Thread by @MalteKurz

1/ 🆕 at Quant's Perspective @ScalableCapDACH @ScalableCapital

Rolling Down the Yield Curve (by @ChrisAndData)

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2/ Upwards sloping yield curves can be explained by several yield curve theories, which imply different future yield curve trajectories. Rolling down the yield curve will maximize future returns when yield curves remain constant over time.

3/ We start of with an artificial scenario in terms of yield curve and forward rates (shown in the graphic). If we now want to invest money for 1 year, bonds of which maturity should we buy?

4/ Two popular theories:

Liquidity Premium Hypothesis: Upward sloping yield curves are a result of people demanding additional compensation when lending money over longer times.

Expectation Hypothesis: Current forward rates are an unbiased estimator of future interest rates.

5/ If we now hold a zero-coupon bond with 10 years maturity for one year: How much compounding do we get under the two theories LP & EH. Under continuous compounding the value can be obtained as an integral over forward rates and be visualized as the area under the forward curve.

6/ Let's now consider bonds of different maturities (blue dots on the forward rates curve in the left graphic). Price trajectories under the Liquidity Premium Hypothesis (LP) and the Expectation Hypothesis (EH) are shown in the right graphic.

7/ If we for a moment assume that yield curves remain constant over time, we now know that the compounding that we harvest is proportional to the area under the forward rate curve. So the sweet spot is the maturity with maximum forward rates and we would need to continuously roll

8/ However in reality this results in a tradeoff between rolling costs and targeting the optimal maturity range. Additionally, yield curves are far from constant over time. Rolling fixed-income securities of long maturities comes with higher returns, but also with higher risks.

9/ This was the fourth article in our fixed-income series on Quant's Perspective. Stayed tuned for the next one about Synthetic Replication of Bond Indices.

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