In this chapter, we’re going to take our first step to try to identify of optimal risk. E-portfolios that is the best portfolio that you can buy for you, so we’re gonna look at several things. Capital allocation is the first process of first step in this process, which essentially is to try to identify or to envision that you only have two assets, a risky asset and a risk-free asset and we want to explore the combinations of risk and return between those two types of investments. Asset allocation is about splitting and splitting your money between different classes of assets That is how much money is in stocks. How much money is in bond’s? Security selection then is about within the risky portfolio that you have. Let’s say we have 75% of our money as in stocks. What should that 75% look like? What are the individual securities in that portfolio? So the idea here is developed what’s referred to as the Markowitz portfolio optimization model? Right, this is the original work done by Harry Markowitz quite a while ago, but it’s still a very strong has very strong impact on the choices that we make when we’re investing the the approach we take as we’ve just been talking about. We’re going to talk about the capital allocation, right the risk return relationship between the risky portfolio and risk free, then we’re going to talk about asset classes and how we distinguish between those and how we should invest in those different classes, and then finally, the last part of this top-down approach is security selection as we’ve talked about in several different courses, There’s two kinds of risk market risk and firm specific risk market risk. As you probably is the stuff that’s left over after we’ve diversified away all of the company specific stuff it’s created by things that are related, right, Everybody is is impacted by inflation and war and interest rates, so market risk comes from those factors that are correlated between investments from specific then comes from company specific things that are, by definition, not correlated, so they’re not correlated with any other factor that could affect risk and return. So when you combine things, ultimately, you eliminate it and we’ve shown this many times here. We have two portfolios or two assets here. Are these probabilities that these returns will occur? This probably looked familiar. Maybe it’s the standalone risk worksheet and this worksheet allows us to calculate the risk and return of these assets. And, of course you can see that they’re very close and return, but asset be a slightly higher risk. We also can see some other statistics that we’ve talked about. Here’s the 95 percent confidence interval You can see, obviously it’s a wider distance for B Then, then a and over here, we have the correlation that you hear. The correlation is negative 0.9 3 6 So what does this mean with respect to portfolios? What’s think about risk if the two assets that we were just talking about if they if all of the risk of those assets was firm specific company specific risk is the only risk you see, then since that risk is uncorrelated by adding those impacts together. If you will, some will be positive, some will be negative, but as we add more and more assets to our portfolio, we ultimately end up with a zero risk portfolio, however, we know that in a real worldthere, there is some systemic risk, so our job is first. Let’s combine things so that we can get rid of as much as the company specific risk as possible, but then we also want to concentrate on. How can we reduce the market risk of the company of the portfolio now? We can do that by combining different asset classes, so this is a study that was done that looks at stocks and they’ve created from. I believe this is from the New York Stock Exchange, different sized portfolios, and we’ve seen this graph. Before, in fact, you saw a picture of a little bit earlier. Just not the research as you get lower and lower more and more stocks in a portfolio, a little risk read, it reduces and at 20 can’t see exactly what the the number is roughly. It looks like around 23 24 percent. Right, but it had a hundred. Listen, let’s go! If you clear out to a thousand shares, right, a thousand choose the the risk is still like 20 percent, so you add roughly nine hundred and eighty stocks and all you get is a is a reduction of one or two percent in risk reduction. And you can see here that you know what happens here is the impact right going down this list. This is what you compare these numbers to over here. 75 percent. If you have a two asset portfolio that has roughly 75% of the risk of the one asset portfolio, so you eliminate 25% of the risk just by going to a two stock portfolio when we think about adding different types again. Think about that same graph. What happens when we add asset classes that are not perfectly correlated, right, so what we ultimately will have is the same graph, except that graph will shift downward so that the market risk is also eliminated. Right, so if you think about stocks in general, those, that’s our security selection as you make that selection have a greater greater number, you reduce risk, but the risk you’re really reducing is the diversifiable risk to get more risk away from your investment. We need to go to different asset classes. So now let’s move on and talk about the statistics and these. I’m sure you recognize these formulas to find the rate of return of a portfolio and take the weighted average of the returns in the portfolio again we’re looking at a two stock portfolio to find the variance. If you remember we have, this represents the risk that comes from the debt portfolio asset. This is the risk that comes from equity now. This part of the formula is a little different because we’re using covariance and the only reason covariance is here is because in the theory, it cuts down on the size of the formulas in reality. If you really wanted to see somehow, this really makes sense for us. This is the formula that we’ve looked at in other classes that this second or this third part of the formula represents the interaction between debt and equity and their correlation. So this is the piece that ultimately determines diversification. And, as you remember, diversification can be between negative 1 and 1 so as diversification goes from 1 down to 0.9 to 0.8 to 0.7 This part of the formula becomes smaller and smaller and smaller and ultimately because negative, we could end up with a portfolio that has much less risk than the assets within that portfolio. So here’s an example from your textbook, and we put it 25 75 split into these assets. This is the portfolio risk and return worksheet. In this case, you see, we have a point. Three correlation and here are statistics and by itself that doesn’t mean all that much to us, but let’s think about what happens when we when if something we’re different, let’s assume we have the identical two assets, except the thing that’s different is covariance and correlation one. If the correlation was a negative point three, what would happen to the return of this portfolio if correlation was negative point three and the answer is nothing would happen to return because correlation is not in that formula, However, we would have changes and all of these numbers would go down. They all would become the reflect a less risk because we’re combining assets that have a greater correlation. That’s negative. How this in theory can work for us is if you could find an asset that had a negative one correlation. Here’s a food. How much money should you put in the equity asset If between debt and equity, it was a negative one correlation standard deviation of D divided by the sum of the standard deviations gives us the proportion. And that’s calculated for us right here. Thirty seven point five percent of this portfolio should be in the equity portion if it had a negative one correlation. So if I put negative one here, put point three, seven five here, that must mean obviously point. Six two five is the weight for the debt. Equity, we see that the return is nine point eight seven five percent, but this is a zero risk portfolio. So let’s see if this can make sense to us if we know today. That the 30-year. Treasury bill, which is risk-free as zero risk, has a three percent rate of return. Which would you rather buy? Would you rather buy the Treasury bond at three percent or the portfolio return at nine point eight percent? Obviously you want the portfolio and everybody would want the portfolio. In fact, people would start selling the risk-free asset people would be borrowing against the United States government, taking that money and all their other investment money and everybody would be piling it into this portfolio and, of course, equilibrium supply and demand is going to eliminate this almost immediately, so this asset, a negative one portfolio. Correlation as cannot exist, certainly cannot list exists for very long, so lets. Now move talk about a three asset portfolio. Look at the data we need for this. We need to have to calculate the return. We need to know three returns for a three asset portfolio. We need to know the weights, right, and how what risk each portfolio asset brings, but then we need a combination correlation number for each of the pairs within the within the portfolio. And as you can see, this gets pretty ugly, fairly quickly, right, A 50 asset portfolio requires 50 rates of returns to be calculated 50 standard deviations and 1125 correlation combinations. So the total data for a 50 stock portfolio is 1225 that amount of data makes this this theory very difficult to to utilize with actual data and in practice. So when we think about this? Markowitz, model one thing to keep in mind is it’s extremely difficult with portfolios of any size, so it will always give us the exact right answer. The problem is the computer strength that we need is far beyond what the average person has that their access. So in the next part of this, we’re gonna move on and talk about how we can use this data to choose portfolios.