Smart Beta and Factor Investing

Smart Beta and Factor Investing#

This assignment refers to the HBS case: Smart Beta Exchange-Traded-Funds and Factor Investing.

  • The case is a good introduction to important pricing factors.

  • It also gives useful introduction and context to ETFs, passive vs active investing, and so-called “smart beta” funds.

1. READING#

  1. Describe how each of the factors (other than MKT) is measured.1That is, each factor is a portfolio of stocks–which stocks are included in the factor portfolio?

  2. Is the factor portfolio…

    • long-only

    • long-short

    • value-weighted

    • equally-weighted

  3. What steps are taken in the factor construction to try to reduce the correlation between the factors?

  4. What is the point of figures 1-6?

  5. How is a “smart beta” ETF different from a traditional ETF?

  6. Is it possible for all investors to have exposure to the “value” factor?

  7. How does factor investing differ from traditional diversification?

Footnote:#

If you need more info in how these factor portfolios are created, see Ken French’s website, and the follow- details:

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_5_factors_2x3.html

https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_mom_factor.html

2. The Factors#

Data#

Use the data found in data/factor_pricing_data.xlsx.

Factors: Monthly excess return data for the overall equity market, \(\tilde{r}^{\text{MKT}}\).

  • The column header to the market factor is MKT rather than MKT-RF, but it is indeed already in excess return form.

  • The sheet also contains data on five additional factors.

  • All factor data is already provided as excess returns

1.#

Analyze the factors, similar to how you analyzed the three Fama-French factors in Homework 4.

You now have three additional factors, so let’s compare there univariate statistics.

  • mean

  • volatility

  • Sharpe

2.#

Based on the factor statistics above, answer the following.

  • Does each factor have a positive risk premium (positive expected excess return)?

  • How have the factors performed since the time of the case, (2015-present)?

3.#

Report the correlation matrix across the six factors.

  • Does the construction method succeed in keeping correlations small?

  • Fama and French say that HML is somewhat redundant in their 5-factor model. Does this seem to be the case?

4.#

Report the tangency weights for a portfolio of these 6 factors.

  • Which factors seem most important? And Least?

  • Are the factors with low mean returns still useful?

  • Re-do the tangency portfolio, but this time only include MKT, SMB, HML, and UMD. Which factors get high/low tangency weights now?

What do you conclude about the importance or unimportance of these styles?

3. Testing Modern LPMs#

Consider the following factor models:

  • CAPM: MKT

  • Fama-French 3F: MKT, SMB, HML

  • Fama-French 5F: MKT, SMB, HML, RMW, CMA

  • AQR: MKT, HML, RMW, UMD

Our labeling of the last model as the AQR is just for concreteness. The firm is well-known for these factors and an unused case study discusses that further.

For instance, for the AQR model is…

\[ \mathbb{E}[\tilde{r}^i] = \beta^{i,\mathrm{MKT}} \, \mathbb{E}[\tilde{f}^{\mathrm{MKT}}] + \beta^{i,\mathrm{HML}} \, \mathbb{E}[\tilde{f}^{\mathrm{HML}}] + \beta^{i,\mathrm{RMW}} \, \mathbb{E}[\tilde{f}^{\mathrm{RMW}}] + \beta^{i,\mathrm{UMD}} \, \mathbb{E}[\tilde{f}^{\mathrm{UMD}}] \]

We will test these models with the time-series regressions. Namely, for each asset i, estimate the following regression to test the AQR model:

\[ \tilde{r}^i_t = \alpha^i + \beta^{i,\mathrm{MKT}} \tilde{f}^{\mathrm{MKT}}_t + \beta^{i,\mathrm{HML}} \tilde{f}^{\mathrm{HML}}_t + \beta^{i,\mathrm{RMW}} \tilde{f}^{\mathrm{RMW}}_t + \beta^{i,\mathrm{UMD}} \tilde{f}^{\mathrm{UMD}}_t + \varepsilon_t \]

Data#

  • Monthly excess return data on n=49 equity portfolios sorted by their industry. Denote these as \(\tilde{r}^i\) , for \(n = 1, . . . .\)

  • You do NOT need the risk-free rate data. It is provided only for completeness. The other two tabs are already in terms of excess returns.

1.#

Test the AQR 4-Factor Model using the time-series test. (We are not doing the cross-sectional regression tests.)

For each regression, report the estimated α and r-squared.

2.#

Calculate the mean-absolute-error of the estimated alphas.

\[\text{MAE} = \frac{1}{n}\sum_{i=1}^n|\tilde{\alpha}^i|\]

  • If the pricing model worked, should these alpha estimates be large or small? Why?

  • Based on your MAE stat, does this seem to support the pricing model or not?

2.#

Test the CAPM, FF 3-Factor Model and the the FF 5-Factor Model.

  • Report the MAE statistic for each of these models and compare it with the AQR Model MAE.

  • Which model fits best?

3.#

Does any particular factor seem especially important or unimportant for pricing? Do you think Fama and French should use the Momentum Factor?

4.#

This does not matter for pricing, but report the average (across \(n\) estimations) of the time-series regression r-squared statistics.

  • Do this for each of the three models you tested.

  • Do these models lead to high time-series r-squared stats? That is, would these factors be good in a Linear Factor Decomposition of the assets?

5.#

We tested three models using the time-series tests (focusing on the time-series alphas.) Re-test these models, but this time use the cross-sectional test.

  • Report the time-series premia of the factors (just their sample averages,) and compare to the cross-sectionally estimated premia of the factors. Do they differ substantially?4

  • Report the MAE of the cross-sectional regression residuals for each of the four models. How do they compare to the MAE of the time-series alphas?

Footnote:#

Recall that we found in Homework 4 that the market premium went from being strongly positive to strongly negative when estimated in the cross-section.

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