Collar Premiums And Initial Cash Flow

Introduction

A collar combines a stock position with a purchased put and a written call. At the start of the strategy, these three transactions create separate cash flows: the stock purchase costs money, buying the put costs money, and selling the call brings in premium. The total initial cash flow depends on getting both the quantities and the signs right.

This tutorial focuses on the cash required to establish the position, not its value at expiration. A useful discipline is to calculate each component separately before combining them. This prevents a call-sale credit from being mistakenly added as a cost, or a quoted premium from being multiplied by the wrong number of shares.

Definition: For a long stock position, a purchased put, and a written call, the net option premium is the put premium paid minus the call premium received. A positive result is an option debit; a negative result is an option credit. The total initial outflow adds the stock purchase cost to that net option premium.

Cash-Flow Model and Sign Convention

Assume the transactions take place at time 0. Let $S_0$ be the stock price per share, $q_s$ the number of shares purchased, $q_p$ the number of underlying-share units covered by purchased puts, and $q_c$ the number of underlying-share units covered by written calls. Let $p$ and $c$ be the respective put and call premiums per share.

A premium quoted per underlying share must be multiplied by the total share units covered by the options. If a contract has a multiplier of 100, for example, one contract covers 100 share units. If a premium is instead quoted as a total dollar amount per contract, use that amount directly and do not multiply it by the contract multiplier again.

For this calculation, treat an outflow as positive when reporting the amount of cash required. Ignore commissions, taxes, margin requirements, financing, dividends, and any other cash flows. These assumptions isolate the purchase price and option premiums; if a problem includes additional initial cash flows, they must also be included.

\begin{aligned} \text{Put premium paid} &= q_p p,\\ \text{Call premium received} &= q_c c,\\ \text{Net option premium (debit-positive)} &= q_p p-q_c c,\\ \text{Total initial outflow} &= q_sS_0+q_pp-q_cc. \end{aligned}

The formula allows different quantities for stock, puts, and calls. In a standard one-for-one collar, the number of put-covered and call-covered share units equals the number of shares held: $q_s=q_p=q_c$. If those quantities differ, the same cash-flow accounting applies, but the options do not form a fully matched one-for-one collar on the entire stock position.

Why the Formula Holds

The result follows by adding the time-0 cash flows using the chosen outflow-positive convention. Buying $q_s$ shares requires $q_sS_0$ dollars, and buying the puts requires $q_pp$ dollars. Selling the calls produces cash, so its contribution to the required outflow is negative: $-q_cc$.

\text{Required outflow} = \underbrace{q_sS_0}_{\text{stock purchase}} + \underbrace{q_pp}_{\text{put purchase}} - \underbrace{q_cc}_{\text{call-sale receipt}}.

This is an addition of initial transaction cash flows, not an assumption about future option exercise or expiration payoffs. It applies when the stated premiums are the amounts paid or received at initiation. It must be modified if the problem specifies transaction charges, premiums quoted on a different basis, or additional initial cash flows.

Worked Calculations

Worked Example: Unequal Option Quantities and Total Outflow

An investor buys 250 shares at $ \$46.00 $ per share. The investor also buys 3 put contracts and writes 2 call contracts. Each contract covers 100 shares; the put premium is $ \$1.80 $ per share and the call premium is $ \$2.30 $ per share. Find the net option premium and total initial outflow. Ignore all fees.

Method. Convert contracts to share units, calculate the put debit and call credit separately, and then apply the debit-positive formula. The different numbers of put and call contracts mean this is not a one-for-one collar over all 250 shares, but the initial cash flows can still be calculated directly.

Step 1: Stock cost.

250(46.00)=\$11{,}500.00.

Step 2: Put cost. Three contracts cover $3(100)=300$ shares. Therefore,

300(1.80)=\$540.00.

Step 3: Call-sale credit. Two contracts cover $2(100)=200$ shares. The cash received is

200(2.30)=\$460.00.

Step 4: Net option premium and total outflow.

\begin{aligned} \text{Net option premium} &= 540.00-460.00=\$80.00\text{ debit},\\ \text{Total initial outflow} &= 11{,}500.00+540.00-460.00\\ &=\$11{,}580.00. \end{aligned}

Check. The option transactions require a net $ \$80.00 $, so the total must be $ \$80.00 $ more than the $ \$11{,}500.00 $ stock cost. That gives $ \$11{,}580.00 $, consistent with the direct calculation. The common mistake this method avoids is adding the call-sale receipt as if it were another payment.

Worked Example: A Matched Collar With a Net Option Credit

A fund buys 400 shares at $ \$52.40 $ per share. It buys 4 put contracts and writes 4 call contracts, each with a 100-share multiplier. The put premium is $ \$3.10 $ per share and the call premium is $ \$2.65 $ per share. Calculate the net option premium and total initial outflow, ignoring fees.

Method. First check that both option positions cover the same number of shares as the stock. Then calculate the option debit and credit and combine them with the stock cost.

Step 1: Check the quantities. Each option position covers $4(100)=400$ shares, matching the 400 shares of stock.

Step 2: Stock cost.

400(52.40)=\$20{,}960.00.

Step 3: Put debit.

400(3.10)=\$1{,}240.00.

Step 4: Call credit.

400(2.65)=\$1{,}060.00.

Step 5: Combine the cash flows.

\begin{aligned} \text{Net option premium} &= 1{,}240.00-1{,}060.00=\$180.00\text{ debit},\\ \text{Total initial outflow} &= 20{,}960.00+1{,}240.00-1{,}060.00\\ &=\$21{,}140.00. \end{aligned}

Check. The option package costs $ \$180.00 $ net, so the total outflow exceeds the stock cost by exactly $ \$180.00 $. This also confirms that the call premium is a receipt, even though the overall option position is a debit.

