Tag: option pricing

Christian Rudder and Corporate Ratings

One of the studdest book chapters I’ve read is from Christian Rudder’s Dataclysm. Rudder is a cofounder of OkCupid, now part of the match.com portfolio of matchmakers. In this book, he has taken insights from OkCupid’s own data to draw insights about human life and behaviour.

It is a typical non-fiction book, with a studmax first chapter, and which gets progressively weaker. And it is the first chapter (which I’ve written about before) that I’m going to talk about here. There is a nice write-up and extract in Maria Popova’s website (which used to be called BrainPickings) here.

Quoting Maria Popova:

What Rudder and his team found was that not all averages are created equal in terms of actual romantic opportunities — greater variance means greater opportunity. Based on the data on heterosexual females, women who were rated average overall but arrived there via polarizing rankings — lots of 1’s, lots of 5’s — got exponentially more messages (“the precursor to outcomes like in-depth conversations, the exchange of contact information, and eventually in-person meetings”) than women whom most men rated a 3.

In one-hit markets like love (you only need to love and be loved by one person to be “successful” in this), high volatility is an asset. It is like option pricing if you think about it – higher volatility means greater chance of being in the money, and that is all you care about here. How deep out of the money you are just doesn’t matter.

I was thinking about this in some random context this morning when I was also thinking of the corporate appraisal process. Now, the difference between dating and appraisals is that on OKCupid you might get several ratings on a 5-point scale, but in your office you only get one rating each year on a 5-point scale. However, if you are a manager, and especially if you are managing a large team, you will GIVE out lots of ratings each year.

And so I was wondering – what does the variance of ratings you give out tell about you as a manager? Assume that HR doesn’t impose any “grading on curve” thing, what does it say if you are a manager who gave out an average rating of 3, with standard deviation 0.5, versus a manager who gave an average of 3, with all employees receiving 1s and 5s.

From a corporate perspective, would you rather want a team full of 3s, or a team with a few 5s and a few 1s (who, it is likely, will leave)? Once again, if you think about it, it depends on your Vega (returns to volatility). In some sense, it depends on whether you are running a stud or a fighter team.

If you are running a fighter team, where there is no real “spectacular performance” but you need your people to grind it out, not make mistakes, pay attention to detail and do their jobs, you want a team full of3s. The 5s in this team don’t contribute that much more than a 3. And 1s can seriously hurt your performance.

On the other hand, if you’re running a stud team, you will want high variance. Because by the sheer nature of work, in a stud team, the 5s will add significantly more value than the 1s might cause damage. When you are running a stud team, a team full of 3s doesn’t work – you are running far below potential in that case.

Assuming that your team has delivered, then maybe the distribution of ratings across the team is a function of whether it does more stud or fighter work? Or am I force fitting my pet theory a bit too much here?

The World After Overbooking

Why do you think you usually have to wait so much to see a doctor, even when you have an appointment? It is because doctors routinely overbook.

You can think of a doctor’s appointment as being a free option. You call up, give your patient number, and are assigned a slot when the doctor sees you. If you choose to see the doctor at that time, you get the doctor’s services, and then pay for the service. If you choose to not turn up, the doctor’s time in that slot is essentially wasted, since there is nobody else to see then. The doctor doesn’t get compensated for this as well.

In order to not waste their time, thus, doctors routinely overbook patients. If the average patient takes fifteen minutes to see, they give appointments once every ten minutes, in the hope of building up a buffer so that their time is not wasted. This way they protect their incomes, and customers pay for this in terms of long waiting hours.

Now, in the aftermath of the covid crisis, this will need to change. People won’t want to spend long hours in a closed waiting room with scores of other sick people. In an ideal world, doctors will want to not let two of their patients even see each other, since that could mean increased disease transmission.

In the inimitable words of Ravishastri, “something’s got to give”.

One way could be for doctors to simply up their fees and give out appointments at intervals that better reflect the time taken per patient. The problem with this is that there are reputation costs to upping fee per patient, and doctors simply aren’t conditioned to unexpected breaks between patients. Moreover, lower number of slots might mean appointments not being available for several days together, and higher cancellations as well, both problems that doctors want to avoid.

As someone with a background in financial derivatives, there is one obvious thing to tackle – the free option being given to patients in terms of the appointment. What if you were to charge people for making appointments?

