Checking Data & Interpreting Regression Outputs

Question

I am looking to check the assumptions and interpretation of the output of a regression that I have run for factor exposures in a long/short equity portfolio:

1. Portfolio is long/short equity with a net of $40\%$ and a Gross of $115\%$
2. Regression variable are 5 market neutral factor indexes (istoxx market neutral Value/Quality/carry/Momentum/Growth)
3. Using 2 years of daily return data

My regression output is the below:

Would I be correct in assuming the following:

1. the Coefficients represent the Beta of the portfolio to each factor
2. only Momentum is statistically insignificant (because of the high p-value)
3. overall the regression output does not effectively model the portfolio in terms of factors (low $R^2$-value)

Is there anything obvious that I could improve - I am trying to reach a useful conclusion on how exposed my portfolio is to each factor?

any wisdom would be greatly appreciated (I am also constrained to do my analysis in Excel, I would have opted for python or R but not available in this case)

Answer 1

I'll first address the three questions.

(1). The 'Coefficients' column represents the point estimates of the betas of the portfolio returns to each factor. These estimates depend on the data you used and on the assumption that there is an intercept, which is standard in regression analysis.

(2). Statistical significance depends on the significance level you choose. If your significance level is $\alpha = 0.05$, as is usual, then the momentum beta is not statistically significant. You can also notice it is the only one which confidence interval contains $0$.

(3). R$^2$ is low but this is quite expected in economics.

Now to address some margins of improvement: you should include the market factor in the regression analysis. As for now, your portfolio has a significant alpha factor (very low but it's there) but you should see if it persists when you include the market factor.

Exposure is captured by the betas. For example a variation $\Delta SMB=x$ in the size factor would affect your expected return as following: $$E[\Delta r] = E[r'-r]=(\alpha + ... +\beta_{SMB}(F_{SMB}+x))-(\alpha+...+\beta_{SMB}F_{SMB})$$ $$E[\Delta r] = \beta_{SMB} \cdot \Delta SMB$$ So if $\Delta SMB=-1$ then $E[\Delta r]=0.4756$, for example.