Download Hewlett-Packard 10BII

Hewlett-Packard 17BII+
Tutorial for Use with Fundamentals 11/e and Concise 5/e
This tutorial was developed for use with Brigham and Houston’s Fundamentals of
Financial Management, 11/e and Concise, 5/e, especially Chapter 2, the Time Value of
Money. The calculator’s 309-page manual covers all of its functions in detail, and it is
worth the time to go through the manual. However, this does take time, and many of the
calculator’s features are not necessary for working the problems in the text. Therefore, we
focus on just what’s needed to work the text problems. We recommend that you read the
text to get an idea about the concepts, then go through the tutorial to learn how to work
the problems efficiently. The examples in the tutorial are identical to the examples in the
text, which makes simultaneous coverage especially efficient.
Although the tutorial focuses on Chapter 2, it does have a section on Statistical
Calculations, which are needed for Chapter 8 of the text. You can defer that part of the
tutorial until you get to Chapter 8 of the text. Also, note that the TVM applications
covered in text Chapter 2 and this tutorial are required for many text chapters, especially
those dealing with bond and stock valuation and capital budgeting. Therefore, it will pay
big dividends to learn how to use your calculator early in the course, like right now.
BASIC CALCULATOR FUNCTIONS
The HP17BII+ performs all the basic arithmetic functions: addition, subtraction,
multiplication, division, exponents, and so on that can be done with any calculator. But it
can also solve TVM problems and do certain statistical and math calculations that simple
calculators cannot do.
The GOLD shift key
Most of the keys have white numbers or lettering on top, then gold lettering on the sloped
front side. The white and gold colors are used because the keys can perform more than
one function. The gold shift key, with no lettering but a gold swatch, allows the user to
activate the gold functions. If the gold shift key is not pressed, then the function keys
perform the function indicated by the white lettering. Also, note that pressing the gold
shift key GOLD places the an “up arrow” symbol in the upper left corner of the LCD
display. Press the GOLD key again and the arrow goes away. The GOLD key is a
toggle key that switches back and forth between the regular and the gold functions, like
typewriter shift keys. After you press GOLD , look only at the gold functions. In this
tutorial, whenever you see the GOLD key, the lettering on the next key corresponds to
the gold function, not the primary (white) function.
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Turning the calculator ON and OFF
To turn on the calculator, press CLR .
Note that the CLR key is in the lower left corner of the keypad—the face of the key has a
white "CLR," while the word "OFF" appears at the bottom of the key in gold. To turn the
calculator off, press GOLD OFF . Thus, the two keystrokes required to turn the
calculator off are (1) press the gold shift key and (2) then press the “CLR” key. Thus, by
pressing the gold shift key first, we are activating the gold function on the “CLR” key,
which turns the calculator off.
To conserve the battery, the calculator turns itself off about 10 minutes after your last
keystroke. Note too that the calculator has a continuous memory, so turning it off does
not affect any data stored in the calculator. However, the display does go to zero.
Calculator language setting
The first time you turn on your HP 17BII+, you will have to define the appropriate
language setting. At the “SELECT LANGUAGE” prompt, you can choose between German,
English, Spanish, French, Italian, or Portuguese. We will assume that you will select
ENGL, for English. However, if you are an international student, you may elect for
another language. If you do so, the instructions in this tutorial will still be generally valid,
but specific details about menu listings will be slightly different.
The menu system
Many of the HP17BII+ calculator’s functions are accessed through an on-screen menu
system. The main menu can be accessed at any time by pressing GOLD MAIN . The
main menu options are:
FIN
BUS
SUM
TIME
SOLVE
CURRX
Below each menu option there is an arrow that must be pressed to select that particular
menu option. This tutorial will focus on using the FIN and SUM functions, but readers are
encouraged to refer to the HP 17BII manual to learn how to use the other menu options.
Press FIN and you will see a list of financial functions, including:
TVM
ICNV
CFLO
BOND
DEPRC
These options represent the time value of money, interest conversion, cash flow
register, bond calculation, and depreciation calculation menus. Remember, pressing
GOLD MAIN will always take you back to the main menu, while pressing EXIT will
allow you to go back one layer in the menu system. For the duration of this tutorial,
whenever you see a command in a box, like EXIT , it may refer to a function on a key or
a menu option. From the context of the tutorial and the other keystrokes, it should not be
difficult to determine which is applicable.
