Call Options Vs. Stocks: Risk/Return Analysis

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Includes: SPY
by: Find My Hedge
Summary

Instead of buying stocks, it is possible to buy call options to improve portfolio performance.

We study returns of call options on SPY using historical data.

It is possible to mimic SPY by allocating only 25% of a portfolio in long-term calls (the rest of the portfolio being kept in cash).

In my previous article "Protective Puts: How To Protect Your Portfolio", many of you suggested several variants to the option strategy I proposed. I will in the following months attempt to test and analyze those strategies. In this article, I am testing a variant of the approach suggested by SilentTrader and inspired by his article "Buy The Bubble".

A call option is a contract allowing a trader to buy a stock at a defined price and on a defined date. For instance, a trader can buy an option of SPDR S&P 500 Trust ETF (SPY) with a strike price of 250 and an expiration date on January 28, 2019. This option will give the trader the ability, not the obligation, to buy 100 stocks of SPY at 250 each on January 28, 2019. If on January 28, SPY is above 250, the trader can exercise the option and buy 100 stocks of SPY at 250 each, sell them at the current price, and pocket the difference. If the price of SPY is below 250, it is not economically viable for the trader to exercise the option.

Making money from call options is not as simple as the previous paragraph could suggest. Call options are of course not free; their price is determined by the market and reflects the upside potential. If traders think that the underlying stock is likely to soar significantly, they buy calls and their price - the premium - tend to go up. On the expiration date, the trader makes a profit if the difference between the stock price and the strike price of the call is greater than the premium paid. This is why buying call options is often associated with bullish speculation, as a significant upside move of the underlying stock is necessary to make a profit.

However, as it is suggested in several articles in Seeking Alpha and by the performance of the Invesco S&P 500 BuyWrite Portfolio ETF (PBP), systematically selling calls (covered or not) seems to produce negative returns in the long run. If that is the case, systematically buying calls should, therefore, produce positive returns. How do option calls perform compared to stocks? What is their risk/reward profile? Those are the questions we will try to answer in this article.

By using historical data, we will analyze how a portfolio exclusively composed of call options and cash performs compared to a fully stock invested portfolio. We will test different strategies, all using SPY as the underlying stock. This backtesting will be done between January 2005 and December 2018; this duration is long enough to formulate a general idea and include the 2008-2009 recession period, allowing us to observe how the strategy holds during bearish markets.

Average performance and risk

In this section, we will first analyze the risk profile of call options individually.

From historical data, we select options with:

  • Number of days to expiration: 30, 60, 120, 180, 365, 730

  • Relative strike price (strike price divided by share price): 70%, 80%, 90%, 95%, 100%, 105%, 110%, 120%, 130%

For each set, we then analyze the distribution of returns if calls were sold after half the original time to expiration: for instance, if we buy a call expiring in 30 days, we sell it 15 days later. This is inspired from my last article: it allows to limit the time value decay of options, as this decay is more pronounced as the expiration of the options approaches.

Overall statistics are shown in the figure below:

Table 1: Returns of call options depending on relative strike price (each line) and time to expiration (each column). In each cell, a histogram first depicts the distribution of returns. There are 6 bins: [-100% to -60%], [-60% to -20%], [-20% to 0%], [0 to +20%], [+20% to +60%], [> +60%]. Then, various metrics are shown: AR -> Average Return, SR -> Success Rate (ratio of options with a positive return), NB -> Number of options in the set. Created by Find My Hedge using data from HistoricalOptionData.

The figure above shows several trends.

First of all, success rate (ratio of options with a positive return) and average return is positively correlated with the number of days to expiration. This could be expected as the time value decrease accelerates as the option's expiration approaches. As we hold them only during the first half of their lifespan, long-term options erode less quickly than short-term options.

Success rate is negatively correlated with the relative strike price: options that are in the money when they are bought are more likely to produce a positive return than options that are out the money. This is not very surprising as time value represents the totality of the value of options when they are out the money, and only a fraction (that decreases as the relative strike price decreases) when they are in the money.

