**Relationship between Diversification and Correlation**

## Diversification

At the heart of diversification is the correlation so we cannot really separate diversification from correlation. You cannot again think about the risk of a portfolio, without thinking the impact of correlation, and that is the relationship between the behaviors of the assets in the portfolio.

Now, one or a couple of important things about diversification.

- This is one of the bedrocks of finance, investment and corporate finance.

**Diversified Portfolio**

The fact that a smart investor should have a **diversified portfolio** is at the very core, at the very heart of just about everything that we do in finance. When we talk about the CAPM, and the way we assess risk about, in that, capital asset pricing model, we are going to go back to the fact that remember, beta is a measure of risk after everything has been diversified away is the measure of the risk that we cannot really escape from that we cannot really **diversify**, again from. So that means that when we think about the expected require return of an asset that is a function of the race that we cannot diversify away and the implication of that is that any investor or any model in finance is going to assume that a smart investor is properly diversified. That is why, at the very beginning of all the financial theory, you have an investor that has a portfolio that is properly diversified and that a lot of that risk has gone actually away. The only risk that he bears is the risk that he cannot diversify away called non-diversifiable risk.

- The second thing that is important in terms of diversification, most people think about diversification in terms of protection or risk reduction, and there is absolutely nothing wrong with that but we are going to look at different ways of thinking about why you may want to diversify.
- Protecting yourself from large fluctuations in your portfolio is a typical one.
- Not putting all your money in an asset, when that asset actually may disappear, you know, like a company that goes bankrupt, or a bond that actually goes into default, well you know, those, those are obvious reasons for diversifying.
- So it is getting away from very large potential losses and it is about the diminishing, decreasing volatility or variability of that portfolio. Most people would justify that typical way.

Diversifying the portfolio, we are going to be a little bit more sophisticated than that. Because, there is a better reason for diversifying, and we are going to see that the result of diversity, diversifying goes to the heart of why investors actually invest and how investors invest in different assets.

Here we will discuss three points about diversification and those three points are point

In general, Investors …

**Do not really want to minimize risk****Do not really want to maximize returns****Want to maximize risk-adjusted returns**

Let us think for a minute about reducing risk, and here is very important that you remember that positive relationship we talked about before between risk and return. The more risk that you are ready to bear, the higher is the expected and return on the assets, which you invest. All right? As an investor, I want to minimize risk and it sounds okay, but once you think about the implications of minimizing risk then it does not sound so because I can always know where the risk of my portfolio, but the cost of that is that I am also lowering the expected return of my portfolio. In the limit, I could put my money safely in the bank and know exactly what I am going to get at the end of any given period but of course, a return that I am going to get is going to be very, very small. On the other hand, if I am willing to bear more risk if instead of putting my money in the bank, I am willing to put it in the bond or even I am willing to put it in a share of a stock. Then, the more risk I am ready to bear and the higher is going to be that expected return. So, now, once you think about it in those terms, minimizing risk it also implies minimizing your expected return. And then it doesn’t sound so good. That is why most people if you really ask them, is the goal of your portfolio to have the minimum possible risk? Once they realize the implications they would say no, no, no it sounds good but, you know, in principle, but now that I realize that then I would have to expect the lowest possible return, then minimize risk is not a very good idea. So I’m going to say and I hope that I convince you, that most investors and I am saying most because there can always be exceptions, but most investors do not really want to minimize risk.

Second thing and this sound shall even a little bit better, which is well, you know most investors want to get their returns as high as possible but again, here is when you have to remember that positive relationship between risk and return. If you want to maximize the expected return of the portfolio that means that, you are going to have to expose your portfolio to a very large amount of risk. Exposing your portfolio to a very large amount of risk might mean that over time, you can make a lot of money or you might lose a lot of money. That is why we call it the risk. Nothing is guaranteed. So a lot of risks might expose you to very large gain or to very large losses. Of course, the longer you remain invested, then the more likely is that risk is going to translate into the return. But at the end of the day, once you think, and once you realize that maximizing expected return or maximizing return goes with maximizing risk, then, as in the first case, it doesn’t sound nearly as good. So if I try to minimize risk, my expected return is going to be very low. If I try to maximize return, my expected risk is going to be very high, and neither of these two things sounds very appealing to investors.

What is very appealing to investors is to actually get the best possible combination of risk and return. That is, to get one, one of the many ways to think about this is, to get the highest possible return for a given level of risk and that is what we call in finance, risk-adjusted return. Taking into account, the return of the assets in which I invest, and the risk of the assets in which I invest by putting them together in a measure of risk-adjusted return.

Now we are going to see one quick way of assessing those risk-adjusted returns that are much fancier and technical ways in finance. The first point to highlight is that investors do not really want to minimize return. Investors do not really want to maximize risk. What investors want to do is to maximize to get the best possible combination of return and risk and that is what we technically call in finance **maximizing risk adjust and returns a**nd guess what that is exactly what you can achieve by diversification. You can never maximize the risk-adjust return of the portfolio if you do not diversify the portfolio. The portfolio that maximizes the risk-adjusted return is going to be a diversified portfolio.