Risk is a challenging subject in the trading and investment world. Depending on who you ask, it can mean a variety of different things. Some consider risk synonymous with volatility, i.e. the more an asset’s price moves, the riskier it is. Others look at it as the probability of losing money. Still others define it as the inherent uncertainty that exists in the world.

Moreover, it’s impossible to measure precisely; the best we can do is get a rough feel for our the amount of risk we’re taking on.

To do this, we’ll rely on a number of metrics and describe their pros and cons. Each of these captures a different facet of risk that you face, and each is incomplete on its own. Good traders are going to look at all of these metrics — and maybe more — before implementing a strategy.

## Sharpe Ratio

This is the classic risk metric that anyone who’s getting into trading is going to hear about at some point or another. The Sharpe Ratio is defined as the returns from a strategy minus the risk-free rate of return and divided by the standard deviation of returns.

It is designed to gauge the excess returns achieved by a strategy by comparing it to a risk-free asset (more on this concept below). It represents the risk of a strategy as the strategy’s volatility, or how much it moves. So a better Sharpe Ratio is achieved with higher returns relative to a risk free asset and with lower volatility.

Mathematically, we can write the formula as:

$$S = \frac{R_a - R_f}{\sigma}$$

where 𝑆 is our Sharpe ratio, 𝑅𝑎 represents the actual returns, and 𝑅𝑓 represents the risk-free rate, and 𝜎 is the volatility.

The Sharpe Ratio is widely used in finance to guage how much risk a strategy took in order to achieve its returns. The higher the ratio, the better the results.

### Pros

The biggest benefit of a Sharpe Ratio is a quick way to gauge systematic strategies after running a backtest. As a rule of thumb, Sharpe Ratios above 1 are quite good for diversified, systematic strategies, and may be possible going forward. If they’re below 0, then you probably don’t want to trade that strategy. If they’re unusually high, say 3, 4 or more, then you likely over-fit your data and you shouldn’t trust your backtest results.

Additionally, because it is so popular, it provides a convenient metric to discuss without much need for interpretation — even if it is a bit esoteric when it’s first introduced.

### Cons

To be honest, the Sharpe Ratio has more cons than pros and certainly should never be relied upon in isolation.

First, the idea of risk employed by the Sharpe Ratio (volatility is necessarily risky), is, in my opinion, misguided. Simply because a price changes, doesn’t mean that you’re taking on more risk! By looking at the standard deviation, the Sharpe Ratio punishes moves up in price and moves down in price. I can’t think of an investor who thinks that their strategy is risky because it made money.

Another issue is the concept of a “risk-free rate.” In practice, high quality bonds such as the US 10-year note, are considered “risk-free” and thus the current rate on these instruments are plugged in for our 𝑅𝑓 value. The trouble with this is assuming that anything is without risk. Contrary to popular belief, the US government has defaulted on its debt multiple times — most recently when Nixon “temporarily suspended” the convertibility to gold in 1971 (which has never been reversed) and when FDR devalued the dollar after confiscating gold, essentially giving bond holders a 66 cents on the dollar. The risk associated with bonds are particularly pronounced in a time of ultra-low yields and rising inflation. Some “risk-free” bonds (e.g. German Bunds) currently have a negative yield, meaning you’re guaranteed to lose money on these assets! That hardly seems like a “risk-free” proposition.

## Sortino Ratio

The Sortino Ratio attempts to solve some of the major problems associated with the Sharpe Ratio, namely by removing the reliance on volatility and only counting losses as a contributor to risk. Additionally, the Sortino Ratio uses a target return rather than a risk-free return for the portfolio — which strikes me as more intellectually honest.

It has a very similar form to the Sharpe Ratio and is written as:

$$S_0 = \frac{R_a - R_f}{DR}$$

Here, we’re using 𝑆𝑜 for the Sortino Ratio — 𝑆 was taken above — 𝑅_𝑎 for the actual returns, 𝑅_𝑡 for the target returns, and 𝐷𝑅 for the downside risk.

### Pros

Because the Sortino Ratio only measures the downside risk of a strategy, we limit ourselves to punishing a strategy only when it actually loses money. For some strategies with normally distributed returns, it will be close to the Sharpe Ratio, which may make it easy to interpret for newcomers to this metric.

### Cons

The Sortino Ratio isn’t as widely used, as the Sharpe Ratio, so there are some discrepancies in calculations at times. For example, it is common to divide the Sortino Ratio by the square root of 2 to make it directly comparable to the Sharpe Ratio. So, if you see the Sortino Ratio from multiple sources, it is important to know how it is calculated if you’re comparing them.

