Description

Homework #6
Case: AQR’s Momentum Funds (A) [9-211-025].
1 The Momentum Product
This section is not graded, and you do not need to submit your answers. But you are expected to consider these issues and be ready to discuss them.
1. What is novel about the AQR Momentum product under construction compared to the various momentum investment products already offered?
2. Name three reasons the momentum investment product will not exactly track the momentum index, (ie. why the strategy will have tracking error.)
3. When constructing the momentum portfolio, AQR ranks stocks on their returns from month t− 12 through t− 2. Why don’t they include the t− 1 return in this ranking?
2 Investigating Momentum
In this section, we empirically investigate some concerns regarding AQR’s new momentum product.
On Canvas, find the data file, “momentum data.xlsx”.
• The first tab contains the momentum factor as an excess return: ˜rmom.
• The second tab contains returns on portfolios corresponding to scored momentum deciles.
– rmom(1) denotes the portfolio of stocks in the lowest momentum decile, the “losers” with the lowest past returns.
– rmom(10) denotes the portfolio of stocks in the highest momentum decile.
• The third tab gives portfolios sorted by momentum and size.
– rmomSU denotes the portfolio of small stocks in the top 3 deciles of momentum scores.
– rmomBD denotes the portfolio of big-stocks in the bottom 3 deciles of momentum scores. Note that the Fama-French momentum return, ˜rmom:FF, given in the first tab, is constructed by FF as,
mom:FF 1 momBU momSUmomBD momSD
r˜ = (r + r ) + r ) (1)
2
1. Is momentum still profitable?
Investigate by filling out the summary statistics below for the full-sample and three sub-samples.
(a) Using the data provided, fill in Table 1 with the appropriate stats for ˜rmom:FF.
Table 1: Momentum performance over time.
Subsample mean vol Sharpe skewness corr. to ˜rm corr. to ˜rv
1927-1993
1994-2008
(b) Has momentum changed much over time, as seen through these subsample statistics?
2. The case is about whether a long-only implementation of momentum is valuable. Construct your own long-only implementation: ,
momU:FF 1 momBU momSU f r˜ = (r + r ) −r
2
Note that this is following the FF approach of treating big and small stocks separately. This would be very similar to a scaled version of,
r˜momU mom(8) + rmom(9) + rmom(10)
For the question below, use the FF-style, ˜rtmomU:FF.
(b) Is long-only momentum as attractive as long-short momentum with respect to mean, volatility, and Sharpe Ratio?
Table 2: Long-only momentum performance.
Long-and-short, (˜rmom:FF)
Long-only (˜rmomU:FF)
v
(c) Is long-only momentum as diversifying as long-short momentum with respect to market and value premia?
3. Is momentum just data mining, or is it a robust strategy?
Assess how sensitive the threshold for the “winners” and “losers” is in the results. Specifically, we compare three constructions:
• long the top 1 decile and short the bottom 1 deciles
r˜momD1 = rmom(10) −rmom(1)
• long the top 3 deciles and short the bottom 3 deciles
r˜momD3 =1 rmom(8) + rmom(9) + rmom(10) mom(1) + rmom(2) + rmom(3)
3
3
k=8 k=1
• long the top 5 deciles and short the bottom 5 deciles
10 5
r˜momD5
k=6 k=1
(b) Do the tradeoffs between the 1-decile, 3-decile, and 5-decile constructions line up with the theoretical tradeoffs we discussed in the lecture?
(c) Should AQR’s retail product consider using a 1-decile or 5-decile construction?
(d) Does ˜rmomD3 have similar stats to the Fama-French construction in (1). Recall that construction is also a 3-decile, long-short construction, but it is segmented for small and large stocks. Compare the middle row of Table 3 with the top row of Table 2.
Table 3: Robustness of momentum construction.
r˜momD1 r˜momD3 r˜momD5
4. Does implementing momentum require trading lots of small stocks—thus causing even larger trading costs?
For regulatory and liquidity reasons, AQR is particularly interested in using larger stocks for their momentum baskets. (Though they will launch one product that focuses on medium-sized stocks.)
Use the data provided on both small-stock “winners”, rmomSU, and small-stock “losers”, rmomSD, to construct a small-stock momentum portfolio,
rtmomS = rtmomSU −rtmomSD
Similarly, use the data provided to construct a big-stock momentum portfolio,
rtmomB = rtmomBU −rtmomBD
Table 4: Momentum of small and big stocks.
All stocks, ˜rmom:FF
Small stocks rtmomS
Large stocks rtmomB
(b) Is the attractiveness of the momentum strategy mostly driven by the small stocks? That is, does a momentum strategy in large stocks still deliver excess returns at comparable risk?
5. In conclusion, what is your assessment of the AQR retail product? Is it capturing the important features of the Fama-French construction of momentum? Would you suggest any modifications?
3 Extensions
1. In Section 2 we analyzed whether Momentum changes substantially when we modify the construction of the factor. Let’s examine that question for the Value factor.
Re-do Tables 2, 3, and 4 but for the decile and size portfolios of the Value factor. Get this data from Ken French’s website.3
Based on these statistics,
(a) Is the long-only version of Value substantially different?
(b) Is the 1 or 5 decile version of Value substantially different?
(c) Does the 3 decile version of Value look like the Fama-French version?
(d) Do the Big Value and Small Value factors look similar?

3
https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html Specifically, see the following data sets:
• Size-sorted portfolios for value. (For instance, “big stocks value”, rvB): “6 Portfolios Formed on Size and Bookto-Market (2 x 3)”
• Decile portfolios for value, rv(k): “Portfolios Formed on Book-to-Market”