you guys are still arguing about tiny leaflets and ignoring the forest
you keep talking about relative probabilities.
that's groovy, but it ignores that larger issue.
risk management (money management) is #1. you can't trade, if you blow out yer capital. 90% or so of traders do so in the first year. why is that?
MONEY MANAGEMENT
it doesn't matter about expectancy etc. when risk of ruin rears it's ugly head.
given N= (enough), the unexpected will be the death of the trader who fails to use proper position sizing, risk management, etc.
of course we can gobble this down to semantics but the original question was "which is riskier - naked calls or naked puts"
one has LIMITED risk.
the other has unlimited risk.
regardless of the relative probability of outcomes, most people would agree , definitionally speaking, that something (naked calls) that can wipe your account out in ONE trade is riskier than something that can't
the probability of it occurring or not occurring is tangential to that issue
put it this way. #'s arbitrary for the sake of explaining the point
trade a: 75% chance of making a small profit. 23% of taking a small loss. 2% chance of taking a hyoooge loss, that could blow out yer account
trade b: 65% chance of making a small profit. 33% chance of taking a small loss. 2% chance of taking a somewhat bigger loss, but still well within the paramaters that will avoid risk of ruin
ANY classic definition of RISK (which is the original question - RISKier trade) would say the 1st trade is riskier.
it's that simple.
all the other stuff is tangential. it's not a matter of which trade is "better" (subjective, and relative to goals, skillsets, etc.), has a higher expectancy, or any of that stuff.
the NUMBER ONE risk that any trader faces is blowing out his account. because when that event happens, no other event matters
50 successful trades in a row, followed by one account blowout = a loss.
and in the long run (we're all dead), the unusual "n" tends to be not so unusual.
so, clearly when you understand what the term RISK means, and you understand simple math, you concede that a trade that risks an INDETERMINATE/UNKNOWN amount of money is RISKier (by any logical and common definition of risk) than one that doesn't
step outside the myopic world that you keep playing in and view the LARGER picture.
nothing is riskier to a trader than the risk of losing all his money.