Case 100Systematic research and dataHard

Build a value factor on the Trivan universe of 12 stocks across three sectors: rank on book to price, go long the top three and short the bottom three. Then build it sector-neutral. The two versions give different returns. Why, and which would you use?

AQR Capital ManagementNew York · 2021

The situation

The Trivan universe is an invented set of 12 stocks, four each in banks, metals and IT services. Banks carry large book values relative to price, IT companies small ones, because their assets are mostly people and software that the balance sheet barely records.

Over the test month the sectors move differently: banks fall 6%, metals rise 1%, IT rises 7%. Within each sector, the cheapest stock by book to price beats its sector by 3 points, the next by 1, the third lags by 1 and the dearest by 3. Positions are equally weighted.

Your task

Build the plain and the sector-neutral value factor, explain why their returns differ, and say which you would use and how you would improve it.

Quick check

Ranking all 12 stocks together, what does the plain factor mainly end up betting on?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The plain factor returns -7.33% and the sector-neutral one +6.00%, because ranking across sectors turns value into a sector bet. The plain version is long two banks and a metal and short three IT stocks, so the banks' 6% fall against IT's 7% rise swamps the value signal. Ranking within each sector removes the sector bet and keeps the cheap-against-dear spread. For a pure value factor, use sector-neutral construction.

Step 1Why does ranking all 12 stocks together pick sectors, not bargains?

Think of comparing house prices per square foot across a city centre and a far suburb. The suburb always looks cheap, not because each house is a bargain but because it is a different market. Book to price works the same way across sectors: banks' assets are on the balance sheet at close to market value, while IT's real assets are people and code that accounting barely records. So the three highest book-to-price stocks are Bank A, Bank B and Metal A, and the three lowest are all IT. The plain factor is long banks and short IT before it is anything else.

Ranking all 12 stocks together puts two banks and a metal on the long side and three IT stocks on the short side, returning -7.33%; ranking within each sector goes long the cheapest and short the dearest in every sector, returning +6.00%.

Step 2How much of each return is the sector bet?

Split each return into the sectors' moves and what is left. The plain factor's longs sit in sectors averaging -3.67% and its shorts in a sector up 7%, a sector bet worth -10.67 points; its stock selection earns +3.33. The sector-neutral factor has one long and one short in every sector, so the sector moves cancel exactly and all +6.00 points come from cheap stocks beating dear ones in the same industry. The value signal worked in both; only one construction let you see it.

The relationship

r_{LS} = \underbrace{(\bar{s}_{long} - \bar{s}_{short})}_{\text{sector bet}} + \underbrace{(\bar{e}_{long} - \bar{e}_{short})}_{\text{within-sector selection}}

s	the sector return of each stock's sector, averaged over each side
e	each stock's return relative to its own sector, averaged over each side

What it says in wordsA long-short return splits exactly into the gap between the sectors you hold and the gap between the stocks you picked inside them.

The plain factor's -7.33% is a -10.67-point sector bet plus +3.33 points of stock selection, while the sector-neutral factor has no sector bet and earns +6.00 points from selection alone.

Step 3Which would you use, and how would you improve it?

Sector-neutral, if the goal is a value factor rather than a sector view. Across sectors, book to price mostly measures accounting differences, so a plain ranking adds a large, unintended and unpaid bet on banks against technology. The trade-off is honest: sector-neutral construction gives up any genuine value effect between sectors, and a manager who believes in that can hold it as a separate, sized sector position. To improve the construction, use z-scores within sector rather than raw ranks, weight positions by signal strength, neutralise beta and size, use finer industry groups than three broad sectors, and cap turnover so trading costs do not eat the spread. Say the limitation: twelve stocks and one month prove the mechanism, not the factor.

Where candidates lose it

The frequent miss is explaining the gap as noise or bad luck. The gap is structural: ranking across sectors on book to price loads on sectors, and in this month the sector bet ran against the long side.

The second is declaring the plain version wrong in every case. It carries a between-sector value bet that some managers want; the answer the interviewer is after is that the choice should be deliberate, sized and measured separately.

What the interviewer asks next

How would you build a value factor that is also neutral to market beta?
Would you rank on book to price, earnings yield or a composite, and why?
The sector-neutral factor turns over 80% a month. What would you change?

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.

1The situation

2Your task