# Is the market price of an asset always lower than the expected discounted value under the REAL WORLD measure?

The risk neutral measure is often said to reflect the risk aversion of investors. So intuitively, I would think that an asset's expected discounted value should be lower under the risk neutral measure (-> market price) than under the real world measure. In other words, a risk averse investor should always prefer a fixed payout equal to the expected discounted value (under the real world measure) to holding the risky asset.

However, in a simple Black/Scholes model with constant volatility, I would expect the expected discounted value of a put option to be higher under the risk neutral measure than under the real world measure. This is because the stock, when modelled under the risk neutral measure, would take more negative paths, giving the put option a greater value.

Is this correct? And how does that fit together with the intuition about investors being risk averse, if we imagine an investor who only wants to buy one put option and has no other assets in this portfolio?

Interested in your thoughts, thanks :)