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Clearing the calculator
To clear the calculator’s memory, press GOLD CLEAR DATA . Clearing the calculator is
important, since leftover data in the calculator’s memory can lead to errors. You should
get into the habit of automatically clearing memory before starting a new calculation.
Occasionally, you may want to save data, but in general you will be entering all new data,
so starting with a clear memory is the safest approach.
There are three different ways to clear data:

clears numbers on the display one at a time.
CLR
clears the entire display, but not the memory.
GOLD CLEAR DATA
clears the display and all memory. This is the safest way to
clear data, and the procedure we generally use.
Changing the decimal and screen display
Depending on what you are doing, you may want no decimal places, two decimal places,
4 decimal places, etc. The number of decimals displayed can be changed easily. To
demonstrate, enter the value 5555.5555 and press the = key.
If your display is currently set for two decimal places, the value is truncated to 5,555.56.
To change the number of decimal places from 2 to 4, press DSP FIX 4 INPUT . The
value 5,555.5555 is displayed instantly.
To change back from 4 decimal places to 2, press DSP FIX 2 INPUT . Now the
value 5,555.56 is displayed. (Rounding is automatic.)
We usually set the display to 2 places, which is convenient when working with dollars and
percentages. However, we often use 4 decimal places when dealing with interest rates
and with rates of return that are entered as decimals.
Finally, to control the brightness of the LCD display, hold down CLR and, depending on
whether you want more or less brightness, press either + or – .
USING THE FINANCIAL FUNCTIONS
Settings: Periods per Year (P/YR)
The HP17BII+ comes out-of-the-box set assuming that when any payment stream is
entered, 12 payments are made each year, or monthly. Generally, though, most textbook
problems are based on one payment per year. So, if you tell the calculator there are 8
payments by setting N = 8, it would assume that they are made monthly, not annually, so
the calculated answer would be wrong—you would be too high on PVs and too low on FVs.
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To check the current payments per year setting, access the time value of money menu, by
pressing FIN TVM . The display shows the setting for periods per year.
To change the setting to one payment per year, press OTHER 1 P/YR (starting from
the TVM menu). Now the calculator is set to assume 1 P/YR. We normally leave the
calculator setting at 1 P/YR. If a problem calls for monthly payments, we adjust the
number of periods and the interest rate as explained later in this tutorial.
Settings: BEGIN and END Mode
Annuities provide payments over a number of periods. For some annuities those
payments are made at the beginning of each period, while for others the payments are
made at the end of the periods. The calculator can be set to deal with either payment
pattern, or at BEGIN or END mode. Most annuities have end-of-period payments.
When you access the TVM menu, you will notice that it shows you the number of
payments per year and it indicates whether you are in BEGIN or END mode. To toggle
between BEGIN and END modes, press OTHER BEG or OTHER END , from the TVM
menu. We recommend leaving the calculator in END mode, then switching to BEGIN
when required, and then switching back to END when you are done.
BASIC TIME VALUE OF MONEY (TVM) CALCULATIONS
When you access the TVM menu (press EXIT to return you to this menu from the begin
and end mode settings), you will see the following options:
N
I%YR
PV
PMT
FV
OTHER .
This is the primary TVM menu and it contains the basic TVM inputs that will be used to
solve many problems. If you know any four of the five TVM variables, the calculator will
solve for the fifth. The OTHER option allows you to access TVM settings (like P/YR and
BEGIN/END mode) and the amortization feature.
FV and PV for lump sums
We first consider TVM calculations with a single (lump) sum.
Example 1: Calculating the FV of a lump sum
What’s the FV of $100 after 3 years if the interest rate is 5%?
First, clear by pressing GOLD CLEAR DATA . This sets all the variables, including PMT,
to zero. Next, enter the following data:
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3
N
5
I%YR
100
+/– PV
The +/- key changes the 100 to -100.
0
PMT
You could skip this step, but it’s safer to enter the 0.
Now press FV to get the answer, $115.76.
