 Apart from historical or realized rate of return, aren't on a particular investment in the past? A particular investor while evaluating a future investment may also expect a certain rate of return on that particular investment in the days to come. So what are the expected rates of returns? Basically the expected rate of return is the rate that is expected by an investor in the future on a particular set of investments or any individual investment. In fact this is expectation is not risk free or free from risk that means there is an element of uncertainty. When the returns expected on a particular investment then how to determine the certainty level of returns on that particular investment for that purpose we analyze this certainty by estimating the possibility of returns on the particular investment. To determine this possibility of the returns we assign probability values to all the possible returns of the particular investment. These probability values range from 0 to 1. Probability value of 0 means there is no return in the future on the investment and probability value of 1 to a particular return means that particular return is certain to happen in the future. When we have a certainty about returns on a particular investment this means that that is a perfect certainty and that perfect certainty allows only one possible return. This means let's say that we have assumed that there is a 100% chance that a particular investment will earn a rate of interest or return of 5%. So that certainty of 5% rate of return is a perfect certainty. Investment with perfect certainty are generally considered as a risk free investment as this is a case of the government securities because there is no chance of default by the government. So every investment security issued by a government authority may be termed as a risk free investment. And for perfect certainty only one value exists for the probability multiplied for the return and that probability is equal to 100 because we are 100% sure that return is certain. This most likely estimate is in fact referred to as a point estimate. In the figure you can see that at the 5% rate of return we have the probability of 1. This means we are 100% sure that this particular investment will earn a rate of return of 5%. We have another scenario and that is the alternative scenario where an investment could have several different rates of return depending on the different possible economic conditions. For that purpose we assign the probability to individual condition and accordingly we assign a rate of return to that probability. Then we multiply individual probability to the individual rate of that condition and the sum of these probability returns is termed as the expected rate of return. In the example we have three scenarios. The weak economy means there is no inflation for that purpose. The probability is 15% or 0.15 the rate of return for that 15% chance is the 20%. Then we have another condition the weak economy there is above average inflation rate is in existence. For that condition we have probability of again 15% then we have third condition means there is no major change in the economy and we assign probability of 0.7 or 70%. Now when we multiply individual probability with the individual rate of return and sum up these probability returns the expected value is 0.07 or the 7%. This is basically the weighted rate of return. If we plot these probabilities and rate of returns on a figure we see that for each probability we have a given rate of return and then we plot this is a probability curve. This means that as we have more of the probabilities then we will be having lesser uncertainty of the expected returns. This means more probability lesser returns that would make the investment more riskier. Similarly we have a worst scenario in which an investment with 10 possible outcomes ranging from 0.40 to 0.50 with the same probability for each rate of returns. And to determine the expected rate of return on this situation we have the expected rate of return of 5%. This 5% means using 10 possible outcomes that the investor is highly uncertain about the actual rate of return. In fact the investment is very much riskier owing to the higher uncertainty as we have 10 possibilities. So 10 possibilities are making this investment more riskier. Now what is risk version? We know that any investor may face a choice between a riskier investment and a certain or risk-free investment. So there are two cases where one investment is much riskier and the other is the risk-free investment and the investor has to choose any investment between the two. The investor would certainly go for the risk-free investment or the alternative case. This means that the investor is a risk-averse investor. This means that if anything else is the same the investor will select the investment that offers higher rate of return with a given level of riskiness. This means if this is the scenario then this assumption says that most of the investors in the market are the risk-averse investors that they want to maximize their rate of return at the lowest level of riskiness. This another means that for a certain level of risk the investor go for an investment that is offering to him the higher amount of return.