Valuing in terms of FRAs
FRAs stands for forward rate agreements. It can be valued by
assuming that forward interest rates are known, as it cannot be more than a
portfolio of an interest rate agreement. There are three main steps to an FRA
valuation. First, determine the forward rate using BBSW or swap zero curves.
Second, find the swap cash flows based on the assumptions that BBSW rates found
in the previous step is equal to the forward rates. Third, discount the swap
cash flows to find the value of the swap.
A ‘Plain Vanilla’
interest rate swap is the most common type of interest rate swap. It is when
one party (the payer) agrees to pay a fixed-rate of interest while the other
party (the receiver) agrees to pay at a floating-rate of interest. They agree
to make payments within the counterparties based on the increase or decrease of
the floating interest rate. In most Australian interest rate swap agreements
the floating rate will be based on the Australian BBSW.
There are potential
benefits and risk for both parties. If the interest rate increases, the payer
will benefit, as their fixed rate is unchanged and the receiver will owe the
payer the difference between the fixed and floating rate. On the other hand, if
the interest rate decreases, the receiver will benefit as their floating rate
will be lower than the fixed rate, and then will be receiving the difference
between the payer.
Generally
between regular retail consumers and banks there are no fees or other direct
costs associated with an interest rate swap. The price of an interest rate swap
is the fixed rate of interest at which the swap is agreed between a bank and a
customer. However, in regards to the relationship between financial firms and
financial intermediaries, the cost associated with an interest rate swap is the
swap spread. The swap spread is the difference acquired between the fixed rate
of interest of a swap and the yield on a fixed-income investment holding with a
similar maturity. Companies enter into swaps with the idea and intention to
hedge risk on a particular cash flow which is dependent on their views about
the fluctuation and volatility of interest rates. Prior to the commencement of
swaps, firms believe that they are able to exchange comparative interest rates
advantageously thus seeking to swap for a rate that would suit the needs of the
firm more appropriately. A firm with a fixed interest rate may seek to swap the
rate of interest with another firm with who is currently experiencing a
floating exchange rate and similarly, a firm with a floating interest rate may
deem it more appropriable to swap interest rates with a firm of a fixed nature.
The swap spread on a given contract reflects the level of risk that is
associated with the swap; the nature of the spread reflects the level of risk borne
by the contract where the spread shares a positive correlation with the risk.
As the spread widens, the corresponding risk increases, equally, if the spread
between the two rates decrease, the risk therefore decreases.
A
swap can be utilised to mitigate and hedge the cost of future borrowings. If a
firm seeks to borrow X amount of dollars over a span of Y amount of years, a
firm can utilise an interest rate swap to minimise the amount owing at the end
of the time period. In a plain vanilla swap, a firm can choose to utilise
either a fixed or floating exchange rate for the repayments of the particular
future borrowing. A firm can speculate the possible future movements of
interest rates and decide whether or not they will be financially advantageous
using a particular cash flow. Whichever option the company decides, there will
be a counterparty who seeks the opposite type of cash flow ready to engage in
the interest rate swap. An interest rate swap acts as a powerful instrument to
help mitigate risk during times of uncertainty, but it is integral that a firm
carefully analyses their financial situation and the possible movements of
interest rates before making any decisions.
“In
an interest rate swap, financial institution as an intermediary exposes two
types of risk, price risk and credit risk” (Gregg 1987). The reason for price
risk is relative to the change in swap price. Usually a change in interest rate
will lead to a gain or loss to the financial institutions. But price change is
a small portion of a swap portfolio to intermediaries. For example, if AMX pays
10% fixed interest rate in exchange for a variable interest rate, a change in
the market interest rate would lead to a change in the payments but no change
in the payments it receives. Hence, there is a capital gain/loss just as use
lower or higher fixed interest rate to exchange floating rate. However, to
facing price risk financial institution always can offset risk from using
futures market, such as hedge Treasury securities and future contracts.
The
most common risk is credit risk. If the interest rate changes, one party will lose
while the other party will profit by same amount. AMX as an intermediary can
hedge against price risk, but it is possible that if one party defaults, then
the intermediary loses the hedging value of against risk and could suffer a
capital loss that mean the AMX has an obligation to support the swaps. However,
no matter which side of end-users default in interest rate swaps, this should
be called credit risk. Typically, intermediaries always are setting swap price
and making portfolio diversification to against the credit risk.
