Category: finance

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!

One Rank One Pension – some thoughts

There has been a lot of debate of late on whether veterans should be moved to a “one rank one pension” system. I won’t bother explaining the whole deal here, I’ll let you read this brilliant post by Ajay Shah about the numbers behind the move. Now that the quant has been outsourced, I can put forth my “qualitative” arguments.

I’m not a fan of this One Rank One Pension (OROP) move. I’m not against paying our soldiers, or veterans, well – I think it must definitely pay above market rates for the skills required for the job. Yet, I think OROP is a “one delta” solution to the problem (previous post here about government’s one delta thinking on agriculture), and can lead to massive unfunded liabilities.

The problem with any kind of pension scheme is that you create liabilities today that need to be funded later on. And at a later date these liabilities might become unserviceable. From this perspective, it is important to try and fund any future liabilities today, or at least have a handle on the precise magnitude of liabilities required. OROP, being “inflation indexed” (that’s Ajay Shah’s nice model to look at it), doesn’t allow for proper budgeting and long-term planning.

It is precisely due to this budgeting issue that the government moved most of its incoming employees to the New Pension Scheme (NPS) in 2004. NPS, unlike previous pension schemes, is a “defined contribution” scheme, where your pension is paid out of a corpus you create by your own saving. From an accounting perspective, it moves liabilities from tomorrow (pensions) to today (higher salary to fund the contributions), and is an excellent move. And there is no reason for it not to apply to the armed forces.

Most of the arguments being made in favour of OROP are emotional (“how can you deny our veterans money” etc.), and not well backed up by logical or economic reasoning. One of those is that lower-level military persons retire when they are 35, and hence need a “one rank one pension” (which I absolutely fail to understand). While I understand that the rigours of the role imply early retirement, I don’t see why defined contribution doesn’t solve the problem. It will have to be matched with higher salaries (to fund the contribution required for a long lifetime of retirement), but that implies liabilities are funded today, which is superior to pushing liabilities under the carpet for future  generations.

The thing with NPS is that it cannot be pushed retrospectively, and hence can apply at best to all forthcoming hires. We still need a solution for the existing employees and veterans, who are already on a defined benefit scheme. Yet, the important thing to consider is that the beneficiaries should be divided into three categories – current veterans, current servicemen and future servicemen, and we should find separate solutions for the three.

It might be argued that without defined benefit pensions, it might be hard to attract talent for a high-risk job like the military, and that is why we might need OROP. This is where the “derivative thinking” comes in. The thing about a job in the military is that there is a higher-than-civilian risk of losing life or limb. The solution to that is not blanket higher compensation – it is risk management.

What we need is generous death and disability insurance for our military, and this too should be purchased by the military from a professional Life Insurance firm. A generous insurance package can help mitigate the risks to life borne by military personnel, and should be sufficient to attract necessary talent. The purchase of such policies from professional insurers is important, for you don’t want the military to be doing an actuary’s job. More importantly, such a purchase will push liabilities to today rather than to tomorrow, and the last thing an army will want during the time of war is increased expenses on account of insurance.

The current debate about OROP has opened the door for a complete overhaul of military compensation. The government should jump at this, rather than simply get bullied by veterans’ groups. As Nitin Pai argues in this editorial in the Business Standard, compensation is an economic decision and should be made based on economic (and financial) reasoning, not based on emotion.

Understanding Stock Market Returns

Earlier today I had a short conversation on Twitter with financial markets guru Deepak Mohoni, one of whose claims to fame is that he coined the word “Sensex”. I was asking him of the rationale behind the markets going up 2% today and he said there was none.

While I’ve always “got it” that small movements in the stock market are basically noise, and even included in my lectures that it is futile to fine a “reason” behind every market behaviour (the worst being of the sort of “markets up 0.1% on global cues”), I had always considered a 2% intra-day move as a fairly significant move, and one that was unlikely to be “noise”.

In this context, Mohoni’s comment was fairly interesting. And then I realised that maybe I shouldn’t be looking at it as a 2% move (which is already one level superior to “Nifty up 162 points”), but put it in context of historical market returns. In other words, to understand whether this is indeed a spectacular move in the market, I should set it against earlier market moves of the same order of magnitude.

This is where it stops being a science and starts becoming an art. The first thing I did was to check the likelihood of a 2% upward move in the market this calendar year (a convenient look-back period). There has only been one such move this year – when the markets went up 2.6% on the 15th of January.

