4. The annually compounded interest rate is 7% per annum (p.a.).

(4.1) What are the holding period returns if you deposit cash at this interest rate for one year, two years, and three years?

4.2 What is the equivalent interest rate compounded semi-annually?

(4.3) What is the equivalent interest rate compounded quarterly?

(4.4) What is the equivalent interest rate compounded daily?

(4.5) What is the equivalent interest rate compounded continuously?

(4.6) What do you conclude from comparing the daily and continuously compounding frequency?

(4.7) Suppose the continuously compounded interest rate for another currency is 4% per annum. What is the equivalent simple interest rate per annum for one year, two-year, and three-year deposits? Are the simple rates per annum higher for longer maturity deposits?

5. The spot price of ABC stock is $50 per share and the risk free interest rate is 5% per annum with continuous compounding. ABC will not pay dividend in the next year.

(5.1) What is the growth rate per annum of ABC stock?

(5.2) Use the growth rate found above and the general forward pricing formula to find the one-year forward price of ABC.

(5.3) Find the initial value of the ten-year forward contract?

6. The continuously compounded risk free rate is 1% per annum and it does not change in the next ten years. A company XYZ does not pay dividend.

(6.1) The two-year forward price of XYZ is $55 per share. Assuming no arbitrage exists, find the five-year forward price of XYZ.

(6.2) Suppose the five-year forward price of XYZ is 57 $/share. Is there an arbitrage opportunity?

(6.3) Clearly describe an arbitrage strategy using two-year and five-year forward contracts given the forward prices listed above. You may not trade XYZ on the spot market. You may long or short only one share of XYZ using the five-year forward contract. You need to describe the trades (amount and direction) and actions you need to take right now, in two years, and in five years. Calculate the amount of arbitrage profit we can realize in five years.

7. You are running the trading desk at a large, high-grade investment bank. You have the following rates available to you:

Spot USDJPY exchange rate: 120.44

3-month Forward USDJPY rate: 119.09

1-month US (Dollar) interest rate: 5.50% per annum

3-month US (Dollar) interest rate: 6.00% per annum

The above interest rates are continuously-compounded.

(7.1) Let rJPY be the annualized 3-month Japanese (Yen) continuously compounded interest rate. Interest rate is effectively the growth rate of the currency. Find the no arbitrage condition involving rJPY based on the general forward pricing formula.

(7.2) What must be the 3-month Japanese (Yen) continuously-compounded interest rate so that there are no arbitrage opportunities?

(7.3) Suppose that the annualized, continuously-compounded 3-month Yen interest rate is -1%. Is there an arbitrage opportunity? If yes, describe exactly what transactions you would undertake at these prices/rates to lock in an arbitrage profit. Describe your actions at time 0 and in three months.

(7.4) Find the one-month forward rate of JPYUSD assuming there is no arbitrage and the one-month continuously compounded JPY interest rate is -1% per annum.