The calculations are based on the swap where an AMX financial institution
pays 10%
p.a and receives three-month BBSW in return on a notional principle of $100
million with payment being exchange every three months. The remaining life on
the swap is 14 months. The average of the bid and offer fixed rates currently
being swapped for three-month BBSW is 12% p.a. for all maturities. The
three-month BBSW rate one month ago was 11.8% p.a.
Time
|
Bfix CF
|
Bfl CF
|
Discount Factor
|
Bfix PV
|
Bfl PV
|
0.1666667
|
2.5
|
102.95
|
0.980487057
|
2.451217644
|
100.941143
|
0.4166667
|
2.5
|
0.951929232
|
2.379823079
|
||
0.6666667
|
2.5
|
0.924203186
|
2.131050797
|
||
0.9166667
|
2.5
|
0.897284693
|
2.243211733
|
||
1.1666667
|
102.5
|
0.871150233
|
89.29289891
|
||
Total
|
98.67765933
|
100.941143
|
The
time periods are 2 months, 5 months, 8 months, 11 months and 14 months.
The
cash flow of the fixed bond can be calculated: 2.5
The
cash flow of the floating bond can be calculated as:
Rc=
11.8235%
Discount
factor: e^(-11.8235%*2/12); e^(-11.8235%*5/12); e^(-11.8235%*8/12);
e^(-11.8235%*11/12); e^(-11.8235%*14/12)
The
present value of the fixed rate bond is 98.68 million and the present value of
the floating interest rate bond is 100.94 million
Since
the floating rate is received and the fixed rate is paid by AMX, the value of
the swap is 100.941143-98.67765933= 2.26348Million.
Time
|
Fixed CF
|
Floating CF
|
Net CF
|
Rc
|
Discount Factor
|
PV of Net CF
|
0.1666667
|
-2.5
|
2.95
|
0.45
|
0.1669
|
0.9808
|
0.44136
|
0.4166667
|
-2.5
|
3
|
0.5
|
0.1183
|
0.9519
|
0.47595
|
0.6666667
|
-2.5
|
3
|
0.5
|
0.1183
|
0.9242
|
0.4621
|
0.9166667
|
-2.5
|
3
|
0.5
|
0.1183
|
0.8973
|
0.44865
|
1.1666667
|
-2.5
|
3
|
0.5
|
0.1183
|
0.8712
|
0.4356
|
Total
|
2.26366
|
Figure 2
The
first row of Figure 2 shows the cash flow
exchange in 2 months, i.e. 0.1667 years from now. In fact the value in 2 months
had been determined already. The financial institution will pay a fixed rate
interest of 10%p.a., a cash outflow (indicated as negative) will be 100 x 0.1 x
0.25 = $2.5 million. Floating rate on the other hand, by the set 3-month BBSW
rate of 11.8% p.a. will lead to a cash flow of 100 x 0.118 x 0.25 = $ 2.95
million. Second row shows cash flow exchange in 5 months, i.e. 0.4167 years
from now. Cash outflow is $2.5 million as before. As stated offer fixed rates
currently being swamped for 3-month BBSW is 12% p.a. for all maturities,
compounded quarterly. Hence the forward rate will be the same as 12% with
quarterly compounding. Cash outflows hence becomes 100 x 0.12 x 0.25 = $3
million. The third, forth and fifth row shows similar, but the cash flow
exchange in 8months, 11months and 14months respectively, i.e. 0.6667, 0.9167
& 1.1667 years from now respectively.
Net flow
is calculated through cash inflow less cash outflow, positive values indicate
inflow and negative values indicate outflow. Rc, the rate of
interest with continuous compounding, is determined through the equation Rc
= mln[1+Rm/m], where Rm is the equivalent
rate with compounding m times p.a..
Discounted factor are calculated through e-Rc x time . Present
Value (PV) of the period is calculated through Net Cash Flow x
Discounted Factor. For instance, PV0.9167
= +0.5 x 0.8973 = + $ 0.44865 million. The total value of the swap is $2.26366
million.
The swap is valued at $2.26348 million by valuing in terms of two bonds and $2.26366 million. The values computed from both methods produce a similar answer with a difference of $0.0002 million. This difference could be due to rounding earlier in the calculations. Both methods of valuing a swap should produce the same value for the same interest rate swap.