Then I looked back a longer period, all the way back to 2007. Suddenly, it seems like the likelihood of a 2% upward move in this time period is almost 8%! And from that perspective this move is no longer spectacular.

So maybe we should describe stock market moves as some kind of a probability, using a percentile? Something like “today’s stock market move was a top 1%ile  event” or “today’s market move was between 55th and 60th percentile, going by this year’s data”?

The problem there, however, is that market behaviour is different at different points in time. For example, check out how the volatility of the Nifty (as defined by a 100-day trailing standard deviation) has varied in the last few years:

Niftysd

As you can see, markets nowadays are very different from markets in 2009, or even in 2013-14. A 2% move today might be spectacular, but the same move in 2013-14 may not have been! So comparing absolute returns is also not a right metric – it needs to be set in context of how markets are behaving. A good way to do that is to normalise returns by 100-day trailing volatility (defined by standard deviation) (I know we are assuming normality here).

The 100-day trailing SD as of today is 0.96%, so today’s 2% move, which initially appears spectacular is actually a “2 sigma event”. In January 2009, on the other hand, where volatility was about 3.3% , today’s move would have been a 0.6 sigma event!

Based on this, I’m coming up with a hierarchy for sophistication in dealing with market movements.

  1. Absolute movement : “Sensex up 300 points today”.
  2. Returns: “Sensex up 2% today”
  3. Percentile score of absolute return: “Sensex up 3%. It’s a 99 %ile movement”
  4. Percentile score of relative return: “Sensex up 2-sigma. Never moved 2-sigma in last 100 days”

What do you think?

Shorting and efficient markets

The trigger for this blogpost is a tweet by my favourite newsletter-writer Matt Levine. He wrote:

And followed up with:

I responded to him with a tweet but thought this is blogworthy so putting it here.

The essential difference between an iPhone and an Apple share is that in the short run, the supply of the former is constantly increasing while the supply of the latter is fixed (follow on offers, stock splits, etc., which increase the supply of shares, are rare events).

The difference occurs because the “default action” (which is “do nothing” – caused due to inertia) has different impacts on the two market structures. In a market with constantly increasing supply, if customers “do nothing”, there will soon be a supply-demand mismatch and the manufacturer will have to take corrective action.

When the supply of the commodity is fixed, on the other hand (like an Apple share), the default action (“do nothing”) has no impact on the prices. You need a stronger method to express your displeasure, and that method is the ability to short the stock.

Means, medians and power laws

Following the disbursement of Rs. 10 lakh by the Andhra Pradesh government for the family of each victim killed in the stampede on the Godavari last week, we did a small exercise to put a value on the life of an average Indian.

The exercise itself is rather simple – you divide India’s GDP by its population to get the average productivity (this comes out to Rs. 1 lakh). The average Indian is now 29 and expected to live to 66 (another 37 years). Assume a nominal GDP growth rate of 12%, annual population increase of 2%  and a cost of capital of 8% (long term bond yield) and you value the average Indian life at 52 lakhs.

People thought that the amount the AP government disbursed itself was on the higher side, yet we have come up with a higher number. The question is if our calculation is accurate.

We came up with the Rs. 1 lakh per head figure by taking the arithmetic mean of the productivity of all Indians. The question is if that is the right estimate.

Now, it is a well established fact that income and wealth follow a power law distribution. In fact, Vilfredo Pareto came up with his “Pareto distribution” (the “80-20 rule” as some people term it) precisely to describe the distribution of wealth. In other words, some people earn (let’s stick to income here) amounts that are several orders of magnitude higher than what the average earns.

A couple of years someone did an analysis (I don’t know where they got the data) and concluded that a household earning Rs. 12 lakh a year is in the “top 1%” of the Indian population by income. Yet, if you talk to a family earning Rs. 12 lakh per year, they will most definitely describe themselves as “middle class”.

The reason for this description is that though these people earn a fair amount, among people who earn more than them there are people who earn a lot more.

Coming back, if income follows a power law distribution, are we still correct in using the mean income to calculate the value of a life? It depends on how we frame the question. If we ask “what is the average value of an Indian life” we need to use mean. If we ask “what is the value of an average Indian life” we use median.