Since the PV was entered as a negative number, the FV is automatically displayed as a
positive number. You will notice that after you enter a variable into the TVM worksheet,
the display shows you what value has been entered. You can recall any input variable by
pressing the appropriate key.
Example 2: Calculating the PV of a lump sum
What is the PV of $115.76 due in 3 years if the interest rate is 5%?
Clear the calculator and then enter the following data:
3
N
5
I%YR
0
PMT
115.76 FV
Pressing PV gives the answer, -$100.00. If we had $100 today, it would grow to
$115.76 after 3 years at a 5% rate.
Example 3: Calculating I%YR
Assume you lend someone $100 today and they must pay you $150 after 10 years. No
payments will occur between now and Year 10. What rate of return would you earn?
10
N
100
+/– PV
0
PMT
150
FV
Convert the 100 to -100 to indicate an outlay.
Press the I%YR key and the calculator provides the earned rate of return, 4.14, which
means 4.14%. Note that the calculator displays 4.14 rather than 0.0414 or 4.14%. Don’t
clear the calculator; we need the data for the next example.
Example 4: Overriding a value to find a new interest rate, I%YR
Suppose you want to modify the preceding example, lending only $95 but still receiving
$150 after 10 years. What rate of return would you earn on the modified loan?
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If you left data from the preceding example stored in your calculator, you can override (or
replace) the PV of 100. Just enter 95 +/– PV , and when you press I%YR , you get
4.67%, the new interest rate on the loan. You could override other variables similarly
and thus do “what if” analyses to see how the output changes with changes in the inputs.
Example 5: Calculating N
Suppose you currently have $500,000 in an account that is earning 4.5%. You want to
find out how long it will take your account balance to reach $1,000,000.
4.5
I%YR
500000
+/– PV
0
PMT
1000000
FV
Press the N key and the calculator returns 15.75, the number of years before you have
$1,000,000 in the account. Note that the calculator requires you to enter the interest rate
as 4.5 rather than either 0.045 or 4.5%.
Recalling information
Now press GOLD OFF to turn off the calculator, and then turn it back on. The display
will show exactly what it showed before being turned off. All the data in the TVM memory
is still there, until it is cleared by GOLD CLEAR DATA .
Annuities
Annuities can also be analyzed with the TVM keys. Now we have a payment, so we must
enter a non-zero value for the PMT. There are 5 terms in the basic TVM equation, and if
we enter data for any 4 variables the calculator will solve for the fifth.
Example 6: FV of an ordinary annuity
What’s the FV of an ordinary annuity of $100 for 3 years if the interest rate is 5%?
0
|
0
5%
1
|
-100
2
|
-100
3
|
-100
There is no beginning amount, so PV = 0. Thus N, I%YR, PV, and PMT are given, and we
must solve for the FV:
3
N
5
I%YR
0
PV
100
+/– PMT
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Now press the FV key to find the answer, FV = $315.25.
Example 7: FV of an annuity due
If the interest rate is 5%, what is the FV of an annuity due where we deposit of $100 at
the beginning of each of the next 3 years?
0
|
-100
5%
1
|
-100
2
|
-100
3
|
After clearing, set the calculator to BEG mode and then enter values for the input
variables:
OTHER BEGIN
(to switch to BEGIN mode, from the TVM menu)
EXIT
(to get back to the main TVM menu)
3
N
5
I%YR
0
PV
100
+/– PMT
When you press the FV key, the answer, $331.01, is displayed, along with the word
“BEGIN.” Most text problems have end-of-period payments, so it’s a good idea to get into
the habit of reverting to END mode after a problem: OTHER END .
Example 8: PV of an ordinary annuity
What’s the PV of the ordinary annuity discussed in Example 6?
Enter the following data:
EXIT
(to get back to the main TVM menu)
3
N
5
I%YR
100
+/– PMT
0
FV
Then, press PV to get $272.32. If you left all the data in the calculator, then pressed
OTHER BEGIN , and then pressed EXIT PV , you would get the PV of the annuity as
an annuity due, $285.94. Again, revert to END mode after finishing this exercise and go
back to the main TVM menu.
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Example 9: Finding the payments for an annuity (PMT)
The future value of an ordinary 5-year annuity is $10,000, and the interest rate is 6%.
