**Return analysis on common stock**

Return is the reward of understanding the investment and risk. There are two main types of return (i) It is the periodic cash receipt as a form of interest and dividends. (ii) Next method is appreciation and depression in the price of security in the form of capital gain or loss. So that total return or investment is also the sum of normal gain and capital gain. The main common stock returns are as follows:

- Realized return:

The realized return is also called historical return and past return. Realized return is an annual returns as a percentage of investment and it is easy to calculate. In simple way it is a calculated as ending price of stock add dividends and subtract the beginning price and divide by beginning price.

- Expected return:

It is a forecast of stocks potential return for a year. It is a predicted return not an actual return. It is the investor’s expectation that they will earn over some future period. It is calculated by adding all rate of return for that period and divided by number of rate of return added. The investor invests only after forecast possible outcome in each interval. It is calculated by multiplying of potential earnings by the chances of them occurring, and sum of those results. The expected return is calculated as follows:

E_{HPR} = n∑ t = 1(P_{j }* HPR_{j})

- Single period rate of return:

It is also called holding period return. A single period also called holding period is the total return earned by investor during the period of holding securities. It is based on a 1 year of calculation. It is the difference of ending price over beginning price and adding receipt during the holding period and divide by beginning price. HPR is calculated are as follows:

HPR = Ending price – Beginning Price + Cash receipt / Beginning price

OR

HPR = P_{1}-P_{0}+d_{1}/P_{0}

Where,

P1 = Ending price

P0 = Beginning Price

D1 = Cash receipt or dividend

- Multi-period or annualized return:

It is a return which is earned during the multiple period of holding securities. In case more than one year of holding securities then annualized return is used. For example if someone holds 3 years of securities the annualized rate of return is used for calculation and valuation. It is concerned with time value of money. The annualized return or Annual Percentage Yield (APY) referred to the rate of interest that is earned when taking into consideration the effect of compounding.

Annual Percentage Yield (APY) = (1+r/n)^{n }– 1

- Required rate of return:

The risk free rate represents the time value of money. A risk premium represents compensation for risk, measured relative to the risk free rate. When we decide on a discount rate that reflects both the time value of money and an asset’s risk, as we perceive it, we have determined our required rate of return. A required rate of return is the minimum rate of return required by an investor to invest in as asset, given the asset’s riskiness. Sometimes we refer to the required rate of return for an asset. Generally we use such required rates of return in discounted cash flow valuation. (Equity Asset Valuation, John D. Stowe, 2007, pg. no. 47-48)

Required rate of also called a hurdle rate is a minimum annual percentage income earned by an investment that will induce individuals or companies to put the money into a particular security. It is the minimum rate of return expected by investor by investment into risky assets. The required rate of return on stock using CAPM/SML is calculated by following formula:

Required rate of return (K) = R_{f} + β(r_{m} – r_{f})