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Is there a difference between buying few shares of an expensive stock vs many shares of an inexpensive one?
Before the prevalence of electronic trading, trading stocks was very costly, dropping from ~15c in the late 1970s to less than a nickel per share today.  Exchange fees for liquidity takers are ~0.3c per share, currently. When orders were negotiated exclusively by humans, stocks used to be quoted in fractions rather than decimal, such as $50 1/2 instead of something more precise like $50.02. That necessary ease of negotiation for humans to rapidly trade extended to trade size as well.  Traders preferred to handle orders in "round lots", 100 shares, for ease of calculation of the total cost of the trade, so 100 shares at $50 1/2 would have a total cost of $5,050.  The time for a human to calculate an "odd lot" of 72 shares at $50.02 would take much longer so would cost more per share, and these costs were passed on to the client. These issues have been negated by electronic trading and simply no longer exist except for obsolete brokerages.  There are cost advantages for extremely large trades, well above 100 shares per trade. Brokerage fees today run the gamut: they can be as insignificant as what Interactive Brokers charges to as high as a full service broker that could charge hundreds of USD for a few thousand USD trade.  With full service brokerages, the charges are frequently mystifying and quoted at the time a trade is requested.  With discount brokerages, there is usually a fee per trade and a fee per share or contract.  Interactive Brokers will charge a fee per share or option only and will even refund parts of the liquidity rebates exchanges provide, as close as possible to having a seat on an exchange.  Even if a trader does not meet Interactive Brokers' minimum trading requirement, the monthly fee is so low that it is possible that a buy and hold investor could benefit from the de minimis trade fees. It should be noted that liquidity providing hidden orders are typically not rebated but are at least discounted. The core costs of all trades are the exchange fees which are per share or contract.  Over the long run, costs charged by brokers will be in excess of charges by exchanges, and Interactive Brokers' fee schedule shows that it can be reduced to a simple markup over exchange fees.   Exchanges sometimes have a fee schedule with lower charges for larger trades, but these are out of reach of the average individual.