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!

Using illegal markets as price discovery mechanism

One of the pet projects of my former MLA (former because I moved residence, not because he was voted out) is to set up a formal mechanism for regulating street vendors. He wants to introduce some kind of a medallion for street vendors so that they have legal sanction, and at the same time subject them to health and food safety checks. Considering this is a fairly common practice abroad, and even in some parts of India (like Goa), it is high time something like this is introduced.

Food cart in Miramar, Goa. Notice the bottom portion – it has a license number

The question, however, is how we will price these “medallions”. Price them too high and existing vendors will not want to get into the new regime, and will remain outside regulatory bounds. Price them too low and it can result in missed opportunities and rent seeking (the current situation, where the price is zero, can be seen as a degenerate case of too low a price).

One way to do this would be through an auction. However, one thing we need to preserve is continuity – current existing street vendors need to get a chance to enter the legal fold without too much disturbance from their current business. An auction might see them being priced out and then continue to operate in the illegal framework – which is not an optimal solution.

The solution lies in status quo, and in illegal markets. Given that street vendors currently operate without a license, they are essentially illegal. The way they manage to keep their carts and not get arrested is by paying off a set of public (and private) officials. Perhaps there is the cop who seeks his weekly rent (hafta). Perhaps a municipal officer seeks the same. Maybe a local thug, too.

If you think about this, the sum total of all these payments is essentially the “license fee” that the vendor pays in order to do his business currently. Can we take this as a proxy for the appropriate license fee in a particular location? Can we do an anonymised survey among street vendors (after having classified them into different “areas”) in order to determine the clearing price?

The basic idea is that illegal markets (like that of the “hafta” for being a street vendor) are markets, too, and their price discovery mechanism is as legitimate as those of more legitimate markets. Thus, the price discovered by these illegal markets are a great starting point for regulated pricing!

There is one thing to examine, though – if we price the license at the same “fee” that the vendors are currently paying different rent seekers, will the rent seekers still be able to seek rent? My hypothesis is “no”. The reason rent seekers seek rent is because in its absence there is a “surplus” that the vendors generate which they are willing to share with the rent seekers. If all the rents that are now being collected by illegal rent seekers are subsequently sought by the state, there is no room left for the illegal rent seekers to operate in!

The question is if this framework can be used for eliminating other forms of rent-seeking, too. The answer, sadly, is no. A large number of the rents that are currently being sought are for “public services” which are not supposed to have a fee. I had to get a document from a court recently, and had to pay rents at different points in the chain in order to get it on time. Using this framework, the way to eliminate this would be by increasing the official court fee, but what one must keep in mind is that court services are inelastic – the increase in fee by a few thousand rupees will not deter me from asking for an order. Thus, even if the court fees are increased, nothing prevents the current rent-seekers from continuing to operate.

In other more elastic markets, however, this approach will work, and better be tried.

Sangakkara and the IPL Auction

Sri Lankan cricketer Kumar Sangakkara has decided to not participate in this year’s IPL auction. In the opinion of this blog, this is an extremely smart decision, for Sri Lankan cricketers are unlikely to be available for a large part of this year’s IPL, thanks to their tour of England starting in May. Let me explain.

The IPL Auction is a strange beast. Each team has a salary cap, and players are auctioned across teams such that a team spends no more than its salary cap (in total). Now, in case a player is not available for a particular part of the tournament (due to a clash in schedules due to international commitments, essentially), the fees paid to the player is pro rated according to the number of matches for which he is available. However, while calculating the team’s salary cap, the player’s full season salary will be counted.

For example, if Sangakkara were to participate in the auction, and win a salary of Rs.5 Crore. Now, if he is available for only 40% of his team’s games, he would be paid Rs. 2 Crore. However, when his team’s total salary is determined, the full amount of Rs 5 Crore is taken into account.

Assuming that the salary cap is the real reason as to why teams don’t bid too much for a player (as opposed to capacity to pay), teams will not want to let go of a large amount of their salary cap for a player who is unlikely to be available for the full tournament. Thus, if Sangakkara were to enter the IPL Auction this year, he is likely to be undervalued, and hence he has decided to not take part in the IPL at all.

