 No expected return is free from uncertainty. This means that there is a level of certain riskiness associated with that particular expected rate of return. Now this riskiness is also associated with the liquidation of that particular investment. But at more importantly, the risk is computed for the expected return. So to determine the riskiness of an expected return of a particular investment, the investor needs to know the tools that can be used in order to measure the riskiness of a particular rate of return that an investor is expected to earn in the future on the intended investment. How to define the term risk? Risk is basically the dispersion of possible returns. This means that any deviation in the expected return is termed as the risk. For a financial analyst, this riskiness is required to be quantified in terms of number so that its level of toughness can be determined. There are certain statistical measures that allow an investor to compare return and riskiness of an investment with reference to the other alternative investments for the particular investor. There are certain measures that can be used to proxy the riskiness of a particular investment. These measures include variance, standard deviation, and coefficient of variation. This means a measurement of spread found between numbers in a dataset. If the variance is larger, this means there is more dispersion and the greater uncertainty which another means that the investment is more riskier in terms of its expected returns. To determine the variance, we basically scare the probability value of the expected returns. For example, we have certain data whose variance is 0.0141. If we convert this figure into percentage, we can see that the variance in this particular case is 1.41% or roughly it is closer to 1.5%. So the variance is much lesser so we can say that the riskiness of this particular investment is much lower. So investment is relatively safer as to its expected returns. There is a point to note that for risk-free investments, the variance is generally 0 because the expected rate of return on such risk-free investment is generally certain. For certainty, the probability value is 100. So this means the return would also be 100%. Then this 100% surety of the expected return means that there is no riskiness. So the variance on these investments is generally the 0. The second measure to compute riskiness of investment is the standard deviation. This is also the measure of volatility or the riskiness of an investment in terms of its expected return. Standard deviation is a quantity that expresses by how much the expected return of an investment can be deviated from its average return. Now to determine the standard deviation of a particular expected return on an investment, we just compute the scale root of the variance of that expected return on the investment. And if we carry the previous example, the scale root of our variance which was 0.0141, the scale root of this figure is 11.87%. Using this standalone figure, let's assume that the investment is relatively less risky. But if we have another investment alternative, then we would be using this standard deviation with this standard deviation of expected returns on that investment. And the investment with lower standard deviation would be termed as the safer investment. The conclusion on this standard deviation discussion says that higher the value of standard deviation, higher the volatility of returns of a given investor on a given investment, which means that investment is relatively riskier one. The third measure to compute riskiness is the coefficient of variation. It is basically a relative measure of riskiness because it compares alternative investment with widely different rate of return and their standard deviation. This coefficient of variation measures risk per unit of expected return and to determine the coefficient of variation, we just divide the standard deviation of returns over the expected return. We have our example that we continue here on the screen. You can see that we have standard deviation of 0.11874 and expected return of 0.07. The coefficient of variation comes to 1.696. This means that to determine one unit of expected return, we have to bear 1.69 unit of standard deviation or riskiness. So the riskiness of this investment is higher than the expected return. This means that investment is highly riskier. We have another example as you can see on the bottom part of the screen where we have two alternatives investment A and investment B. The expected return on investment A is 7% and on B it's 12%. The standard deviation on investment A is 5% and on B is 7% apparently. The B has higher standard deviation so the B is looking higher riskier than the investment A but if we compute coefficient of variation for both of the investments, we can see that for the investment A, the coefficient of variation is 0.71 and for investment B, this coefficient of variation is 0.58 as we have seen that higher coefficient of variation means higher riskiness. Now using this criteria, we can say that investment B is lesser riskier than investment A as the per unit riskiness of investment B is lesser than the per unit riskiness of investment A because investment B is yielding lesser riskiness which is as low as half unit of the risk against one unit of the return earned by the investment B. So we can conclude that investment B is relatively lesser riskier than the investment A. How to measure risk for the historical returns? As we have just seen the measurement of risk for the expected returns. In fact, same riskiness measures like coefficient of variation, standard deviation and variance can be used to measure the riskiness of some past returns or historical returns. For that purpose, again we can use the variance which is standard deviation basically and it is the scale root of the variance of the probability values of the historical returns. This measure indicates that how much individual holding period yields over the time deviated from the series expected value of time t. This means there to determine the riskiness of historical returns we compute its standard deviation, the standard deviation of holding period yield and then we compare the standard deviation of holding period yields against the expected return and the deviation computed through the measure of coefficient of variation, measure of standard deviation and measure of variance. That measure tells how riskier was the particular investment in the past.