Portfolio Theory And The Invisible Option On Hobbies

In summer of 2020, I published a short post (4 min read) that I believe holds several deeply important investing meta-lessons. It’s called You Don’t See The Whole Picture.

Using the dad voice I use on my sons when I think they are sandbaggin’, I’ll say: you should really read it.

I’ll wait.


Ok, just so we are on the same page, I’ll spell out its lessons:

  1. The impact of correlations is not intuitive. The investment universe is mind-blowingly vast so the returns to concentration along with the narratives will grab the headlines. But boring risk management is the “blocking and tackling” of winning the long game.

    Prescription:  Take portfolio construction seriously. Because it’s not intuitive, grokking it can give you an edge1.

  2. Smart investors understand correlations and portfolio theory. In their battle to construct the most efficient risk-adjusted portfolios, they arb away the reward for idiosyncratic risk.

    Prescription: Diversify so you are only left the irreducible systematic risks that you do get paid for2.

  3. The correct reflex for a price that doesn’t make sense is not “that’s stupid”, but “what am I missing?”

    Prescription: Mind your dashboard3. Are the tools you look at capable of showing you the correct picture? A dissonant price means your model of how things work is incomplete. 

These three ideas point to a subtle implication which extends beyond investing but is [to me at least] most legible from the lens of portfolio and options theory:

The value of an asset viewed in isolation is actually a floor.

DCF As The Zero Strike

Let’s stay in the business world for now.

A company’s value can be much higher than a DCF-based valuation if it improves the portfolio of its most efficient holder. In that post, the SUN shareholder’s portfolio is the highest and best use of RAIN shares. I’d expect the SUN shareholder to set the marginal price of RAIN.

Meanwhile non-holders of SUN are looking at RAIN in a vacuum and concluding it’s an overpriced coin flip not an investment. It’s gotta be a bubble, right?

They just don’t see what SUN shareholders see. It’s like when a market maker gets their bid hit on a slug of super cheap XYZ vol, only to find out that some hedge fund bought a convert or ASR at a much lower implied XYZ vol. Just like the person selling RAIN shares to SUN holder, the market maker is getting arbed by someone who sees a fuller picture.

So when we value a business, say using DCF (“discounted cash flow” he said as he dismounted a dinosaur), that’s the floor price. Even if there were no other potential investors that could be a strategic buyer for our business, we know it’s worth its DCF4.

So there is optionality struck at the DCF value!

The option represents the gap between the DCF and the price a strategic investor would pay.

Understanding The Option

The value of a traditional call option depends on several easily observable inputs: the strike, distance from the strike, interest rates, and time to expiry. The input we cannot observe is the volatility of the underlying asset during the the life of the option.

If you have heard of the “greeks” they are just measures of sensitivity of the price of an option with respect to one of these inputs5.

So the big question: what does this option to be acquired by a more efficent portfolio or strategic investor depend on?

Connectivity and divergence

I don’t have any formal or quantitative explanations but the reasons feel intuitive.

Connectivity

If “DCF in isolation” is our lower bound, the option struck from that point starts to accrue value as the number of entities in the world grow. A seesaw is worthless until a second kid shows up. More interconnections means more possible portfolio combinations. And the value of the option is maximized by the portfolio that can find the best combination on the frontier of risk/reward. 

Embedded in connectivity is how networked information is. You could have a world with many companies, but if they don’t know about each other. That information bottleneck would impair the value of the option even if there were theoretically many combinations.

Divergence

This goes back to how counter-correlations lower the risk of portfolios. If your business looks like every other, than there is no room for you to marginally improve the portfolio of a suitor. They already would have acquired one of the businesses you resemble. The premium to your DCF value is a function of your divergence or scarcity.

To recap so far:

  • Straightforward valuation methods like DCF set a floor on a company’s value. 