And for the purpose of awarding compensation after a tragedy, the compensation amount should be based on the value of the average Indian life. Since incomes follow a Power Law distribution, so does the value of lives, and it is not hard to see that average of a power law can be skewed by numbers in one extreme.

For that reason, a more “true” average is one that is more representative of the population, and there is no better metric for this than the median (other alternatives are “mean after knocking off top X%” types, and they are arbitrary). In other words, compensation needs to be paid based on the “value of the average life”.

The problem with median income is that it is tricky to calculate, unlike the mean which is straightforward. No good estimates of the median exist, for we need to rely on surveys for this. Yet, if we look around with a cursory google search, the numbers that are thrown up are in the Rs. 30000 to Rs. 50000 range (and these are numbers from different time periods in the past). Bringing forward older numbers, we can assume that the median per capita income is about Rs. 50000, or half the mean per capita income.

Considering that the average Indian earns Rs. 50000 per year, how do we value his life? There are various ways to do this. The first is to do a discounted cash flow of all future earnings. Assuming nominal GDP growth of about 12% per year, population growth 2% per year and long-term bond yield of 8%, and that the average Indian has another 37 years to live (66 – 29), we value the life at Rs. 26 lakh.

The other way to value the life is based on “comparables”. The Nifty (India’s premier stock index) has a Price to Earnings ratio of about 24. We could apply that on the Indian life, and that values the average life at Rs. 12 lakh.

Then, there are insurance guidelines. It is normally assumed that one should insure oneself up to about 7 times one’s annual income. And that means we should insure the average Indian at Rs. 3.5 lakh (the Pradhan Mantri Suraksha Bima Yojana provides insurance of Rs. 2 lakhs).

When I did a course on valuations a decade ago, the first thing the professor taught us was that “valuation is always wrong”. Based on the numbers above, you can decide for yourself if the Rs. 10 lakh amount offered by the AP government is appropriate.

 

No Chillr, Go Ahead

This is yet another “delayed post” – one that I thought up some two weeks back but am getting down to write only now. 

After some posts that I’ve done recently on the payments system, I decided to check out some of the payment apps, and installed Chillr. This was recommended to me by a friend who has a HDFC Bank account, who told me that the app is now widely used in his office to settle bills among people, etc. Since I too have an account with that bank, I was able to install it.

The thing with Chillr is that currently they are tied up with only HDFC Bank. You can still sign on if you have an account of another bank, but in that case you can only receive (and not send) money through the system. So your incentive for installing is limited.

Installation is not very straightforward since you have to enter some details from your netbanking which are not “usual” things. One is a password that allows you to receive money using the app, and the other is a password that allows you to send money. Both are generated by the bank and sent to your phone as an SMS which the app automatically reads. I understand this is part of the system itself and this part won’t go away irrespective of the app you use.

Once you have installed it, you will then be able to use the app to transfer money to your contacts who are also on the app without requiring to know their account number. The payment process is extremely smooth with an easy to use second factor of authentication (a PIN that you have set for the app, so it is instant), so if more people use it, it can ease a large number of payments, including small payments.

The problem, though, is that it is currently in a “walled garden” in that only customers of HDFC Bank can send money, and hence the uptake of the app is limited. The app allows you to see who on your contact list is there on the app (since that is the universe to which you can send money using the app). The last time I checked, there were four people on the list. One was the guy who recommended me the app, the second was another friend who works in the same organisation as this guy, the third a guy who works closely with banks and the fourth a Venture Capitalist. And my phonebook runs into the high hundreds at least.

In terms of technology, the app is based on the IMPS platform which means that in terms of technology there is nothing that prevents the app from transferring money across banks using its current level of authentication. This is very good news, since it means that once banks are signed on, it is a seamless integration and there are no technological barriers to payment.

The problem, however, is that the sector suffers from the “2ab problem” (read my  argument in favour of net neutrality using the 2ab framework). Different tech companies are signing on different banks (Chillr to HDFC; Ping Pay to Axis; etc.) and such banks will be loathe to sign on multiple tech companies (possibly due to integration issues; possibly due to no compete clauses).

Currently, if HDFC Bank has a users and Axis Bank has b users, and they use Chillr and Ping Pay respectively, the total value added to the system by both Chillr and Ping Pay is proportional to a^2 + b^2 (network effects, Metcalfe’s law and all that). But if these companies merge, or one of them gets the account of the other’s bank, then you have a single system with a+b users, and the value added to the system by the combined payments entity is (a+b)^2 which is a^2 + b^2 + 2 ab. Currently the sector is missing the 2ab. The good news, however, is that there are no tech barriers to inter-bank payments.