Worked Example: Applying a Contract Multiplier

An investor buys 150 shares at $ \$87.60 $ per share, buys 3 put contracts, and writes 3 call contracts. Each contract covers 50 shares. The premiums are quoted per share: $ \$4.20 $ for the put and $ \$5.10 $ for the call. Find the net option premium and total initial outflow, ignoring fees.

Method. Convert the contracts using their 50-share multiplier. Do not assume a multiplier of 100 simply because that is common in some markets.

Step 1: Convert option contracts to share units.

3(50)=150\text{ share units for each option position}.

The options therefore match the 150 shares held.

Step 2: Calculate stock cost and option cash flows.

\begin{aligned} \text{Stock cost} &= 150(87.60)=\$13{,}140.00,\\ \text{Put cost} &= 150(4.20)=\$630.00,\\ \text{Call receipt} &= 150(5.10)=\$765.00. \end{aligned}

Step 3: Combine the amounts.

\begin{aligned} \text{Net option premium} &= 630.00-765.00=-\$135.00,\\ \text{Total initial outflow} &= 13{,}140.00+630.00-765.00\\ &=\$13{,}005.00. \end{aligned}

The negative net option premium means the option package produces a $ \$135.00 $ net credit. It does not mean the whole position produces a net receipt: the stock purchase is much larger, leaving a $ \$13{,}005.00 $ initial outflow.

Check. Starting with the $ \$13{,}140.00 $ stock cost and subtracting the $ \$135.00 $ option credit gives $ \$13{,}005.00 $. The common mistake this example avoids is using the wrong contract multiplier or multiplying the contract count by the multiplier twice.

Interpreting Debits, Credits, and Quantities

The phrase “net option premium” can be used with different sign conventions. To avoid ambiguity, state the convention explicitly. Here, put cost minus call receipt is debit-positive: a positive value is cash required, and a negative value is a cash credit. If a question instead asks for the net cash received from the options, reverse the sign.

Option comparison	Net option premium	Interpretation
Put cost exceeds call receipt	Positive	Net option debit
Put cost equals call receipt	Zero	No net option cash flow
Call receipt exceeds put cost	Negative	Net option credit

The stock cost remains a separate term. A net option credit reduces the total stock-and-options outflow; it does not automatically make the entire position a credit. Likewise, a net option debit increases the required cash above the stock purchase price.

Always check the unit of each quoted premium. If a premium is stated per share, multiply by the number of share units covered. If it is stated per contract, multiply by the number of contracts only. In a problem with different multipliers or different option quantities, calculate each option leg separately before netting them.

Common Sign and Unit Traps

Adding the written-call premium as a cost. A call writer receives premium at initiation, so subtract that receipt from the outflow. In the first worked example, the incorrect calculation $11{,}500+540+460=\$12{,}500$ treats the receipt as a payment. The correct calculation is $11{,}500+540-460=\$11{,}580$.
Netting premiums before checking their units. The put and call premiums may cover different numbers of shares. Convert each leg into dollars first, then subtract.
Using the stock quantity for both option legs automatically. This is valid only when the contract quantities actually cover that many shares. Read each contract count and multiplier.
Confusing option credit with total position credit. A call receipt larger than the put cost creates a net option credit, but the stock purchase can still make the total initial cash flow an outflow.
Multiplying twice. A per-share premium needs the covered share units; a premium already quoted per contract does not need the contract multiplier applied again.

Initial cash-flow accounting is a basic but important part of derivative analysis aligned with the SOA Exam FM (Financial Mathematics) syllabus. The same sign discipline applies whenever a position combines purchases and sales: record each cash receipt and payment from the perspective of the investor, then add them consistently.

Key takeaway: With an outflow-positive convention, calculate total initial cash required as stock cost plus put cost minus call-sale proceeds. Convert each option position to the correct share units before applying its per-share premium.

Check Your Understanding

For each problem, use an outflow-positive convention and ignore fees unless stated otherwise.

An investor buys 300 shares at $ \$32.50 $, buys 3 put contracts, and writes 3 call contracts. Each contract covers 100 shares. The put premium is $ \$1.20 $ per share and the call premium is $ \$0.85 $ per share. Find the net option premium and total initial outflow. (Answer: $ \$105.00 $ net option debit; $ \$9{,}855.00 $ outflow.)
A portfolio buys 500 shares at $ \$74.20 $, with 5 put contracts and 5 written call contracts, each covering 100 shares. The put premium is $ \$2.60 $ per share and the call premium is $ \$3.15 $ per share. Find the net option premium and total initial outflow. (Answer: $ \$275.00 $ net option credit; $ \$36{,}825.00 $ outflow.)
An investor buys 800 shares at $ \$109.25 $, buys 8 put contracts, and writes 6 call contracts. Each contract covers 100 shares. The put premium is $ \$5.40 $ per share and the call premium is $ \$6.10 $ per share. Find the net option premium and total initial outflow. (Answer: $ \$660.00 $ net option debit; $ \$88{,}060.00 $ outflow.)
A matched position consists of 200 shares at $ \$41.75 $, 2 purchased put contracts, and 2 written call contracts. Each contract covers 100 shares. Premiums are quoted as total amounts per contract: $ \$225 $ for each put and $ \$180 $ for each call. Find the net option premium and total initial outflow. (Answer: $ \$90.00 $ net option debit; $ \$8{,}440.00 $ outflow.)
An investor buys 1,000 shares at $ \$63.80 $, buys 10 put contracts, and writes 8 call contracts. Each contract covers 100 shares. The put premium is $ \$1.95 $ per share and the call premium is $ \$2.40 $ per share. Find the net option premium and total initial outflow. (Answer: $ \$30.00 $ net option debit; $ \$63{,}830.00 $ outflow.)

What You'll Learn