Calculating Betas Using Regression on HP 10B,

HP 12C, or Texas Instruments Calculators

For most purposes, you should use Excel or statistics software for running regressions. But you should know how to run regressions on calculators. Since there are so many calculators, I cannot provide instructions for all of them. Indeed, I recommend that you use the HP-10B, which has enough functions to be useful for most situations. Other more expensive calculators obviously have more functions (like the 12C), but often take longer to learn how to use. As a result you will not use the full capabilities of these "high-powered" calculators. In your work (job), most of the complex calculations will be done with Excel anyway! Here are some simple steps on the two popular HP calculators and for the popular Texas Instruments calculators. In all cases, you should also consult the owner's manuals for further directions, and work through examples with one another. Supppose that we have the following returns for 5 weeks in percentages:

Week	Index %Return (x values)	Company %Return (y values)
1	3%	5%
2	3%	4%
3	-2%	-2%
4	5%	6%
5	-2%	-1%

Note that the company's returns tend to be more "extreme" than the market's. This means that the company's beta should be greater than 1. If you calculate a beta less than 1, you did something wrong! To calculate a firm's beta, regress the company's percentage returns (daily, weekly,or monthly) against the market's returns; where we have the equation: Y = a + bX. Y represents the company's returns and X represents the market index (percentage) returns. Even though the equation has Y on the left, the Company returns are on the right above, because we enter the X data first for the HP-10B.

In all cases, enter the data in pairs (the x-y pair for week 1, then the x-y pair for week two, and so on) in the order suggested below, then proceed to calculate the y-intercept and the slope (beta).

Regression using an HP 10B. Use the data above to calculate the firm's beta. See the HP-10B manual on pages 86-87 and 91 for the instructions that are summarized here. Enter the 1st x-value with the INPUT key and then the corresponding y-value with the Sum+ key. These are the percentage values above of (3,5). Do this for each pair of values. Once each of the five pairs of values is entered, then see page 91 for the Linear Regression instructions. Calculate the y-intercept (b) by pressing the following three keys in order:

the last key is the second-key for the 5-key. This sequence gives you the y-intercept; which we often do not need. Your answer for the above values should be 0.83. If you don't get this as an answer, try again!

The slope (the m of the y-hat, m key) is the BETA! Just after you calculate the y-intercept, press the following two keys in order:

the SWAP key is the second-key for the K-key, just above the orange key.

The beta for the above company equals 1.12, which is greater than 1.00 for the market, which means that the company is more risky than the market.

Regression using an HP 12C. See Section 6 of the Owner's Handbook and Problem-Solving Guide, pgs. 87-91. The directions for entering y-values and x-values are on page. 87. You should enter the y-value of each pair first. Enter the 1st y-value with the ENTER key, and then the corresponding x-value with the SUM+ key. These are the percentage values above of (5,3). Do this for each pair of values. Unfortunately, the 12C does not have a beta key. However, several procedures will give you a beta once you enter the data. The procedure explained below depends upon the fact that the beta is the slope of the regression, which equals the "rise over the run." Carry out the following steps:

1. Press the (0) (g) (y-hat,r) keys to find the value of y at x=0, which equals 0.8301 for our example (the y-intercept).

2. Press the (STO) (0) keys to store the value of the Y intercept for use in calculating the slope (beta).

3. Press the (0) (g) (x-hat,r) keys to find the value of x at y=0, which is the value of the X-intercept, which equals -0.7403.

4. Press (RCL) (0) (CHS) (x><y)(division) keys to calculate and display the value of the slope, which equals 1.12.

Note that the beta of 1.12 is the same as for the HP-10B. Other methods exist for calculating a beta with the 12C, and other calculators will be easier (like the 10B).

Regression using an HP 17B. See pgs. 124-25 for an example of inputing data, and p. 121 for the beta calculation (under forecasting).
The basic steps:
Entering Data

1. Press: SUM, and Item 1 will appear. Then enter all of your x-values in a row, pressing INPUT after each value. When you are finished entering your x-values, press EXIT. [Next you have to name the values -- as a variable.]

2. Press: NAME (WXYZ), and then choose the X and press INPUT, so that you tell the calculator that the set of values you entered is your x-variable.

3. Press: GET, then NEW ; and then enter all of your y-values as in step 1, and name this set of values your y-variable,
following step 2.

You should now have your x-variable (set of index percentage return values) and your y-values (your company percentage return values) entered into the calculator. To get the beta (and intercept), remember that the elementary school equation is used: y = mX + b; where m is the slope (beta) and b is the y-intercept of the linear equation.

4. Press: CALC (^)
     Press: MORE (^)
     Press: FRCST (^) -- for forecasting with linear regression.
     Select: the X-variable (you will be given the two options, X and Y, if you entered the data according to the directions!).
     Select: the Y-variable.

5. Press: M to get the beta for your company, and the b for the y-intercept (note that these are from the grade school equation: y = mX + b).

Regression using Texas Instruments Calculators (BA, BA-II or MBA). See the Owner's Manuals for more details and additional examples. Carry out the following steps.

1. Press the 2nd Mode keys until "STAT" shows in the display.

2. Enter the first x-value (3) and press the x><y key; then enter the first y-value (5) and press the SUM+ key.

3. Continue entering the x and y-values as in step 2 until all observations are entered.

4. Press the 2nd b/a keys to find the value of y at x=0, which is the value of the y-intercept (equals 0.8301).

5. Press the x><y key to display the value of the slope (beta), which is 1.12.

Using the TI BA II PLUS:

1. Press 2nd DATA to enter the data. You are then actually "prompted" for the X01 and Y01 data points, etc. When you enter one value (e.g. for the X01, the press ENTER, and then the ARROW DOWN (actually pictured as an arrow in the top row of your calculator).

2. When you have completed entering the data, press: 2nd STAT, then 2nd CLRWork. After that, all you have to do is press the ARROW DOWN key successively, until you see the display for b = (beta!). When you press the ARROW DOWN key the first time, your display will show a = ... , which is the y-intercept of the regression equation. You have to press the Arrow Down key many times to have the beta displayed.

Regression on a calculator is easy! But remember that OLS regression includes many technical assumptions. Should you need additional help, please use the Owner's Manual that comes with your calculator especially if you use something other than an HP! And remember to review regression mathematics in a statistics or finance textbook.