Postscript: The title is a direct translation of a popular and perhaps derogatory Kannada phrase.

Revenue management in real estate

Despite there continuing to be large amounts of unsold inventory of real estate in India, prices refuse to drop. The story goes that the builders are hoping to hold on to the properties till the prices rebound again, rather than settling for a lower amount.

While it is true that a number of builders are stressed under bank loans since banks have pretty much stopped financing builders, this phenomenon of holding on to houses while waiting for prices to recover is actually a fair strategy, and a case of good revenue management. Let me illustrate using my building.

There are eight units in my building which was built as a joint venture between the erstwhile owner of the land on which the building stands and the builder, both receiving four units each. The builder, on his part, sold one unit from his share very soon after construction began.

Given the total costs of construction, the money raised from sale of that one apartment went a long way in funding the construction of the building. It wasn’t fully enough – the builder faced some cash flow issues thanks to which construction got delayed,  but since he managed to raise that cash, he didn’t need to sell any other units belonging to his share. He continues to own his other three units (and has rented out all of them).

The economics of real estate in India are such that the cost of land forms a significant part of the cost of an apartment. According to a lawyer I had spoken to during the purchase of my property (he also has interests in the construction industry), builders see a significant (>100%) profit margin (not accounting for cost of capital) in projects such as my building.

What this implies is that once the builder has taken care of the cost of land (by paying for it in terms of equity, for example, like in the case of my building), all he needs to do to fund the cost of construction is to sell a small fraction of the units. And once these are sold, there is absolutely no urgency to sell the rest.

Hence, as long as the builder expects prices to recover (when it comes to house prices, builders are usually an optimistic lot), he would rather wait it out (when he can realise a higher price) than sell it currently at depressed prices. Hence, downturns in housing markets are not characterised by an actual drop in prices (few builders are willing to drop prices) but by a drop in the volume of transactions.

While there might be a large number of housing units that remain unsold, it is unlikely that there are apartment complexes which are completely unsold – there will be a handful of bargain-hunting early buyers who would have bought and funded the construction of the complex. And given the low occupancy rates, these people are losers in the deal, for it will be hard for them to move in.

And it is also rational for the builder to invest in new projects even when they are currently holding on to significant inventory. All they need to do is to find a willing partner who can contribute the necessary real estate in the form of equity. And new projects will inevitably find the first set of early buyers looking for a bargain, irrespective of the builder’s track record.

And so the juggernaut rolls on..

China, Reporting and Bias

The amount of attention that the rising Chinese stock market received over the last one year is nothing close to the attention that the falling market has received over the past month or so.

While the markets have fallen by at least a fourth, which is more than what the Dow Jones Industrial Average (DJIA) fell on Black Monday, the fact is that this followed nearly a year of insane rise in the markets, the fact is that markets are still up 80% over a year ago.

I hereby present two charts. Both are time series and hence drawn as lines, and both start from 1st of January 2014. The first shows the SSE Composite Index  (refer to Yahoo finance for a more interactive plot. I couldn’t embed the chart here).

chinaThe second shows the Google Trends for “China Stock Markets” over the same time period.

 

 

I don’t think I need to explain much further. On the way up, there was little commentary on China’s markets, apart from that there might be a bubble. On the way down, though, there is so much more!

The asymmetry in markets is rather intriguing!

Cake cutting, Dutch auctions and chit funds

Last night at what started off as high tea but ended up as dinner (for me, at least), Baada and I shared a cake. The cake was delivered to our table along with a (rather sharp) knife. I used the knife to cut  the cake into two, and Baada chose one of the two pieces (inexplicably he chose the smaller one). That way, we had achieved the most efficient method of splitting a piece of cake between two people.

It has been an interesting mathematical problem as to how to split a piece of cake between three people, since the above algorithm doesn’t work. The problem has been solved, but is rather complicated with several cases, involving one person cutting a piece, the second person trimming it and offering it to the third, followed by further complications. I won’t bother describing it further here. And then you have the problem of extending the solution to N people sharing a piece of cake.

