Case 017Factor investing and quantHard
From a universe of 12 stocks with book to price, market value and a month's return, build a value factor long the top third and short the bottom third, show that it is mostly a small cap bet, then rebuild it as a size-neutral two by three sort.
1The situation
The Dakshin Twelve is an invented universe of twelve Indian stocks. Six are small, with market values from Rs 800 crore to Rs 3,000 crore, and six are big, from Rs 15,000 crore to Rs 80,000 crore. The table in the solution gives each stock's book to price ratio and its return in one month, in which small caps as a group had a strong month.
Use equal weights inside every portfolio to keep the arithmetic visible.
2Your task
Build the naive value factor, show what it is really exposed to, rebuild it so it is neutral to size, and explain the construction choices you would defend.
Quick check
The naive value factor returns 5.25% in the month. Roughly how much of that is value, once size is taken out?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The naive value factor returns 5.25%, but about 2.00 points of that is a size bet, and the size-neutral factor returns 3.25%. Three of the four value stocks are small and three of the four growth stocks are big, so in a month small caps rallied the naive factor looks better than value really did. Sorting on book to price inside small and big separately, then averaging, gives a value return of 3.25% and a separate size return of 5.08%.
Step 1What does the naive sort give?
Rank all twelve by book to price, buy the top four and sell the bottom four. The value leg earns 6.125% and the growth leg 0.875%, so the naive value factor returns 5.25% for the month. It looks like a strong month for value, and that is the claim the rest of the case tests.
| Stock | Code | Market value, Rs crore | Book to price | Return, % | Naive leg |
|---|---|---|---|---|---|
| Kavya Textiles | S1 | 800 | 1.20 | +9.0 | value |
| Nirav Castings | S2 | 1,200 | 0.95 | +7.5 | value |
| Tapti Paper | S3 | 1,500 | 0.80 | +6.0 | value |
| Ushma Foods | S4 | 2,000 | 0.55 | +5.0 | |
| Vedika Labs | S5 | 2,500 | 0.40 | +4.0 | |
| Yashvi Retail | S6 | 3,000 | 0.30 | +3.5 | growth |
| Aranya Power | B1 | 15,000 | 0.85 | +2.0 | value |
| Bhargav Cement | B2 | 22,000 | 0.60 | +1.5 | |
| Chitrak Finance | B3 | 30,000 | 0.45 | +1.0 | |
| Devika Telecom | B4 | 40,000 | 0.35 | +0.5 | growth |
| Ekaant Software | B5 | 55,000 | 0.25 | +0.0 | growth |
| Falguni Consumer | B6 | 80,000 | 0.15 | -0.5 | growth |
Step 2What is the naive factor really betting on?
Look at who is in each leg. 3 of the 4 value stocks are small and 3 of the 4 growth stocks are big: the value leg's average market value is Rs 4,625 crore against Rs 44,500 crore for the growth leg. Cheap stocks tend to be small, so a pure value sort quietly buys small and sells big. It is like judging whether a coaching method works by comparing its students with another centre's, when its students were also younger: two differences are tangled together.
Step 3How does a two by three sort separate value from size?
Split the universe at the median market value into small and big, then within each half sort on book to price into value, neutral and growth, two stocks each. The value factor is the average of the two value cells minus the average of the two growth cells, so every rupee long value in small stocks is matched by a rupee short growth in small stocks, and the same in big. Small value beats small growth by 4.50 points and big value beats big growth by 2.00 points, so the size-neutral value factor is 3.25%. The same grid gives a size factor, small minus big across the three columns, of 5.08%.
| SV, BV | small value and big value cells |
| SG, BG | small growth and big growth cells |
Step 4Which construction choices would you defend in an interview?
Four, each with its reason. Weight by market value inside each cell, not equally, so the factor can be traded without piling into the smallest, least liquid names. Set the size breakpoint using larger stocks only, so a flood of tiny listings does not move it. Use accounting data with a lag of several months, so the factor never uses a book value that was not yet published. And consider sorting within industries, so value is not just a bet on whichever sectors are cheap. This construction follows the approach Fama and French set out in 1993; its limit is that one characteristic, book to price, is a blunt measure of cheapness for asset-light businesses.
Where candidates lose it
Candidates build the naive long-short, report 5.25%, and call it the value premium. The interviewer is testing whether you check what else the factor is exposed to; a factor is only useful if it measures one thing.
The second miss is fixing size by throwing out small stocks altogether. That changes the universe instead of neutralising the exposure, and leaves value measured only among big stocks.
What the interviewer asks next
- How would the answer change with value weights inside each cell?
- Momentum also correlates with size in this universe. How would you build a factor neutral to both?
- Why might you use earnings to price or cash flow to price alongside book to price?
- How would you test whether the size-neutral value factor earns a premium over time?
Asked at AQR Capital Management, Investment Research, New York, 2021 (Wall Street Oasis): Explain to me the construction of certain factors. Why do you choose the method and how to optimize it.
Company names and figures are illustrative.