What are the annual end-of-year payments? What would each payment be if they were
made at the beginning of the year?
Since payments are made at the end of each year, make sure the calculator is set to END
mode. N, I%YR, PV, and FV are given, so we solve for the PMT:
5
N
6
I%YR
0
PV
10000 FV
Now, press the PMT key to get the answer, PMT = -$1,773.96.
To find PMT if the annuity were an annuity due, then we would leave the data in the TVM
register, switch to BEGIN mode by pressing OTHER BEGIN , go back to the main TVM
menu by pressing EXIT , and then press PMT to get -$1,673.55.
Example 10: Calculating the number of periods (N)
Suppose you plan to deposit $1,200 at the end of each year in an account that pays 6%
interest each year. How long will it take for your account to reach $10,000?
First clear the calculator, make sure you are in END mode, and you are back at the main
TVM menu. Then make these data entries:
6
I%YR
0
PV
1200
+/– PMT
10000
FV
Now press the N key to find the number of years, 6.96, which you might round to 7.
Notice that the PMT is entered as a negative because you are making a deposit, while FV
is positive because you can withdraw it. Either PMT or FV must be negative—otherwise,
the calculator will produce a nonsensical answer, in this case -11.90 years. Note too that
if the payments occur at the beginning of each year, you would follow the same
procedure, but here your calculator would be set to BEGIN mode. The answer would then
be 6.63 years.
Example 11: Calculating the interest rate (I%YR)
Continue with the previous example, but now assume you can only save $1,200 at the
end of each year. You still want to accumulate $10,000 by the end of 5 years. What
interest rate would you have to earn to reach this goal? Here are the keystrokes:
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5
N
0
PV
1200
+/– PMT
10000 FV
Make sure the calculator is in END mode, and press the I%YR key. The required rate of
return, or interest rate, is 25.78%. If the payments occurred at the beginning of the
years, you would use the same keystrokes, but with the calculator set to BEGIN mode, the
answer would be 17.54%.
Example 12: Uneven cash flows: annuity plus a lump sum
Assume that you can buy a security that will make the payments shown on the following
time line. What is the PV of this stream if the interest rate is 12%?
0
|
12%
1
|
100
2
|
100
3
|
100
4
|
100
5
|
100
1,000
1,100
Here we have a 5-year ordinary annuity plus a $1,000 lump sum at the end of Year 5.
The calculator finds the PV of the annuity, the PV of the Year 5 lump sum payment, and
then sums them, using the basic TVM keys as follows:
5
N
12
I%YR
100
PMT
1000
FV
Now press the PV key to find the PV, -$927.90, which shows up as a negative because
PMT and FV were entered as positive numbers.
Example 13: Irregular series of cash flows
Assume that you can buy a security that will make the payments shown on the following
time line. At an interest rate of 12%, what is the PV of the security?
0
|
12%
1
|
100
2
|
300
3
|
300
4
|
300
5
|
500
This problem requires us to use the calculator’s “cash flow register,” where we enter a
series of inputs and then perform a calculation based on those inputs. Access the cash
flow register by pressing FIN CFLO (you may need to press EXIT a couple of times to
get back to the main menu), and make sure the cash flow register’s memory is clear by
pressing GOLD CLEAR DATA . You will be asked if you want to clear the list, just say
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yes to clear the register. Then, enter the cash flow data from above. You will be asked
for the cash flows that occur and how many times they occur (notice the $300 cash flow
occurs 3 times).
The calculator asks for the initial cash flow by displaying: “FLOW(0)=?”. After you enter a
value, you are prompted for “FLOW(1)=?”, and then asked how many times it occurs:
“#TIMES(1)=?”. This procedure continues until all cash flows are entered. The
keystrokes required are:
0
INPUT
(Initial cash flow)
100
INPUT
1
INPUT
(1st cash flow, occurs once)
300
INPUT
3
INPUT
(2nd cash flow, occurs three times)
500
INPUT
1
INPUT
(3rd cash flow, occurs once)
These keystrokes tell the calculator to store the cash flows shown on the time line into the
cash flow memory. Notice the number in the parentheses of calculator’s prompts changes
to reflect which cash flow is being entered into the calculator. At any point, you can
review the values entered in the cash flow register using the  or  keys.
