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Calculate Return on Investment

How we calculate periodic return?

A periodic return is referred to as the return on any given period. In finance, we always look at multiple periods rather one period. At times, we may look for any specific purpose but when we want to assess the performance of assets, what we do is to aggregate the performance over time. And in order to do that we need to aggregate information into statistics into measures that tell us something about the risk and return characteristics of different assets. Therefore, we will discuss here

Return:

Risk:

• Beta
• Standard Deviation

We will define periodic return first.

For example, we buy an asset or a share of stock at the beginning of the year and then we sell it at the end of the year. When we compare the price at which we buy and the price at which we sell that asset, that price might have gone up or it might go down, so one of the two sources of return is capital gain or a capital loss. If the price goes up, then we obtained a gain, and we call that a capital gain. And if the price went down, then we obtained a loss and we call that a capital loss.

Now on top of that, many assets actually pay us a cash flow. Some companies pay dividends. Some bonds pay coupons and that is the cash flow that we put into our pocket. And it will be part of our return. So again, if we buy a share at the beginning of the period and sell it at the end of the period, not only we can get that capital gain or loss, which is given by the change in price between the beginning and the end of the period, but we also can pocket the cash flow, which again could be a dividend, could be an interest payment if it is a bond. Once we put together these two sources of returns, then that is what we actually get our return.

Capital Gain Example

Except for the fact that we need one more step. And the one more step that we need is typically we express everything, both the change in price and the cash flow that we get, relative to the price at the beginning of the period. Well, that the reason for this is simple is, it’s not the same thing to actually get a capital gain and a cash flow when we paid \$2 for a share of the stock than when we paid \$10 for a share of the stock. So suppose that between the beginning and the end of the period and there was a capital gain of \$1. And we actually got a dividend of \$1. Well, that’s a \$2 gain that we actually got. One from the changing price and one from the cash that we put in our pocket. So if we paid\$2 for that share of the stock then we actually got a very big return. That is, we got \$2 in terms of gain compared to \$2 that we paid at the beginning, but if we had paid 10 or 20, or \$30 for that share, in proportional terms what we actually got in terms of return is much lower when we pay 10, 20, or \$30.

So what we typically do, in order to calculate that return, is to standardize, to divide everything by the price that we paid at the beginning of the period.

How to calculate Return?

In order to calculate a return, we need two things.

• First, a change in price between the beginning and the end of the period.
• Second, we need to know the cash flow that we are putting in our pocket if any between the beginning and the end of the period, and once we have those two, components we add them up and we divide the whole thing by the price that we paid at the beginning of the period.

So, these are the two sources of gains that we get when we buy a share of stock.

Now, we are going to look at a set of data.

 Year USA Spain Egypt World 2004 10.7% 29.6% 126.2% 15.8% 2005 5.7% 4.9% 161.6% 11.4% 2006 15.3% 50.2% 17.1% 21.5% 2007 6.0% 24.7% 58.4% 12.2% 2008 -37.1% -40.1% -52.4% -41.8% 2009 27.1% 45.1% 39.7% 35.4% 2010 15.4% -21.1% 12.4% 13.2% 2011 2.0% -11.2% -46.9% -6.9% 2012 16.1% 4.7% 47.1% 16.8% 2013 32.6% 32.3% 8.2% 23.4%

Let me clarify a few things about the data that we are seeing.

We are seeing there three equity markets. It is important that we understand that this is equity. This is not debt. So, these are stock markets. These are broadly diversified indices. This is not, for example, in the case of the US, the widely used S&P 500 all these are Morgan Stanley indices and it does not really matter, Morgan Stanley, Financial Times, Dow Jones. There are many providers of data, this just happens to be Morgan Stanley data. These are basically broad indicators of the performance of the equity market in each of the three countries that we are seeing there. Now, in the last column, we have the world market, and that is basically an aggregation of all the equity markets, developed markets and emerging markets put together into one. So that world equity market is basically the composite of developed and emerging markets altogether and all expressed in the same currency to which I would get to in just a minute. So. A couple of characteristics about those returns. Characteristic number one they are, all of them, what we call total returns.

What is Total Return?

Total returns basically mean that we don’t leave anything out. That means that we are putting together the change of price, between the beginning and the end of the period. But we are also putting together the cash flows, paid by the companies in the index. So when we look at, for example, that 10.7% for the year 2004. In the case of the US, that means that when we put together the change in the value of the index between the beginning and the end of the period, and we put together the cash flow, the dividends paid by all the companies in the index. When we aggregate those two things and put it relative to the value of the index at the beginning of the period we get that 10.7%. Okay. So characteristic number one of those returns is that they, they are again they are total returns and that means we’re putting together all of the sources for which we can get a return and that means capital gains or losses and dividends paid by these companies. Characteristic number two. All of them are expressed in terms of dollars. If we were actually looking at those three first countries, the local currency in each country’s different and typically we would express the returns in that particular currency. Now because we want to make some comparisons, and we will make those comparisons a few minutes from now.

We want to put everything in the same currency and that currency is the dollar. And we also do that because if we look at the last column, that world market portfolio we’re aggregating many countries with many different currencies and that is like adding apples and oranges, it doesn’t really make any sense. Unless we add the map in the same currency and that is why we are, again we are using the dollar as that particular currency. So keep in mind that the characteristics of those returns. Number one is that they are expressed in the dollar, number two that they still have their total returns and that they are put together all the sources from where we can get gains. All right? Now, we are going to go back. If we are asked to tell something about the performance of the US Market or the Spanish Market or the Egyptian Market, well we are not going to be looking at one year we, we ideally would like to be looking at a relatively long period of times. Which means that we are going to have a series of many returns they could be annual returns, they could be monthly returns, they could be daily returns. What we have here are annual returns, the ones that we looking at, but ideally, if I want to be able to tell we something about the relative performance of the U.S. market, the Spanish market or the Egyptian market or any other market then I would like to look at a longer period of time. The problem is not a problem but what happens is that when I am looking at a long period of time we know, just looking at a series of returns is not going to help me. So what I need to do is to summarize information. And summarizing information basically, implies bringing all the numbers together into one specific measure. And that measure could be something that describes returns, or something that describes risk, or something that describes, as we’re going to discuss in the next session, risk-adjusted returns.