Articles on investing and capital management, with a quantitative focus.
What is Risk?
As far as I know, there is no universally accepted definition of "risk" for investment modelling. Modern Portfolio Theory (MPT), introduced by Markowitz, uses standard deviation to measure volatility and risk. In the MPT world, risk = volatility.
There are also other measures of risk. Maximum drawdown, the maximum loss from peak to trough, measures the severity of worst case declines that span arbitrarily long periods. I personally like this measure because it describes the emotional pain of human investors much better than standard deviation. Humans respond very differently to good volatility (gains) and bad volatility (losses). In the real world, pain/fear/capitulation occur due to losses, not due to pure volatility. Standard deviation measures good and bad volatility equally, whereas maximum drawdown only measures bad volatility.
What do people really mean by "risk", though? Here's my own definition:
Risk: the likelihood of losing capital permanently
It's hard to convert this definition into a mathematical measure due to individual factors. What does permanent mean? An investor who is forced to take money out of a depressed portfolio experiences a permanent loss, even if the portfolio later recovers. There are also historical instances of true permanent losses, such as when the Russian stock market was wiped out during the Russian Revolution.
In addition to the time horizon issue, there's individual investor psychology to consider. People will sometimes abandon their investment (capitulate) due to fear of more losses, or disillusionment. Whether it's due to a short timeframe panic, or longer timeframe exhaustion, this action causes permanent losses.
If we assume that we're only investing in things that won't cause permanent capital loss in the very long term, this leaves the following shades of risk:
- investor is forced to pull money out before the asset recovers
- investor abandons the asset due to fear or disillusionment
In recent years, I got a taste of the first risk. Although my investments were meant to be very long term, tax complications due to moving between countries forced me to liquidate some assets. If my investments had been down at the time, I would have incurred a permanent loss. There are many other situations that could force someone to pull money out: surprise expenses, job loss, retirement, etc.
I think that standard deviation and maximum drawdown are reasonable estimates of risk. Greater volatility (standard deviation) swings the price farther from the mean, making it less certain that prices will normalize in a constrained time frame.
I still prefer maximum drawdown because it more closely matches the definition of Risk (losing capital) and is more directly linked to investor fear, as described above.
You've already lost money
There's another way to look at portfolio values which makes no distinction between temporary and permanent losses. One might say that the current value is the most meaningful number because it's what you actually have. When an investment portfolio drops sharply, you've already lost the money. There's never any guarantee that the value will rise again. If that were guaranteed, the value wouldn't have dropped.
From this perspective, volatility or maximum drawdown closely match the definition of Risk.
— Jem Berkes