DM41X: Interest Rate of a Forward-Forward Agreement
A Future Interest Contract: Forward-Forward Agreement
A forward-forward agreement (yes, forward-forward is not a typo, that is what’s really called) is a financial transaction which starts on a forward date and ends on another forward date. An example transaction involves one party borrowing a sum amount to be paid back, only at the same time to deposit such amount in another short-term investment. The forward-forward rate, which I designate as FFR, is combined interest rate taking both transactions at the same time. The FFR is calculated as such:
FFR = [ (1 + IL * DL ÷ 365) ÷ (1 + IS * DS ÷ 365) – 1 ] * (365 ÷ (DL – DS))
IL: interest rate for the longer period, in decimal
DL: length of the long period
IS: interest rate for the shorter period, in decimal
DS: length of the short period
365: number of days in a year. It gets replaced with 360 if a 30/360 year is used.
If the loan lasts longer, the FFR represents the interest cost.
If the deposit lasts longer, the FFR represents the interest earned.
DM41X and HP 41C Code: FFR
01 LBL T^FFR
02 ^T FWD-FWD RATE
03 AVIEW
04 PSE
05 ^T LONG TRM DYS?
06 PROMPT
07 STO 01
08 STO 06
09 ^T LONG TRM %?
10 PROMPT
11 STO 02
12 %
13 365
14 /
15 1
16 +
17 STO 05
18 ^T SHORT TRM DYS?
19 PROMPT
20 STO 03
21 ST- 06
22 ^T SHORT TRM %?
23 PROMPT
24 STO 04
25 %
26 365
27 /
28 1
29 +
30 ST/ 05
31 RCL 05
32 1
33 -
34 365
35 *
36 RCL 06
37 /
38 2
39 10↑X
40 *
41 STO 07
42 ^T FFR=_
43 ARCL 07
44 AVIEW
45 RTN
Notes:
^T: It starts an alpha string.
Line 42: ^T FFR+_: The underscore is used as a space
Alpha strings are abbreviated in attempt for the message to fit the screen without scrolling.
Periods are assumed to be one year or less, and a 365-day year is assumed.
Examples
Example 1:
Longer Period (borrow): 49 days, 11%
Shorter Period (deposit): 30 days, 8%
Result: FFR= 15.6340
Example 2:
Longer Period (borrow): 63 days, 10.2%
Shorter Period (deposit): 31 days, 11.1%
Result: FFR= 9.2410
Source
Steiner, Bob. Mastering Financial Calculations. Second Edition. Prentice Hall: Financial Times. 2007. ISBN 978-0-273-70444-7. pp. 68-70
Eddie
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