The Museum of HP Calculators


True Annual Growth Rate of an Investment Portfolio

This program is Copyright © 1978 by Hewlett-Packard and is used here by permission. This program was originally published in "HP-38E/38C Personal Finance Applications" book. This program was transcribed by Kris Collins.

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

Finding the true rate of return on an investment portfolio where variable amounts are invested or withdrawn at indefinite or irregular intervals is a complicated calculation.  However, it is a highly useful tool in money management.

This program uses "Fisher's algorithm", a powerful technique to solve for the true realized rate of return.

Notes:
 

Reference:

1)    Lawrence Fisher, "An Algorithm for finding Exact Rates of Return", The JOURNAL OF BUSINESS, University of Chicago Press, Volume XXXIX No. 1 part 2, January 1966.
 
 
KEY ENTRY
DISPLAY
KEY ENTRY
DISPLAY
g P/R g CLP 00- g LASTX 25 31
RCL PMT 01-24 14 g FRAC 30-25 61
f Change DAYS 02-24 41 2 31-2
3 03-3 g yx 32-25 21
6 04-6 f SQRT X 33-25 21
5 05-5 g EEX 34-25 32
0 06-0 2 35-2
0 07-0 x 36-61
/ 08-71 ENTER 37-31
RCL PV 09-22 13 ENTER 38-31
g x<>y 10-25 5 RCL i 39-22 12
g GTO 15 11-25 7 15 x 40-61
/ 12-51 g ex 41-25 22
g CFi 13-25 14 RCL PV 42-22 13
g GTO 00 14-25 7 00 x 43-61
x<>y 15-33 STO / 0 44-21 51 0
- 16-41 x 45-61
g GTO 13 17-25 7 13 STO / 1 46-21 51 1
1 18-1 RCL n 47-22 11
0 19-0 3 48-3
n 20-11 g x<>y 49-25 5
0 21-0 g GTO 24 50-25 7 24
STO 0 22-21 0 RCL i 51-22 12
STO 1 23-21 1 RCL FV 52-22 15
RCL g CFi 24-22 25 14 RCL 0 53-22 0
g x=0 25-25 6 - 54-41
g GTO 24 26-25 7 24 RCL 1 55-22 1
f INTGR 27-24 61 / 56-71
PV 28-13 / 57-51

 
 
KEY ENTRY
DISPLAY
KEY ENTRY
DISPLAY
i 58-12 CHS 66-32
g LASTX 59-25 31 g x<>y 67-25 5
g PSE 60-25 4 g GTO 18 68-25 7 18
2 61-2 1 69-1
g yx 62-25 21 RCL i 70-22 12
f SQRT x 63-24 21 f %T 71-24 22
g EEX 64-25 32 g P/R
7 65-7

 
 
REGISTERS
R0 Sum numerator R1 Sum denominator R2 CF1 R3 CF2
R4 CF3 R5 CF4 R6 CF5 R7 CF6
R8 CF7 R9 CF8 R.0 CF9 Rn n
Ri ik RPV T RPMT pj RFV VT

Instructions:
 

  1. Key in the program.
  2. Set switch to M.DY and press f CLEAR ALL.
  3. Key in the date of the final fund evaluation and press PMT.
  4. Key in the final fund value and press FV.
  5. Key in an initial guess for the interest rate, .1, and press i.
  6. Key in 2, press n.
  7. Key in the transaction (whole dollars only) and press PV.
  8. Key in the date of that transaction and press R/S.
  9. Repeat steps 7 and 8 until all transactions are entered.  Then press g GTO 18 R/S to compute the continuously compounded interest rate.
  10. To compute the annual rate, use the following keystroke sequence: RCL i 1 / g LN 100 x.

Example:

You invest in a pension fund and after anumber of year you are told that the fund value was 9,050 dollars on 7/01/1977.  Determine the effective (continuously compounded) and nominal rate of return from the record of your transactions which are as follows:

    an investment of $4,150 on 1/01/1972;
    an investment of $2,005 on 1/01/1973;
    a withdrawal of $950 on 1/01/1974;
    a withdrawal of $3,111 on 1/01/1975;
    an investment of $2,000 on 10/01/1975;
    an investment of $2,005 on 1/01/1976; and
    a final investment of $1,000 on 7/01/1976.
 
 
Keystrokes
Display
D.MY/M.DY = M.DY
f CLEAR ALL 0.00
7.011977 PMT 7.01
9050 FV 9,050.00
.1 I 0.10
2 N 2.00
4150 PV 4,150.00
1.011972 R/S 4,150.06
2005 PV 2,005.00
1.011973 R/S 2,005.04
950 CHS PV -950.00
1.011974 R/S -950.03
3111 CHS PV -3,111.00
1.011975 R/S -3,111.02
2000 PV 2,000.00
10.011975 R/S 2,000.02
2005 PV 2,005.00
1.011976 R/S 2,005.01
1000 PV 1,000.00
7.011976 R/S 1,000.01
g GTO 18
R/S (-.04)                Differences between
(-0.004)            successive approximations
(-0.00005)        of the correct interest rate.
(-0.00000001)
5.90                effective continuous rate

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