery periods since MOM yields positive returns in crisis and its returns plunge in recovery. Carry-Gold are mostly positively correlated, which might be used to form more enhanced trading and hedging strategies. Carry-S&P are mostly very positively correlated, and their jump probability correlations peak during big financial events. Delta Carry, on the other hand, distinguishes from other portfolios as a possible hedging instrument. It is not prominently correlated to any of the portfolios. These correlations motivate us to search for common factors deriving the 11 portfolios under consideration. We find through the Principal Component Analysis that there are four main components to explain their returns and two main components to explain their vols. Moreover, the first component in volatility is the common factor deriving all risky asset vols, explaining 75% of the total variance.
To model this dynamic relationship between these portfolios, we estimate a multivariate normal Markov switching (MS) model using them. Then we develop a dynamic trading strategy, in which we use the MS model estimation results as input to the mean-variance optimization to find the optimal portfolio weights to invest in at each period. This trading strategy is able to dynamically diversify between the portfolios, and having a sharp ratio of 1.25, it performs much better than the input and benchmark portfolios. Finally, MS results indicate that Delta Carry has the lowest variance and positive expected return in both states of the MS model. This supports our findings from risk analysis that Delta Carry performs well during volatile periods, and vol elevations have a direct positive impact on its returns.