Assignment Task:
Task:
Question 1
The picture below shows the output from the training of a decision tree where:
The outcome variable is a binary outcome 0, 1 where zero indicates that in the following month the stock has underperformed the market and one indicates that the stock has outperformed.
The predictors are three common investment factors (normalized:
o N_Beta is defined the historical beta of the stock (with negative sign, ?????) o MOM is the 12-months momentumo EP is the E/P ratio of the stock
The tree has been trained on a sample of US stocks.
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a) Using the information contained in the picture try to provide the economic intuition behind the investment strategy described in the tree. Assume that your audience is generally sceptical of machine learning and you need to show that the algorithm’s decision process can be explained and understood in terms of traditional investment factors.
b) Explain what the different numbers contained in a typical node of three mean.
c) Explain how to read the gini number
Question 2
Different portfolio managers can take a different approach to building a multifactor model. Russel Investment (see Q2_Russel.pdf, p. 10) combines 4 well known factors with unequal weights, while Citigroup (see Q2_Citigroup.pdf, p. 2) combines 3 well known investment ideas with equal weights.
a) Briefly introduce the concept of “overfitting” in the context of developing a quantitative Investment Strategy.
b) Explain for which of the two approaches described above overfitting is more likely to be a problem and why.
Question 3
Investment factors allow to generate profits by:
Going long (investing) in the “Good” stocks
Going short (short-selling) in the “Bad” stocksThe picture below shows, for three well known investment factors, the result of a simple back testing exercise.
For each factor the picture shows:
The performance of the “Long Portfolio” that invests in the stocks in the top 10% of the factor ranking (black bars in the graph).
The performance of the “Short Portfolio” that short-sells the stocks in the bottom 10% of the factor ranking (striped bars in the graph).
a) Explain for which of these factors there is a higher risk that the real investment return will be lower than the simple paper return from the back-testing and why.
b) How would you structure the back-testing to minimize the difference between back-testing return and real return?
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Question 4
The file Q4_Factors.pdf contains an article that appeared on the Financial Times in March 2020. The article describe a number of hypothesis on why traditional investment factors have underperformed the stock market in the recent past. For example the article says that
While investors in the market cap-weighted S&P 500 enjoyed annualised net total returns of 8.6 per cent in the five years to the end of February, those following the S&P 500 Value index eked out just 5.8 per cent. Likewise the S&P 500 Quality index has delivered just 6.9 per cent by the same metric…
Among the different hypothesis, Prof Noel Amenc argues that…
“many factors have a market beta of less than 1 — that is, they are less volatile than the market — due to a defensive bias, at least when implemented in a long-only format. As a result they tend to underperform in bull markets (but outperform when markets fall, so may prove their worth this year)”.
After reading this article your boss asks you to build an experiment to verify if what professor Amenc says is true. Assuming that you have at your disposal all the data that we have used in our exercises (including data on factors, returns and betas) how would you use the data to verify this claim?
ATTENTION: you do not have to actually do the calculation or write the code. You just need to describe in plain language what type of calculation you would do to verify if the claim of professor Amenc is true with respect to a specific factor, for example value.
Try to be as precise as possible in describing your experiment.
Question 5
The picture below shows the Table 5 from Fama and French (1992). You do not have to download the paper but if you are interested you can find it HERE (https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.1992.tb04398.x) . The table reports average monthly returns (in percentage points) of for 100 portfolios built based on Book-to-Market ratio and Size (ME stands for Market Capitalization). Every number represents the average monthly return of a specific “bucket” of stocks defined by a specific size (in row) and B/M ratio (in column).
a) What conclusions can you draw about the existence of size and value investment factors in this country?
b) Are the two factors (size and value) independent? If not, how would you describe their relationship?
c) If an investor was looking to build a long-short portfolio (for example 130/30) to beat the market without any additional risk which investment advice would you give (in terms of which factor/factors to use)?
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