Every person wants that his money grows and with this, it becomes one of the major reason as to why people are investing in various securities. A return is the gain or loss of a security in a particular period. There is a rule that the more risk you take the more is the return and vice versa. So risk and return are directly proportional to each other. There are two types of returns:

- Expected return: it is the return that the investors expect from their investments over some future period. Expected return is usually based on historical data and is not guaranteed.
- Realised return: it is the return that was or could have been earned. The realized return has occurred and can be measured with the proper data.

Return has two components-Yield and Capital gain/loss

- Yield: yield refers to income from a particular asset in the form of interest and dividends.
- Capital gain/loss: it refers to the appreciation (or depreciation) in the price of the asset. It is the difference between the purchase price and the price at which the asset is sold or can be sold.

**Types of Returns**

**Total return**

Total return helps the investor to know the percentage gain or loss for the investment vehicle in which he/she has invested in. As we know that return has two components-yield and capital gain/loss. So the total return equals the sum of the yield plus capital gain or loss over a given period.

**Returns = Income Received ± Price Change**

**Total Return = End Price – Initial Price + Income Received/ Initial Price = Returns/ Initial price**

**Income received=yield i.e. income from the asset in the form of interest and dividends.**

**Price change= End price- Initial price (can be negative also)**

Example: An investor buys 100 shares of Stock A at Rs.20 per share for an initial value of Rs.2,000. During the year the stock paid a dividend of Rs.1.5 per share. At the end of the year stock, A was sold for Rs.25.

To calculate the investment’s total return following calculation has to be done

Total return = (25*100)-(20*100)+(1.5*100)/ (20*100)

= 2500-2000+150/ 2000

= 650/ 2000

= 0.325

Total return (%) = 0.325*100 = 32.5%

**Compounded Annual Growth Rate (CAGR):**

It refers to the rate expressed on an annualized basis. It takes into consideration the effect of compounding. It helps to find out the per year growth rate of an investment vehicle.

**Yield To Maturity (YTM):**

YTM is generally used in relation to bonds. It refers to the total return anticipated on a bond purchased at the current market price if it is held until the end of its lifetime. Calculations of yield to maturity assume that all coupon payments (payouts from bond) are reinvested at the same rate as the bond’s current yield, and take into account the bond’s current market price, face value, coupon interest rate and term to maturity.

**Arithmetic average return:**

Arithmetic average return is the return calculated by dividing the sum of periodic returns by the number of returns. The periodic returns mean that the returns must have the same periodicity, i.e., all must be of a daily, weekly, monthly, quarterly, or yearly frequency. Calculating an investment return using the arithmetic mean is suitable for historical return measurement, but not the projection of the future value of an investment (as it doesn’t take into account the compounding of returns over time).

Arithmetic average return = ∑ Sum of periodic returns/No. of returns (Count of returns)

For example, if we have the following annual returns:

The arithmetic mean return is: [(11%+20%+10%+9%)/4]= 12.5%

**Geometric average return:**

The geometric mean is used to calculate average rate per period on investments that are compounded over multiple periods. The geometric mean is more accurate than arithmetic average return as the former takes into consideration the effect of compounding also.

Geometric Average return = [(1+ TR1) (1+ TR2) … (1+ TRn)] 1/n – 1

TR = Total Return

Example: For instance, consider a Rs.10 stock that increases by 100% to Rs.20 after the 1st year, then declines by 50% in the 2nd year. The average return for the 2 years would be (100% – 50%)/2 = 25%, but the actual return is 0% because the stock is at the same price at the end of the holding period as it was at the beginning.

Geometric return= ((1 + 1) × (1 – .5))^(1/2) – 1 = (2 × .5)^(1/2) – 1 = 1 – 1 = 0%.

**The nominal rate of return:**

The nominal interest rate is the periodic interest rate times the number of periods per year. It is the simple return earned on an investment. For example, A nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal rate without the compounding frequency is not fully defined.

Nominal rates are usually contractual or pre-fixed in nature, for example, the loan rates and the Fixed Deposit rates quoted by a bank.

**The effective rate of return:**

The effective rate of return takes the effect of compounding into account. The higher the frequency of compounding, the higher is the Effective Rate of Interest.

For example, Mr. A makes an investment of Rs.100000 at an interest rate of 10% p.a. compounded monthly. Here the nominal interest rate is 10% whereas the effective interest rate would be 10.47%.

**Real Rate of Return:**

A real rate of return is an interest rate that has been adjusted to remove the effects of inflation and to reflect the real yield to an investor. The real rate of return is an interest rate that is adjusted for inflation. , the real interest rate is a reflection of the change in purchasing power derived from an investment based on the change in the rate of inflation.

**Real interest rate = (1+ Interest rate ) /(1+ inflation rate )-1**

**Post-tax return/Return after tax:**

Return calculated by taking into consideration the effect of expected or paid income taxes into account.

Post-tax return = Nominal Rate * (1-tax rate)

For example: If nominal rate of interest on security is 8%, the individual tax rate is 30% then after-tax return is = 8 (1-0.30) = 8 * 0.7 = 5.6%

**Holding period return:**

The holding period is the time interval that an investment is held. The holding period return is the investment return during the holding period.

Holding Period Return = Income + (End value-Initial value)/ Initial value

Example: Mr A bought 100 shares of stocks A on 3rd Jan 2017 for Rs.120 each. He sold 100 Shares of stocks A on 25th Feb 2018 for a price of Rs.140 each. He also received Rs.250 as dividend during this period.

Holding period return = 2.5+(140-120)/ 120

= 22.5/ 120

= 0.1875

Holding Period Return (%) = 18.75%