Now, taking credit card details at the time of booking is not efficient. However, assuming that most patients a doctor sees are “repeat patients”, just keeping track of who didn’t turn up for appointments can be used to charge them extra on the next visit (this needs to have been made clear in advance, at the time of making the appointment).

My take is that even if this appointment booking cost is trivial (say 5% of the session fee), people are bound to take the appointments more seriously. And when people take their appointments more seriously, the amount of buffer built in by doctors in their schedules can be reduced. Which means they can give out appointments at more realistic intervals. Which also means their income overall is protected, while still maintaining social distancing among patients.

I remember modelling this way back when I was working in air cargo pricing. There again, free options abound. I remember building this model that showed that charging a nominal fee for the options could result in a much lower fee for charging the actual cargo. A sort of win-win for customers and airlines alike. Needless to say, I was the only ex-derivatives guy around and it proved to be a really hard sell everywhere.

However, the concept remains. When options that have hitherto been free get monetised, it will lead to a win-win situation and significantly superior experience for all parties involved. The only caveat is that the option pricing should be implemented in a manner with as little friction as possible, else transaction costs can overwhelm the efficiency gains.

Tiered equity structure and investor conflict

About this time last year, I’d written this article for Mint about optionality in startup valuations. The basic idea there was that any venture capital investment into startups usually comes with “dirty terms” that seek to protect the investor’s capital.

So you have liquidity preferences that demand that the external investors get paid out first (according to a pre-decided formula) in case of a “liquidity event” (such as an IPO or an acquisition). You also have “ratchets”, which seek to protect an investor’s share in the company in case the company raises a subsequent round at a lower valuation.

These “dirty terms” are nothing but put options written by existing investors in a firm in favour of the new investors. And these options telescope. So the Series A round has options written by founders, employees and seed investors, in favour of Series A investors. At the time of Series B, Series A investors move to the short (writing) side of the options, which are written in favour of Series B investors. And so forth.

There are many reasons such clauses exist. One venture capitalist told me that his investors have similar optionality on their investments in his funds, and it is only fair he passes them on. Another told me that “good entrepreneurs” believe in their idea so much that they don’t want to even consider the thought that their company may not do well – which is when these options pay out, and so they are happy to write these options. And then you know that an embedded option can increase the optics of the “headline valuation” of a company, which is something some founders want.

In any case, in my piece for Mint I’d written about such optionality leading to potential conflicts among investors in different classes of stock, which might sometimes be a hindrance to further capital raises. Quoting from there,

The latest round of investors usually don’t mind a “down round” (an investment round that values the company lower than the preceding round) since their ratchets protect them, but earlier investors are short such ratchets, and don’t want to see their stakes diluted. Thus, when a company is unable to find investors who are willing to meet its current round of valuation, it can lead to conflict between different sets of investors in the company itself.

And now Mint reports that such conflicts are a main reason for Indian e-commerce biggie Snapdeal’s recent struggles, which has led to massive layoffs and a delay in funding. The story has played out exactly as I’d written in the paper last year.

Softbank, which invested last in Snapdeal and is long put options on the company’s value, is pushing the company to raise more funds at a lower valuation. However, Nexus and Kalaari, who had invested earlier and stand to lose significantly thanks to these options, are resisting such moves. And the company continues to stall.

I hope this story provides entrepreneurs and venture capitalists sufficient evidence that dirty terms can affect everyone up and down the chain, and can actually harm the business’s day-to-day operations. The cleaner a company keeps the liabilities side of the balance sheet (in having a small number of classes of equity), the better it is in the long run.

But then with Snap having IPOd by offering only non-voting shares to the public, I’m not too hopeful of equity truly being equitable any more!

Valuing Global Fashion Group

Yesterday, in Mint, I wrote about ratchets in option valuation (a pet topic of mine), and gave alternate valuations of different Indian “unicorns” by accounting for the downside protection clauses that come with startup investment.

Money quote:

This implies that a share of the company held by [investors] includes a long put option, while a share of the company held by earlier investors includes a short put option (since they have implicitly written this option). In other words, a share held by the new investors is worth much more than a share held by earlier investors.

Now comes news that Global Fashion Group (that includes Jabong and a few other fashion houses started by Rocket Internet) has raised money at a “down round”. This gives me a good opportunity to put my theory to practice.

