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# 1. What is return?

The annual return a person gets in an investment expressed as a percentage of the total amount invested is called Return.

# 2. What are the components of return?

Capital Gains and Yield together combine to make returns for an investor.

Capital gain: When there is appreciation in the price of the asset it is capital gain. There can also be depreciation in the price of the asset then it is called capital loss.

Yield: The most common form of return for an investor is called yield. Such as interest from bonds or dividends from stocks.

# 3. Total Return

It refers to the sum of all the returns earned in a given time period.

Total Return = Yield + Price change

TR = [Dt + (Pt – Pt-1)]/ Pt-1

Where, TR = Total return

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Dt = dividend received in cash at the end of time period t

Pt = Price of stock at time period t

Pt-1 = Price of stock at time period t-1

Example

Ram purchased a stock for Rs 5,000. At the end of the year the stock is worth Rs 6,500. If ram was paid a dividend of Rs. 250 then calculate the total return received by ram.

Solution

Using above formula

Total return = [250 + (6,500 – 5,000)]/5,000

= 0.35 or 35%

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# 4. Expected Return

It refers to the weighted average of possible returns with the weights being the probabilities of occurrence. This is because the amount an investor expects can vary as there are many possibilities.

E(R) = ∑ X*P(X)

Where X means the various values of return and P(X) means the probability of various returns.

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Example

Suppose, if you know an investment has 40% chance of earning return of Rs 10, 30% chance of earning return of Rs 20 and 25% chance of bearing a loss of Rs 10. Then what is the expected return?

Solution

Using above formula

Total return = (10*0.4) + (20*0.3) + (-10*0.25)

= 7.5

# 5. Relative Return

It is the difference between absolute return achieved in the investment and the benchmark return achieved or set up for the same investment.

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Example

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The benchmark return for XYZ stock is 10% for a given time period, whereas you earned a return of 6% on the same stock in the same time period.

So the relative return for you is 6% - 10% which is -4%. And XYZ stock didn’t give the same return as expected.

It refers to the returns on an investment after removing the effect of inflation. And hence is also called Real rate of return.

Inflation adjusted return = (1+Return)/ (1+Inflation rate) -1

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Example

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Return on an investment is 8% and the current rate of inflation is 5%. Calculate inflation adjusted return?

Solution

Using above formula

Total return = (1+0.08)/ (1+0.05) -1

= 1.0285 -1

= 0.0285 or 2.85%

# 7. Alternate Return

It refers to a simple approximation of inflation adjusted return which means it is calculated by simply subtracting the inflation rate from the rate of return on an investment.

Example

Return on an investment is 8% and the current rate of inflation is 5%. Calculate Alternate return?

Solution

Simply Rate of return – inflation rate

= 8% - 5%

= 3%

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1. # Return Concepts

• Actual return – It is the realized return or ex post facto return.

• Expected return – It refers to ex ante or predicted return. These are based on probability.

• Required return – It refers to return for compensation for time and risk.

According to theory Expected return is equal to required return, if security price is equal to its fair value and if expected return is not equal to required return, security is mispriced.

While making an investment decision always buy a security if expected return > required return. Greater than sign is due to margin of safety.

# 1. Measures for Return

Few measures for realized return are as follows:

• Holding period return: It refers to total return or annualized return

• Return relative and cumulative wealth index

• Average return over multiple periods: It is a statistical measure which involves arithmetic mean and geometric mean (which involves time weighted return).

• Real life factors which impact such as inflation, taxes and exchange rates: Inflation includes real v/s nominal return, then taxes on income /dividend and capital gains and impact of exchange rates for international investments.

Estimation of expected return

• Expected holding period return is based on target price

• Expected return based on probability distribution of return

# 2. Holding period return

It refers to total returns one gets on holding an asset or portfolio of assets over a long period of time. It is expressed in terms of percentage.

