Definition of a Forward Curve

Suppose you want to purchase a beach house in exactly one year and will need a five-year loan at that time. If a five-year mortgage loan is available today for 6 percent, a lender might offer you a forward contract on a five-year loan to be settled in one year. This rate is known as the __forward rate__, and it will most likely be greater than 6 percent. Your forward loan is referred to as a "one-year forward, five-year tenor." If your neighbor also wants a beach house but wants a six-year loan that will occur in two years, what do you think this is called?

Right. The first part represents the forward period, and the second part represents the loan period. In practice, it is frequently referred to as a "2y6y" loan.

No. The six-year tenor part is correct, but the forward period is not four years.

No. The two-year forward time period is correct, but the tenor of the loan is not four years.

This is how it works in the bond market as well. Forward rates are determined from government bond spot rates. This means the forward curve is derived from the spot curve, but the interesting thing is that although forward rates are usually computed using the spot curve, known forward rates can be used to create the spot curve. Forward rates are very important for many financial market participants. Examples include a firm with an expected positive NPV project with a deferred starting date. This firm would use the forward market to predict what its future borrowing costs would likely be, which will ultimately affect the wealth of the project. Forward rates are frequently computed using spot rates, but can also be inferred from derivative securities.

The __forward curve__ is a series of forward rates along the term structure. A major difference between forward and spot rates is that forward rates are considered to be break even reinvestment rates, mostly because they are marginal returns for increasing the loan or bond issue by one period.

Suppose you are approached by a financial institution willing to offer you two different investment choices. The first option is two consecutive one-year investments in which you could earn 10 percent during the first year, and an unknown return during the second year. The alternative is a two-year investment in which you could earn 12 percent. What is the one-year forward rate implied from these spot rates?

No. It is not mathematically possible to invest at 10 percent during the first year and then less than 12 percent for the second year to generate a return equal to 12 percent earned during each year for two years.

Yes. The math is $$\displaystyle \frac{(1.12)^2}{(1.10)} - 1 \approx 0.14036 \approx 14.04 \% $$.

No. The second option provides a return of 12 percent for each of the next two years. The first option offers only a 10 percent return during the first year, which implies the second year's expected return must be higher than 12 percent.

When interest rates are expected to rise, the forward curve will be upward sloping, and when rates are expected to fall, the forward curve will be downward sloping. In the first case, the forward curve will lie above the spot curve, and in the second case it will lie below it.

In summary: [[summary]]

Once an analyst has the forward curve, it can be used to find arbitrage opportunities, especially when comparing spot and derivative markets. The curve can be used to price option and swap contracts. It can also be used to make decisions about appropriate maturities for fixed income investors.

A two-year forward, six-year tenor

A four-year forward, six-year tenor

A two-year forward, four-year tenor

Less than 12 percent

Greater than 12 percent

Equal to 12 percent

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