# Yield/Bond Price Changes

If you were going to evaluate the effect of a shift in interest rates on say a 1yr, 5yr, 10yr bond, and don’t know what the current interest rate is, would you start with 0 as your current rate? For instance, the 1yr rate goes up 20 basis points, and the 5yr rate goes down 20 basis points. Would you start with 0 and thus the new rates are .002 and -.002? Does it effect the % change in price if you started with 0% or 5% as your base case?

This is a tricky question and one that I would approach from two angles: first, from the POV of a coupon-bearing bond; and second, from a zero coupon POV. Duration will be affected by the time left to maturity (positive relationship, longer maturity ==> higher modified duration/sensitivity), coupon (negative relationship) as well as the bond’s original yield (negative relationship). If you do not know prevailing rates, you aren’t going to be able to calculate the duration of coupon bearing bonds; this is because duration changes as rates change. For example, as rates increase a bond’s duration will actually decrease, making the same bond less senstive to the same further rate increase than previously. For example, a bond trading at a premium is less sensitive to a decline in interest rates than a comparable par or discount bond, so the subjectivity involved in measuring a coupon bond makes the question nearly impossible. Without knowing the current level of rates, you will not know the duration of a coupon-bearing bond.

On the other hand, if you have a non-interest bearing bond like a zero, you could do this calculation since the only variable you’d be concerned with is the bond’s time left until maturity (no cashflows to worry about). So if you had a 1-yr, 5-yr and 10-yr bond you coud do the calculations to determine each bonds’ duration. A 10-yr bond would have an approximate modified duration of 10 (a 1% rise (fall) in interest rates would decrease (increase) the bond’s price by approximately 10%)

Just an FYI, I work in fixed income trading/strategy and this question is definitely not something I would consider basic. In fact, this is a very advanced question to ask without much additional information (like having each bond’s key-rate duration or general modified duration).

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45e3

duration has several meanings, try to use the simplest. By the way textbook gives some insight into similar problem. The value of this question should be higher IMO…

For zeros, and a parallel shirft you take the weighted average duration of the portfolio (which is now just each bonds maturity in years multiplied by its % of the portfolio’s total value) and you simply calculate the change this way. For key-rate duration, a non-parallel shift in which specific rates change, it will be a little trickier to determine which portfolio will perform the best/worst. Basically, longer-dated maturities are much more sensitive, so if we have a barbell we have short and long maturities, a ladder has an equally weighted blend (so the duration of the portfolio is likely the average or middle bond’s duration, and for a bullet it only depends on that particular bond’s maturity. For example, an equally weighted barbell of 2 bonds with maturities of 10-yrs and 30-yrs would have an average duration around 20-years; an equally weighted ladder of 10 to 30-yrs bonds at each year would have an approx. duration of around 20 as well; while a bullet (single bond) has a duration equal to that bonds’ maturity (in years).

Hope this helps clarify. Let me know if you have any other questions and I’ll see what I can help with.