Financial Risk Manager Part 1

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Explanation:

Here is the updated, accurate explanation for FRM Part I students preparing for this question. I have corrected the errors from the original reference (wrong interest amount and slightly imprecise strategy description).

Question Summary

The treasurer expects to receive GBP 800,000 in 3 years and plans to invest it for one additional year (from t=3 to t=4).
The current 3-year spot rate is 1.5% and the 4-year spot rate is 2%, both with continuous compounding.
The company can borrow and lend at these rates.

Required:

Calculate the interest income the company will earn in the 1-year period beginning 3 years from today (i.e., during the fourth year), after locking in today’s forward rate.
State what transactions the treasurer should enter into today to lock in this rate.

Step-by-Step Correct Solution

Step 1: Calculate the 1-year forward rate from year 3 to year 4 (continuous compounding)
The formula for the forward rate $f_{3,4}$ is:

f_{3,4} = \frac{r_4 \times 4 - r_3 \times 3}{4 - 3} = \frac{0.02 \times 4 - 0.015 \times 3}{1} = \frac{0.08 - 0.045}{1} = 0.035 \ (3.5\%)

Step 2: Calculate the actual interest income earned in the fourth year
Because the rates use continuous compounding, the interest income on GBP 800,000 is:

\text{Interest} = 800,000 \times (e^{0.035 \times 1} - 1) \approx \textbf{GBP 28,495.77}

(This is the precise figure; the original reference wrongly used the simple approximation 800,000 × 0.035 = 28,000.)

Step 3: Transactions to lock in the forward rate today
To synthetically lock in lending (reinvesting) at the 3.5% forward rate from t=3 to t=4, the treasurer should:

Borrow today the present value of GBP 800,000 for 3 years at the 3-year spot rate (1.5% continuous).
Lend (invest) that exact same amount today for 4 years at the 4-year spot rate (2% continuous).

Outcome at t=3:

Receive GBP 800,000 from the insurance inflow.
Repay the 3-year borrowing with it → net cash flow = 0.
The 4-year lending position continues, effectively making the GBP 800,000 grow at the locked-in 3.5% continuous rate during year 4.

At t=4: The position yields GBP 800,000 × e^{0.035} ≈ GBP 828,495.77, producing the locked-in interest income of GBP 28,495.77.

This is the standard cash-and-carry strategy to lock in a future lending (reinvestment) rate.

Explanation:

Question Summary

Required:

Calculate the interest income the company will earn in the 1-year period beginning 3 years from today (i.e., during the fourth year), after locking in today’s forward rate.
State what transactions the treasurer should enter into today to lock in this rate.

Step-by-Step Correct Solution

Step 1: Calculate the 1-year forward rate from year 3 to year 4 (continuous compounding)
The formula for the forward rate $f_{3,4}$ is:

f_{3,4} = \frac{r_4 \times 4 - r_3 \times 3}{4 - 3} = \frac{0.02 \times 4 - 0.015 \times 3}{1} = \frac{0.08 - 0.045}{1} = 0.035 \ (3.5\%)

Step 2: Calculate the actual interest income earned in the fourth year
Because the rates use continuous compounding, the interest income on GBP 800,000 is:

\text{Interest} = 800,000 \times (e^{0.035 \times 1} - 1) \approx \textbf{GBP 28,495.77}

(This is the precise figure; the original reference wrongly used the simple approximation 800,000 × 0.035 = 28,000.)

Step 3: Transactions to lock in the forward rate today
To synthetically lock in lending (reinvesting) at the 3.5% forward rate from t=3 to t=4, the treasurer should:

Borrow today the present value of GBP 800,000 for 3 years at the 3-year spot rate (1.5% continuous).
Lend (invest) that exact same amount today for 4 years at the 4-year spot rate (2% continuous).

Outcome at t=3:

Receive GBP 800,000 from the insurance inflow.
Repay the 3-year borrowing with it → net cash flow = 0.
The 4-year lending position continues, effectively making the GBP 800,000 grow at the locked-in 3.5% continuous rate during year 4.

At t=4: The position yields GBP 800,000 × e^{0.035} ≈ GBP 828,495.77, producing the locked-in interest income of GBP 28,495.77.

This is the standard cash-and-carry strategy to lock in a future lending (reinvestment) rate.

Comments (1)

Yash ParwaniApr 8, 2026 1:18 PM

The answer is incorrect. With continuous compounding the interest income will be 28,495.77

LeetQuiz .Apr 10, 2026 10:56 AM

Hi Yash, Thanks for pointing out. We mixed the continuous compounding forward rate calculation with a simple interest approximation. We've updated it to be the precise figure GBP 800,000 × e^{0.035} ≈ GBP 828,495.77.

The finance director of a London-based insurance firm expects to receive GBP 800,000 in three years. The plan is to invest this amount for an additional year at the one-year forward rate applicable at that time. Currently, the 3-year spot rate is 1.5%, and the 4-year spot rate is 2%, both with continuous compounding. Using this information, calculate the interest revenue the company will earn during the fourth year from this investment. What steps should the finance director take immediately to lock in this rate of return?

Exam-Like

Last updated: April 10, 2026 at 10:58

Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,495.

53.6%

Lend at the 3-year spot rate and borrow at the 4-year spot rate to earn a return of GBP 28,000.

13.1%

Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,119.