How to calculate loan duration
In the financial field, loan duration (Duration) is an important indicator that measures the sensitivity of loan or bond prices to interest rate changes. It not only helps investors assess risk, but also provides a reference for loan pricing. The following is a detailed calculation of loan duration and its application.
1. Definition of loan duration
Loan duration refers to the weighted average time of loan or bond cash flows, and the weight is the proportion of the present value of each period's cash flows to the total present value. It reflects the sensitivity of the loan to interest rate changes. The longer the duration, the more sensitive it is to interest rate changes.
2. Calculation formula of loan duration
The formula for calculating the loan duration is as follows:
| symbol | meaning |
|---|---|
| D | loan duration |
| t | Time when cash flow occurs (year) |
| CF_t | cash flow in period t |
| r | Discount rate (annual interest rate) |
| P | The present value of a loan or bond |
Formula:
D = Σ [t * (CF_t / (1 + r)^t)] / P
3. Calculation steps of loan duration
1.Determine cash flow: Lists the cash flows (such as interest and principal) of a loan or bond each period.
2.Calculate present value: Discount the cash flows of each period to the current point in time according to the discount rate.
3.Calculate weighted time: Multiply the time of each cash flow by the present value and divide by the total present value.
4. Application of loan duration
1.Interest rate risk management: The longer the duration, the more sensitive the loan is to interest rate changes, and investors can hedge interest rate risks by adjusting the duration.
2.loan pricing: Banks can adjust loan interest rates based on duration to reflect their risk levels.
3.Portfolio Management: Investors can optimize the risk-return ratio by combining loans or bonds with different durations.
5. Examples of loan duration
Assume that the loan term is 3 years, the annual interest rate is 5%, the interest is paid once a year, and the principal is repaid at maturity. The cash flow is as follows:
| Time (year) | Cash flow (yuan) | Present value (yuan) | Weighted time (years) |
|---|---|---|---|
| 1 | 50 | 47.62 | 47.62 |
| 2 | 50 | 45.35 | 90.70 |
| 3 | 1050 | 907.03 | 2721.09 |
| Total present value (P) | 1000 | - | |
| Duration (D) | - | 2.86 |
Calculation process:
1. Present value calculation: CF_t / (1 + r)^t (r=5%)
2. Weighted time calculation: t * present value
3. Duration: Weighted sum of time / total present value = (47.62 + 90.70 + 2721.09) / 1000 = 2.86 years
6. Limitations of loan duration
1.Assume that interest rates move in parallel: The duration assumes that interest rates change uniformly across all maturities, but in reality the interest rate curve may not move parallel.
2.Ignore convexity: Duration only measures first-order interest rate sensitivity, higher-order effects (such as convexity) may affect the results.
3.Cash flow fixed: The duration is applicable to loans or bonds with fixed cash flow, but not applicable to floating rate products or bonds with rights.
7. Summary
Loan duration is an important tool in financial risk management, helping investors assess interest rate risk by calculating the weighted average time of cash flows. Despite its limitations, its simple and intuitive nature makes it widely used in loan pricing, portfolio management and other fields. Mastering the duration calculation method will help you better manage the risks and returns of financial assets.
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