There seems to be a relative strike price that optimizes average return. Buying at the money options seems to work best when they expire in less than one year. For one-year options, the average return is optimized when buying them 10% out the money. For two year options, the average return is best when buying them 20% out the money.

The optimal relative strike price is different when optimizing average return or success rate. In-the-money options are less risky and have a larger success rate, but they don’t have as large upsides as at-the-money and out-the-money options. This is a classical risk vs. returns trade-off.

But how does this performance varies during bullish and bearish markets? The two following figures show the distribution of returns when options were bought when the price of SPY was less than 10% below its all-time high (bullish) and more than 10% below its all-time high (bearish). We chose 10% instead of a more consensual 20%, as otherwise the number of bearish cases would be too low for statistically significant results, especially for long-term options.

Table 2: Returns of call options depending on relative strike price (each line) and time to expiration (each column) during bullish markets (price of SPY > 90% of its all time high). In each cell, a histogram first depicts the distribution of returns. There are 6 bins: [-100% to -60%], [-60% to -20%], [-20% to 0%], [0 to +20%], [+20% to +60%], [> +60%]. Then, various metrics are shown: AR -> Average Return, SR -> Success Rate (ratio of options with a positive return), NB -> Number of options in the set. Created by Find My Hedge using data from HistoricalOptionData.

Table 3: Returns of call options depending on relative strike price (each line) and time to expiration (each column) during bearish markets (price of SPY < 90% of its all time high). In each cell, a histogram first depicts the distribution of returns. There are 6 bins: [-100% to -60%], [-60% to -20%], [-20% to 0%], [0 to +20%], [+20% to +60%], [> +60%]. Then, various metrics are shown: AR -> Average Return, SR -> Success Rate (ratio of options with a positive return), NB -> Number of options in the set. Created by Find My Hedge using data from HistoricalOptionData.

Overall, performances of calls are lower when bought during bearish markets than during bullish markets. In other words, calls seem to be of better use for trend following strategies during a bullish market than for contrarian strategies when a correction has occurred. This might be explained by the higher implied volatility during bearish markets. Still, this surprised me as until now I used call options to boost my positions when there was a dip in the market.

Long-term performance evaluation

In the previous section, we have seen that the average returns can reach up very high values (+66.4% for two years' calls). However, these high returns are associated with high risk: a significant portion of calls have returns that are lower than -60%. Traders should therefore only allocate a portion of their portfolio in calls, and keep the other portion in cash so they are still able to invest if such loss should occur. In this section, we will estimate:

  1. The optimal calls - cash allocation maximizing returns during the 2005-2018 period.

  2. The minimum calls - cash allocation obtaining similar returns to the underlying SPY stock. It will allow us to compare the risk of a calls + cash portfolio versus a stock portfolio on similar returns.

The strategy used here is simple and easily actionable. We will test our strategy on multiple relative strike prices (strike price divided by share price) - 80%, 90%, 95%, 100%, 105%, 110%, 120% - and multiple times to expiration - 60 days, 180 days, 365 days, 730 days. For each variant, we will find the optimal calls ratio: the percentage of the portfolio allocated to calls.

As for describing the strategy, we will suppose that we are testing it with the following parameters:

  • Relative strike price: 95%

  • Time to expiration: 60 days

  • Starting date: 2005-01-11

  • Cash ratio: 30%

Day 1 (End Of Day)

Here is concretely what happens on 2005-01-11 with the parameters chosen earlier:

  • We suppose that the investor initially doesn’t hold shares or options of SPY. The price of SPY on 2005-01-11 is $118.18.

  • The investor allocates 30% of his portfolio to buy calls with a time to expiration close to 60 days and with a strike price close to 118.18 x 95% = 112.27.

Each following trading day (end of day)

There are two possible outcomes:

  • As long as the time to expiration of the call is larger than half of the original time to expiration (60/2 = 30 days), the investor doesn’t update his/her position.

  • When this isn’t the case anymore, the investor sells the calls he/she owns, and allocates again 30% of the portfolio in calls as he/she did in day 1.

