# Naive question: how do factor models inform portfolio construction?

I have read plenty on the topic of factor modelling, but, in the end, after one has decided upon the factors to include in a model, how do all the Betas how tell one how to weigh each asset in a portfolio to maximize return?

For example: as a portfolio manager, I have $$n$$ (let's say 10) securities in the universe of securities that I can invest in, $$k$$ (let's say 20) factors that explain those securities, and the following factor model for each security: $$r_i = \beta_0 + \beta_1*factor_{i,1} + \beta_2*factor_{i,2} + \ldots + \beta_k*{factor}_{i,k} + \epsilon$$

After having regressed the following factor model for each asset, for the current period $$i$$, how should one construct a portfolio with weightings for each asset? I imagine that the $$\beta$$'s are helpful in making this decision?

$$w_i = base weight_i + ((N+1)/2 - rank_i)*R$$
Here $$baseweight_i$$ are predetermined for each asset, if you can no certain preference, you can take it to be equal weighted. $$rank_i$$ is the rank of a certain asset, average rank is calculated by $$(N+1)/2$$ where $$N$$ is the number of assets. So a lower rank means more weight to that particular asset class, 1st rank being the highest. The parameter $$R$$ is defined by your individual preference to tilt from the base weights. High $$R$$ will lead to higher turnover.
• Nice answer. Could you provide some typical values you are using for $R$? Jun 25 '19 at 8:29
• $R$ is highly dependent on your personal preference, you can optimize it on a risk adjusted basis but I dont suggest it. For a no-short constraint, the maximum value of R can be $2*baseweight_i/(N-1)$. It can also be used according to turnover constraints. Jun 25 '19 at 8:33