What Sangakkara is betting on is that in the auction teams will have a short-term perspective, and will be looking at only this year’s commitments in order to determine a player’s availability . Ideally, since the auctions are for purchase of a player for three years, teams should be taking into account the tours scheduled for the IPL seasons of those years (the gap in India’s schedule will show when the IPL will take place, and a player belonging to any country that has cricket scheduled at that time according to this chart will not be available for the IPL). However, perhaps due to the uncertainty in next year’s schedules (thanks to the proposed ICC revamp), teams are only going to take into account this year’s commitments in order to guide their bidding.

Sangakkara has said that he plans to take part in next year’s IPL, and he hopes for a much better valuation then compared to this year, for he will be free of international commitments. Given that the salary cap for the teams increases by only 5% (Rs. 3 Crore) next year, what he will be banking on is that teams might release some high value players they will be employing this year.

Tailpiece: Given that the English domestic calendar invariably clashes with the IPL, English Test players are going to be forever undervalued in the IPL. At least they should be if teams are intelligent about their bidding.

Tailpiece2: Samit Patel and Alex Hales have a deal with their county Nottinghamshire that they will be allowed to play in the IPL only if they can get a fee of USD 400000 (INR 2.5 Crore). They have both put their base prices as Rs. 2 Crore. It will be interesting to see if and how teams go about picking them!

Who should the IPL franchises retain?

I have a proprietary algorithm for evaluating cricket matches. This algorithm analyzes matches ball-by-ball and then computes the “impact” of each player on the game, in terms of both batting and bowling.

I’ve been intending to do this for a while now but I finally got down to calculating the impact of different players in the past editions of the IPL, and who it makes sense for franchises to retain (incidentally, today is the last day for franchises to announce to the IPL who the players are who they are going to retain).

Let us go franchise by franchise and see who the best players are. The numbers in the brackets represent the impact of each player according to my proprietary system.

1. Chennai Super Kings

By a long way, their two best players are MS Dhoni (3.53) and Ravindra Jadeja (3.46). Interestingly, the primary reason for the latter’s high score is his batting (2.86)- he has been bowling well, too (0.6), but it is his batting that has had significant impact.

These two are followed some distance behind by Raina (2.02) and the now retired Mike Hussey (1.75). Ashwin is some way behind at 0.7 (his bowling is at 1 and batting at 0.33; the algorithm tends to unfairly penalize bowlers for their batting abilities, or the lack of it).

Chennai have already made their decision on who to retain. They are going to retain Dhoni, Jadeja, Raina, Ashwin and Dwayne Bravo. The last is a bit of a puzzle, at -1.09. His batting has been excellent – he has contributed 1.52 but his bowling has been utter crap at 2.61. CSK would do well to use him as a batsman only

2. Delhi Daredevils

This is a team that has performed rather badly in the last bunch of IPLs, so they might be expected to dispense with some players. Virender Sehwag (3.14), though, has performed exceptionally in the rot, though this season’s domestic performance (or the lack of it) might go against him. Next is the injury-prone Irfan Pathan (1.72). Shahbaz Nadeem is a surprise package at 1.56. I wouldn’t expect them to retain anyone.

Umesh Yadav (-1.77) and Mahela Jayawardene (-2.33) have been especially poor performers

3. Kings XI Punjab

Another franchise that didn’t do particularly well in the last set of IPLs. David Miller (2.05) was their standout performer, followed by Gurkeerat Singh (1.24), Shaun Marsh (1.11) and Praveen Kumar (1.02). The latter two are highly injury prone and they may not want to part with a large part of their budget for the yet uncapped Gurkeerat. So if you expect them to retain any players, it would only be Miller.

At the other end, Parvinder Awana (-1.92) has been the standout performer.

4. Kolkata Knight Riders

Sunil Narine (4.48) and Gautam Gambhir (4.22) tower over the rest. Following them are Shakib al Hasan (1.63) and Iqbal Abdulla (1.13). One would expect them to hold on to the first two (Narine and Gambhir) and try to use their trump card to match a price for Shakib.

