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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?

Thank you in advance.

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One common way to construct portfolio is a high - low factor portfolio. First you sort the asset classes based on a particular factor. For example if the regression co-ef is positive implying positive risk premia, you sort them in ascending order of the factor, and opposite for negative co-ef. After that you percentile this sorted series and decide a threshold percentile for low and high. Common thresholds are 30/70, meaning assets with percentile lower than 30 are in the low bucket and higher than 70 are in the high bucket. You can then long the high bucket and short the low bucket, the middle range you can either ignore or equal weight.

If you have no-short constraints, then you can design a weighted strategy by ranking them based on a factor, one way is:

$$w_i = base weight_i + ((N+1)/2 - rank_i)*R$$

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.

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  • $\begingroup$ Nice answer. Could you provide some typical values you are using for $R$? $\endgroup$ – JejeBelfort Jun 25 at 8:29
  • $\begingroup$ $R$ 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. $\endgroup$ – Dhruv Mahajan Jun 25 at 8:33

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