2. Calculate the returns of each rate using the following:

r

t

= 100 ln

P

t

P

t

1

where

P

t

is the rate at time

t

. Plot the returns for each rate.

3. Create a histogram for each of the returns series and report their descriptive

statistics including mean, median, mode, variance, standard deviation, skewness

and kurtosis. What conclusion can you draw by examining the kurtosis in each

case?

4. Under the assumption that the returns of each rate are drawn from an indepen-

dently and identically distributed normal distribution, are the expected returns

statistically di erent from zero for each rate? State clearly the null and alterna-

tive hypothesis in each case.

5. Assume the returns of each rate are independent from each other, are the mean

returns statistically di erent from each other?

6. Calculate the correlation matrix of the returns.

7. Is the assumption of independence realistic? If not, re-test the hypotheses in

Question 5 using appropriate test statistics. Compare the results to the results

obtained in Question 5.

8. If you can only choose maximum of two rates into a portfolio, which will you

choose? What are the optimal weights and the optimal expected returns? State

clearly your objective function and provide step-by-step derivations.

9.

Bonus question:

Why is it not realistic to assume these rates follow a normal

distribution? Moreover, is Treasury Bill safer than the other three exchange

rates