## Thursday, November 13, 2014

### Stock Prices

I recently read "Flash Boys", a 2014 book by Michael Lewis about stock trading.  I intend to review it but for now just wish to discuss one point, the issue of what a "fair" price for a stock trade is.  Consider the market for IBM stock.  Suppose for example the market bid and offer prices are \$159.99 and \$160.01 (per share).  So there are people offering to sell shares for \$160.01 and others offering to buy shares for \$159.99.  So it seems plausible that a fair price is \$160.  And if you should happen pay \$160.01 or receive \$159.99 the penny a share profit to a market maker providing liquidity doesn't seem outrageous to me.

But this analysis only makes sense if the amount of stock you are buying or selling isn't enough to move the price significantly.  Suppose there are a billion shares of IBM stock outstanding and the elasticity of demand is 1 for IBM stock (this is just an illustrative example, the actual values will vary).   Then a small order like one thousand shares can be expected to move the price by one part in a million (since one thousand is one part in a million of one billion) or \$.000160.  Since this is small compared \$.01 it won't materially affect a market maker's profit.  But a large order like a million shares will move the price by one thousand time as much or \$.16.  This is enough to turn an anticipated \$.01 per share profit into a \$.15 per share loss if  a market maker should be so unwise as to sell a million shares at \$160.01 (or buy a million shares at \$159.99).

So what is a fair price for a large order?  It seems to me that it is the midpoint between the before and after prices.  Or \$160.08 if you are buying, \$159.92 if you are selling.  If you could obtain better prices than this then you could profit by repeatedly buying (driving up the price) and then selling (at a higher price) a large block of shares.  And you should be able to obtain near to this price just by splitting up your order and feeding it into the market slowly buying (or selling) at gradually increasing (or decreasing) prices.

Much of the behavior of high frequency traders that Lewis complains about in this book just seem to be attempts of market makers to protect themselves from being blindsided by large orders.  Without endorsing every specific tactic this doesn't seem unreasonable in general.  And it benefits small investors (like myself) as the alternative is larger bid ask spreads (like for example \$159.90 bid, \$160.10 asked).