Suppose you developed a stock trading system which gives you 1% per trade. It is a good system even if you take into account stock bid-ask spreads which are usually less than 1%.  You can ask yourself - what will happen if I buy options instead of stocks?  Will my average return be greater? How about the risk?

In this article we will answer these questions.

Option return strongly depends on stock volatility and striking price. In-the-money and out-of-the-money options will give you very different returns and risk/return ratios (read more about risk and returns in our book How to Win the Stock Market Game) and this is why we will consider option returns as function of striking price and stock volatility. 

Assumptions:        

1. Stock returns have the normal distribution with the average return SR and the standard deviation SIGMA.

2. Risk/Return ratio SIGMA / SR  for stocks will be assumed equal to 4. It is typical for good trading strategies.

3. We will consider striking price S varied from 0.8 to 1.2 of stock purchase price P₀.

4. Volatility will be varied from 0.3 to 1.4. A typical volatility for active stocks is about 0.8.

5. Time before option expiration will be equal to 1 month at the moment of purchase and this time will not change significantly during the option holding period (short-term trading is considered)

6. Short-term interest rate is equal to 3%.

Figure 1 shows the option returns for 1% stock return. The left panel shows the returns when bid-ask option spreads are equal to zero. In this case the out-of-the-money options, when striking price is 20% larger than the stock price, give fantastic returns. However, this is not realistic. And it is a typical mistake of inexperienced option traders. One must consider bid-ask spreads during calculations of options returns and risk. 

In our previous publication we have showed that in average the bid-ask spread can be described by following equation

Option Spread = 0.24 P ^ 0.36

where P is the option price. So for P = $1 the spread is equal to $0.24.

The right panel on Figure 1 shows the average returns when the bid-ask option spread have been taken into account.  One can see that the most profitable option strategy with S = 1.2 P₀ became the worse. Very little positive option returns are observed at small values of stock volatility. These volatilities are nor realistic and one can conclude: for the average stock return about 1% it is better to trade stocks than options.

The situation is changing dramatically if the average stock return becomes larger. Figure 2 shows the average option returns and risk/return ratios in case when the average stock return is equal to 1.5%.

One can see that buying out-of-the-money options become profitable and risk/return ratios of option with S = 1.1P0 are minimal. Figure 3 shows similar results for the average stock return = 2%.

For stock volatility = 0.8 the option risk/return ratios are comparable with the risk/return of stock trading strategy but the average option return is 3-5 times larger. The minimal option risk/return ratios are observed for the out-of-the-money options and for S = P0. 

Conclusion: 
If the average stock return is less than 1% it is better to trade stocks than stock options. For higher stock returns it is better to trade out-of-the-money-stock options.