Risk and Return in Context to an Individual Asset (With Formula)

Read this article to learn about the concept of risk and return in context of an individual asset and portfolio of assets.

i. Return:

An individual or business enterprise invests money to make earnings there from over a period of time-say a year. If an investment of Rs. 100 is made in a security promising income Rs. 10 a year, the return would be Rs. 10.


Return is always expressed in terms of percentage of earnings on investment. There is another source of return i.e., price appreciation of Rs. 100. Suppose, the security held does not pay any dividends, but at the end of one year, it is sold in the market, it fetches Rs. 110.

The increase of Rs. 10 in value of security during a year constitutes return on investment. Thus, return equals the amount of dividend plus value of security sold. Algebraically, return on an investment can be expressed as below.

where, R = rate of return;


Dt = cash dividend at the end of time period t,

Pt = the price of security at the time period t;

Pt-1 = the price of security at time period t-1

It may be noted that the term in parentheses in the numerator of the above equation represents capital gain or loss. If the price of the security at the end of the period is higher than at the beginning, capital gain is said to have occurred.


On the contrary, capital loss would take place if the ending price were less than the beginning price. Even if capital gain is not realized because the security is not sold, the same should also be taken into consideration while determining return on investments.

ii. Risk:

Risk may be defined as variability of returns that are expected from a given investment. The greater the variability, the riskier the security is said to be and the vice-versa. Investment in Treasury bill carrying 8 percent interest is risk free because of the government guarantee. In contrast, investment in equity shares, which do not assure certainty of return, is risky investment because the cash dividend that is anticipated may or may not materialize.

Some shares are riskier than others and even in years when overall stock market buoys up, many individual shares register decline in price. Therefore, putting all your money in one share is extremely risky. Risky assets rarely fetch the expected rate of returns. They earn either more or less than was originally expected. Investment risk, then, is related to the probability of actually earning a low or negative return. The higher the probability of earning low or negative return, the riskier the investment.

No investment should be undertaken unless the expected rate of return is high enough to compensate the investor for the perceived risk of the investment. It is, therefore, necessary to measure degree of risk associated with the investment.


Riskiness of an investment can be assessed with the help of probability distribution. Probability of an event is the likelihood of occurrence of an event. If an investor invests in a stock, there is 60 percent possibility that it will fetch dividend @ 15 percent at the year-end, 20 percent possibility to get dividend @ 10 percent.

If these possible outcomes are listed, the listing is called probability distribution. This probability distribution can be summarized with reference to the expected return and the standard deviation, as shows in Table 5.1 Expected.

Probability Distribution of the Rate of Return on Stock

Return is simply a weighted average of the possible returns, with the weights being probabilities of occurrence, thus, the expected return R is:

where, Ri is the return for ith possibility,

Pi is the probability of that return occurring and

n is the total number of possibilities.

The expected return in the above case is 17 percent.

To be more precise and clear, we need a definite value a measure of the dispersion or variability around our expected return. One such measure is the Standard deviation (0). The higher the standard deviation of returns, the greater is the riskiness of an investment.

The standard deviation can be algebraically expressed as:

Where √ represents the square root. The square of the standard deviation, σ2, is termed as the variance of the distribution. Operationally, variance of probability of distribution is first computed and then the square root of this figure provides us with the standard deviation.

Table 5.1. shows our example distribution’s variance to be .0297. Taking the square root of this value, we find that the distribution’s standard deviation is .172. Thus, the standard deviation is basically a weighted average of the deviations from the expected value, and it provides insight into how far above or below the expected value the actual value is likely to be.

Where a probability distribution is normal, the actual return will be ±1 standard deviation of the expected return as 68.26 percent of the time. Fig. 5.1. explains this point and also shows the situation for ±2.0 and ± 3.0.

Probability Ranges for a Normal Distribution

iii. Coefficient of variation:

Standard deviation measuring dispersion of expected return can help an investor to make a choice between two or more investment alternatives. For instance, an investor would go for an investment having lower standard deviation over the one with higher standard deviation but the return remaining the same.

Investors invariably want as much return and as little risk as possible. But the pertinent issue plaguing an investor is which one of the two investments he should choose if one has the higher expected return while the other lower standard deviation. Likewise, problem arises where alternatives differ in size.

For instance, there are two projects, X and Y, having normal probability distributions of one-year returns, with the following characteristics:

Expected Return and Standard Deviation of Two Projects

On the basis of standard deviation, we can erroneously conclude that project Y is more risky than project X. However, in relation to the size of the expected return, project A has a greater variation. Thus, to assess the magnitude of risk of projects, the size of the project needs to be adjusted. For this purpose, another statistical technique will have to be used.

This technique is ‘Coefficient of Variation’ (CV) which is computed by dividing standard deviation by the expected return:

With the help of CV, an investor can precisely surmise the risk per unit of return and can thereby compare the expected returns on the two alternate projects to reach more logical decision. The higher the CV, the larger the relative risk of the investment. Using the CV as the risk measure, project A with a return distribution CV of .66 is considered as being more risky than project B, with CV of 0.33.

iv. Risk Averse and Required Returns:

Most of the investors are risk averse and certainly the average investor is risk averse with respect to his/her money. An investor is risk averse if he chooses less risky investment. Risk aversion has implications for security prices and rates of return. Other things being the same, the higher security’s risk accompanies lower price and higher required return.

To explain the effect of risk aversion on security prices, let us assume company X and Y’s stock sold for Rs. 100 per share and each had an expected rate of return of 20 percent. Investors are risk averse. They would go for X’s stock because of its less risk and start selling Y’s stock to buy X’s stock. This will result in risk in price of X’s stock and decline in price of Y’s stock.

Price changes in stocks of the two companies would lead to change in the expected rates of return on these securities. For example, X’s stock was bid up from Rs. 100 to Rs. 10, while Y’s stock price declined from Rs. 100 to Rs. 75. As a result, the X’s expected return would decrease to 10 percent, while Y’s expected return would rise to 20 percent. The difference in returns, 20%—10% = 10%, is a risk premium (RP). RP represents the additional compensation investors require for assuming the additional risk of Y’s stock.

Thus, risky investments in a market dominated by risk-averse investors, must offer higher expected returns than less risky investments so as to entice people to buy and hold them. Investors seeking low risk must be willing to accept lower return. Thus, there is no free lunch when it comes to investments. If this situation does not occur, buying and selling in the market will force it to occur.

Since the utility score for B is higher than A, the investor would go for it.

1. Renault Manufacturing Ltd. forecast returns on its share with the following probability distribution:

Calculate the expected return for Renault


Expected Return

2. The following information are available for two companies:

(a) Compute the correlation between the two shares

(b) What is the expected return and risk of a portfolio in which X and Y have been combined in equal proportions?


(a) Correlation (r) = Covariance of x and y/σx σy

= 120/(10 × 10) = 1.20

(b) Expected return = W × X return x + Wy X return y

=0.5 × 20% + 0.5 × 25% = 22.5%

(c) Risk (0) = (W2X02 + W2 y02 y+2PXyWX0X, Wy0y)1/2

= [(0.5 X 20%)2 + (0.5 X 25)2 + 20 X 120%]1/2

= (100 + 193.75 + 240)1/2

= 23%

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