  • There is additional optionality value that comes from the fact that the idiosyncracies of a business may offset risks of other businesses in an investor’s portfolio. The investor can afford to pay a premium to DCF for this diversification and come out ahead6

  • The value of that extra optionality depends on how many possible combinations exist (ie how networked the world is) and how divergent the company’s risks or opportunties are. While any attempt to compute “greeks” for these sensitivites is above my paygrade (this is a blog post and my pay is zero) they feel like useful concepts to consider. I’d also recommend, in the spirit of option greeks, to consider them in an “all else equal” manner7.

Beyond Investing

A business is just an instance of the wider category “generating”. Businesses generate solutions. A car is a  solution.

Every activity from playing sport or writing a song or cooking is generating. Some of these activities are useful to others. But the value can also be isolated. If you decide to hike across the country, it generates intrinsic value for you. Before you did it, you considered the value and decided on its own it was a worthwhile endeavor.

But as connectivity increased, the idea that you could blog about a hike (perhaps even funding it) expanded the value of this otherwise narrow but concentrated endeavor. The hiker always owned a call option on the rewards of this endeavor, but the internet gave that option value.

A graphic designer. An orater. A mind that excels at games. All of these concentrated endeavors are generating functions. But the leverage embedded in connectivity maximizes their value. A nerd with a niche interest in cryptography suddenly finds their hobby of significant complementary value to the finance establishment.

In an age of side-hustles, doing something for its own sake can seem wasteful. Or some people might feel “I don’t want to do X unless I’m going to get really good at it”. I feel that way sometimes too. For a certain type of person, it’s an encouraging reminder, that as the world continues forming synapses, those “selfish” hours spent doing something “weird” might have a lot more value than what you think they do today. I suspect the value of these options can only be seen in hindsight8.  But take heart.

At worst, they are their own reward and any upside, no matter how remote, is yours too.




  1. If you found SUN/RAIN eye-opening, Your Portfolio Intuition Is Poor will reinforce what you learned
  2. For more on this idea see The Diversification Imperative
  3. Warren Buffet doesn’t look at a chart before buying a business. An option market maker doesn’t look at a company’s revenue before delta-hedging. Your decision inputs should match your strategy and horizon. Many disagreements about price come from differint time horizons or investors operating at different levels of abstraction. My most widely read post is about this idea:  Why Investing Feels Like Astrology
  4. This does’t mean the company doesn’t have downside risks, it’s just that DCF allegedly compressed all of those into a discount factor and this discussion is taking the baton from that point on
  5. Some examples of important “greeks”:

    • delta: change in option price as a function of change in underlying

      An option with a 40% delta means that it will increase $.40 in value if the stock goes up $1.00

    • vega: change in option price as a function of change in implied volatility

      Implied volatility is the market’s assessment of how much a stock can move around. It represents a n annual standard deviation. So if an option has 16% implied vol, the market thinks the stock’s annual SD is 16%. If an option has $.25 of vega that means if the market believes the annual standard deviation has increased by one point from 16% to 17%, then the option’s value will increase by $.25

  6. I’m not discovering planets here. FB bought IG because of portfolio thinking. IG was likely never valued by DCF even by its own founders. The price of the acquisition balanced plenty of optionality for the founders, above any notion of DCF at the time, and the plain reality that it was worth much more than even that to FB.
  7. There’s an easy-to-anticiapate caveat that some companies’ sensitivities to these “greeks” is actually negative (for example, a monopoly operating in a closed market being disrupted in the way the internet’s price transparency eiliminated low-hanging arbitrages from the system). It’s a fair caveat because the line between a risk captured in the discount factor and the negative sign of the greeks for such a company is blurry. I think the “ceteris paribus” feature of greeks comes to the rescue here, but I wouldn’t die on that hill.
  8. I doubt the Spoonman ever saw himself as the star of a music video. That’s a weird example but I’m still waiting for my hobby of watching music videos [I stil watch music videos pretty much daily], to pay off.

Leave a Reply