How to measure risk?

Risk vs reward measures are typically used for performance evaluation of a strategy or portfolio. But what does risk really mean? Presumably we're talking about risk of loss. But risk of loss means that you actually exit a position at a loss. So really, then, we're talking about the risk of making a decision to take a loss. That means to measure risk using a statistical measure of past prices, like standard deviation (used in sharpe ratio) or negative semi-deviation (used in sortino ratio), you're ignoring any behavioral economic aspects in making that decision.

The implicit assumptions in using a price-derived statistical measure of volatility in a performance evaluation are (1) that we make decisions at fixed-width intervals (because the mathematical definitions of those measures use such intervals), (2) that measure is the same in the past as it will be in the future, and (3) average return compensates for having to tolerate the volatility in real time.

Assumption (1) depends on the freedom of investors (or portfolio manager) to withdraw funds or exit positions. (2) is definitely false, and generally just used for convenience. My main focus for a new measure of risk is on (3). The average return is the best estimate of future return, given that the future is unknown. But surely risk tolerance is path dependent. It's one thing for a portfolio to be up one day, down the next, for e.g. 30 straight days. And it's another for a portfolio to be down for 15 consecutive days, then up for 15 consecutive days; that may incur different behavioral economic aspects for investors. Many risk models assume that prices have no memory, but investors surely do have memory. And no matter what the average or expected return is, I would argue that it's the Probability(return will be x% greater than a volatility-free portfolio) that matters most. And that probability may depend on factors other than the statistics of past prices. Surely neuroeconomics will bring us to a new definition of risk, which does a better job of measuring how we anticipate future outcomes.

The managed macro portfolio is +5.4%, with its worst drawdown at -2.56% on May 15. The drawdown was 1 day after I moved to full leverage, so clearly I was not worried about the possible volatility. If I had outside investors, I would have told them that the probability of having a good return within 1-3 months was 100%. I said over a month ago that the russell will rally back to 1200, that the dax will get to 10k, and they are on their way. The stock market will continue higher this year, with a few bumps and detours along the way, to be sure. As Laszlo Birinyi says, it's like driving from NY to LA. You're sure to get there, and don't sweat the possible traffic or flat tire along the way.