Latest / VoraPrep Audio — Professional Licensure & Certification Exam Prep / CFP-INV: Portfolio Diversification & Correlation: Covariance, Non-Systematic Risk, and the Efficient Frontier
Transcript
- Hey, welcome to VoraPrep Audio. If you're studying for the CFP exam, one of the biggest ideas you have to get your head around is diversification. Not just the buzzword, but the math behind it. Why does it actually work? This is one of those topics that can feel a little abstract until it clicks, and when it does, it shows up everywhere on the exam. It's the bedrock of how we build portfolios. So let’s start with the big idea, which comes from a guy named Harry Markowitz. Back in the 1950s, the old way of thinking was pretty simple: buy good stocks, avoid bad ones. You looked at each company on its own. But Markowitz came along and proved, mathematically, that that’s completely the wrong way to look at it. He said you should never judge an investment in isolation. Its real value is how it behaves next to all the other things in your portfolio. Think of it like building a basketball team. You wouldn't just pick the five best shooters in the league. That team would be a disaster. You need a rebounder, a defender, a playmaker… people with different skills that work together. That's a portfolio. By combining assets that don't move in perfect lockstep, you can lower your team's overall volatility. That's your risk. And you can do this without giving up expected points, or in our case, expected return. This is what people call the only "free lunch" in finance. You get a benefit, risk reduction, without a cost. The key to this whole thing is a single number: the correlation coefficient. It’s just a measure of how two assets move together. And it's always on a scale from negative one to positive one. Let's start at one end of the spectrum. A correlation of positive 1.0. This is perfect positive correlation. It means the two assets are basically identical twins. When one goes up 10 percent, the other goes up 10 percent. When one zigs, the other zigs. If you combine these two, you get absolutely zero diversification benefit. Your portfolio's risk is just the simple weighted average of the two assets' individual risks. It's like having two great shooters who only stand in the same spot on the court. It doesn't help. Now, what if the correlation is zero? This means the two assets are completely independent. Their movements have nothing to do with each other. Think of something like the U.S. stock market versus… say, the price of agricultural timberland. One doesn’t really affect the other. When you combine assets like this, you get a huge diversification benefit. The portfolio's risk will be way, way lower than the weighted average. And then you have the holy grail, a perfect negative correlation of negative 1.0. This means the two assets are a perfect seesaw. When one goes up by five percent, the other goes down by exactly five percent. In theory, you could find two assets like this. If you combine them in just the right way, you could completely eliminate all your company-specific risk. You could create a risk-free return. Now, this is mostly a theoretical idea. But it shows you the power of finding things that move in opposite directions. The important thing for the exam is that any correlation less than positive 1.0 gives you some benefit. Even if it's positive 0.60. As long as they aren't marching in perfect lockstep, you are getting some risk reduction. Now, the exam might try to trip you up with the difference between covariance and correlation. This is a classic trap. You might see a question that says the covariance between two stocks is, like, positive 150. And your brain might want to think, "Wow, that's a really high number, they must be super correlated." But that's wrong. Covariance is an unbounded number. It could be plus 500 or negative 0.02. It tells you the direction—positive or negative—but it doesn't tell you the strength of the relationship. Correlation is just the standardized version of covariance. It takes that raw number and puts it on that clean, easy-to-understand scale of negative one to positive one. So correlation tells you the strength; covariance does not. Let's walk through a quick scenario to see this "free lunch" in action. Let’s say your client has all their money in Stock A. It has an expected return of 12 percent and a standard deviation, our measure of risk, of 20 percent. Now, you propose adding another asset, Asset B. It just so happens to have the exact same numbers: 12 percent expected return, 20 percent risk. But here's the magic key: the correlation between them is zero. They are totally independent. So you build a portfolio that's 50 percent Stock A and 50 percent Asset B. What's the new expected return? Well, that's the easy part. It's just the weighted average. Half of 12 percent plus half of 12 percent… is still 12 percent. The return hasn't changed. But what about the risk? To figure this out, we first need to use variance, which is just standard deviation squared. So, a 20 percent standard deviation means a variance of 20 squared, which is 400. Both assets have a variance of 400. The formula uses the weights and the variances. We take the weight of Stock A squared, which is 0.5 times 0.5, or 0.25. Then we multiply that by its variance of 400. That gives us 100. We do the same for Asset B. Its weight squared is also 0.25, multiplied by its variance of 400, which gives us another 100. Normally, there's a third part of the formula that involves correlation. But since the correlation here is zero, that whole part of the calculation just disappears. So, we're left with the first two parts. We add them together: 100 plus 100 equals 200. This 200 is the portfolio's variance. To get back to standard deviation, we just take the square root. The square root of 200 is about 14.14 percent. Think about that. The return is still 12 percent, but the risk plummeted from 20 percent down to 14.14 percent. That’s a nearly 30 percent reduction in volatility, and it cost nothing. That is the free lunch. So what kind of risk did we just get rid of? We got rid of what's called unsystematic risk. This is the company-specific stuff—a bad CEO, a lawsuit, a factory strike. It’s the risk you can diversify away by holding about 25 to 30 well-chosen, non-correlated stocks. The other kind of risk is systematic risk, or market risk. This is the big stuff that affects everyone: a recession, high inflation, a war. You cannot diversify this away. The market only compensates you for taking on systematic risk, because it assumes you're smart enough to get rid of the unsystematic risk for free. All of these optimal portfolios—the ones that give you the highest possible return for a certain level of risk—can be plotted on a graph. That curve is called the Efficient Frontier. It's basically the menu of the best possible combinations of assets you could own. Okay, quick check for you. Let's say Stock X has a standard deviation of 15 percent, and Stock Y has one of 25 percent. You put them in a 50/50 portfolio, and I tell you their correlation is a perfect positive 1.0. What’s the portfolio's standard deviation? … It’s 20 percent. Because the correlation is positive 1.0, there’s no diversification benefit. You just take the simple weighted average: half of 15 plus half of 25 is 20. Simple as that. And a final tip for exam day: remember that in a real crisis, like 2008 or the flash crash in 2020, correlations can do funny things. Asset classes that you thought were non-correlated can suddenly all start moving together, spiking toward positive 1.0, as everyone rushes for the exits at the same time. VoraPrep is a full exam-prep app — lessons, practice questions, and an AI tutor in one place. Get started at Vora Prep dot com.