Spot rate means the rate at this moment. It can be the rate for 90 days, for half years or for 10 years. Forward rate means the expected rate at a particular time in the future. Similarly, it can have rate for 90 days, for half years or for 10 years. As the forward rate is the expected rate in the future, the forward rate will become spot rate at that moment if the expectation is correct. For example, on Jan 1, 2007, the 90-day forward rate for Jan 1, 2008 may be 5% (annualized). If the expectation is correct, the 90-day spot rate on Jan 1, 2008 will still be 5%.

Spot rate and forward rate can be both represented as _nf_m where n is the period from this moment and m is the period of investment/contract. Moreover, n, m are usually represented in multiples of 30 days. For example, ₀f₁ means the spot rate (0 days from this moment) for 30-day contract. ₄f₁ also means a 30-day contract but 360 days from now. 

Traps and Tips:

You will be asked to find the forward rate of a particular n, m pair in the CFA exam. The concept they are testing you is whether you understand how a investor will be indifferent  of 2 investment schemes or how arbitrage can be prevented. The point is 2 consecutive investments should have the same yield as 1 investment with the same total period. Otherwise, there is arbitrage opportunity. (Remember, in finance, there is an equation of balance, i.e. arbitrage-free. This is the fundamental force in finance).

Several points have to be bore in mind:

1. n, m are multiples of 90 days.
2. Remember the meaning of _nf_m
3. Understand whether the given rate is annualized!

E.g. There is a bond with 5 periods left. And 0f5 = 5.6%. Another bond has 3 periods left with 0f3 = 5.3%. What should be the rate the 2^nd bond has to be re-invested with so that the investor will be indifferent?

The rate being asked is the 2-period forward rate 3 periods from now (3f2). We have to equate:

0f5 ^ 5 = 0f3 ^ 3 x 3f2 ^ 2

(1.056)^5 = (1.053)^3 x 3f2 ^2

Therefore, the forward rate should be 6.052%. (Note, here it didn’t mention days/years. So we just have to treat the given rate as the rate of a period.)