# 6. Risk vs. Return  One of the oldest questions in finance is: “How much risk a person is willing to tolerate in order to receive a particular level of return?” In order to answer this question we must answer two additional questions: “How to estimate risk?” and “How to assess return?”

The return side is quite simple. Take the average daily, weekly or monthly returns, sum all of them, and divide them by the number of observations you have, . To increase the credibility of the estimated returns, one could increase the number of observations in the data set; however, one should take in mind that companies change and, for example, Apple today might be completely different than apple five years ago.  Thus, it is up for the analyst to decide which time period represents the company best.

The estimation of risk is a little bit trickier than return. There are many approaches one could employ to assess it. For example, one could use the Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) model using the option’s market to look at the future volatility, or simply take the historical returns and calculate the standard deviation of them. In this post we will focus on assessing it using the standard deviation of assets returns.

As you have already calculated the average return, one could subtract it from a one particular day’s return and would get how much in this particular day the return deviated from the mean return. Further, we could square this subtraction and do the same thing for all the returns in our data set. By summing the squared deviations and dividing them by the number of observations we get the average volatility or the average risk that this asset posses,

As we have calculated risk and return, the investor must decide if he/she is willing to hold the asset. Thus, the answer of the question proposed at the beginning of the article depends on the individual’s tolerance towards risk.

Further on, this sounds good in theory, but how to do it practically? First, go to finance.yahoo.com then select a company, click on the historic prices, select the time frame of your choosing and at the bottom of the page you can download it to your excel spreadsheet.  Open it, and crunch the numbers.

The beauty of this approach is that you can use it for any of the asset classes. The only thing that you need is the data. For more information about financial markets see previous posts.

Happy investing! 