option auctions

Although slowed down, the privatization program is still ongoing in Turkey. One of the last auctioned assets was a closed-down raki factory that is located right on Bosporus. The point of interest was not the factory itself but the precious 54,870 square meters land that the factory had been built on. (Since none of the buildings are historical, the prospective investor is free to demolish everything and to use the land as he wishes.)

The winner of the auction was an obscure company with a bizarre and very long name: As Asya Gayrimenkul Pazarlama İnşaat Taahhüt Otomotiv Oto Kiralama Turizm Kamuoyu Araştırmaları Reklam Hizmetleri ve Matbaacılık Dayanıklı Tüketim Mamülleri Gıda Maddeleri İthalat İhracat Sanayi ve Ticaret Ltd. Şti.

Their bid was 303,100,000 TL. The result was shocking. After 40 rounds of fierce bidding, the prices had climbed to such high levels that even the government was caught by surprise.

A couple of weeks later the winning company made it to the headlines. Everyone was wondering who these obscure millionaires were. The fact that their company had only 50,000 TL of registered capital rendered the situation even more mysterious.

I was surprised, not by the result of the auction, but by the reaction of the newspapers. These guys were no millionaires. The government had lowered the entry barrier to such ridiculous levels that anybody who was willing to risk 50,000 TL (i.e. the collateral amount) could join the auction and bid for the small-but-realizable prospect of making millions of dollars. The goal was to attract more participants and to stimulate greater momentum and competition. Secretly the government hoped that the amateur investors would push up the prices and that the asset would nevertheless end up in the hands of a professional investor who will be able to close the deal by paying the promised amount.

However, in an almost paradoxical fashion, the design of the auction discouraged the serious investors who anticipated right from the beginning that the presence of obscure investors would lead to an irrational bidding war.

Claim: The behaviour of the winning company was aggressive but not irrational.

A privatization auction does not immediately result in a completed sale. There is a deadline for paying the promised amount. (The deadline is usually a year away from the auction date.) If the winner changes his mind, then he is forced to hand the entire collateral to the government. In other words, the auctioned object is not the asset itself. It is the strike price of the American call option to buy the asset before the deadline. This price is Y minus W where W is the value of the collateral and Y is the bid. (The collateral counts towards the purchasing price.) Since W is fixed from the beginning, the participants are essentially bidding for the strike price of the option. (Note that they are not bidding for the price of the option!)

Now let's look at how the bidding behaviour changes as the required collateral amount decreases.

Since the price of an American call option is close to that of an European one with exactly the same qualities, we can safely employ the classical Black-Scholes formula during the rest of our analysis. This is not an uncontroversial move. There may be monetary gains from an early payment to the government. (e.g. In numerous privatizations, early payment has been encouraged by a provision of discounts.) Nevertheless, the assumption that the early exercise of our American call option is non-optimal is harmless. The conclusion of our argument will be analytically independent from it.

If the value of the asset is greater than Y-W at the deadline date, then the option will be exercised. If it is not, then the option will expire and W will go wasted.

The Black-Scholes option price at time "t" is:

where

and where "S" is the value of the asset at time "t", "K" is the strike price of the option, "r" is the continuously-compounded annualized risk-free interest rate, "σ" is the volatility of the value of the asset, and N(x) is the standard normal cumulative distribution function:

In our case, we have K=Y-W, T=1 and t=0. (i.e. Deadline is a year away from the auction date.)

Without losing generality let's fix "σ" at 20% and "r" at 5%. And for convenience let's express both "Y" (the bid) and "W" (the collateral) as percentages of "S" (the value of the asset at t=0): Y=m*S and W=n*S where both "m" and "n" are strictly positive real numbers.

Note that the value of S at t=0 is universally observable and everyone agrees on it. You may ask: "Wait... Revealing the true value of S at t=0 was the whole purpose of the auction!" Nope. The auction is concerned with the value of S at t=1, not at t=0.

Moreover let's assume that auction participants and government share the same ideas about the dynamics that drive the evolution of "S" and "r". (In particular, they can agree on the values assigned to "σ" and "r".) This is indeed a strong assumption... (In economics, granted that its conclusions are instinctively realistic, the contents of a model do not matter much!)

During the auction, the bidders will never violate the following inequality:

This is simply because the auction participants are trying to make a profit. "W" is set by the government and it will be the cost of the option no matter what the winning bid is. (Here we implicitly take for granted that the interest earned on the collateral goes into the account of the government even if the winner ends up purchasing the asset before the deadline.) Hence participants will bid in a way that renders the value of the option greater than "W".

Since "S" is positive, dividing both sides by "S" preserves the inequality:

The term "ln(S/K)" in "d" is now "ln(1/(m-n))". Hence "S" has completely disappeared from the inequality. Since the government fixes "n" before beginning of the auction, the only unknown variable left here is "m".

Due to the competitive spirit reinforced by numerous rounds of bidding, the participants will be pressured to increase their bids (i.e. their "m") until the inequality above turns into an equality. In other words, once the government fixes "n", the above equation spits out a unique "m" that depicts the bidding behaviour of participants:

Independent variable "n" is located on the x-axis and dependent variable "m" is located on the y-axis.

Note that the relationship between the two variables is non-linear. As the government decreases the amount of collateral required as a percentage of the value of the auctioned asset, the bidding becomes more aggressive. The sensitivity of this interaction becomes greater at the lower ends of "n".

During the privatization of the raki factory, "n" was set incredibly low. Today the value of a square meter land on the Bosporus is about $2,000. Hence S at t=0 is roughly equal to 164,610,000 TL (=54,870*2,000*1.5). In other words, the government had set "n" equal to 0.02% (=30,000/164,610,000).

With the above assumptions for "σ" and "r", the corresponding "m" for 0.02% is 235%! In other words, the winning bid is 386,833,500 TL (=2.35*164,610,000). If the winning company has friends in the government, it may be able to extend the deadline to two years. (This has happened before!) In that case, "T" becomes 2 and the corresponding "m" increases to 360%!

Conclusion: The bidding behaviour was not irrational.

P.S. In retrospect we already know that "m" was 184% (=303,100,000 /164,610,000). Plugging 12% into "r" as a more realistic risk-free rate for the Turkish market, we can calculate the "expected σ": 12.5%

P.S. The owners of the winning company do not have fat offshore bank accounts. They need to find a real investor to whom they can pass the option before the deadline, or with whom they can finance the exercise of the option at the deadline. I am pretty sure that they are desperately flying around the world at the moment. Since they are virtually unknown in the investment community, it will be tough for them to find an interested foreign partner.