After the CFs have been entered, press EXIT to return to the CFLO menu, select
CALC and enter the interest rate by pressing 12 I% . Next, to find the PV of the cash
flows, press NPV to find NPV = PV = 1,016.35.1
Unlike many other financial calculators, the HP 17BII+ also has a net future value
(NFV) function. The NFV feature finds the future value of each cash flow and sums the
future values. Press NFV to solve for the net future value of $1,791.15.
Example 14: The Internal Rate of Return (IRR)
Assume that we invest $1,000 today (t = 0) and expect to receive an uneven set of cash
flows in the future. Here is the CF time line:
0
1
12%
|
|
-1000
100
2
|
300
3
|
300
4
|
300
5
|
500
What rate of return will we earn on the $1,000 investment? Here are the entries:
GOLD CLEAR DATA YES
To clear entire cash flow list to put new data
in cash flow register
1000
+/–
INPUT
100
INPUT
1
INPUT
300
INPUT
3
INPUT
500
INPUT
1
INPUT
NPV stands for Net Present Value. Our stream has no negative cash flows, but if there were
some negative flows, the calculator would net them out to produce the NPV. There is a negative
flow in the next example.
1
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To get to the CFLO menu press EXIT , and then press CALC IRR% to solve for the
interest rate, which is 12.55%. So, if we make this investment, we will earn 12.55% on
our money. At 12.55%, the sum of the inflow PVs is equal to the $1,000 investment.
Leave the data in the calculator, and we will show you how to calculate the NPV
without entering new data except for the interest rate. Assuming I% = 12%. Simply
press 12 I% NPV and you will get the NPV, which is $16.35. The NPV and IRR are
used in capital budgeting, and we virtually always calculate both with a given set of cash
flow data. The important point is that you need to enter the cash flow only once to get
both the NPV and the IRR.
Example 15: Effective Annual Rate (EAR, or EFF%)
If interest is paid more than once per year, then we often need to calculate an effective
annual rate for use in TVM calculations. The following equation is used to convert
nominal rates to effective rates:
M
I 

EAR  EFF%  1  NOM   1 ,
M 

Here INOM is the stated rate and M is the number of compounding periods per year. The
calculator is programmed to solve this equation, as we illustrate with this example: What
is the EAR (or EFF%) on a bank account that pays a stated (or nominal) rate of 5% but
with semiannual (twice yearly) compounding? Here are the keystrokes:
To access the interest conversion (ICNV) menu, go back to the main menu by pressing
GOLD MAIN and then press FIN ICNV . There are two compounding options to
choose from. Either you can specify the number of periods per year (PER) or you can
assume continuous compounding (CONT). Here, we will deal with discrete
compounding that requires you to specify how many payments per year. Select PER ,
and enter the nominal interest rate and number of compoundings as follows:
5
NOM%
Enters the nominal rate
2
P
Changes the compounding periods per year to 2.
EFF%
Gives the EAR or EFF%, 5.0625%.
If there had been 12 compounding periods per year, the effective rate would have been
5.1162%.
If you want to find the effective rate using continuous compounding, just select CONT
and enter a nominal rate and solve for the effective rate. Continuous compounding is
discussed in Web Appendix 2A.
Example 16: PV with semiannual compounding
A $100 lump sum is due in 10 years. Our funds could be invested at 5%, compounded
semiannually. What is the PV of the future $100 payment?
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Access the TVM menu. We can find the PV in two ways. First, we could use the EFF% of
5.0625% as calculated above and then enter N = 10, I%YR = 5.0625, PMT = 0, and FV =
100. Then, when we press the PV key we find PV = -$61.03.
Alternatively, we could divide the nominal rate by 2 to get the semiannual rate and
multiply the number of years by 2 to get the number of semiannual periods and then
proceed as shown below:
10 x 2 =
N
(enters 20 periods for N)
5÷2 =
I%YR
(enters the 2.5% semiannual rate)
0
PMT
(because there are no annual payments)
100
FV
(this is the one payment we will receive as an inflow)
Pressing PV provides the answer, -$61.03. Note that it’s the same as the answer found
using the EFF% and 10 years rather than 20 semiannual periods. (Remember, the PV
shows up as a negative because PMT and FV were entered as positive numbers.)
