# Portfolio Theory – Part 4 (Math Concepts)

In this video we walk through the equation for Portfolio Theory.

VIDEO SUMMARY

In this video, we are going to continue our conversation about Portfolio Theory. Now I think this video is going to blow your mind. In some of the previous videos we have talked about things like risk and diversification and negative correlation and why that is important. But in this video, what I am going to do is I am going to walk through the math equation for Portfolio Theory and put all the pieces together and show you how this works. So to get started, I am going to throw up the equation. What this is, is it is looking at a two asset portfolio. So you have a portfolio with two different assets. That is asset A and asset B. Based on the percentage each asset takes up, as well as the individual characteristics of those assets, that is going to determine the performance of your overall portfolio. So that is the goal here with this equation. You are trying to gain this understanding of your portfolio’s performance.

The key concept here is that Portfolio Theory separates the concepts of risk from return. Now previously I have always talked about risk and return as related concepts, and they are. Because if you were to go out and buy an individual investment, you would assess the riskiness of that investment and you would build that into the price you would be willing to pay. So if you are looking at an investment with ten percent risk you would want to discount the future cash flow by ten percent and receive that ten percent interest. So this idea of risk and return are very related concepts. But what we see when we put investments together in a portfolio, risk and return start to separate from each other. The reason why this is, is because if assets or investments are negatively correlated, the uncertainty between these investments will cancel each other out. Because when one investment goes down, another investment will go up. And so the overall portfolio risk will be reduced. So we are trying to figure that out here.

Let us take a look back at the equations. What you see here is there are two equations. The top equation is the equation for your portfolio return, and the bottom equation is the equation for your portfolio variance (or your portfolio risk). So looking at the first equation, this is a pretty simple equation to understand. This is just a weighted average of your expected returns of your investments. So it is taking the weighted average. So if you have a portfolio that’s 60%/40%, or 50%/50%, or 70%/30%, you are going to plug that into this equation. So you take the weight of asset A times the expected return of asset A plus the weight of asset B times the return of asset B and that will give you the overall return for the portfolio. That is pretty straightforward, and I think most people understand that. Where things get interesting is when you look at portfolio risk, because we need to factor in this netting out of assets based on negative correlation. So what you see, when you look at the second equation, is it starts out in a very similar way. You are taking the weight of the variance of your portfolio for each of these assets, asset A and asset B. But then there is this piece of the equation at the end, and this is what is factoring in the correlations. So the most important part of this is the very last piece of the equation. This is the correlation coefficient. So the correlation coefficient is going to range between 1 and negative 1. So one is completely positively correlated and negative one is completely negatively correlated. So you are going to look at the expected movement of your assets and determine the correlation coefficient for them. When you plug it into this equation, what you see is, as the correlation coefficient reduces below zero, this whole part of the equation becomes negative. So what it does, is it starts reducing the risk. It reduces your overall portfolio risk. So what happens if it is perfectly correlated? If your coefficient is 1, your portfolio risk is going to be pretty close to the weighted average of the variance. So because your assets are moving in the same direction all the time, it is almost as if you have one asset. But the further you get away from a coefficient of 1, as you get towards 0, your risk starts to reduce. Then you go below 0, the closer you get to negative 1, you can reduce your risk almost completely. Because as one asset drops in value, the other assets are going to gain in value. So overall, the riskiness of your portfolio can be very, very low.

I hope you realize the significance of this equation, because what it is telling you, is that you are creating value without having to pay for it. Based on the financial choices you make on putting together your portfolio, you can create value there. If you just went out and bought an individual investment, you would pay the appropriate price based on the risk. But if you combine it into a portfolio in a smart way, you are actually not holding as much risk as you pay for. So I hope you realize the significance of this and how powerful it can be. In the next video, I am going to break down some of the issues that are in Portfolio Theory and some of the things you should be aware of.

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Neither Zach De Gregorio or Wolves and Finance Inc. shall be liable for any damages related to information in this video. It is recommended you contact a CPA in your area for business advice.