**The interest rate curve or yield curve is the graphic representation of the temporary structure of interest rates , which relates the interest rate and the term of indebtedness.**

The interest rate curve allows us to observe how the cost of financing varies according to its duration. It also serves to show how the expected return of a **financial asset** changes according to the investment horizon. To prepare this graph, the **interest rate** or return will be placed on the vertical axis . Also, the horizontal axis will correspond to the period of the **loan**or investment.

**Usefulness of the interest rate curve**

The usefulness of the interest rate curve is that it makes it possible to elucidate the expectations of investors at any given time. That is, the graph reveals the **profitability** that economic agents expect towards the future. This, based on the information offered by the market today.

Specifically, interest rate curves are recurring when investment alternatives are evaluated. These can be **corporate bonds** , **sovereign debt** or even indices such as **Euribor** .

Suppose we have the data on the **sovereign bond** yields of a given country.

Period | Annual interest rate |

1 year | 2,16525% |

2 years | 2.20400% |

3 years | 2,28063% |

5 years | 2.32388% |

7 years | 2.40963% |

10 years | 2,62350% |

20 years | 2.90688% |

30 years | 2.95688% |

So, the chart would look like this:

**Interest rate curves according to their form**

Interest rate curves, depending on their form, can be:

**Increasing:**The slope of the curve is positive, showing that the longer a loan is, the more expensive it will be. This is the most common because in the longer term, the greater the perceived risk and the**lender**(or the investor) will demand a higher return. It usually occurs in moments of optimism. Moments in which the economy is growing properly.**Inverted:**The slope is negative, that is, longer term, lower yield. This situation is not very usual and may indicate that agents foresee a fall in returns in the future. It indicates pessimism. Investors expect falls in the stock markets and take refuge in**state bonds.****Flat:**The interest rate remains fixed regardless of the period of indebtedness or investment. It is an even less common case than the previous one and considered even unreal.**Oscillating or with humps:**When increasing and decreasing sections are observed in the interest rate curve. This happens when there is economic instability that generates uncertainty in the market.

**Interest rate curves according to the time horizon**

The interest rate curves, according to the time horizon evaluated, are:

**Cash:**On the vertical axis, the interest rates applied today to a loan or investment that expires in a given period are considered.**Forward or forward: It**takes as a starting point, or zero period, a moment after the present, In this way, you can observe the cost of borrowing or the return on an investment in a period of time between two future dates. For example, in January I can project data for a loan that I will request in the second quarter of the year.

**Zero Coupon Curve**

The zero coupon curve is a kind of interest rate curve that shows the return demanded by the market to a **risk-free asset** . This, for different investment terms.

The zero coupon curve serves to evaluate **fixed income** investment instruments such as **public debt** . These assets offer a small, but stable return over time. For that reason, it is ideal for individuals with high **risk aversion** .

To graph this curve we are guided by the following equation:

Where:

The reverse way is:

The great contribution of the zero coupon curve is to simplify the analysis, either of the performance of an instrument or the cost of financing. For this, it is assumed that what is invested or borrowed is only a monetary unit, for example, US $ 1.

Let’s look at the following example of a zero coupon curve. Suppose we have the following data for the **state bonds** of different terms issued by a Latin American country.

Duration | Annual interest rate |

1 year | 0.1817656% |

2 years | 1,3481343% |

3 years | 2,0994051% |

5 years | 2.5712547% |

7 years | 2.8585209% |

10 years | 3,0264087% |

20 years | 3.1191177% |

30 years | 3.1391177% |

The interest rate curve would be as follows: