Same Constants when adding more dependent variables.

[emilpuiu]

Hi guys,

First time poster here.

I am working on my dissertation and I came up with some odd, although interesting, results.

There are two models I am using with regression analysis:

The first:

y = a + bx1 + bx2 + ... + bx7

The second:

y = a + bx1 + bx2 + ... +bx8

So, the 2 attachments show the results for 10 different regressions, the first using 7 independent variables and the second using 8 independent variables. The dependent variables (REH, REMN, RCA, RMEA, etc) are all monthly returns for 10 different strategies used by hedge funds during the financial crisis of 2007. The dependent variables (alpha, RSPY, RSIZE, R10Y, etc) are all factors that presumably should be affecting the returns for the different strategies.

The 7 factors and 8 factors regressions are using the same factors, but the 8 factors has as an addition a new factor (REMERG).

The constant, alpha, is what I am interested in. If the value of alpha, the constant, is found to be positive and significant, it means that the returns for a specific strategy were due because of skill of the manager in selecting the most efficient investments. If negative and significant, it means that the manager of the strategy was not able to produce this skill.

The main problem is that if you look carefully at the results for both the 7 and 8 factors regressions, the alpha values are identical for some of the strategy.

Now, define alpha, the constant, as an excess return above the market return for the strategy.

My question is, how is it possible for alpha, the constant, to not change when I add one independent variable to the model? Shouldn’t it change as well (as the other independent variables do)?

My only explanation is that by adding an additional variable (REMERG) to the model, it does not influence the amount of excess return (alpha) produced by the strategy, as the model is robust in the sense that can accurately explain the amount of alpha for each of the strategy.

However, as we can see, the REMERG factors is statistically significant (the 2 ** means that the value of the independent variable is statistically significant at the 1% c.l., while * is at the 5%), so by being statistically significant IT MUST HAVE INFLUENCE on the constant (or ultimately in explaining the dependent variable, which MUST lead, in my mind, to a change in the value of the constant).

Anyone care to share their opinions?

P.S. The dependent variables are as follows:

-RSPY = monthly return on the S&P500

-RSIZE = Size spread between Small Cap stocks and Large Cap stocks

-R10Y = change in the level of yield for the 10year T-Bill constant maturity

-RSPREAD = credit spread (calculated as monthly change in BAA Moody’s Corporate Bonds - *10y T-Bill Constant Maturity)

-RBOND = *monthly return on a lookback option on a 10y T-Bill

-RFX = monthly return on a lookback option on dollar spot rate

-RCOM = monthly return on a lookback option on the commodity index

-REMERG = monthly return on the MSCI Emerging Market Index

- constant, alpha, C = Excess return produced by the independent variables.

Regards,

emilpuiu