*"Price is what you pay. Value is what you get."*- Warren Buffett

This simple statement speaks volumes about return on investment. Take an instance: You grow a sapling and water it regularly. The sapling finally matures into a big tree that yields you fruits. Now compare this with the business perspective in the modern world. It is quite similar. Here, business is the sapling, water is the money, and fruits are the returns on investment.

**The Concept**

Usually, the term 'rate of return' is most frequently used when making investments in business or securities. It can be termed as the rate at which the returns are earned on a capital invested, in a given time period. These returns can be positive or negative. Expected rate of return is the anticipated value of future returns. For example: You buy 10 notebooks each costing USD 2. So, your investment is USD 20. Now you plan to sell each notebook for USD 3. So, the amount you earn at the close of business is USD 30, which is the return on your capital, of which USD 10 is your profit. Therefore, your return rate is (30-20)/20x100 which is 50%. This was a very simple example to understand the concept. But then if you peep into the functioning of the stock market, although the concept remains the same, calculating rate of return becomes more challenging. Say, you make an investment of USD 100. A year later its value is worth USD 200. So, your rate of return is 100%. But then a year later due to some economic debacle, your investment falls to USD 100 again. So, now your return drops by 50%. Expected rate of return in stock markets and bonds follow the theory of probability as well.

**Formula**

Expected rate of return (∑i) = 1

^{n}[P(i) x r

_{i}]

where:

r

_{i}= rate of return

P(i) = probability of achieving the return (r

_{i})

n = number of probable outcomes anticipated

For instance, you own a stock ABC. Its current value is USD 10. The experts predict that by the end of this year, there is a 25% probability that it might soar by 15% if the economic growth goes up. They feel that there is a 40% chance that the stock value may increase by 12% if the economic growth is good. However, they also believe that there is a 35% probability of the economy falling leading to a decline of 5% in the stock value. Now the rate of return will be:

(25% x 15%) + (40% x 12%) + (35% x (-)5%) = 0.0375 + 0.048 + (-)0.0175 = 0.068

Here, 6.8% is the expected rate of return.

This calculation is an integral part of any business and for people who invest in securities.