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You may have heard people say that investing involves a tradeoff between risk vs. return. And that’s typically true. Investors usually need to take on greater risk to achieve higher returns.

But what do investors really mean when they talk about risk?

It turns out there are a few different ways to think about risk. Today, we look at some common ways that risk is typically measured.

**Is it the risk of loss? **

Most investors probably think risk is related to the risk of ‘loss,’ whether that’s a percentage loss or the amount of money an investor could potentially lose.

For example, **Chart 1** below tracks the historic **drawdowns** for the S&P 500 (based on SPY) from 1993 to the present. Drawdowns reflect the cumulative loss that an investment has experienced from its peak.

What we see is that drawdowns:

- Of 5% are reasonably common.
- Reaching 10%, commonly known as a “correction,” happen much less often.
- Exceeded 20%, commonly known as a “bear market,” in four separate periods – two of which saw the index fall around 50% (in the Dot-com bust and the Great Financial Crisis of 2008).

Knowing that you may lose half of your investments is important. However, focusing only on the downside misses all the upside. Over this whole period, an investor saw price gains of around 1800%, or around 10% per year (despite all the drawdowns).

**Chart 1: Drawdown Risk for the S&P 500 since 1993**

**What is volatility? **

Professional investors, instead, typically think about portfolio risk in terms of uncertainty or the range of possible outcomes. Often, they measure a portfolio’s volatility to understand its risk.

Volatility is a *per-annum* measure of the *standard deviation* of *daily* returns. This sounds complicated, but let’s break it down.

First, an easy way to think about the standard deviation of daily returns is to look at the daily returns of the two stocks plotted below. In the chart below, where each day’s return is a dot, the:

**Blue stock**has returns that are clustered in a tight range. Visually, the average deviation looks to be close to ±1% from a zero daily return. In fact, the standard deviation is 1.3% per day.**Orange stock**has a much wider range of returns. That translates to a much higher standard deviation, at 4.0% per day, making that stock “more risky.”

As this shows, standard deviation is a statistical measure that simply quantifies how much returns deviate from their average each day.

**Chart 2: Low risk vs. high risk**

**What does standard deviation in daily returns really mean? **

One of the interesting features of returns in most financial assets is that “small moves” are typically much more common than “large moves.” We see that for drawdowns in Chart 1 and even for the dots in Chart 2 above.

For example, if we look at daily returns for the S&P 500 over the past 30 years and count the different-sized daily returns (Chart 3), we see that:

- The highest bar is for slightly positive returns.
- The majority of days, the S&P returns around ±1%. In fact, the dark blue bars represent 68% of all dates. This is also statistically close to the standard deviation of daily returns, at around 1.2%.
- If we look at larger returns, the chart includes almost 95% of all dates (light and dark blue bars) at a level that is around double the standard deviation (around 2.4%).
- Some days have even better or worse returns (orange zones). The average return of all the negative orange bars is around -3.6%, which we will return to later.

**Chart 3: The historic distribution of daily S&P 500 returns**

What we are looking at in Chart 3 is a “distribution” of realized returns. This is close to what statisticians call a “normal distribution,” which has a number of predictable properties, even over longer timeframes, and is used as a base for options pricing math.

**What happens to daily standard deviation over longer times?**

Interestingly, if we look at the distribution of actual returns over longer periods (say weekly or monthly), we see a similar pattern (**Chart 4)**. But there are a few things are worth noting:

**Deviation of returns increases at a decreasing rate:**The range of one-year returns is much less than 252 days x one-day range. This is due to mean reversion of news and, ultimately, traders based on relative valuations.**Average market returns are positive:**In fact, the average becomes more positive the longer the time window. This makes sense given the stock market tends to increase over time, too.**Deviation of returns is still both above and below zero**. Although very good returns start to exceed very bad returns over longer timeframes, there are still many 12-month periods with quite negative returns.

**Chart 4: The historic distribution of S&P 500 returns over increasingly longer periods**

**Volatility is a per-annum risk measure **

When professional investors talk about “volatility,” they are talking about the expected portfolio distribution as a “per-annum” number. Although that is similar to the 252 trading days return shown in the chart above, it is actually calculated using daily returns.

The math to “annualize” the standard deviation of daily returns is:

Volatility = Daily Standard Deviation x square root (# of days).

For example, if we use the data from Chart 3, where the standard deviation of daily returns was 1.2%, we get expected volatility of the index of around 19% per annum:

Volatility = 1.2% x square root (252) = 1.2% x 15.9 = ~19%

Not surprisingly, 19% is also pretty close to the average value of the VIX index over the past 30 years. In fact, the average daily VIX level was 19.8 over the period. Although these two measures of volatility are related, they are not the same:

- The VIX represents what options traders are expecting future volatility to be.
- While volatility uses the actual (or historical) daily returns.

Importantly, this doesn’t mean an investor stands to lose (or gain) 19% in a year. What it really means is that the portfolio will return somewhere between ±19% in 2 out of every three years. That’s similar to looking at the dark blue area in the charts above.

In the other one-third of the years, the returns will be stronger, sometimes much stronger, than that – as we see in the light blue and yellow bars.

**What is Value at Risk? **

Professional risk managers might be more concerned with large losses than the range suggested by portfolio volatility. For example, an investor may have a limited amount of reserves or a set tolerance for a large daily loss.

Two common ways to measure the cost of large losses build upon the statistical approaches we noted above:

**Sortino Ratio**is a variation of the Sharpe Ratio but only considers downside deviation. As we noted above, standard deviation moves in both directions, positive and negative. The Sharpe Ratio measures returns relative to total volatility, whereas the Sortino Ratio only considers “bad” volatility, or downside risk.**Value at Risk (VaR)**calculates an**average dollar loss**in times when a portfolio is expected to experience an extreme return.

Both of these methods use the concept of uncertainty in returns but focus on the negative returns. In the case of VaR, the focus is quantifying the average losses on the “worst” of all expected returns.

**Understanding and managing risk affects portfolio returns **

Overall, risk is a key concept in finance.

While most people think of risk in terms of losses, practitioners generally use statistical measures that have to do with measuring the range of outcomes, or “uncertainty” of returns.

Either way, risk and return are fundamental tradeoffs for investors – as usually a portfolio with higher returns is more risky (meaning losses can also be higher).

Investors should know that there are also a number of ways to reduce risks in a portfolio – including diversification, which can reduce volatility, and buying options to protect a portfolio against losses.