9/23/2017
Interest rate hedging spot forward rates
Financial System Edition 2 Perdisco
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1 of 3
ID: FMW1.10.109a
An investor wants to make a two period investment and investment and is presented with the following investment options:
(a)
Invest for one period at 3.67% pa and then for a further single period at 3.99% pa
(b) Invest for two periods at 3.83% pa
Which investment option should be chosen to maximise profit? Assume that the interest rates are compound interest rates. Round all percentage calculations to 2 decimal places.
Select investment option (b) Select investment option (a) Select either because both investment options will return the same result
Feedback
[1 out of 1]
You are correct.
Discussion To solve this question, we must determine the two period spot rate that is equivalent to investment option (a). That is, what two period spot rate is financially equivalent to the one period spot rate and the future one period spot rate offered in investment option (a)? This is done as follows:
9/23/2017
Interest rate hedging spot forward rates
(1 + 0r2
)2
0r2
= (1 + 0r1) × (1 + 1r2) = [(1 + 0r1) × (1 + 1r2)]1/2 - 1 = [(1 + 0.0367) × (1 + 0.0399)] 1/2 - 1
= 0.0383
= 3.83%
Therefore, the implied two period spot rate that is financially equivalent to investment option (a) is 3.83% pa. Since this is the same as the rate offered for investment option (b), the two investment options must be identical. Therefore, the investor can select either because both investment options will return the same result.
2 of 3
ID: FMW1.10.105
Given the following spot and forward interest rates, use the drop down lists to indicate what is expected to happen to interest rates in the future. a) 0r1 = 5.0% and 0r2 = 5.1%
he future one period spot rate will rise
b) 0r1 = 5.0% and 1r2 = 5.0%
he spot yield curve is flat
c) 1r2 = 5.1% and 2r3 = 5.0%
he spot yield curve is inverse
Feedback
[3 out of 3]
a) You are correct. b) You are correct. c) You are correct.
Discussion Consider each scenario in turn: 0r1 = 5.0% and 0r2 = 5.1%
These are both spot rates for 1 and 2 periods respectively. They indicate that 1r2 = 5.2% and hence that next periods, one period spot will rise.
9/23/2017
Interest rate hedging spot forward rates
0r1 = 5.0% and 1r2 = 5.0%
The one period spot = 5.0% while the one period forward rate = 5.0%. This suggests that future interest rates will not change and hence that the spot yield curve is flat. 1r2 = 5.1% and 2r3 = 5.0%
These are both one period forward rates that respectively start 1 and 2 periods hence. Since the second rate is lower than the first they suggest that interest rates will decline over time and hence that the spot yield curve is inverse.
3 of 3
ID: FMW1.10.106
The period in most forward rate calculations is taken to be one month (30 days). Use the drop down lists to select the correct interest rate definition symbol for each of the descriptions below:
Symbol
Description
a) 0r2
he 60-day spot rate
b) 1r2
he 30-day spot rate beginning in 30 days
c) 1r3
he rate for a 60 day investment in 30 days time
Feedback
a) You are correct. b) You are correct. c) You are correct.
Discussion
[3 out of 3]
9/23/2017
Interest rate hedging spot forward rates
For interest rate notations n1rn2, the prefix subscript n1 indicates the time at which the rate is available and the investment commences, and the suffix subscript n2 indicates the time at which the investment matures. a) 0r2: the 60-day spot rate All spot rates have n1 as 0 because they commence their life immediately, while the 2 suffix indicates that the spot rate applies over two periods (when t = 2). b) 1r2: the 30-day spot rate beginning in 30 days The 1 prefix indicates that the interest rate is available one period from now; that is, the next period. The 2 suffix indicates that the spot rate applies until t = 2, which is two periods from now. Thus, the interest applies for one period, or 30 days, beginning 30 days from now. This rate can also be called the one-month forward one-month rate. c) 1r3: the rate for a 60 day investment in 30 days time The 1 prefix indicates that the interest rate is available one period from now; that is, in 30 days. The 3 suffix indicates that the spot rate applies until t = 3, which is three periods from now. Thus, the interest rate is available 30 days from now, and applies for two periods, or 60 days, from that time.
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