In the previous note on the lecture series of financial institutions and markets, we have understood what risk is in the financial system and how to measure it. This note will cover what return is and how to compute expected returns from the financial system.
What is Return?
Whenever we put our money, time, effort, etc., we hope to get certain benefits or gain that we call the return or reward of investment in layman terms. These returns may be in the form of monetary or non-monetary terms that depend on where we are investing.
Return is the amount or rate of produce, proceeds, gain, profit which accrues to an economic agent from an investment. It is a reward for and a motivating force behind investment and the broader objective of the investor is usually to maximise return.
Investment is always associated with risk because we may not get the return or lose the entire capital. However, we still put the money on the financial system with the hope of getting a better return with minimum risk.
Return Components
Whenever we talk about returns specifically when invested in the financial market, so return on a typical investment has two components:
- the periodic cash or income receipts, either interest or dividend. The income component is usually but not necessarily received in cash viz., stock divident.
- the appreciation or depreciation in the price or value of the asset, called the capital gain or the capital loss. The capital gain (or loss) is the difference between the purchase price of the asset and the price at which it can be or is sold.
The total return on an investment thus can be defined as income plus/minus price appreciation/depreciation.
For example, suppose we purchased a stock A at Rs. 500 and after one year, it becomes Rs. 750. So the net capital gain is 750-500 = 250. In terms of percentage: (250/500)* 100 = 50%. We can see that the net return is 50% within a year. In the above example, there is no income component as a company has not given any dividend, and the actual component is stock value appreciation.
Types of Return Concepts
The types of return concepts exist for the different kinds of instruments. For example, stocks, bonds, derivatives, etc., In this section will discuss the types of return concepts in general. However, in the forthcoming sections, we will discuss different return concepts based on a particular kind of instrument.
Expected Return
It is an anticipated, predicted, desired, ex-ante return that is subject to uncertainty. Here expected return is probable as there is an uncertainty associated with the return.
Realised Return
At the investment time, we can expect a certain percentage of returns based on a specific probability distribution computed from the historical data. However, realized return is the actual earning at the withdrawal of the invested amount.
Holding Period Return (HPR)
It measures the total return from an investment during a given or designated period in which the investor holds the asset. There are two things: Holding Period Yield (HPY) and Holding Period Return (HPR). HPR = HPY + 1.
HPY is defined as the sum of any cash payments received and price change over the holding period divided by the price at which the asset is purchased at the beginning.
- Any cash payment is related to dividends
- The price change is related to how much price is appreciated or depreciated during the holding period.
- The actual cost of the instrument
Nominal return
Nominal return is the return in nominal rupees. For example, suppose we purchased a stock A at Rs. 500 and after one year, it becomes Rs. 700. So the net capital gain is 700-500 = 200. In terms of percentage: (200/500)* 100 = 40%. We can see that the nominal return is 40% within a year.
Real Return
Real return is equal to the nominal return adjusted for changes in prices. i.e., the rate of inflation. The relation between nominal and real return is defined as: (1+ Nominal Return) = (1 + Real Return) + (1 + Inflation Rate)
Inflation is defined as the price adjusted for changes in the price level. So the nominal return has to be adjusted for the market’s price level or inflation rate. As we know, that price value gradually depreciates as time goes. For example, ten years ago (in 2010) average price for a 2BHK apartment was 50L, and currently, it touches 1CR. We can easily see that price power has depreciated.
Real return = Nominal return – Inflation rate
Required Rate of Return (RRR)
The required rate of return is more or less similar to the expected return. RRR needed to pursue when the investors purchased the security given its risk. It is like they are hoping to take the risk in the market to get the expected returns. It motivates the investor to participate in the financial system.
It is defined as the minimum expected rate of return needed to induce or persuade an investor to purchase the security, given its risk. It has two components. First, the risk-free rate of return and second, the risk premium.
The risk free instruments example are government treasury bills and government bonds. These kinds of instruments are free from defaultery and also probably risk free.
RRR = Risk-free rate of return + Risk premium
Where Risk premium as a function takes input as macroeconomic fundamentals, industry specific variables, and company specific variables.
Risk premium = f(macroeconomic fundamentals, industry specific variables, company specific variables)
The risk premium means the additional risk or return expected from the market. The risk can arise due to change in the macroeconomic fundamentals, like inflation, growth of GDP, change in monetary policy, etc.
For example, suppose the Reserve Bank of India changes the monetary policy. They decided to change the interest rate, i.e., the repo rate has to increase. As a result, and cascading effect, call money rate will change, banking lending rate will change, the market interest rate will change, the money supply in the system will change, and effectively there will be the impact on total investment. And finally, the output will change. Here output means the price of a security and the other instruments. So this way, we can see that any changes in the macroeconomic impact the market, and either it may increase or decrease the risk.
Industry-specific variables are like some industries are seasonal and cyclic, or impact due to oversupply of goods, shortage of goods and raw material, etc.
Company-specific variables are like changes in the internal management, policies, etc.
Calculation of RRR (Capital Asset Pricing Model)
The Capital Asset Pricing Model (CAPM) is used in finance to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset’s non-diversifiabile risk. The model takes into account the asset’s sensitivity to non-diversified risk (also known as systematic risk or market risk), ofter represented by beta (
).
The CAPM can be represented in equation as follows:
Where, 
is expected return of individual security, 
is a risk-free rate of return, represents market risk of individual security, 
represents market return.
Testing CAPM
According to Capital Asset Pricing Model (CAPM) the market risk is the sole factor which determine the expected return of the stock, which is used as the cost of equity of the company. For testing the validity of CAMP, generally we follow a two step procedure.
Step 1: Run the time series regression to estimate the market risk following the equation:
Where, 
is expected return of individual security, and represents market return.
Step 2: After getting the for each company/portfolio we run a cross sectional regression to examine whether is statistically significant and for this, we have used the function,
Where, 
is premium: if the will be statistically significant, then we can conclude that gives the premium and the CAPM holds good.
References
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