GFG has now raised $339M for a headline valuation of $1.13 billion. In its earlier round, it had raised $169M for a headline valuation of $3.5 billion. Let us look at a hypothetical employee of GFG who owned 0.1% of the company before the previous round of investment, and see what these shares are worth now.

Absence of ratchets

GFG had a “pre-money” valuation of $3.33 billion, and 0.1% of that would have been worth $3.33 million. As of that round of investment, existing investors had 95% stake in the company, so our friend’s share of the company would have come down to 0.095% (95% of 0.1%).

The new round shows a pre-money valuation of $791 million, and so our friend’s stock would be worth $750,000 after the latest round of valuation. This is a comedown from the previous valuation, but is still significant enough.

Presence of ratchets

Let’s assume that the previous round of investment into GFG came with a full ratchet (we’ll look at other downside protection instruments later). This would mean that its investors in that round would have to be compensated for the drop in valuation.

Investors in the previous round put in $169M for a headline valuation of $3.33Bn. The condition of the full ratchet is that is that if this round’s pre-money valuation were to be less than last round’s post-money valuation, the monetary value of last round’s investors has to be the same.

So despite this round showing a pre-money valuation of only $791M, last round’s investors would claim that $169M of that belongs to them (the way this is achieved in an accounting context is that the ratio in which their preferred shares convert to common shares changes). So the earlier investors (who came before last round) see the value of their shares go down to a paltry $622M. From owning 95% of the company, the down-round means they only own 79% now. And that is before the new round has come in.

Investors in the new round have put in $339M for a headline valuation of $1.13Bn, giving them a round 30% stake. Earlier investors have a 70% stake, of which investors who came before the previous round (which includes employees like our friend) have a 79% stake, giving them a net stake of 55%.

Coming back to our friend, remember that he owned 0.1% of the shares before the last round of investment. The ratchet means that he owns 0.1% of 55% of the company’s current headline valuation. This values his shares at $622,000.

But not so fast – since this assumes that the latest round of investment has no ratchets. If we need to take into consideration that this round has a full ratchet as well, the option formula I used in the Mint piece says that GFG is now worth $760M, far lower than the $1.13Bn headline valuation.

This implies that the stock held by investors prior to this round is now worth only $421M ($760M – $339M). Investors prior to the last round held 79% of these shares, so their stake is worth $331M now. Our friend held 0.1% of that, so his stake is only worth $331,000.

In other words, if both the previous and current rounds of investment in GFG came with a full ratchet protection, the shares held by ordinary investors such as our friend would have lost 56% of its value on account of optionality alone! Notwithstanding the fact that the remaining shares are held in a company whose value is on the downswing!

Then again, downside protection for investors could have come by other means, which were less harsh than full ratchet. Nevertheless, this can help illustrate how much of founders’ and employees’ shareholder value can be destroyed using ratchets!

More optionality in startup valuations

Mint reports that Indian e-commerce biggies Flipkart and Snapdeal are finding it hard to raise more money at the valuations at which they raised their last funding rounds. One line from the report:

Despite Morgan Stanley’s markdown in February, Flipkart is still approaching investors asking for a valuation of $15 billion, but it hasn’t had any takers yet, the first two people cited above said.

The problem with the valuations is that it includes significant option value. It is common in startup funding to include implicit options in favour of the new round of investors to protect them from the downside of any future decrease in valuation.

Typically designed in the form of “ratchets”, when the firm raises a fresh round at a lower valuation, the investors in the previous round will get additional shares so that their overall share in the investment remains the same (won’t go into the exact mechanics here). This downside protection allows investors to be more aggressive on their valuations of the company, and the company is able to report higher headline numbers.

Ratchets have two problems, both of which are illustrated in the difficulty of Flipkart and Snapdeal in raising more funds. Firstly, optionality in funding means an automatic markdown of funds held by investors in progressively earlier rounds. This is not explicit, but a ratchet is basically existing investors writing an option in favour of the new investors. While the cost of this option is not explicit, it is the earlier investors who bear the cost.

So Series C (and earlier) investors bear the cost of the optionality given to Series D investors. Series B and earlier investors bear the cost of Series C’s optionality. And so on. Notice that this telescopes, so the founders (original owners of equity) have written options to everyone who has invested (of course they also benefit from the higher overall valuation).

