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Auction Prices and Risk Premium

Quotation

Bargain hunters paid a total of $53,630 yesterday morning at an unusual auction of stocks seized by the State Franchise Tax Board from delinquent taxpayers.

That was $800 less than the stocks were worth when the market closed yesterday.

More than 40 bidders turned out for the auction, conducted by San Francisco County Deputy Sheriff Paul Speckenheuer at a state building in the city.
. . .
A 363-share lot of stock in Charles Schwab, the San Francisco discount broker, was bought by an unidentified Schwab staffer for $13,500, or $37.19 per share. That turned out to be one of the better bargains because Schwab stock rose $1.75 yesterday to $38.88.
...
Successful bidders had to pay immediately with cash or certified checks.

Source: San Francisco Chronicle, March 7, 1997

Question
Given the information in the above quotation, were these stocks necessarily a bargain?

Answer
I would like to point out below a few reasons why they might not have been a "bargain" after all.

Let’s compare buying Charles Schwab shares through a broker to the above auction results.

First, most likely the bidders had no access to instantaneous price quotes. Thus, the investors at the auction were left in the dark. Actually, if the auction had been held two days later when the Dow dropped about 160 points, my feeling is that the bidders would have over bid.

Second, as a bidder you were constrained as to the quantity of shares you could buy. It had to be 363 shares or nothing. They were also constrained in their payment method, as they had to "pay immediately with cash or certified checks."

You can look at these two constraints as undesirable or "bad." Thus, in comparative shopping, a rational investor would pay less for an item that has a less desirable feature than an otherwise identical item. Hence, the lower price expected to be paid for the item does not necessarily constitute a "bargain." An alternative way of analyzing the "bargain" is that investors would require a higher rate of return -- an additional risk premium -- on the items with more restrictions so as to compensate for the undesirable feature. But, price and required return, or yield, move in opposite directions. Therefore, if the required return increases, its price should go down, other things being equal.

The San Francisco auction had one advantage, namely that the investors did not have to pay commission to a broker.

To determine whether these discounts constituted "fair’ compensation for the constraints of the auction compared to stock exchanges, one needs a large repeated sample of such auctions to determine how much more return investors would require to be compensated for the additional sources of risk inherent in the auction.