Assuming it’s calculated properly, it is a backwards looking metric and can be biased as a result. For example, we only see the outcome of the decisions made by the strategy, we don’t actually know what the true probability distribution of the outcomes were, so we can’t actually determine the risk we took, or the risk our strategy will take in the future.

## Gain/Pain Ratio

As the name implies, this metric captures the upside gains relative to the downside losses a strategy has incurred. It is the summation of all returns divided by the absolute value of the sum of all losses.

We can write it as:

$$G = \frac{\sum_{t=1}^T r_t}{\sum_{i=1}^T \left| L_t \right|}$$

where 𝐺 is the gain to pain ratio, 𝑟𝑡 are our returns (daily, weekly, monthly, whatever you’re using), and 𝐿𝑡 are the losses (same time frame as the returns).

Values over 1 are quite good, greater than 2 are tremendous. At 𝐺=1, you have every dollar of loss giving you a dollar of profit, at 𝐺=1 you know have two dollars of profit relative to every dollar you lose, and so forth. The key is to keep this above 0 to remain profitable.

### Pros

The gain to pain ratio gives you an idea of how much you’re risking on each trade and is a key metric to keep an eye on to ensure you’re able to maintain your strategy. It can also be improved with better money management, potentially by tightening up stops or decreasing trade size until you’re comfortable with the amount of risk you’re taking.

### Cons

Some strategies, such as short gamma strategies where the trader is selling options, can game the gain to pain ratio and inflate the value. For a simple example, if you sell out of the money put options, most of the time, you’re going to continually collect the premium associated with those puts and very rarely take a loss at all. In times of crisis, however, this strategy is going to blow up when you’re suddenly on the hook to buy rapidly free-falling shares at above market prices.

## Maximum Drawdown and Drawdown Duration

Drawdowns are simple and inevitable. The maximum drawdown measures the largest value lost from the peak of a strategy until it recovers that value — if it ever does. And the longest drawdown duration measures how much time it takes for a strategy to recover from a drawdown.

When looking at a backtest, most novice traders just go for the total returns. If it made 10% per year (or whatever their target is), then they’re happy and go ahead and deploy that strategy and excited about all the money they’re going to be making. A few months later though, they abandon this strategy and go back to the drawing board or to picking random stocks they hear touted on CNBC.

Inexperienced traders do this time and time again because they don’t count the psychological cost of their drawdowns when judging a backtest.

If a backtest is any good, then it certainly has some drawdown associated with it. No strategy is perfect. A drawdown may have lasted 6 months, a year, or maybe even more, before it gets back to its previous levels. Can you, as a trader, handle that? If that strategy that gets you 10% annual returns in your backtest endured an 18-month drawdown, and you couldn’t take it psychologically and would have given up on the strategy before it recovers, then this is not an accurate test. You need to find something else or build enough confidence in your strategy to overcome these pits.

Similarly, if you have a strategy that lost 50 or 60% over the course of a drawdown, but eventually rebounded — could you continue to trade your system to get the returns you hope for? If not, then change the system to find something that you can stomach.

Don’t underestimate the challenge of holding on through losing periods — they will happen! And if you abandon a good system in the middle of it, then you’re only going to set yourself up for worse outcomes in the future.

### Pros

Drawdown metrics are critical for wrestling with the most challenging psychological aspects of trading — loss. Counting the cost and preparing for the worst will make it easier to endure, even if it is still difficult when that time comes.

### Cons

A backtest’s drawdown metrics aren’t necessarily indicative of the experience you’re going to have trading a strategy in the future. It’s good to tell yourself that your biggest loss and longest drought is still ahead of you.

It is also hard to divorce yourself from looking at the end result of a backtest when gauging a drawdown. Let’s say there’s a massive, 70% drawdown that lasts more than 2 years, but everything else in your strategy makes sense and your backtest shows a 20% annual return over 20 years. Looking at that huge equity curve is going to make it hard to be honest with yourself when you contemplate over 2 years of consistent losing and asking if you can handle it.

## Total Loss to Stop

Do you know the maximum you stand to lose on any given day? The total loss to stop captures this (for those trading with stops) by looking at the stops for each open position in your portfolio, and assuming all of them get stopped out. If you have stops that are 10% below the current price for each position, then you have a 10% total loss to stop, or could lose 10% of your portfolio that day.

### Pros

This is a useful metric to track while trading to ensure your stops are in place and prepare yourself psychologically for the worst-case-scenario each day. You can always keep an eye on your potential downside and be sure that you’re able to handle it.

### Cons

During a market crash, prices often gap downward, meaning the market could blow through your stops if the worst case scenario actually occurs. So while your total loss to stop metric is supposed to be a maximum loss metric, it’s more like the best outcome during the worst case scenario.