Deck 5: Determination of Forward and Futures Prices

Question 1

An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% per annum respectively both expressed with continuous compounding). What is the six-month forward rate? Give four decimal places. _ _ _ _ _ _

Answer 1

To calculate the six-month forward rate, we can use the interest rate parity (IRP) formula, which relates the spot exchange rate, the domestic interest rate, and the foreign interest rate. The formula for the forward rate (F) when interest rates are continuously compounded is:

$$F = S \times e^{(r_d - r_f) \times t}$$

Where:
- $F$ is the forward exchange rate
- $S$ is the spot exchange rate
- $r_d$ is the domestic interest rate (continuously compounded)
- $r_f$ is the foreign interest rate (continuously compounded)
- $t$ is the time in years

Given:
- The spot exchange rate ( $S$ ) is 0.7000
- The domestic interest rate ( $r_d$ ) is 5% per annum, or 0.05 when expressed as a decimal
- The foreign interest rate ( $r_f$ ) is 7% per annum, or 0.07 when expressed as a decimal
- The time ( $t$ ) is six months, which is 0.5 years

Plugging these values into the formula, we get:

$$F = 0.7000 \times e^{(0.05 - 0.07) \times 0.5}$$

$$F = 0.7000 \times e^{-0.01}$$

$$F = 0.7000 \times e^{-0.005}$$

$$F = 0.7000 \times 0.9950125$$ (using a calculator for the exponential term)

$$F \approx 0.6965$$

Therefore, the six-month forward rate, to four decimal places, is approximately 0.6965.

Question 2

Which of the following is a consumption asset? choose one)

A) The S&P/ASX 200 Index
B) The Canadian dollar
C) Copper
D) BHP shares

Answer 2

C

Question 3

The spot price of an investment asset that provides no income is $30, and the risk-free rate for all maturities with continuous compounding) is 10%. What to the nearest cent) is the three-year forward price? _ _ _ _ _ _

Answer 3

$40.50

Question 4

The spot price of an asset is positively correlated with the market. Which of the following would you expect to be true? choose one)

A) The forward price equals the expected future spot price.
B) The forward price is greater than the expected future spot price.
C) The forward price is less than the expected future spot price.
D) The forward price is sometimes greater and sometimes less than the expected future spot price.

Question 5

The spot price of Australian barley is AUD$240 per metric tonne, whereas the futures price of barley for delivery in nine months is AUD$252 per metric tonne. Suppose that storage costs are 8% per annum and the interest rates are 4% per annum for all maturities both rates are continuously compounded). Determine the convenience yield per annum continuously compounded) implied by the futures price. Answer as a per cent with two decimal places. ________

Question 6

Repeat question 2 on the assumption that the asset provides an income of $2 at the end of the first year and at the end of the second year. _ _ _ _ _

Question 7

Which of the following is true? choose one)

A) The convenience yield is always positive or zero
B) The convenience yield is always positive for an investment asset
C) The convenience yield is always negative for a consumption asset
D) The convenience yield measures the average return earned by holding futures contracts

Question 8

An investor shorts 100 shares when the share price is $50 and closes out the position six months later when the share price is $43. The shares pay a dividend of $3 per share during the six months. How much does the investor gain? _ _ _ _ _ _

Question 9

A short forward contract that was negotiated some time ago will expire in three months and has a delivery price of $40. The current forward price for a three-month forward contract is $42. The three-month risk-free interest rate with continuous compounding) is 8% per annum. What to the nearest cent) is the value of the short forward contract? _ _ _ _ _ _

Question 10

In question 2 what is the value to the nearest cent) of a three-year forward contract with a delivery price of $30? _ _ _ _ _ _