Applying Expected Value Concepts to Option Investing
What is expected value?
Expected value is the average result that would occur
if an experiment were to be repeated a very large number of times.
For
example,
given
a
fair
coin, if you gained $2 for each outcome of heads, and you lost
$1 for each outcome of tails. If you flip the coin many many times,
the average gain per toss (expected value) would be $0.50. This
is computed by multiplying the probability of each outcome by its
profit(loss) and summing these results.
(.5 x $2) + (.5 x $1) = $0.50
If you flipped the coin one million times, you should expect to have gained about
$500,000. Note that this result is not certain, you could lose $1,000,000 or
gain $2,000,000, but the odds of either extreme occurring are miniscule. For
any game of chance, if the expected value is in your favor and you
can keep playing, you will accumulate winnings. If the "expected value" is
against you, you will eventually go bankrupt.
Applying expected value to option investments
Expected value is computed by multiplying the profit(or loss)
of each outcome by the probability of that outcome, then summing
all of those results. Consider the below Bull Put Spread trade
for ABC (now at $28.50)
Buy Put ABC ($24 strike expiring in 45 days)
for $.20
Sell Put ABC ($26 strike expiring in 45 days)
for $.45
Price Range 
Profit(Loss) 
Probability 
Profit x Probability 
>$26 
$.25 
78% 
$0.195 
$25.75 to $26 
$.12 
5% 
$0.006 
$22 to $25.75 
$.85 
5% 
$0.043 
<$24 
$1.75 
>12% 
$0.210 


Sum = 
$0.052 
Breakeven is at $25.75. In the price ranges of $24 to $25.75
and 25.75 to $26, the profit continuously changes. (When profit
continuously changes, the analyzers cut each range into many
very narrow slices to accurately calculate probability. To
simplify this example an average profit for each range is
used.) The expected value of $.052 means that if you independently
repeated this investment a large number of times, the average
result of the investment would be a loss of $.052 per share
($5.20 per contract). The larger the expected value, the better
your average profits will be. Avoid investments with negative
expected values unless you know something that is in your
favor that the analyzers have not considered. When the analyzers
compute expected value, they include the effects of brokerage
fees both in the reduction in your profit and in the likelihood
that an option will be exercised. (The software offsets the
exercise trigger point by $0.05 to account for the fees charged
to the person exercising the option. Example: A Put option
with a strike price of $26 will not be exercised if the stock
finishes above $25.95 (strike price minus $.05), because such
a trade would not be profitable to the person exercising the
option once brokerage fees are considered.) Because these
effects are included, the expected value displayed in reports
is labeled "Net Expected Value".
Annualized Net Expected Return
The "Net Expected Value" of an investment is made more useful
by taking into account the
amount being placed at risk by the investment and the time period
of the investment. Dividing "Net Expected Value" by the
amount risked, yields the "Net Expected Return on Risk".
Comparing investments requiring different time
periods is facilitated by annualizing this return. The result is
the "Annualized Net Expected Return".
"Annualized Net Expected Return" is intended to be used
along with "maximum profit", "safety
margin"
and "probability of profit" as the primary means of ranking investments.
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Next Section: Simple
Call and Put Option Analysis
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