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Forward Curve

What is a Forward Curve?

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The financial world is a vast and complex landscape where numerous elements come together to shape and influence decisions, policies, and strategies. One such key concept often employed by traders, investors, and financial analysts is the Forward Curve – an abstract yet immensely critical tool in understanding financial markets. While it may seem daunting at first, once understood, the forward curve can become a valuable part of your financial toolkit.

A forward curve is essentially a graphical representation of the prices of a series of forward contracts for a particular commodity, security, or currency over a specified time period. Forward contracts are agreements that enable buyers and sellers to lock in a specific price for the asset to be delivered on a future date. This tool helps market participants anticipate future price movements, assess the cost of holding assets, and navigate investment strategies with greater confidence.

Spot Curve vs Forward Curve

What is a Forward Curve?

A forward curve is a line plot that represents the prices of forward contracts over time. Forward contracts, a type of derivative, are agreements between two parties to buy or sell an asset at a specific price at a future date. These contracts are traded in over-the-counter (OTC) markets.

The forward curve, then, visualizes these agreed-upon future prices. It’s a tool that traders and financial analysts use to understand market sentiment about future price movements, manage risk, and shape their investment strategies.

For instance, let’s say we’re dealing with crude oil. Each point on the forward curve corresponds to a specific forward contract for crude oil with a particular delivery date and agreed-upon price.

For example, the forward curve for crude oil might show that the price for delivery in one month is $70 per barrel, the price for delivery in six months is $72 per barrel, and the price for delivery in one year is $75 per barrel.

The shape of this forward curve can provide valuable insights. If the prices are increasing over time (as in our example), we would say that the market is in “contango.” This could suggest that the market expects the price of crude oil to rise in the future. On the other hand, if the prices were decreasing over time, we would say that the market is in “backwardation,” indicating the market expects future prices to fall.

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Remember, though, that the forward curve does not predict future spot prices; it merely reflects the current market consensus based on available data and expectations.

What is the Difference With a Spot Curve?

A spot curve (also known as a zero curve or term structure of interest rates) and a forward curve are important concepts in finance, particularly in fixed income and derivatives markets. While they are related, they serve different purposes and provide different information about market conditions.

The Spot Curve illustrates the relationship between the yield (interest rate) and the time to maturity of zero-coupon bonds (bonds that don’t pay periodic interest but are sold at a discount and redeemed at face value at maturity). Each point on the spot curve represents the current yield for a zero-coupon bond for a specific maturity.

The Forward Curve, on the other hand, represents the series of forward rates over a certain time period. Forward rates are the agreed-upon rates for lending or borrowing money at a future point in time. The forward curve is derived from the spot curve and represents the market’s expectations for future interest rates.

For example, let’s consider a simplified scenario. Suppose we have a spot curve with yields for one-year and two-year zero-coupon bonds. The one-year yield is 2%, and the two-year yield is 3%.

From this, we can derive the one-year forward rate one year from now. If we assume annual compounding, we would solve for the forward rate that equates the return from investing in a two-year bond with the return from investing in a one-year bond and reinvesting at the forward rate. The resulting curve would reflect this calculated forward rate.

Now, let’s summarize these concepts in a table:

Spot CurveForward Curve
DefinitionA graphical representation of the interest rates on debt for a range of maturities. It shows the yield an investor is expected to earn if they were to buy a bond and hold it until maturity.A series of forward rates over a given time period. It represents expected future spot rates, given the current term structure.
Example1-year yield: 2%, 2-year yield: 3%1-year forward rate starting one year from now, calculated from the 1-year and 2-year yields from the spot curve.
What it representsCurrent yields for zero-coupon bonds for specific maturities.Market’s expectation of future interest rates.
PurposeUsed to price bonds and to extract discount factors necessary for pricing other securities.Used to speculate or hedge on future movements in interest rates. Helps in managing risk related to interest rate changes.
Spot Curved vs Forward Curve

Keep in mind this is a simplified example and real-world calculations would involve additional factors and could get complex.

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An Example of Data

let’s illustrate a forward curve for a commodity, like crude oil, using a table of forward prices.

Delivery MonthForward Price (per barrel)
June 2023$70
July 2023$71
August 2023$72
September 2023$73
October 2023$74
November 2023$75
Forward Prices

In this example, we can see that the forward price for crude oil is expected to increase over time, from $70 per barrel in June 2023 to $75 per barrel in November 2023. This suggests that the market participants expect the price of crude oil to rise over this period.

If you were to plot these points on a graph, with the Delivery Month on the x-axis and the Forward Price on the y-axis, you would get a forward curve that slopes upward. This is a situation referred to as “contango” in commodity markets, which occurs when future prices are expected to be higher than the current price.

It’s important to remember that a forward curve represents market expectations at the time of calculation, based on the prices of forward contracts. It’s not a prediction of future spot prices, but rather a reflection of what the market currently expects future prices to be.

The forward curve is a valuable tool in financial analysis. It helps traders and investors anticipate future price movements, assess the cost of holding assets, and navigate their investment strategies with greater confidence. However, actual future prices may end up being different due to a myriad of factors that can influence market dynamics.

Plot the Curve

Let’s use Python with the help of the pandas and matplotlib libraries to plot this data:

import matplotlib.pyplot as plt
import pandas as pd

# Create a dictionary of forward prices
data = {
    'Delivery Month': ['June 2023', 'July 2023', 'August 2023', 'September 2023', 'October 2023', 'November 2023'],
    'Forward Price': [70, 71, 72, 73, 74, 75]

# Convert the dictionary to a pandas DataFrame
df = pd.DataFrame(data)

# Convert 'Delivery Month' to datetime format
df['Delivery Month'] = pd.to_datetime(df['Delivery Month'])

# Plot the forward curve
plt.plot(df['Delivery Month'], df['Forward Price'])
plt.title('Oil Forward Curve')
plt.xlabel('Delivery Month')
plt.ylabel('Forward Price (per barrel)')

This script first creates a pandas DataFrame from the dictionary of forward prices. The ‘Delivery Month’ column is converted to datetime format so it can be used for the x-axis of the plot. Then, the forward curve is plotted using Matplotlib, with the delivery month on the x-axis and the forward price on the y-axis.

The resulting plot should show an upward-sloping curve, which indicates that the forward prices for oil are expected to rise over time. This situation is called “contango”.

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