Example 17: Loan amortization
In this example we show how to use the calculator to create an amortization table for a 5year, 6%, annual payment, loan of $100,000 as shown in Table 2-4 in the textbook. You
should look at that table as you work through the following calculations.
First, we find the required loan payment. After checking to be sure P/YR is set to 1
payment per year and that you are in End mode, access the TVM menu, and make these
entries:
5
N
6
I%YR
100000
PV
0
FV
PMT = -$23,739.64. This is the required annual payment.
To access the amortization feature, press OTHER AMRT . Next, enter the number of
payments you want to analyze. Let’s begin with the first payment, so enter 1 #P .
“#P=1 PMTS: 1-1" is displayed. This indicates that you are about to see Year 1 data.
Press PRIN to see the amount of principal repaid in the first year, -$17,739.64.
Press INT to see the amount of interest, -$6,000. Press BAL to see the balance at
the end of Year 1, $82,260.36. You could write out these numbers to get the first
year data for the amortization schedule shown in Table 2-4.
Now press NEXT to see Year 2 data. Press PRIN , INT , and BAL to get the Year 2
principal repayment, interest, and ending balance. You could repeat this procedure to find
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data for years 3, 4, and 5. If you wrote all this out, you would have the Table 2-4
amortization schedule, and you would see a final balance of 0.00.
More can be done with the amortization feature, including working with monthly payment
loans, but we refer you to the calculator manual for these applications.
USING THE STATISTICAL FUNCTIONS
The HP17BII+ can also perform several statistical functions. In this tutorial, we will focus
on the mean (or arithmetic average), the standard deviation, and regression analysis. To
begin, note that there are two types of data—complete population data and sample data.
We have population data if we have information on every possible data point. For
example, if there were 5,000 publicly traded companies and we knew last year’s rate of
return for each one, then we would be dealing with population data. However, if we
collected data on just 200 of the 5,000 firms, we would have sample data.
Another example of population data is where you are given a probability
distribution of a particular stock’s expected returns. If all possibilities are included, which
means that the probabilities sum to 1, then we have population rather than sample data.
Here’s an example of probability data:
Outcome
Terrible
Poor
Expected
Good
Excellent
Probability
0.10
0.20
0.40
0.20
0.10
1.00
Return
-18%
-6
12
30
42
We generally use statistical analysis in two ways: (1) To get an idea about something that
occurred in the past, like the average rate of return on publicly owned stocks and the
extent to which different firms deviated from that average. We would use the mean
(average) to get an idea of the central tendency of returns and the standard deviation to
get an idea about the variations about that mean. (2) To predict future outcomes, like the
rate of return on a stock during the coming year. For predictions, we typically rely on
regression analysis.
We are most concerned with the mean (average expected return) and the
standard deviation (which measures the dispersion of possible returns from the mean).
These values can be calculated with the HP17BII+ as shown below.
The 12% has the highest probability, the -6% and +30% are next, and the -18%
and +42% have the lowest probabilities. We can then enter each return into the calculator
in proportion to the probability of its occurrence. From the main menu, press SUM . Like
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the cash flow register, this function asks you to enter a series of data. Make sure the
memory is clear, by pressing GOLD CLEAR DATA and select YES . Then press:
18
+/– INPUT
10% probability, or 1 in 10, so enter once.
6
+/–
20% probability, or 2 in 10, so enter twice.
6
+/– INPUT
12
INPUT
12
INPUT
12
INPUT
12
INPUT
30
INPUT
30
INPUT
42
INPUT
INPUT
40% probability, or 4 in 10, so enter four times.
20% probability, or 2 in 10, so enter twice.
10% probability, or 1 in 10, so enter once.
As you enter the data, the display keeps prompting you for “ITEM(1)=?”, and so on for
your entire list. Here our probabilities were all divisible by 10 and hence were easy to
work with. If the probabilities had been irregular, say 6% for one return, 13% for
another, etc., this procedure would be more trouble than it would be worth, and it would
be easier to just use the formulas to calculate the mean and standard deviation.
If we have sample data, like annual stock market returns, each data point has an equal
chance of occurring, so we would just enter each one once.