HPR = [(P1 – P0) + C]/ P0

Where P0 is the price of the asset at the beginning of the holding period (or simply the purchase price of the asset), P1 is the price of the asset at the end of the holding period, C is the cash flow to the investor during the period (dividend paid on share/interest paid on bonds)

Further the formula becomes => P0 = (P1 + C)/(1+R)

(P1 + C) = P0(1+R)

Now if r denotes annual return and t denotes holding period in years then

(1+HPR) = (1+r)t

HPR= (1+r)t - 1

R = (1+HPR)1/t - 1

And real return = [(1 + Nominal return)/(1 + Inflation)] – 1

Another formula for HPR is when an investor holds an investment for T years and the return for 1st year is R1 and so on. Then

HPR = (1+R1)* (1+R2)*…….* (1+RT) - 1

Example

Suppose an investment in ABC Company gives returns of 20%, 10%, -5%, 10% in 1st, 2nd, 3rd and 4th year respectively. Then calculate the holding period return?

Solution

Using above formula

HPR = (1+ 0.20)*(1+ 0.10)*(1 – 0.05)*(1 + 0.10) – 1

= (1.20)*(1.10)*(0.95)*(1.10) – 1

= 0.3794 or 37.94%

# 3. Average Returns

• Arithmetic average return – It refers to return earned in an average period over multiple periods.

Arithmetic average return = (R1+R2+……+RT)/T

• Geometric average return – It refers to average compound return per period over multiple periods.

Geometric average return => (1+Rg)T = (1+R1)* (1+R2)*…….* (1+RT)

• The geometric average will be less than the arithmetic average unless all the returns are equal.

• Which one among arithmetic and geometric mean is better?

The arithmetic average is overly optimistic for long horizons whereas the geometric average is overly pessimistic for short horizons. So one should use both the measures wisely.

Example

Suppose an investment in ABC Company gives returns of 20%, 10%, -5%, 10% in 1st, 2nd, 3rd and 4th year respectively. Then calculate the holding period return?

Solution

Using arithmetic average return formula

AAR = (20% + 10% - 5% + 10%)/4

= 8.75%

Using geometric average return formula

(1+Rg)4 = (1+ 0.20)*(1+ 0.10)*(1 – 0.05)*(1 + 0.10)

Rg = 4√[(1.20)*(1.10)*(0.95)*(1.10)] – 1

Rg = 0.0837 or 8.37%

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# 1. Risk

Risk refers to the probability of variability between the expected and actual returns in an investment.

# 2. Total Risk

Total risk is simply summation of Systematic and unsystematic risk where systematic risk refers to the variability of return on stocks or portfolios associated with changes in return on the market as a whole and unsystematic risk refers to the variability of return on stocks or portfolios not explained by general market movements. Unsystematic risk can be avoidable through diversification of investment in a portfolio.

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Total Risk = Systematic Risk + Unsystematic Risk

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# 3. Concepts of Risk

All investments are risky, in whichever sector you make for example stock market, banking and financial sector, real estate, derivatives, gold, etc. The degree of risk however is based on different assets, investment instruments, and the mode of Investment Even the so called riskless assets like-bank deposits carry some cost at the time of realization of proceeds or in conversion into cash. While systematic risk is common to all companies and has to be borne by investors and compensated by the risk premium. Whereas the unsystematic risk can be reduced by the investor through proper diversification and planning a proper investment strategy for the purpose.

# 4. Systematic Risk

It arises on account of the economy-wide uncertainties and the tendency of individual securities to move together with changes in the market. It is also known as market risk. It arises out of external and uncontrollable factors, such as the market, nature of the industry, economy and other factors. These risks cannot be uncontrollable by an individual.

Examples of systematic risk

Market risk:-

• This arises out of changes in demand & supply which create pressure in the market.

• The totality of investor perception and subjective factors influence the events in the market which are unpredictable and non-controllable.

Interest Rate Risk:-

• The return on investment depends on the interest rate received on it and changes in market rates of interest from time to time.

• This interest rate depends on the nature of instrument, stocks, bonds, etc. maturity of the periods and creditworthiness of the issuer of security.

Few other examples of systematic risk can be governmental changes in the interest rate policy, increase in inflation, changes in monetary policy by RBI, government changing the foreign exchange rates, government withdrawing tax on dividend payments by companies and others.

# 5. Unsystematic Risk

Unsystematic risk arises from unique uncertainties of individual securities. These uncertainties are diversified if a large number of securities are combined to form well-diversified portfolios. It is also known as a unique risk. It arises out of known and controllable factors, internal to the issuer of the securities or companies. These risks can be controllable.

