**Question:** To what extent have the stock prices of four companies – Duke Power, Bank of America, IBM and Proctor and Gamble – moved with the overall stock market? Do lagged movements in the overall stock market also impact the current period stock price?

How have changes in the 10-year government bond interest rate impacted the stock price for the four companies?

**The Data**: The analysis presented here is based on monthly data starting with the fourth month of 1980 and ending with the seventh month of 2018. N=456.

**The Model**: The dependent variable is stock price at period t divided by the stock price at time t-1. The explanatory variables are S&P 500 at period t divided by S&P at time t-1, three lags of this S&P ratio, and the ratio of the current 10-year government bond interest rate to the lagged 10-year government bond interest rate.

**Results:** The results for the return equations for the four companies are presented below.

Duke Power |
||

dukror |
Coef. | P>t |

spror |
0.33556 | 0 |

lag1spror |
0.0365767 | 0.546 |

lag2spror |
0.058777 | 0.335 |

lag3spror |
-0.0211995 | 0.725 |

tenyrch |
-0.1645325 | 0.001 |

_cons |
0.7624648 | 0 |

Bank of America |
||

bacror |
Coef. | P>t |

spror |
1.392815 | 0 |

lag1spror |
0.0396445 | 0.68 |

lag2spror |
0.1671838 | 0.085 |

lag3spror |
-0.0386275 | 0.686 |

tenyrch |
0.1329733 | 0.079 |

_cons |
-0.6889676 | 0 |

IBM |
||

ibmror |
Coef. | P>t |

spror |
0.9212106 | 0 |

lag1spror |
-0.051747 | 0.444 |

lag2spror |
-0.0875875 | 0.199 |

lag3spror |
-0.0776229 | 0.248 |

tenyrch |
0.0725273 | 0.172 |

_cons |
0.2299272 | 0.089 |

Proctor & Gamble |
||

pgror |
Coef. | P>t |

spror |
0.5961397 | 0 |

lag1spror |
-0.0131834 | 0.844 |

lag2spror |
0.0276608 | 0.682 |

lag3spror |
-0.0264788 | 0.692 |

tenyrch |
-0.0543051 | 0.173 |

_cons |
0.4844197 | 0 |

**Observations on Beta or Systematic Risk**

The short-term beta is the coefficient of the current mark variable.

The long-term beta is the sum of the coefficients for the current market variable and the three lagged market variables.

Below is a chart comparing betas (both short and long term) from this model to betas published by yahoo finance.

Different Measures of Beta |
|||

Yahoo Finance Beta | One Period Beta from Model | Long Term Beta from Model | |

Duke |
0.03 | 0.336 | 0.410 |

BAC |
1.67 | 1.393 | 1.561 |

IBM |
1.04 | 0.921 | 0.704 |

PG |
0.43 | 0.596 | 0.584 |

The order of betas from this model and from Yahoo finance across the four companies least to highest are identical.

Both estimates reveal that Duke Power has the lowest beta and BAC the highest one.

Even though Duke Power still has the lowest beta, the estimates presented here indicate that Duke Power has far larger systematic risk than the Yahoo finance beta estimates.

In two cases, (Duke and BAC) the long-term beta is smaller than the short-term beta. The long-term beta for IBM is lower than the short-term beta. The long and short term betas for PG are similar.

Need to do more research on reasons difference in companies that might cause this result.

**Observations on the Interest Rate Coefficient**

The 10-year interest rate is negatively related to stock price for only one company Duke Power. This coefficient is significantly different from zero for a two-tailed test with alpha equal to 0.05.

The interest rate coefficients for the other three companies are positive but not significantly different from zero at a two-tailed test with alpha equal to 0.05.

**Concluding thoughts**: The impact of interest rates on firm returns can be very complicated. First, the direct impact on the S&P 500 should be modeled. Changes in short rates could have a much different impact on rates than changes in long rates but this impact could be difficult to separate because of collinearity.

More empirical work on how interest rates impact stock prices will follow.