Jacques Kallis performed particularly badly (-2.81) and is unlikely to be retained.

5. Mumbai Indians

If you were to rank all players in descending order of impact, the standout player across teams would be Harbhajan Singh (5.04; 3.64 bowling, 1.41 batting). Despite his axing from the national team, one would expect him to be retained by the franchise. He is followed some way behind by Lasith Malinga (2.01), Kieron Pollard (1.97; with 3.05 in batting and – 1.09 in bowling) and Rohit Sharma (1.74). One would expect all of those three to be retained. Dinesh Karthik at 1.31 might also be retained, for they will only need to give up Rs. 4 Crore from their salary cap to get him.

6. Rajasthan Royals

If one goes by the gossip, the Royals are expected to retain a large number of players. They are the “moneyball” team of the IPL. They don’t spend too much on salary but try to get otherwise undervalued players to play for them.

Brad Hodge (1.91) has been their star performer but his age might go against him – they might prefer to match him using their trump card. They are expected to retain Shane Watson (1.55 with 3.83 batting and -2.28 bowling), though. Stuart Binny at 1.34 is also a good bet to be retained.

Interestingly, the system shows a negative impact for the otherwise highly rated Sanju Samson (-0.17)! He is, however, another player they might retain.

7. Royal Challengers Bangalore

The Royal Challengers have already made their decision – they will retain Chris Gayle (4.93; with 6.51 batting and -1.58 bowling), AB de Villiers (3.12) and Virat Kohli (1.95 with 2.22 batting and -0.27 bowling). The one highly rated player they are not retaining is Zaheer Khan (3.69). Khan has been exceptional considering that his partners in the RCB pace attack are Vinay Kumar (-3.59), RP Singh (-2.83) and Abhimanyu Mithun (-1.69).

Their only other highly rated bowler is Murali Kartik (1.05). They will need to completely rebuild their bowling attack in order to compete this IPL

8. Sunrisers Hyderabad

Dale Steyn (3.43) is the standout performer and they would do well to retain him. The next best is Shikhar Dhawan, who is some distance away at 0.72. Given the paucity of quality Indian players, though, they might end up retaining Dhawan also.

I’m willing to share the full results of my analysis. Do reach out to me if you want to play around with it and I’ll send it to you. And let me know what you think of these ratings.

Spending on Indian Players in IPL Auctions

In the first IPL Auction in 2008, teams spent an average (median) of 47% of their overall spend on Indian players, the rest going to foreign players. By the time of the auction in 2011, however, they had wisened up to the fact that only four foreigners can play in the eleven, and the average (median) spend on Indian players went up to 65%.

How did different teams fare on this count? The following graph describes this (I’m generally not a big fan of “dodged” bar graphs but couldn’t think of a better way of representing this data. If you have any ideas, do let me know).

As you can see in this graph, most teams significantly increased their spending on Indian players. The only teams that failed to do so were Deccan Chargers (who performed really badly and then dropped out of the IPL), Kings XI Punjab (performed badly all three seasons) and Rajasthan Royals (who built their team around “uncapped” Indian players who were not part of the auction).

It will be interesting to see what this ratio is like in the following auction.

Analyzing the IPL Auction Rules – 1

So finally after a really long delay the rules for the IPL Auction 2014 are out. Each franchise has the option of retaining up to five players, with additional “trump cards” that allow them to match the price of a winning bid in the auction for players that were part of their teams in the earlier IPLs.

At the outset, the rules of the auction look loaded towards teams that already have strong squads and want to retain as many players as they can – for example, given the rules of the auction, a team can retain up to 6 players from their existing squads, and this significantly biases the auction in favour of teams that want to retain players.

Looking a bit deeper, though, it is clear that this luxury of retention comes at a price. For example, irrespective of what the team negotiates with its number one player, Rs. 12.5 Crore (125 million), or a little more than 20% of the cumulative salary cap will be debited from the team’s account. For the next player, Rs. 9.5 Crore (95 million) will be debited. There is a sliding scale and the fifth player a team retains will cost them Rs. 4 Crore in terms of their budget.

