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017

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.

ACAQR Capital ManagementNew York · 2021

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.

StockCodeMarket value, Rs croreBook to priceReturn, %Naive leg
Kavya TextilesS18001.20+9.0value
Nirav CastingsS21,2000.95+7.5value
Tapti PaperS31,5000.80+6.0value
Ushma FoodsS42,0000.55+5.0
Vedika LabsS52,5000.40+4.0
Yashvi RetailS63,0000.30+3.5growth
Aranya PowerB115,0000.85+2.0value
Bhargav CementB222,0000.60+1.5
Chitrak FinanceB330,0000.45+1.0
Devika TelecomB440,0000.35+0.5growth
Ekaant SoftwareB555,0000.25+0.0growth
Falguni ConsumerB680,0000.15-0.5growth
The Dakshin Twelve: the naive value leg, the four highest book to price stocks, holds three small stocks, and the growth leg holds three big ones; small stocks returned more than big ones in the month.
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.

The naive value leg sits in the small cornersmall halfbig half0.00.51.0Rs 1,000 crRs 10,000 crRs 100,000 crMarket value, log scale; book to price on the vertical axisS1S2S3S4S5S6B1B2B3B4B5B6value leggrowth legmiddle
In the Dakshin Twelve, three of the four highest book to price stocks are small and three of the four lowest are big, so the naive value leg averages Rs 4,625 crore of market value against Rs 44,500 crore for the growth leg.
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%.

Sort on value inside each size group, then averageValueNeutralGrowthSmall+8.25%S1 + S2+5.50%S3 + S4+3.75%S5 + S6Big+1.75%B1 + B2+0.75%B3 + B4-0.25%B5 + B6Value factor = average of the two value cellsminus average of the two growth cellsNaive sort5.25%Size-neutral3.25%Size factor5.08%2.00 points of the naivevalue return were a size bet
Sorting on value within small and big stocks gives a value factor of 3.25% against the naive 5.25%, and a separate size factor of 5.08%, so 2.00 points of the naive value return were really small caps beating large caps.
The relationship
HML=12(SV+BV)−12(SG+BG)=12(8.25+1.75)−12(3.75−0.25)=3.25%\text{HML} = \tfrac{1}{2}(SV + BV) - \tfrac{1}{2}(SG + BG) = \tfrac{1}{2}(8.25 + 1.75) - \tfrac{1}{2}(3.75 - 0.25) = 3.25\%
SV, BVsmall value and big value cells
SG, BGsmall growth and big growth cells
What it says in wordsThe value factor is the average cheap portfolio minus the average expensive portfolio, each averaged across size groups so size cancels.
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.

← Case 016A Rs 2,000 crore pension fund holds 50% listed equity, 35% bonds and 15% private assets, with Rs 180 crore of unfunded commitments. Equities fall 30% and private assets are marked down 10%. What is the new private weight, can it meet its capital calls, and what should it do?Case 018 →A payroll software company has earned a 28% return on capital against a 12% cost of capital for ten years, with 4% annual customer churn. What are its competitive advantages and barriers to entry, can it sustain 18% revenue growth, and how much is the excess return worth?

Company names and figures are illustrative.

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