What is the Forward Rate?
Usually reserved for discussions about, the forward rate (also called the forward ) is the theoretical, expected on a several months or years from now.
Forward Rate Example
For example, let's assume you receive Treasuries to keep safe and , you still have two choices: You could either buy a that matures in one year, or you could buy a that matures in six months, and then buy another six-month when the first one matures.that you would like to use for a tuition bill you know arrive in exactly one year. If you invest the in
If both options generated the same outcome, you would probably be indifferent and go with whatever was easiest. However, there is the chance that rates money by buying a six-month now and rolling it over into another six-month to take advantage of those potentially higher rates. Or maybe rates be lower, and you'd make more money locking your money up now for the full year. So the real question is, how much a six-month cost six months from now? That is, what is the forward rate on that six-month ?be higher in six months. If so, you'd make more
The answer isn't clear. After all, by simply looking online you can ascertain how much a one-year T-Bill and a six-month T-Bill yields right now. But there is no way to tell for sure what a six-month T-Bill in six months. However, there is a way to determine what the market is expecting, and that is by calculating forward rates.
Forward Rate Formula
Mathematically, the forward rate is the rate at which you would be indifferent to the two alternatives in our example. In other words, if you just bought the one-year Treasury, which you know from the newspaper is yielding 3% right now, you can easily calculate the price of this T-Bill:
$100/(1+.015)2 = $97.09
So you know that if you invest $97.09 today, you'll have the $100 you need in a year.
Now, how much do you need to invest if you purchase a six-month T-Bill and then reinvest that after six months in another T-Bill? You don't know for sure unless you know what that second six-month T-Bill is going to earn. If the annualon a six-month T-Bill purchased today is 2%, which is 1% semiannually, then the price of purchasing one six-month T-Bill today and then rolling it over into another six-month T-Bill would be:
required today = $100/((1+.01)(1+f))
Where f is the forward rate -- the rate on a six-month T-Bill six months from now.
In order for you to be indifferent about your two alternatives, you would have to be sure that$97.09 in both scenarios would generate the $100 you need in a year. Thus, the returns on the two have to equal.
$100/(1+.015)2 = $100/((1+.01)(1+f))
$97.06617 = $100/((1+.01)(1+f))
What is the rate that makes theseequal? We must solve for f:
f = ((1+.015)2/(1+.01))-1 = 2.00% for six months, or 4.00% for one year.
The forward rate is 4% per year. Thus, we know that the market believes today the six-month T-Bill is going to yield 4% per year in six months. Thus, if you chose to buy a six-month T-bill and reinvest the proceeds in another six-month T-Bill, that second T-Bill would need to have a 4% annual yield to make you indifferent between doing this and just purchasing a one-year T-bill at the going rate. Now the question is, do you think you're really going to get 4%?
Why the Forward Rate Matters
If there is anything to be learned from forward rates, it is that they areillustrations of how interest rates tie together across the spectrum. Forward rates can be calculated further into the future than just six months. It's just a matter of doing the math. For example, the investor could calculate the three-year implied forward rate four years from now, the seven-year implied rate two years from now, etc.
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