Optimal calls - cash ratio for maximizing returns

The objective here is to find the percentage of calls vs. cash that maximizes returns, without considering risks taken. The following table shows this percentage when using the previous strategy on different relative strike prices and time to expiration.

Table 4: Maximum annualized returns depending on relative strike price (each line) and time to expiration (each column). For each cell, the first line represents the annualized return, the second line represents the ratio of calls vs. cash allowing to obtain such a return. MAX DD: Max Drawdown (observed only when the position is renewed). STD: standard deviation (observed when the position is renewed). How to read the table: if an investor followed the strategy outlined above with options with an expiration time to expiration of 730 days and with a relative strike price of 90%, his maximum annualized return would have been 11.2% and would be achieved if he allocated 68% of his portfolio in call options and 32% in cash. Cells are empty when there is no amount of calls that could provide positive returns in the long run.

When evaluating the strategy, using long-term call options seems to be better, as observed in the previous section. For 365 days and 730 days options, the best seems to focus here on at-the-money options.

The following graph shows the performance of the best-performing strategy with an annualized return of 12%. It is clear that the higher returns observed come with higher risk and volatility. It is important to point out that an advantage of that approach compared to classic leverage is that the risk is limited to the percentage of the portfolio invested in call options - 65% in our case. It is not possible to lose more money than invested.

Source: Created by Find My Hedge using data from HistoricalOptionData

The minimum calls - cash allocation obtaining similar returns than SPY

In order to compare the risk-adjusted returns of our strategy to the returns of SPY, we have computed for each relative strike price and time to expiration the minimum percentage of calls allowing to get a similar return than SPY. As the performance of each strategy is the same, we can compare their risk with each other and with SPY.

Table 5: Minimum calls/cash ratio necessary to obtain similar returns than SPY depending on relative strike price (each line) and time to expiration (each column). For each cell, the first line represents the annualized return, the second line represents the ratio of calls vs. cash allowing to obtain such a return. MAX DD: Max Drawdown (observed only when the position is renewed). STD: standard deviation (observed when the position is renewed). How to read the table: if an investor followed the strategy outlined above with options with an expiration time to expiration of 730 days and with a relative strike price of 90%, he would achieve a similar return than SPY if he allocated 32% of his portfolio in call options and 68% in cash. Cells are empty when there is no ratio allowing to get similar returns than SPY.

The story gets more interesting. Very long-term call options seem to be working best, as we can achieve a similar performance than SPY by allocating only 25% of our portfolio in calls and 75% in cash. As SPY can drop more than 50%, using this strategy can be a great way to protect a portfolio from large drops. The following charts show the performance of the strategy for two years' calls and different relative strike prices.

Source: Created by Find My Hedge using data from HistoricalOptionData.

It is important to note that, with similar returns, the volatility of the strategy seems to be always greater than SPY, except when large drops occur such as during the 2008-2009 recession period. The higher the relative strike price, the higher the volatility observed, but also the lower capital at risk (except with a relative strike price of 120%, which is too high for the strategy). Indeed, there is a trade-off to choose between a lower volatility but a higher call/cash ratio on low relative strike prices and a higher volatility but a lower call/cash on high relative strike prices. Those are different types of risk that should be chosen depending on the economic context and the investor personality.

Conclusion

Using historical data, we have studied the returns of calls with different time to expiration and relative strike prices. The best solution seems to use long-term calls that are at the money or slightly out the money, especially during bullish markets.

It is possible to mimic the performance of SPY using a portfolio comprised of cash and long-term call options. Volatility is greater, but the investor only needs to invest and risk a quarter of his portfolio. This provides a protection against market crashes.

Several improvements could be made on the strategy. First, we have supposed that the uninvested part of the portfolio is only comprised of cash. It might be a good idea to invest this part in risk-free investments or low-risk bonds. The strategy also doesn’t adapt to the market conditions: we have seen that long-term calls perform better during bullish markets than bearish markets, so the strategy could also take that into account.

Disclosure: I am/we are long SPY. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.