Question

Discuss the relationships among spot rates, forward rates, inflation rates, and interest rate?

Give evidences for each situation.

Answer 1

Spot rate is the rate of interest contracted or applied on a deposit, loan or investment, for a stated period, at the time of entering into the arrangement. This is the nominal interest rate which comprise of the compensation towards time value of money and inflation. For example, if a loan is quoted now, at 4% for a period of 1 year and at 4.2% interest rate for 2 years, the 4% and 4.2% are the spot rates prevailing now for 1 year and 2 years respectively.

Forward rate is the rate of interest applicable for a future period implied, in a rate contacted now. In other words, it is the spot rate implied, applicable for the future period, commencing after a specified time, but quoted now.

In the example above, the interest rate for the 2^nd year embedded in the 4.2% rate applicable for 2 years, is the forward rate for one year, after one year from now. Forward rate for 2^nd year can be arrived at from the spot rates for 1 year and 2 years, as follows:

             (1+s_t)²

F_1,2 = ------------- - 1

              ( 1+_st-1)

Where f_1,2 =Forward rate from year 1 to year 2.

s₁ and s₂ arespot rates for years 1 and 2 respectively, ruling now.

In the given example, s₁= 4%, s₂= 4.2%

Applying these rate n the formula, forward rate for 2^nd year = [(1+4.2%)^2/(1=4%)^1 ]-1

= (1.042^2/1.04)-1 = (1.085764/1.04)-1 = 4.400385%

Inflation is the measure or rate at which price levels increase in the economy in general. In effect, it is the deterioration in purchasing power of a unit of money, over the given period. Inflation rate is the part of interest rate quoted, in order to compensate for the price increase.

Interest rate, or more specifically the nominal rate is the rate quoted or contracted for a deposit, loan or investment, for a stated period. This comprise of compensation for time value of money (real interest rate) and for inflation.

For example, if the inflation rate is measured at 3% and the interest rate quoted is 4.2%, then the real interest rate is 1.2% and the nominal rate is 4.2%.