Mastering Duration of a Bond Portfolio | CFA Level I Fixed Income

Today, we’ll take a quick dive into calculating the duration of a bond portfolio. So far, we’ve covered different duration measures and how to calculate them for a single bond. But what happens when fund managers invest in multiple bonds? Let’s find out!

Two Methods to Estimate Duration of a Portfolio

Imagine a portfolio with two bonds:

• Bond A: 8% annual coupon, 1-year maturity, yield-to-maturity (YTM) of 20%, price of 90 per 100 par, and $100,000 par value (market value: $90,000).
• Bond B: 5% annual coupon, 2-year maturity, YTM of 12%, price of 88.17 per 100 par, and $400,000 par value (market value: $352,680).

Now, let’s explore the two ways to estimate the duration of this portfolio:

1. Aggregated Cash Flows Approach

Here, we treat the portfolio as one big bond with many cash flows. To calculate the Macaulay duration, we first find the cash flow yield (IRR) for the aggregated cash flows. For our example, the IRR is 12.929%.

Next, we discount the aggregate cash flows using the IRR to find their present values and weights. Multiplying the weights by the time to the respective cash flows and summing them up gives us a Macaulay duration of 1.744. Finally, dividing this by (1 + IRR) gives us a modified duration of 1.544.

However, this method has limitations:

• It’s only accurate if the future cash flows are predictable.
• Interest rate risk is usually expressed as a change in benchmark interest rates, not as a change in the cash flow yield.

2. Weighted Average Method

This method is more commonly used in practice. We start by calculating the weight of each bond in the portfolio based on its market value.

Next, we calculate the Macaulay duration and modified duration for each bond. For our example, the weighted average Macaulay duration is 1.756, and the weighted average modified duration is 1.556.

While this method is an approximation, it’s more practical for real-life applications. However, it assumes a parallel shift in the yield curve, which might not always be true.

Conclusion

So, there you have it! The two approaches to calculating the duration of a bond portfolio are the aggregated cash flows approach and the weighted average method. Make sure you understand the fundamental differences and limitations of each approach.