Examples of unsystematic risk:--

• This is related to the variability of the business, sales, income, and profits etc. which in turn depend on market condition for a product.

• This risk sometimes is external to the company such as due to changes in government policy, change in strategies of competitors.

Financial Risk:-

• This is related to a method of financing, adopted by companies like delayed receivables and fall in current assets.

Few other examples of unsystematic risk are company workers declaring strike, any top management personnel leaving the organization, company losing any important contract, any lack in technological advancement, issue in procurement of raw material and others.

Purchasing power risk refers to risk which arises due to inflation or rise in prices leading to rise in cost of production, lower margins, wage rise etc. The return expected by investors will change due to change in real value of returns.

# 7. Insolvency Risk

Insolvency risk refers to risk arising due to the borrower becoming insolvent or in future may default, or delay the payments due, such as interest installments or principal repayments. In such cases, the investor may get no return or negative return.

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# 1. Beta

Beta is a measure of the volatility, or systematic risk, of an individual security or a portfolio in comparison to the market as a whole. In other words, beta gives a sense of a stock's market risk in a particular stock or a group of stock compared to the whole market. Beta is also used to compare a stock's market risk to that of other stocks. Investment analysts use the Greek letter 'ß' to represent beta. Beta is used in the capital asset pricing model (CAPM) which is a very important tool in valuation of a business.

# 2. What changes the Beta?

The beta of a firm is determined by three variables:

• The degree of operating leverage in the firm

• The firm’s financial leverage.

# 3. Historical Market Beta

It is calculated using regression analysis, and it can be said as the tendency of a security's returns to respond to swings in the market. The standard procedure for estimating betas is to regress stock returns (R) against market returns (RM). So R = a + b(RM)

where a is the intercept and b is the slope of the regression.

• A beta of 1 indicates that the security's price will move with the market.

• A beta of less than 1 means that the security will be less volatile than the market. For example, if a stock's beta is 0.9, it's theoretically 10% less volatile than the market.

• A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market.

# 4. Historical Beta variables

Firstly decide on an estimation period

• Services use periods ranging from 2 to 5 years for the regression

• Longer estimation period provides more data, but firms change

• Shorter periods can be affected more easily by significant firm specific event that occurred during the period

Then decide on a return interval for example daily, weekly, monthly. Usually shorter intervals yield more observations, but more noise.

Then estimate returns (including dividends) on stock using formula

Return = (PriceEnd - PriceBeginning + DividendsPeriod)/ PriceBeginning

Included dividends only in ex dividend month

Lastly choose a market index, and estimate returns (inclusive of dividends) on the index for each interval for the period.

# 5. Types of Beta

The various types of betas are as follows:

• Negative beta - A beta less than 0 - which would indicate an inverse relation to the market - is possible but highly unlikely. Some investors used to believe that gold and gold stocks should have negative betas because they tended to do better when the stock market declined, but this is not always true and it hasn't been proved yet.

• Beta of 0 - Basically, cash has a beta of 0. In other words, regardless of which way the market moves, the value of cash remains unchanged (given no inflation).

• Beta between 0 and 1 - Companies with volatilities lower than the market have a beta of less than 1 (but more than 0).

Beta of 1 - A beta of 1 represents the volatility of the given index used to represent the overall market against which other stocks and their betas are measured. The S&P 500 is such an index. If a stock has a beta of 1, it will move the same amount and direction as the index. So, an index fund that mirrors the S&P 500 will have a beta close to 1.

• Beta greater than 1 - This denotes a volatility that is greater than the broad-based index. Many companies in the technology sector on the NASDAQ have a beta higher than 1.

• Beta greater than 100 - This is impossible as it essentially denotes a volatility that is 100 times greater than the market. If a stock had a beta of 100, it would be expected to go to 0 on any decline in the stock market. If you ever see a beta of over 100 on a research site, it is usually either the result of a statistical error or a sign that the given stock has experienced large swings due to low liquidity, such as an over-the-counter stock. For the most part, stocks of well-known companies rarely have a beta higher than 4.

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