DCF As A Lower Bound

Sunblock stock (SUN) makes 10% in a sunny year. Loses 2% in a rainy year.

Umbrella stock (RAIN) loses 2% in a sunny year. Makes 2% in a rainy year.


  • The year is 50% to be sunny.
  • The risk-free rate is 0%

A few things to think about

  1. SUN has a higher expected return and Sharpe than RAIN
  2. We can see the stocks have -1 correlation
  3. There is an arbitrage. You can put 50% into each stock and earn 4% in sunny years and 0% in rainy years for an EV of +2% on the portfolio

What can we expect?

The market prices of these stocks will adjust.

Let’s keep it simple and presume:

  1.  SUN’s price stays constant. Its returns characteristics are unchanged.
  2. RAIN’s price is to be bid up so it returns only 1% in a rainy year and loses 3% in a sunny year. Note that RAIN’s expected value is now -1% per year instead of zero.

Why would the market bid that much?

This is the subject of my latest post, You Don’t See The Whole Picture. (Link)

Expect to find:

  • A simple math example to show how the diversification benefits of an asset can benefit a portfolio EVEN if the asset has a negative expected return
  • Examples from the market-making and option trading worlds which describe the “supply chain of edge”. When you see prices that don’t make sense it’s possible you don’t see the info embedded in a higher link in the chain. Whether that’s due to analytical or structural limitations, incentives, or something else is a question you need to consider.

Some Musings I Left Out 

If I felt comfortable larping as an actual businessperson I might have included a few more thoughts in the post:

ComplementsFB can pay up for WhatsApp because they are the most efficient buyer. So the price to a bystander, who can’t see Zuckerburg’s dashboard, looks insane. And in fact, in isolation, the price might be insane. But to the party where its value is highest, it can be a bargain.

Disney paid $4b to buy Star Wars rights. It was a win/win for Lucas and Mickey. The synergies lower the effective price.


Sometimes tech giants scoop up small firms as acqui-hires or to leap-frog R&D time/cost. But I imagine sometimes it’s just defense. Kill Simba before he grows up to inherit the Sahara. Once again, the price looks high in isolation but this “strategic buying” is informed by a wider context.

A Lower Bound

The stand-alone value of a business is the intrinsic value of a call option. But, there is a non-zero chance that some combination makes the asset worth even more. An excessive price is a mix of intrinsic and extrinsic. Going further, is it possible the extrinsic premium increases in proportion to connectivity?

Louis Pasteur wasn’t doing R&D at chocolate chip cookie company, but he would have been paid more at a Nabisco than at his local French universities. But they need to find each other.

In a connected world, awash in capital, the DCF of any business in isolation might be just where the bidding starts.

The most practical implication of these ideas is that you are not paid for diversifiable risks, so you incinerate theoretical money when you don’t diversify. This is true regardless of your actual investment performance.

The Diversification Imperative is a reminder of the only free lunch in investing. (Link)

One thought on “DCF As A Lower Bound

Leave a Reply