established, the theta is 0.009, just under a penny. If Disney share price is
unchanged when three weeks pass, his theta will be higher. Exhibit 4.16
shows how thetas and theoretical values change over time if DIS stock
remains at $35.10.
EXHIBIT 4.16 Disney 35 put—thetas and theoretical values.
Mick needs to be concerned not only about what the theta is now but what
it will be when he plans on exiting the position. His plan is to exit the trade
in about three weeks, at which point the put theta will be −0.013. If he
amortizes his theta over this three-week period, he theoretically loses an
average of about 0.01 a day during this time if nothing else changes. The
average daily theta is calculated here by subtracting the value of the put at
23 days to expiration from its value when the trade was established to find
the loss of premium attributed to time decay, then dividing by the number
of days until expiration.
Since the theta doesn’t change much over the first three weeks, Mick can
eyeball the theta rather easily. As expiration approaches and theta begins to
grow more quickly, he’ll need to do the math.
At nine days to expiration, the theoretical value of Mick’s put is about
0.35, assuming all other variables are held constant. By that time, he will
have lost 0.45 (0.80 − 0.35) due to erosion over the 35-day period he held
the position if the stock hasn’t moved. Mick’s average daily theta during
that period is about 0.0129 (0.45 ÷ 35). The more time he holds the trade,
the greater a concern is theta. Mick must weigh his assessment of the
likelihood of the option’s gaining value from delta against the risk of
erosion. If he holds the trade for 35 days, he must make 0.0129 on average
per day from delta to offset theta losses. If the forecast is not realized within
the expected time frame or if the forecast changes, Mick needs to act fast to
curtail average daily theta losses.