But then, there is an elegant solution, after all, which I found in Alex Bellos‘s excellent book Alex Through the Looking Glass a couple of days back. As Bellos describes,

One ingenious method invented in the 1960s, which can be used for any number of people, concerns a moving knife. The knife is positioned at the side of the cake and then moves very slowly across it. When someone shouts ‘STOP!’ the knife slices at that position. The person who shouted out receives the slice. The knife then continues for the remaining participants.

It is not hard to see how this works (it assumes that the players, unlike Baada last night, want the largest possible piece of cake while being fair). If you call too early, you end up with a smaller piece of cake than you’re entitled to, and so you wait. You call too late, and someone has already called for it. So with every player playing the optimal strategy, this moving knife strategy results in each person getting their fair share.

While reading this cake-cutting strategy, I got reminded of the Dutch auction. In such an auction, the house starts with a very high price, which drops slowly (represented by a clock, usually). And as the price drops, when one of the buyers is willing to pay the price at that moment, they bid for it, and the object gets sold at that price. While it is a “first price auction” and buyers may not disclose their true willingness to pay (in the hope of getting the item for a lower price), the advantage is that it’s quick, and hence used for auctioning things such as flowers.

It works the same way as the cake-cutting algorithm in that if there is a well-defined value for the object being auctioned (this is rarely the case in practice), it makes sense to bid exactly at the point when the price equals this well-defined value.

This method of cutting cakes and auctioning flowers is also similar to how chit funds work in India. In a chit fund, you have N people who invest money into a pot at N different points in time. Each time, the money thus collected is auctioned to the person who needs it the most, and the price of the auction is determined by the amount that the person is willing to “let go” of the maximum amount. This amount that is thus let go of is distributed to the other participants (with the house taking a commission).

This is exactly similar to the cake cutting case. Think about it!

So it is very interesting that a fundamental feature of Indian homegrown finance, the chit fund, draws from important concepts in maths and game theory. We’re truly great!

 

Genesis, the Nile and the Nifty

So I’ve written on the financial markets for Mint. This is not part of my usual mandate – which is to write data/quant stories related to politics and the economy and suchlike, I believe this is very different from the kind of markets pieces Mint normally writes.

For starters, I see that there is very little “quant” stuff in mainstream financial reporting. You have tonnes of writing on “fundamentals” (“Company A got this new deal so expect their stock price to increase” or “Company B has regulatory trouble, so short their stock” level) and tonnes on “technicals” (“the nifty will find resistance at 7891” and “we are seeing a head-and-shoulders market (sponsored by P&G)” type), but none on quant.

In fact, if you were to learn finance by reading the newspapers (admittedly a stupid thing to do), you wouldn’t know of how bankers work, of the models they use, of random walks, and of the Black-Scholes-Merton equation. You would think of finance as a rather boring accounting-related fundamentals or voodoo technical stuff. All the cool quant stuff will be lost to you.

So in my attempt to remedy that, I’ve gone all the way and introduced readers of Mint to Fractional Brownian Motion. No, really. I tell a story from Genesis (I actually looked up and read this chapter from the Old Testament so that I could quote it properly), and then relate it to the flooding of the Nile, and that to the work of hydrologist Harold Edwin Hurst, and how that can help us understand the markets. An extract:

Hurst was to remain in Egypt and be associated with the Nile for 62 years (the Egyptian government retained his services after the country’s independence). Looking through 847 years of Nile overflow data (existence of this data tells us much about the farsightedness of the Mameluke and Ottoman rulers of Egypt), Hurst managed to crack the puzzle. The model he built was one of long-range dependence. It is a model that has far-reaching effects, most importantly in the financial markets.
And another:
Turning this around, analysing the rescaled range of a time series as a function of number of time periods will tell us about its long-range dependence. All we need to do is to find the exponent of N, according to which the rescaled range grows. If this exponent is half (in which case the rescaled range grows with the square root of N), we have a regular random walk (or Brownian motion). If the exponent is greater than half, we have positive long-range time dependence, and the value of the exponent tells us the degree of such dependence. Similarly, if the exponent is less than half, we have negative long-range time dependence, which is known as fraction Brownian motion.
Go read the whole thing! And while you’re at it, pick up Benoit Mandelbrot’s The (Mis)Behaviour of Markets and read that, too. It’s a fantastic book on financial markets, and while it has been written by a mathematician, contains no math. And it’s absolutely fascinating stuff. Oh, I’ve read that book twice. And refer to it quite often.