29 Nov

# Risk Return & Portfolio Theory | CA Final SFM

**Investment Objectives**

**Rate of Return on “Single Security”**

Present Value of Future Cash Flows

**Rate of Return on “Single Security”**

**Question 1**

**Mr. X is to decide regarding whether he should invest in equity share of NJ Ltd. Expected dividend receivable by year end on share of NJ Ltd. is 45. Expected Market Price of this equity share by year end is 300. The expected rate of return by Mr. X is 25% p.a. Determine the current market price of equity share.**

**Question ****2**

**NJ Ltd. has been showing a consistent growth in the share price as well as dividends in the recent past. Such growth rate is about 10% per annum. Price of this share prevailing today is ` 200 per share. The company is expected to declare a dividend of ` 36 by end of the year. You are required to determine the expected rate of return for the shareholder at present.**

**Average Rate of Return on “Single Security”**

- When the information is available about the individual rate of return of a security over past few years
- The average rate of return of such security can be determined by
__Simple Arithmetic Mean__

**Question 3**

**Determine the average rate of return based on the following data:**

Presently the price of the share is ` 200.

**Average Rate of Return **

**Expected Rate of Return on “Single Security” (In a Probability Series)**

**Consider the example given below:**

**Measurement of ****Risk**

**Measurement of ****Absolute Risk**

**Standard Deviation of Returns of a Security (In a Simple Individual Series)**

**Question 4**

**The following rates of returns have been observed on stock X over past 8 years:**

Determine standard deviation of returns on stock X.

**Standard Deviation of Returns of a Security (In a Probability Series)**

**Question 5**

**The expected returns on stock X are given as below:**

Determine the standard deviation of returns from the above given data.

**Risk Associated with Investment**

While comparing the performance of any security with the other, standard deviation may not always be sufficient for analysing the performance in terms of __Relative Risk__.

In such situation, the performance of two securities can be better compared through measure of relative risk.

**Question 6**

**A stock, costing ` 120, pays no dividends. The possible prices that the stock might sell for at the end of the year with the respective probabilities are:**

**Required:**

- Calculate the expected return.
- Calculate the standard deviation of returns.

**Co-efficient of Variation**

**Example:**

**Question 7**

**Consider the following cases:**

You are required to analyse the above four cases and observe whether standard deviation will be effective tool for decision on selection of one out of the two securities X and Y.

**Case 1:**

Both the securities X and Y have same rate of return but risk of both the securities are different. X has low risk as compared to Y as represented by the standard deviations of both the securities. Between the two, X will be preferred.

**Case 2:**

Both the securities X and Y have same degree of risk, as represented by their standard deviations. Security X offers higher returns as compared to Y. Therefore, X will be preferred.

**Case 3:**

The risk involved in Security X is lower than that of Security Y, as represented by their standard deviations. Security X has higher returns as compared to Y. Security X is preferred from both risk and return view point.

**Case 4:**

Security Y offers higher returns but also has higher risk as compared to X. The standard deviation of Security Y is higher than that of X, indicating high risk. However, simply looking at the risk and returns, it cannot be decided as to which security shall be preferred. A relative measure of risk in the form of coefficient of variation will be required.

**Determining Covariance and Correlation Between Two Stocks**

- Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.
- A positive correlation indicates the extent to which those variables increase or decrease in parallel;
- A negative correlation indicates the extent to which one variable increases as the other decreases.

Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated.

**Note:**

*Covariance Between Two Stocks x and y (In a simple individual series):*

**Question 8**

**Consider the following data about returns of two stocks X and Y:**

You are required to determine the following:

- Average rate of return of both the stocks
- Standard Deviation of returns of both stocks
- Covariance and correlation between two stocks

**Variance of Returns**

**Standard Deviation **

**Determining Covariance between returns of two stocks in Probability Series:**

**Question ****9**

Consider the following data regarding two securities *X* and *Y*:

You are required to determine the following:

- Expected rate of return for Security
*X*and*Y* - Standard Deviation of returns for both the Securities
- Covariance and Correlation between returns of
*X*and*Y*

**Determining Correlation Between Returns of a Particular Stock and Market**

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