Observations and Speculations (Assignment, Part I)
1. Correlation. All currencies were positively correlated with each other. Correlations varied from approximately +.25 to nearly +.90. The Canadian Dollar consistently correlated least with each other currency. The Deutsche Mark correlated highly with each of the remaining three currencies, and most highly with the Swiss Franc. The universal positive correlation may reflect pricing in US Dollars. Changes in US Dollar value would appear as a correlated movement in all other currencies. The market value of the Canadian Dollar may correlate more closely with the US Dollar than the other five currencies (see Variance, following). If so, the data depict a market world somewhat polarized between US Dollar and Deutsche Mark.
2. Variance. The Canadian Dollar displayed variance roughly an order of magnitude less than the other four currencies. This may reflect affinity with the US Dollar (see Correlation, preceding).
3. Mondays, Thursdays and All Days. The variance of the log of daily return (price change) for Thursdays differed little from the variance for All Days, and it was slightly higher measured for All Days than when measured for Thursdays alone. We observed that the variance for Mondays was roughly half again higher than the variance for Thursdays. This suggests that traders may be making up for two extra days of price movement on Mondays. It also suggests that annual volatility may be better estimated, from a sample of n days, as sqrt(365/n)*std instead of sqrt(250/n)*std.
4. Data Errors. We observed the year number in the data dates 870903, 871122 and 870704 causes these observations to fall far outside the temporal range of the data, while leaving no data for 840903, 841122 and 850704. As we had over 3000 observations in our data set for each currency, and over 640 for each trading day, we believe this will have no significant effect on findings. Because we discovered the error late in the project, and we expect little value in correcting it, we have noted the error and left it unchanged.