Now, if a “down round” (funding round at lower overall valuation than previous round) happens, this optionality gets immediately gets “paid out”. So if the Series D valuation is lower than Series C valuation, Series B and earlier investors (and founders) immediately “pay” the difference to the Series C investors (these options are American, and usually without an expiry date). So Series B and earlier investors (and especially founders) will not like this round. And they will hunt around for offers that will ensure that they don’t have to pay out on the options they’ve written. I suspect this is what is happening at Flipkart and Snapdeal now.

The second problem with ratchets is that stated valuations are inflated. A common share in Flipkart (don’t think one exists. All investors in that firm are effectively either long or short an option in the same stock) is not valued at $15 billion, so that valuation is essentially a misnomer. When Morgan Stanley says on its books that Flipkart is actually worth $11 billion, it is possible that that is the “true value” of the stock, without accounting for the optionality that latest round of investors receive. In other words, the latest round of investors invested at a price, which if extended to all stock, would value the company at $15 billion. But the rest of the company’s stock is not the same as the stock these investors hold! 

The problem, though, is that the latest “headline valuation” (inclusive of optionality) is anchored in the minds of founders and other earlier investors, and they see any lower price as unacceptable. And so the logjam continues. It will be interesting to see how this plays out.

With IPO being way too far off an event for determining if a company has “arrived” I propose a new metric, with shorter horizon. A company can be declared as having arrived if it manages to raise a round of equity with no embedded options. Think about it!

VC Funding, Ratchets and Optionality

A bug (some call it a “feature”) of taking money from VCs is that it comes in with short optionality. VCs try to protect their investments by introducing “ratchets” which protect them against the reduction in valuation of the investee in later rounds.

As you might expect, valuation guru Aswath Damodaran has a nice post out on how to value these ratchets, and how to figure out a company’s “true valuation” after accounting for the ratchets.

A few months back, I’d mentioned only half in jest that I want to get into the business of advising startups on optionality and helping them value investment offers rationally after pricing in the ratchets, so that their “true valuation” gets maximised.

In a conversation yesterday, however, I figured that this wouldn’t be a great business, and startups wouldn’t want to hire someone like me for valuing the optionality in VC investments. In fact, they wouldn’t want to hire anyone for valuing this optionality.

There are two reasons for this. Firstly, startups want to show the highest valuation possible, even if it comes embedded with a short put option. A better valuation gives them bigger press, which has some advertising effect for sales, hiring and future valuations. A larger number always has a larger impact than a smaller number.

Then, startup founders tend to be an incredibly optimistic bunch of people, who are especially bullish about their own company. If they don’t believe enough in the possible success of their idea, they wouldn’t be running their company. As a consequence, they tend to overestimate the probability of their success and underestimate the probability of even a small decrease in future valuation. In fact, the probability of them estimating the latter probability at zero is non-zero.

So as the founders see it, the probability of these put options coming into the money is near-zero. It’s almost like they’re playing a Queen of Hearts strategy. The implicit option premium they get as part of their valuation they see as “free money”, and want to grab it. The strikes and structures don’t matter.

I have no advice left to offer them. But I have some advice for you – given that startups hardly care about optionality, make use of it and write yourself a fat put option in the investment you make. But then this is an illiquid market and there is reputation risk of your option expiring in the money. So tough one there!

New line of business

I’m considering a new line of business. This is basically advising startups on option valuation and how to account for different conditions and optionalities that venture capitalists put in in term-sheets.

Aswath Damodaran has an extremely interesting piece on valuation of the so-called “unicorns” and how such valuations are inflated on account of optionality in favour of investors. He takes a stab at valuing such optionality, but I think there’s scope for going deeper and helping companies figure out the valuations in each individual case. Money quote from the piece:

As an outsider with an interest in valuation, I find venture capital deals to be jaw-droppingly complex and not always intuitive, and I am not sure whether this is by design, or by accident. When it comes to investor protection, the stories that I read for the most part are framed as warnings to owners about “vulture capital” investors who will use these protection clauses to strip founders of their ownership rights. I think the story is a far more complex one, where both investors and owners see benefits in these arrangements, and where both can expose themselves to dangers, if they over reach.

Do you think this is a good line of business to get into? Will startups be willing to pay for a service that allows founders to get value for money for the equity they are giving away? Or will they be so focussed on execution that trifles such as a change in valuation by a few percentage points don’t matter to them any more?

And what are the odds that if I get into this business and do a good job of it, a VC will want to hire me just so that I stop damaging their carefully designed ratchets?