The wheel strings two trades you already know into a loop: the cash-secured put from the last lesson and the covered call from Module 12. Sell a put. If it expires worthless, sell another. If you are assigned, you own 100 shares, so sell a call against them. If the call expires worthless, sell another; if the shares are called away, you are back in cash and start again with a put. This lesson follows one turn in numbers, tracks what the shares really cost, and names what the wheel is underneath.
One turn, in numbers
- The put. The stock is at $100. You sell the 30-day $95 put, about a 25-delta put, for $1.33 and set aside the cash. At expiry the stock is at $92, so you are assigned: you buy 100 shares at $95.
- The call. You own the shares with the stock at $92. You sell the 30-day $95 call for $2.04. Setting the call at or above what you paid is the usual rule; the downtrend section shows why.
- Called away. At expiry the stock is at $97. The call is exercised and your shares are sold at $95.
You bought at $95 and sold at $95, so the shares made nothing. The whole profit is the two premiums: $1.33 plus $2.04 is $3.37 a share, $337 on the $9,500 the turn tied up for 60 days. That is about 3.5% for two months, or 21.6% annualized.
A 25-delta put finishes in the money roughly one month in four, so a year of monthly puts can expect to buy the stock about three times, more in a falling market.
The range for a $100 stock at 30% volatility, 30 days out. About two outcomes in three land between about $91.76 and $108.98, so a $95 strike sits well inside the likely range. Drag days to 365 to see how far a year of wheeling can wander, or volatility up to see why jumpy stocks pay bigger premiums.
Tracking the cost basis
Wheel traders keep one running number per stock, the cost basis: the price paid for the shares less every premium collected along the way. After assignment in the example it is $95 minus $1.33, $93.67. After the call it is $93.67 minus $2.04, $91.63. Every call you sell while you hold the shares lowers it again.
The cost basis is the price at which selling the shares leaves you even on the wheel so far, nothing more. Treating it as a target, and refusing to sell below it, is how a wheel turns into holding a falling stock for months.
What the wheel really is
Parity from Module 2 says stock plus a short call is the same position as a short put at the same strike, apart from interest and dividends. So the wheel never changes shape: with cash it is a short put, and after assignment it is stock plus a short call, a short put again. The whole wheel is one short put, re-struck each month near wherever the stock has gone, on a stock you have agreed to own.
It is short volatility: short gamma and short vega, paid by theta, earning when implied volatility turns out higher than the movement the stock delivers, the volatility risk premium. And it carries a view, because a short put's delta is positive: the wheel is always long some of the stock, and it gets longer as the stock falls.
Delta of one short $95 put against the stock price, 30 and 7 days before expiry. Hover at $100 and then at $90: the position goes from about a quarter of the shares to most of them. With a week left the curve is nearly a step. Raise volatility and the curve softens, but the direction never changes.
At $100 the short $95 put behaves like about 25 shares. At $90 with a month left it behaves like about 71, and at expiry below $95 it is the full 100. Adding exposure as the price falls is what short gamma means: the wheel buys every dip, whether or not the dip is worth buying.
The downtrend risk
The wheel does best on a stock that drifts sideways. Its bad case is a steady fall. Say you are assigned at $95 with a cost basis of $93.67, and the stock keeps going to $80. Now both choices for the call are poor.
- Sell at or above your cost basis. The 30-day $95 call, 19% above the market, pays about $0.07. You are sitting on a $1,367 loss on the shares and collecting almost nothing for it.
- Sell near the market. The $85 call pays about $1.07. If the stock bounces to $90 you are called away at $85 and lock in $85 minus $93.67 plus $1.07, a loss of $7.60 a share, $760, and miss the rest of the bounce.
The premiums are small next to the move. One month's $1.33 is 1.4% of the strike; climbing back from $80 to a $93.67 cost basis takes more than ten such months. The income arrives in small amounts and is taken back in large ones, so choosing stocks you would hold through a fall, and sizing so that holding them is bearable, matters more than the strike. Module 13 set out sizing and when to roll or close.
The maths: cost basis, cycle return and the short put underneath
Sell a put at strike Kp for a credit P, get assigned, then sell calls for C1, C2 and so on: the cost basis per share is Kp - P - C1 - C2 - .... Called away at Kc, the turn makes Kc - Kp + P + C1 + ... a share, and the return is that over Kp, times 365 over the days taken. In the example: 95 - 95 + 1.33 + 2.04 = $3.37, 3.37 / 95 = 3.55%, and 3.55% × 365 / 60 = 21.6%.
Parity is why the two phases are one position. With no dividend, S - C = K e^(-rT) - P at the same strike and expiry: stock and a short call equal cash worth the strike and a short put. The Greeks agree. At the $95 strike with the stock at $92 and 30 days left, the call's delta is 0.385, so stock plus the short call has a delta of 1 - 0.385 = 0.615, and the short put's delta is also 0.615.
Your turn
Open AMZN on the Options Chain at the monthly expiration. Find the put with a delta nearest -0.25 and work out your cost basis if assigned. Then read the Mid of the call with a delta nearest 0.25, and put all four numbers into the Wheel Calc.