Once the data have been entered, we can find the mean and standard deviation as
discussed below.
Example 18: Population mean and standard deviation
With the data stored in the calculator as shown above, we can find the expected return
(mean, or average) and the standard deviation () by pressing EXIT and CALC .
Press MEAN for the mean, or expected, return, 12.00%.
Press EXIT and enter the value of the mean into the list (this makes the 11th entry),
by pressing 12 INPUT then press EXIT CALC STDEV to obtain the population
standard deviation, 17.60%.2
Working with sample data
We often work with historical stock market returns and other sample data. Procedures
here are nearly identical to that for the population data, but there are a few differences.
2
This procedure for standard deviation is so complicated because the prepackaged standard
deviation operation assumes a sample standard deviation. In this case, we needed a population
standard deviation and a couple of extra steps were required. You will see in the next example
when we calculate a sample standard deviation, it is a lot easier.
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We use a 5 data point example for simplicity, but we would normally want more
observations to increase our confidence in the results.
Return
Year
2001
2002
2003
2004
2005
Market
23.2%
-10.1
-8.3
28.2
10.1
Stock Y
56.8%
-23.1
-31.0
32.8
11.1
Example 19: Sample mean and standard deviation
What is the mean (average) and standard deviation (s) of returns on the market and on
Stock Y over the past 5 years?
First, the data must be entered into the calculator. Now, we are entering two fields of
data: market returns and stock returns. First, we must enter the entire list of market
returns (the X variable).
Access SUM by entering GOLD MAIN , clear the data by entering
GOLD CLEAR DATA YES , and then begin entering the X variables (like above):
23.2
INPUT
10.1
+/–
8.3
+/–
INPUT
INPUT
28.2
INPUT
10.1
INPUT
Now, we must store this list in the calculator’s memory. Press EXIT NAME . Here you
can specify a name. You can give the data a descriptive name, like Mkt returns, but
sometimes it is best to keep it simple. Name the list “X”. Press WXYZ X INPUT .
Now, the list is saved as “X,” and the Y variable data needs to be entered.
Press GET *NEW to start a new list. Enter the Y variable data:
56.8
23.1
31.0
32.8
11.1
+/–
+/–
INPUT
INPUT
INPUT
INPUT
INPUT
Name the new list “Y” by pressing EXIT NAME WXYZ Y INPUT .
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To determine the means and standard deviations of the two variables, you have to
retrieve each list and calculate the mean and sample standard deviation of each list as
follows:
GET X
CALC MEAN
The mean of the X variable (X’s return) is 8.62%.
STDEV
The standard deviation of the market is 17.57%.
EXIT GET Y
CALC MEAN
The mean of the Y variable (Y’s return) is 9.32%.
STDEV
The standard deviation of Stock Y is 37.03%.
Linear Regression
Regression analysis shows the relationship between two variables, in this case the returns
on the Market and on Stock Y, and the regression is given in the form of Y = a + bX.
The b term in this equation is the beta coefficient, which is used in the CAPM to show the
relationship between returns on an individual stock and returns on the market. We can
use the data you just entered in the calculator to find Stock Y’s beta. These same
procedures can be used for any simple linear regression.
Example 20: Determining the regression parameters
After the data is entered and after calculating each lists mean and standard deviation in
Example 19, press MORE FRCST . You are now asked to select the “X Variable.”
Choose the “X” list you created. You are now asked to select the “Y Variable.” Choose
the “Y” list you created. Now press MORE MODL LIN . To solve for the Y-intercept
and beta coefficient press:
B
The Y-intercept is -7.74%.
M
The beta coefficient is 1.98.
Therefore, the regression line is: Stock Y’s return = -7.74% + 1.98 (Market
return).
Example 21: Correlation coefficient
What is the correlation coefficient between Y’s return and the market return? What is the
R2 of the regression?
With the data still stored in the calculator and from the linear model results menu (that
you should still be in after working Example 20), press:
CORR The correlation coefficient is 0.94.
In a simple regression (one independent variable), the R2 of a regression is just the
square of the correlation coefficient.
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R2 = (r)2 = (0.94) = 0.88.
Finally, note that the HP17BII+ cannot do multiple regressions, where there are two or
more independent variables.