Dealing with fixed income is becoming a headache for managers who would like to know when it is a good moment to invest. Some tend to analyse the relationship between fixed-income assets and **external factors**. There may be numerous factors that have influence in the fixed income series, such as, interest rates, currencies movements, politics, and so on. This post focuses on interest rates and their influence over fixed income funds.

## Interest rates as external factors

Firstly, let’s know something about interest rates. In a country, the set of terms of interest rates is called **the zero coupon curve**. This curve varies along the time, containing a great deal of information. Common sense says that the more information you use, the better. However, it is difficult to deal with a big set of variables which change along the time.

The problem is not only to deal with a great number of data but also with the fact that all series are related to each other. On the other hand, we work with funds which invest in assets with different terms. Then it is hard to determine the term that funds are related to.

Now let’s see how to solve some of those problems.

## Birds of a feather flock together

If we are not sure which term is related to a fund, we could **regress the fund and the zero coupon curve**. Then we capture the significance of each term and, paying attention to the highest p-values, we know how the relationship is.

For example, let’s take 14 fixed-income funds in the USA that are classified in short-medium term and long term. We’re expecting that the long term funds are related to long term series in the zero coupon curve. Nevertheless, making a linear regression between the series, the coefficients with higher significance are mixed between short and long terms interest rates.

In the graph below the long term, funds are painted in pink and the short term ones in green. There are representative of each kind of series in every term of the zero coupon curve, and moreover, some of them have a high significance in a term that we don’t expect.

Considering the results, it is not intuitive to relate the funds with the terms that they represent. This is because the funds invest in different kind of assets.

## Summarising information

In this context, it is vital to reduce the number of series we treat. In this line, the PCA technique is really useful because it brings all the information **together in a few factors**.

This method reveals something curious about interest rates. That is, the information can be summed up in only three factors which represent the level, the slope and the curvature of the zero coupon curve, and they preserve around 95% of the information. This is very interesting because we don’t need to use all the interest rates series but only 3 features.

If we apply the PCA technique over the zero coupon curve in the USA, the weights given to each term can be plotted as follow:

## Conclusion

The dependencies between interest rates and fixed income funds are so high that we must tread warily in this matter. Nevertheless, here we have some guidelines to start.