Lesson 12 of 25 · 7 min
A protective put: what it does to the distribution
A floor rewrites every outcome below one price and leaves every outcome above it alone, minus a fixed amount.
A protective put is two positions held together: the shares, and a put on those shares. Track 2 lesson 7 covered what the put obliges each party to do. This lesson does one thing only — states what the pair does to the range of outcomes.
Take 12,400 shares of a single large-company holding at $84.50, so $1,047,800 of market value. A put struck at $75 with nine months to expiry costs $4.15 per share, which is 12,400 × $4.15 = $51,460. Below $75 the put's gain offsets the shares' further decline, so the pair is worth 12,400 × $75 = $930,000, less the $51,460 already spent, which is $878,540.
That is the floor, and it corresponds to a maximum loss of $1,047,800 − $878,540 = $169,260, or 16.15 percent of the starting value. Compare an unhedged 45 percent decline: $1,047,800 × 0.55 = $576,290, a loss of $471,510. Everything worse than a 16.15 percent loss has been removed from the distribution and replaced with a 16.15 percent loss.
Above $75 nothing is removed. Every outcome is the shares' outcome minus the same $51,460, which is 4.91 percent of the starting value. So the distribution has been truncated on one side and shifted down uniformly on the other. Those are the two effects, and neither of them is a statement about whether the shares will fall.
Key terms
- Protective put
- Holding shares and a put on the same shares, so the pair cannot be worth less than the strike minus what the put cost.
- Floor
- The lowest value the pair can reach at expiry. It equals shares times strike, less the premium paid.
- Truncation
- Removing a range of outcomes from a distribution and replacing them with a single outcome at the boundary.
Worked example
Where the outcomes stop
12,400 shares at $84.50, so $1,047,800. One put per 100 shares, struck at $75, nine months, $4.15 per share. Illustrative prices.
- Premium paid
- $51,460
- Value of the pair at any price below $75
- $878,540
- Maximum loss
- $169,260
- Maximum loss as a percentage
- 16.15%
- Unhedged value after a 45% decline
- $576,290
- Amount every upside outcome is reduced by
- $51,460
12,400 × $4.15.
(12,400 × $75) − $51,460.
$1,047,800 − $878,540.
$169,260 ÷ $1,047,800.
$1,047,800 × 0.55.
4.91% of the starting value.
The distribution now ends at a 16.15 percent loss instead of continuing to zero, and every gain is 4.91 points of starting value smaller.
Check yourself
You hold 8,600 shares at $62.00 and hold a put struck at $55 that cost $3.40 per share. What is the largest loss the pair can produce by expiry?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.