13. Cross-sectional strategies

• So far we have looked at strategies that go in and out of a particular asset according to a signal.

• We looked at past returns and past realized volatility.

• You can think of these as strategies as “timing” because they change how much risk they take over time.

• Now we will look at strategies that do not change their net exposure to the stock market over time, but changes which assets it buys.

The Quantitative space is mostly about “cross-sectional” strategies

• Size- Low market cap stocks earn high abnormal returns

• Value- High Book-to-market stocks earn high abnormal returns

• Momentum – High Prior 12 month returns earn high abnormal returns

• Profitability- High Profitability firms earn high abnormal returns

• Beta – Low market beta firms earn high abnormal returns

• Idiosyncratic Volatility – High indio vol firms earn low abnormal returns

• Investment- Low investment growth firms earn high abnormal returns

• Short-term reversals-Low last week returns earn high abnormal returns

The recipe

1. Construct a signal for each stock. We call this a stock “characteristic”

   • It can be based on accounting data, return data, or whatever

   • What is important is that for each stock in each date you have a value for this characteristic

2. On a given date sort stocks by this characterisitc.

   • It is key that this characteristic is infact known at sorting date!

   • Extremely careful not to introduce “look-ahead” bias

3. Construct portfolios by dividing stocks in deciles/quinties and form portfolios of stocks that have similar characteristic

   • You can either equal weight or value weight within portfolio

   • But what is important is that each portfolio will have stocks of have ver different chracteristic values

4. Construct the long-short where you go long portfolio 10 and short portfolio 1 (or vice versa) but the point is to take a bet on the characteristic spread

Quantitative investing is going from “names” to characteristics

The sorting by date keeps the stocks inside the portfolios with similar characteristics

• This sorting will “work” if these chracteristics are good proxies for risks that the average investor cares about

  • will lead to spread in returns

  • will lead to a factor

• But it doesn’t work always, if you use the first letter of stock ticker to construct 26 portfolios you are unlikely to get spread in average returns and most likely each portfolio will resemble the market portfolio but with much more volatility.

• And even if you do find something–> likely garbage, very hard to think about an economic model that would deliver that pattern!

Lets look at the portfolios’ characteristics, i.e. Size, Book-to-Market, momentum,… of the different portfolios

• These are the characterisitcs that were used to create the portfolios.

• Indeed, the key is that each portfolio has stocks of vastly different characterisitcs and keeps churning as firms change

  • Let’s take MSFT (microsoft) as an example:

  • MSFT transitioned from being small in the 80’s to be gigantic in the 90’s, as a result, it moved up from the small portfolio to the big portfolio

  • Duing the Tech boom when MSFT had a huge valuation relative to it’s book value, it went to the low BM portfolio

  • But then MSFT transtioned back to the high BM portfolio once it’s market valuation collapsed in the aftermath of the techbubble

• The key is that firms’ characteristics change over time, by constructing portfolios, we hope to estimate some stable relationship between risk and return