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What exactly is the theory behind deep-in-the-money calls? You say this implies being risk-averse...what does that exactly mean?

The simple answer is that the higher the strike price the more risk involved in the calls.
If the strike price is zero, you are basically just buying the stock. As you increase the strike price, the daily fluctuations of the stock are a bigger percentage of the price of the option, so your leverage is increased. You can gain more and loose more.
The deeper in the money (closer to zero) strike prices therefore will be less volatile (though more volatile than the stock)

For example lets say you think apple will trade at 330 by end of next year (about 25% higher than today's close of 265ish to keep it round numbers)

If you buy the stock, you will get 25% returns.
If you buy a jan 2021 call for apple at 150, they only cost you 117/share (includes some time premium)
If the stock hits 330, by then, they would be worth 180 so that's 53% gain.
If you buy a jan 2021 call for apple at 250, they only cost you 39, but would be worth 80 if the stock reaches 330, for 105% gain.

If you guess wrong, and the stock goes to 250,
buying the stock looses about 6%
the 150 call would loose 15%
the 250 call would loose 100%

You can choose your time and strike price to control the level of risk / reward you want to
assume. The shorter the timeframe and close to the current stock price, the more you are gambling instead of investing.

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