Variance

Variance is a statistical measurement that quantifies the spread of a set of data points around their average value. In the world of investing, it's a key ingredient used to measure the volatility of an asset's returns over a specific period. Imagine two stocks, both averaging a 7% annual return. Stock A's returns have been 6%, 7%, and 8% over the last three years. Stock B's returns have been -10%, 7%, and 24%. While their average is the same, Stock B's returns are all over the map. Variance captures this “wildness” mathematically. A higher variance indicates that the returns are more spread out from the average, implying greater volatility and, in the eyes of many academics, higher risk. While it's a foundational concept in finance, especially in Modern Portfolio Theory (MPT), value investors often view its usefulness with a healthy dose of skepticism.

For decades, the financial industry has used variance—and its close cousin, standard deviation—as the primary proxy for an investment's risk. The logic is simple and intuitive: the more an asset's price bounces around (high variance), the less certain you can be about its return at any given point in the future. This unpredictability is defined as risk. A fund manager might tell you a portfolio has “low variance,” meaning its returns have been historically stable and predictable. Conversely, a startup tech stock will likely have a very high variance, with its price experiencing dramatic swings. This framework helps in constructing diversified portfolios, where assets with different variance characteristics can be combined to smooth out the overall journey. However, equating this price turbulence directly with true investment risk is a point of major debate.

You don't need to be a math whiz to understand how variance is calculated. It's a simple, four-step process:

1. 1. Find the Average: First, calculate the average (or mean) return of an investment over a period. Let's say a stock's returns over three years were 5%, 15%, and 10%. The average return is (5 + 15 + 10) / 3 = 10%.
2. 2. Calculate the Differences: Next, find how far each year's return was from the average.
   • Year 1: 5% - 10% = -5%
   • Year 2: 15% - 10% = 5%
   • Year 3: 10% - 10% = 0%
3. 3. Square the Differences: Square each of these differences. Squaring serves two purposes: it gets rid of the negative signs (since a negative number squared becomes positive) and it gives much more weight to larger deviations.
   • Year 1: (-5%)^2 = 25
   • Year 2: (5%)^2 = 25
   • Year 3: (0%)^2 = 0
4. 4. Find the Average of the Squares: Finally, calculate the average of these new squared values. This result is the variance.
   • Variance = (25 + 25 + 0) / 3 = 16.67

While variance is the engine of the calculation, it has a major drawback: its units are “squared percentages,” which makes no intuitive sense. What does “16.67 squared percent” even mean? This is where standard deviation comes to the rescue. It is simply the square root of the variance. In our example, the square root of 16.67 is approximately 4.08%. This number is far more useful because it's back in the same unit as our original data (percentage returns). It tells us that, on average, the stock's annual return has tended to deviate from its 10% average by about 4.08%. For this reason, you will almost always hear investors and analysts talk about standard deviation rather than variance, even though one is directly calculated from the other.

Here’s where we pump the brakes. Legendary investors like Warren Buffett and his mentor, Benjamin Graham, would argue that variance is a deeply flawed measure of risk. For a value investor, risk is not about how much a stock price wiggles; it's about the probability of a permanent loss of capital. Think about it: is a high-quality, dominant business that you bought for 50% of its intrinsic value “risky” just because its stock price is volatile in the short term? The value investor would say no. The volatility is just market noise, creating an opportunity to buy more at a cheaper price. Conversely, is a stable, “low variance” stock that is trading at 300% of its intrinsic value “safe”? The value investor would scream no! The risk of a permanent loss is enormous, because there is no margin of safety if the business falters or the market sentiment changes. As Buffett famously said, “I would much rather have a lumpy 15 percent return than a smooth 12 percent return.”

Before you build your entire risk assessment around variance, be aware of its critical limitations:

• It Looks Backward, Not Forward: Variance is calculated using historical data. It tells you how volatile an asset was, not how volatile it will be. A sleepy utility company could suddenly face a disruptive new technology, making its low historical variance utterly meaningless for predicting its future.
• Good and Bad Volatility Are Treated the Same: A stock that jumps 40% above its average return contributes just as much to its variance score as a stock that plummets 40% below. This is absurd from an investor's standpoint. A sudden price surge is a wonderful surprise, not a “risk” in the same way a crash is. More advanced metrics like downside deviation attempt to fix this by only focusing on negative returns.
• It Ignores the Possibility of Catastrophe: Variance calculations often assume returns follow a “normal distribution” (a bell curve). This model works well for everyday market jitters but fails spectacularly at predicting rare, extreme events like the 2008 financial crisis. These so-called Black Swan events live in the “tails” of the distribution and can cause devastating losses that historical variance fails to anticipate.