Interest Rate Duration of a Rolling Five-Year Investment

Summary

The document considers a rolling investment, such as a guaranteed investment certificate, whose rate resets to market rates at each renewal. The investor asks how to measure duration after most of the current term has elapsed, given that the investment is automatically renewed and its value is reset to face amount at renewal.

The answer defines duration through price sensitivity to an immediate interest-rate change. Because a rate reset at a future renewal date does not add sensitivity to today’s instantaneous rate shock, the answer treats the instrument’s duration as that of the remaining current investment period. In the example, with one year left in the current term, it gives a duration of one. This conclusion uses the stated reset and valuation assumptions; it does not model interim cash flows, changes in credit risk, or other features that could affect the actual value or duration of a particular product.

Key ideas

• Duration measures an instrument’s price sensitivity to an immediate interest-rate change.
• A future rate reset does not, by itself, add present price sensitivity to today’s rate shock.
• The answer equates the rolling investment’s duration with the remaining current investment period.
• Under the stated example assumptions, the remaining term is one year.
• Product-specific cash flows and other risks are not analyzed.

Tags

# What is the duration of a rolling 5 year investment?


# What is the duration of a rolling 5 year investment?












I have difficulty with the duration of a 5 year investment (like GIC). In such an investment, the investment (GIC) rate is reset as the current market rates. So the market value is equal to the face amount at the beginning of each rolling period. The investment is automatically renewed every 5 years in the future. Now the investment is in its 4th anniversary (i.e. after 4 years of purchase). What is the duration of the investment? Is it approximately 1 year or 5 year or something in the middle?

## Answer by sqrt2sqrt2 (score 2)

https://quant.stackexchange.com/a/60869

The duration represents the sensitivity of the price of a financial instrument to current interest rates. Since at the rolling date the price will be equal to the face value no matter what happens to interest rates today (the interest rate will be reset at a future date), the rolling does not add any price sensitivity to an instantaneous interest rate shock. So the duration of your rolling investment is equal to current investment, i.e. 1.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.