# Asset Allocation: Expected Returns, Standard Deviations and Correlation

In this video, we will discuss asset allocation and introduce you to key concepts such as expected returns, standard deviations and correlation.
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In our discussion of robo-advisors, the first thing that we want to discuss is asset allocation, which is one of the key concepts in finance, and it’s the main thing that a robo-advisor is going to do for us. Asset allocation refers simply to how much of your money you’re going to put into different classes of securities. So that is to say, how much of your money you’re going to put into broad groups of securities like stocks and bonds as opposed to each individual stock or each individual bond. Therefore, this is more about types of assets than about individual assets.
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So it’s thinking about financial instruments that conform to a specific type as opposed to thinking about a specific stock, like say Apple’s stock or Microsoft stock. Examples of asset classes include domestic stocks. So those equities that are traded in the United States, United States treasury bonds, emerging market stocks, stocks that are trading in emerging markets such as Mexico or the Philippines and so forth, and real estate. The principles of finance suggests to us that we ought to determine an allocation to meet our financial goals.
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So when thinking about a particular investing strategy, we want to think about what we want to achieve when we set that particular strategy, and then think about an allocation that is going to help us to best meet those goals. Examples of these types of problems include things like how much to save for retirement, or how much to save for children’s education, and so on and so forth. So how do we go about determining an allocation? The first thing that we need to think about, according to the principles of finance, is what expected return do we need to meet our goals.
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That is to say, what rate of return do we think that we need in order to achieve whatever goal it is that we set out to do? To take an example, let’s suppose that we have $500 to save per month over the next 40 years. We’d like to have a million dollars at the end of those 40 years. So again, this is a typical retirement saving example, where we know how much we have to save, we know how long we’re going to save it for, and we have a goal as to what the amount is that we need to have at the end of our saving period. What return do we need to earn to make this happen? 169 This again is a very typical finance problem, and the answer to it comes from the time value of money problem from principles of finance, where we think to ourselves, if we invest at some rate of compound interests, how much are we going to have when we’re finished investing? The future value that we’re looking for here is a million dollars. The amount of the payment is$500. The number of payments that we’re going to have is \$480, and the question is what return do we need to achieve in order to get to this goal? The answer turns out to be 1.5 of one percent per month. This can be easily achieved in a financial calculator or in Excel.
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So when we are trying to solve this problem or think about this particular goal, we know that we need to find an investment or an asset allocation that’s going to return to us a 0.5 percent per month, or approximately six percent per year.
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The other consideration when we’re thinking about an asset allocation is that we usually think that there’s a trade-off between the return that you can expect and the risk that you have to bear. So for a higher expected return, we expect that you’re going to have to bear more risk, and we usually quantify that risk with a concept called the standard deviation, the variance, or the volatility. All refer to roughly the same concept. As an example, let’s think about stocks and treasury bills. So equities are usually thought of as relatively high risk investments that have high expected returns.
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On the contrary, treasury bills which are paid by the United States government and promised an expected return, are usually thought of as being relatively low-risk, and in fact usually thought of as being default free, because it is expected that the US Treasury will not default on its obligations. Asset allocation is all about reaching your goals. So again, that one million dollars for retirement for example, with an expected return and risk that you personally are comfortable with. To get a little bit of a sense of the risk and return of different asset classes, this particular table shows us for five different asset classes, what returns have averaged over the past several years, and what their standard deviation is.
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I’ve listed the different asset classes according to their average return, and you can see that there’s a broad relation between the average return that we realize on the different asset classes and the risk involved in the asset class or its standard deviation. This relation isn’t perfect, but it doesn’t have to be the case that an asset with the highest average return always has the highest standard deviation. So starting from US residential real estate, you can see that as a broad class, residential real estate has had an average return of 1.6 percent per year, with a standard deviation of 5.82 percent per year.
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This may come as a surprise to many investors as we hear a lot about really large returns to investing in residential real estate. But when we take a look at US real estate as a whole, the return on investing in real estate is actually not especially high, it just happens to be very high in some marquee areas. As I mentioned above, treasury bills are usually thought of as the safest asset, and you can see here that they have an average return of 4.73 percent. They do have some standard deviation, but this occurs because interest rates change over time, and during different times, we can invest at treasury bills at a different rate.
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The next average return comes to treasury bonds, which again are considered fairly safe and relatively risk free, with an average return of about 7.5 percent and a standard deviation of about nine percent. US corporate bonds come next, and then the riskiest and highest returning asset class is US stocks, which have an average return of about 11.5 percent, and a standard deviation per year of about 18 percent. Again, what these numbers are trying to show to us is that there’s generally some trade-off between the return that we can get on a particular asset class and the amount of risk that we have to bear. There’s another concept that’s important when thinking about asset allocation, and that’s diversification.
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One of the biggest insights of finance theory is that holding multiple asset classes produces what we call a diversified portfolio. What this means in simple terms is that sometimes when one asset class has bad returns, another may have good returns. So we may be in a situation, for example, in which bonds have good returns, but stocks are having relatively bad returns. In 1952, Harry Markowitz showed that investors can reduce the risk of their portfolios through diversification, and this is part of what earned him a Nobel Prize. In order to quantify the degree to which an asset class can help diversify a portfolio, we need one more piece of information, which is the correlation of the returns amongst the asset classes.
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Again, here is a sample of what historically the correlation between different assets have been. Again, I have the same five asset classes that I had before; real estate, treasury bills, T bonds refers to treasury bonds, C bonds to corporate bonds and stocks. As we look across the first row, we can see that one of the advantages to real estate is that it has a relatively low correlation with other asset classes. The correlation always ranges between minus one, which essentially says that when one asset class goes up, the other asset class goes down to positive one, which says that when one asset goes up, the other asset class goes up.
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You can see with real estate that relative to bills and treasury bonds, it has a negative correlation. This essentially means that it’s diversifying relative to those securities. It has virtually no correlation with corporate bonds, and a slightly positive correlation with stocks. I won’t go through every single number on this particular table, but a couple of places to highlight are for example the correlation between treasury bonds and corporate bonds. If you look in the fourth column and the third row, you can see that the correlation between corporate bonds and treasury bonds is about 0.7.
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This is because the level of interest rates is one of the major determinants of the return on both corporate bonds and treasury bonds, and so as interest rates go up and down, corporate bonds and treasury bonds tend to move together in terms of their price. The other one to highlight is the correlation between corporate bonds and stocks, which is about 0.47. What we’re seeing here is that, since both of these securities are issued by corporations, they tend to be positively correlated. So when corporations are doing well, the returns on their bonds do relatively well, and the returns on their stocks do relatively well.
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We use this information, the expected return, the standard deviation, and the correlation to form what we call efficient portfolios.