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A Rate of Return (RoR) is the loss or gain from an investment that is held over a certain period of time. In other words, the rate of return of an investment is the loss (or gain) compared to the initial cost or investment. The net gain or loss is typically expressed in percentage terms. When the RoR is negative, it is considered a loss and when the ROR is positive, it reflects a gain on the investment.

RoR is calculated with the following formula −

$$\mathrm{RoR =\frac{End\:Value\:of\:Investment − Initial\:Value\:of\:Investment}{Initial\:Value\:of\: Investment}× 100}$$

The point to note here is that any gains or losses made during the holding period of the investment should be considered in the formula. For example, if a share costs INR 10 and its current price is INR 15 with a dividend of INR 1 paid during the period, the dividend should reflect in the RoR formula. It would be calculated as follows −

$$\mathrm{RoR =\frac{(15 + 1) − 10}{10}× 100 = 60 \%}$$

The historical returns are usually recorded from the beginning of a year (i.e., January 1^{st}) to the end of the year (i.e., December 31^{st}) to find out the annual return of the particular year. A compilation of several past annual returns is required to calculate historical returns over many years. With the historical returns data, analysts and investors can compute the average of historical returns on a set of data of a financial asset.

It is simple to calculate historical data if all the past annual performance is available.

The data given below is of the historical performance of the S&P 500 index. It is for educational purpose and does not show original data.

- December 31, 2016: 2,105
- December 31, 2017: 2,550

To calculate the historical returns, first find the difference between the most recent price and the past price. The difference is then divided by the past price and then multiplied by 100 to get the result in a percentage form. The calculation is also done iteratively to cater for longer time periods, for example, 5 years or more.

Hence, the historical return for the S&P 500 based on the data provided above is calculated as −

$$\mathrm{Historical\:Returns =\frac{2550 − 2105}{2105}× 100 = 21.4 \%}$$

Treasury bills or T-bills, also known as money market instruments, are short-term debt instruments issued by the Government of India. These are now offered in three tenors, viz., 91 days, 182 days, and 364 days. Treasury bills are, in fact, zero coupon securities and they pay no interest.

Instead, they are issued at a discount presently and redeemed at the face value at maturity. For example, a 91-day Treasury bill of INR 100 (face value) may be issued at say INR 98.20, that is, at a discount of say, INR 1.80 and would be redeemed at the face value of INR 100.

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