# Position Sizing by Using Max Loss: Part II

An e-mail came from a student who read my article on the topic of position sizing and still feels that the concept is not clear to him. The topic of proper position sizing is of utter importance to any trader, option trader or not; therefore, we shall delve deeper into this subject and use several mathematical examples from the current market, as the student requested. The focus will be placed on both long calls and long puts, as the e-mail asked.

There are several steps to an options trade:

1. Fundamental Analysis = what to trade

2. Technical Analysis = when to trade (timing)

3. Implied Volatility = which option strategy to use

4. Proper Position Sizing

5. Entry & Active Monitoring

6. Exit & Learn from the trade

This article will focus on Step 4 – Proper Position Sizing.

In order to delve deeper, we need to know the account size, and for simplicity’s sake we will use two examples. The first account will have 50,000 dollars in it and a trader that is willing to risk 2% of the account, or a grand (50,000 x 0.02 = 1,000). The second account is much smaller at 10,000 dollars and the trader is more conservative so the risk is only 1% of the account, or a hundred dollars (10,000 x 0.01 = 100).

The formula for finding out the number of contracts is quite simple: divide the specific portfolio risk by the trade risk (cost of trade); we will go over this math three times.

Position Sizing for a Long Call

Assuming that technical analysis was properly done, and that reasons for a bullish entry are valid, we proceed to the readings of Implied Volatility which point out that the IV is in the lower range; therefore, the premium is relatively inexpensive. From the option chain we pull out the May cycle (72 days to expiry) and look for 70 cents Delta. The premium on the Ask for a May 30 call with a Delta of 76 is 2.41.

Once we know with certainty how much the May 30 call costs, $241 per contract, we can figure out the number of contracts we can purchase. The first account with 50K and allowed risk of 1K qualifies for this trade because 1,000 divided by 241 equals four contracts that we can purchase (4.15 rounded down). The second account that allows for a loss of only 100 dollars does not work with this particular position sizing based on the max loss. [However, if an option trader still wants to take this trade, there is another way to handle the position sizing by placing the stop loss at an acceptable percentage of the premium value. This might be the topic of a future article.]

Position Sizing for a Long Put

Assuming that we want to short a stock that trades around eight dollars, and the technical as well as the IV reading (being in the lower range) supports a long put purchase, then the same procedure applies. The May option chain with 72 days to expiry should be opened and the 70 cents Delta or higher should be selected.

The May 10 put with 72 cents Delta at the Ask costs 2.09, hence the most a single contract could lose is 209. Of the two accounts, only the larger one qualifies. From 1,000 divided by 209 we get (4.78) – again only four contracts. Next let us move to spread trading.

Position Sizing for a Credit Spread

Once again assuming that the timing of our Bearish trade is impeccable technically and according to the IV reading, we would place the following spread trade. The goal of the trade is to have the DIA close below 130. Currently it is at 128.30. Figure 3 shows the option chain.

The essential info from the above option chain is pulled out and placed in table below

DIA at Entry |
Action & Contracts |
Option Strikes |
Premium |

128.30 | BTO + 1 [Delta +0.35 |
Mar Qt 131 call |
0.56 (debit) |

128.30 | STO – 1 [Delta – 0.41] |
Mar Qt 130 call | 0.84 (credit) |

Max L = 1 – 0.28 = 0.72 | Aggregate Delta -0.06 | Maximum Profit | 0.28 (credit) |

Figure 4

The position sizing for this spread trade is permissible in both accounts (50K and 10K) but the contract size will vary. The max loss is only 72 dollars. The first account calculation is: 1,000/72 = 13.89; so round it down to get 13 contracts. For the second account, 100/72 = 1.39 which is in reality one contract. Notice that we can trade a higher priced underlying in a smaller account by using a more complex option trade.

In conclusion this article used three different examples to highlight how position sizing according to the max loss truly works. The total cost of the contracts, either spread or singles was used. Buying a single legged call is riskier than spread trading, so when the account size is small, spread trading with one lot (single contracts) can work well. Moreover, do not be under the impression that position sizing according to the max loss is the only possible way to trade options. However, if you want to keep things simple, especially at the initial entry, then position sizing according to the max loss is one of the ways you could approach option trading, since we are clear on the max loss and also max gain at the expiry from the outset.