The question is if this pricing is appropriate – is charging 20% of the team budget for the number one player enough compensation for the benefit the team gets by way of retention? Is charging two thirds of the total salary cap (Rs. 39 Crore) enough for retention of five players?

At first look, this pricing looks appropriate – after all, why would someone want to forego two thirds of their auction kitty for keeping just five players, when the total squad size is 16 to 27? However, looking at the previous auctions tells a different story.

The two graphs here shows the proportion of total auction money spent by each team on each player in the last two auctions. The graph might appear complicated so let me explain. For each team, I ordered players bought in the auction in the descending order of price. Then I looked at how much the top player cost as a proportion of the total money spent at the auction. Then, how much the top two players cost and so on.

ipl11

(click on images for full size. For the 2008 auction, marquee players have been included in the analysis)

In the 2008 auction, teams spent between 60 and 85% of their budgets in order to select their five most expensive players, with a median of 72%. In the 2011 auction, teams spent between 65 and 90% of their budgets for their top five players (takes into account retained players), and the median spend was 71%.

Given that the “top 5” players for each team cost them upwards of 70% of their total budgets in the last two auctions, charging teams only Rs. 39 Crore (65%) for retaining five players is blatantly unfair, and biased towards the teams that want to retain. Also, considering that retained players are “known devils”, there is more value for money for teams from retained players. So in the ideal case, the fee for retaining 5 players should have been definitely upwards of 75% of the total budget (Rs. 45 Crore).

The following table helps to show the undervaluation of each retained player:

The second and third columns in the above table shows the median percentage of total budget teams spent in order to buy their top N players. The last column shows what percentage of their budget they would have to spend if they are to retain players in the auction.

The message for teams is clear: retain as much as you can. It is cheaper to retain your top players rather than building a new team from the available pool. The challenge, however, is to negotiate a good price with these players.

PS: I have a solution that can help teams plan their auction strategy. If you are an IPL team and you are interested in this, contact me through the contact form.

Successful IPOs

Check out this article in the Wall Street Journal. Read the headline. Does this sound right to you?

MakeMyTrip Opens Up 57% Post-IPO; May Be Year’s Best Deal

It doesn’t, to me. How in the world is the IPO successful if it has opened 57% higher in the first hour (it ended the first day 90% higher than the IPO price)? To rephrase, from whose point of view has the IPO been the “best deal”?

What this headline tells me is that makemytrip has been well and truly shafted. If the stock has nearly doubled on the first day, all it means is that MMYT raised just about half the cash from the IPO as it could have raised. If not anything else, the IPO has been a spectacular failure from the company’s point of view.

The US has a screwed up system for IPOs. Unlike in India where there is a 100% book-building process where there is effectively an auction to determine the IPO price (though within a band) in the US it is all the responsibility of the bank in charge of the IPO to distribute stock (as far as I understand). Which is why working in Equity Capital Markets groups in investment banks is so much more work there than it is here – you need to go around to potential investors hawking the stock and convincing them to invest, etc.

Now, the bank usually gets paid a percentage of the total money raised in the IPO so it is in their incentive to set the price as high as they can (and the fact that they are underwriting means they can’t get too greedy and set a price no one will buy at). Or so it is designed.

The problem arises because the firm that is IPOing is not the only client of the bank. Potential investors in the IPO are most likely to be clients of other divisions of the bank (say, sales and trading). By giving these investors a “good price” on the IPO (i.e. by setting the IPO price too low), the bank hopes to make up for the commission it loses by way of business that the investors give to other divisions of the bank. If most of the IPO buyers are clients of the bank’s sales and trading division (it’s almost always the case) then what all these clients together gain by a low IPO price far outweighs the bank’s lost commission.

It is probably because of this nexus that Google decided to not raise money in a conventional way but instead go through an auction (it made big news back then, but then that’s how things always happen in India so we have a reason to be proud). Unfortunately they were able to do it only because they are google and other companies have failed to successfully raise money by that process.

The nexus between investment banks and investors in IPOs remains and unless there are enough companies that want to do a Google, it won’t be a profitable option to IPO in the US. Which makes it even more intriguing that MMYT chose to raise funds in the US and not here in India.