Question

Calculate the benefit, based on the forward rate agreements, that an investor can derive if his / her expectations of future interest rate movements are verified:

a. 3% after two months

b. 2.8% after three months

c. 2.5% after one month

d. 1% after five months

e. 2.9% after six months

Fowrard rate agreements
Terms	Bid	Ask
1 x 4	2.840	2.860
2 x 5	2.815	2.835
3 x 6	2.795	2.815
4 x 7	2.800	2.820
5 x 8	2.805	2.825
6 x 9	2.815	2.835
1 x 7	2.835	2.855
2 x 8	2.830	2.850
3 x 9	2.825	2.845
4 x 10	2.840	2.860
5 x 11	2.860	2.880
6 x 12	2.885	2.905

Answer 1

In an FRA (Forward Rate Agreement) , Investor will benefit if the FRA's rate is lower than his/her expected rate by taking a Long position(Borrow).

Similarly, If the FRA's Rate is higher than Expected rate , taking a Short Position (lending) will benefit the Investor.

However if the expected rate is between bid and ask rates no benefit can be derived

The Question has both BID(lend) and ASK(borrow) Rates given.

Assuming : given rates are per year

A.Expected rate = 3% after 2 Months (hence 2x5,2x8 rates are taken)

i ) FRA rate of 2X5 (ASK) =2.835 % (since expected rate is more than FRA rate, investor shall borrow hence relevant rate is ask rate)

Benefit in % for 3 Months = (3%-2.835%)*3/12 =0.04125%

ii ) FRA rate of 2X8 (ASK) =2.850 % (since expected rate is more than FRA rate, investor shall borrow hence relevant rate is ask rate)

Benefit in % for 6 Months = (3%-2.850%)*6/12 =0.075%

B.Expected rate = 2.8% after 3 Months (hence 3x6,3x9 rates are taken)

i ) FRA rate of 3x6 (expected rate is in between bid and ask rate hence NO Benefit)

  ii ) FRA rate of 3x9 (BID) =2.825 % (since expected rate is less than FRA rate, investor shall lend hence relevant rate is BID rate)

Benefit in % for 6 Months = (2.825%-2.8%)*6/12 =0.0125%

C.Expected rate = 2.5% after 1 Month (hence 1x4,1x7 rates are taken)

i ) FRA rate of 1x4 (BID) =2.840 % (since expected rate is less than FRA rate, investor shall lend hence relevant rate is BID rate)

Benefit in % for 3 Months = (2.840%-2.5%)*3/12 =0.085%

ii ) FRA rate of 1x7 (BID) =2.835 % (since expected rate is less than FRA rate, investor shall lend hence relevant rate is BID rate)

Benefit in % for 6 Months = (2.835%-2.5%)*6/12 =0.1675%

D.Expected rate = 1% after 5 Months (hence 5x8,5x11 rates are taken)

i ) FRA rate of 5x8 (BID) =2.805 % (since expected rate is less than FRA rate, investor shall lend hence relevant rate is BID rate)

Benefit in % for 3 Months = (2.805%-1%)*3/12 =0.45125%

ii ) FRA rate of 5x11 (BID) =2.860 % (since expected rate is less than FRA rate, investor shall lend hence relevant rate is BID rate)

Benefit in % for 6 Months = (2.860%-1%)*6/12 =0.93%

E.Expected rate =2.9% after 6 Months (hence 6x9,6x12 rates are taken)

i ) FRA rate of 6x9 (ASK) =2.835 % (since expected rate is more than FRA rate, investor shall borrow hence relevant rate is ask rate)

Benefit in % for 3 Months = (2.9%-2.835%)*3/12 =0.01625%

ii ) FRA rate of 6x12 (expected rate is in between bid and ask rate hence NO Benefit)

to get the benefit in value multiply given notional loan value with resultant percentages.