1. Suppose that the spot rate of EUR is 1.1250 USD for 1Euro. 1 year forward rate is 1.1440 USD for 1 Euro. Suppose that the 1 year USD interest rate is 1.50% annualized and Euro interest rate is 0.001% annualized (rates are compounded annually that means for example that 1USD a year from now grows to 1*(1+1.50%) USD). Is there an arbitrage opportunity? If there is describe it.
2. Suppose that the spot exchange rate of EUR is 1.1245 USD for 1Euro. Suppose that the 3 months USD interest rate is 0.85% annualized and Euro interest rate is -0.3% annualized (rates are continuously compounded). What is 3 month forward exchange rate? What does it mean for interest rate to be negative?
3. What is the six-month forward price for a stock providing no income if the stock price is 100 and the continuously compounded interest rate is 1%? What is the forward price if the stock pays a 2% continuously compounded dividend yield?
4. What is the difference between a forward contract and a futures contract?
5. Make futures margin table similar to the class handout using oil futures prices spreadsheet Oil_CLZ6.xls on courseworks. Suppose that initial margin is 3,190 USD and a maintenance margin 2,900 USD. You sell short 3 contracts at the close on March 16, 2016 and buy back at the close on September 14, 2016 . Oil futures point value is 1000$. When are the margin calls?
6. Consider following futures symbols on Bloomberg. ESZ6 Index, NQZ6 Index, TYZ6 Comdty, CLZ6 Comdty, NGZ6 Comdty, GCZ6 Comdty, SIZ6 Comdty, SX6 Comdty, CZ6 Comdty. Print the futures curves for these markets, for example: ESZ6 Index CCRV. Get descriptions of each future: ESZ6 Index DES. Submit printouts. Write down what of the futures markets are in contango, what are in backwardation and what are mixed. What markets show seasonality?
7. Go to http://finance.yahoo.com, chose Chart and type AAPL in the box. Click Historical Quotes below the chart. Input dates: Start January 25, 2014, End September 14, 2016. Click download spreadsheet format in the bottom of the page. Data is in the Excel format Date, Open, High, Low, Close, Volume, Adjusted Close. Make and submit the printouts of 2 plots: cumulative distribution functions of returns and approximate probability density function of returns using 0.2% horizontal intervals. Calculate mean, variance, standard deviation, mean absolute deviation, kurtosis and skewness of daily returns in Excel. Use only adjusted close prices.
8x. a) Calculate and plot 50day, 30 day and 10 day Moving Average of SPY Close from January 2, 2008 to September 14, 2016 in a spreadsheet similar to HW1SPYMovingAve.xls. Submit printout.
b) Calculate and plot 25 day, 45 day, 60 day and 90 day volatility of SPY Adjusted Close in a spreadsheet similar to the HW1SPYvol.xls. Submit printout.
9. Let X be a continuous random variable taking values between 0 and 10 with probability density function p(x) = 0.1. Find E(X) and Var(X). Plot its Cumulative Distribution Function.
10. Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation 1. Y has mean µ = 3 and standard deviation = 3. Their correlation is 0.4. What is the mean and standard deviation of X + Y ? What is the distribution of X + Y ? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed?Explain your answer.
11 This is not a Math Finance question but a frequent interview question. What is the first time after 9pm when the hour and minute hands of a clock are exactly on top of each other.
12. Suppose you are applying to graduate schools. Your chances to be admitted to each one school are 15% and are the same for any school. To how many different schools you need to apply if you want your chances to be admitted to at least one school to be above 95%.