Question

1. A. What are the stock market indices? What do they measure? How do we measure stock market’s overall performance? B. What are the EAR and APR? What’s the difference? How to convert APR to EAR under different frequencies of compounding? C. The relation between interest rate and pricing of financial securities. D. What’s the purpose of building investment portfolios? What’s the difference between firm’s specific risk and market risk. Which one is diversifiable? Which risk is systematic? Which one could be reduced by forming portfolio? How does the diversification work, including high or low correlated stocks?

Please explain key points for each.

Answer 1

(A)- A stock market index is a basis used to measure the changes that take place in a stock market over a period of time. It is used to measure market fluctuation. The same is done by taking similar types of listed securities into consideration. The various factors considered while choosing the securities are: type of industry, market capitalisation of the company, P/E ratio, etc.The value of fluctuation of the index is equal the sum total of fluctuations of all these underlying shares. Thus if most of the underlying shares move in an upward direction, so will the index. The same holds true for vice versa.

The measurement of a stock index is done as follows:

That is we find the appreciation of stock index over a period of time. Suppose we want to measure the appreciation in a stock index between 1 Jan 2018 and 31 Dec 2018. This we calculate it as the difference in prices between both the dates and then divide it by Jan 1 price.

(b) APR refers to Annual Periodic Rate and is referred as per month rate of interest to be charged ultiplied by the number of periods. For example- If a car loan has 1% interest per month and the interest is to be paid after 6 months, APR will be 6%. It involves no compounding, but includes other costs, for example in this case it'll be additional costs such as loan fees ,etc.EAR on the other hand refers to APR in which compounding is done.Thu, the difference between these two is APR excludes interest on interest that is compund interest while EAR includes it.Calculation of EAR from APR: can be done by adding compounded interest to APR.

(C)There is an INVERSE relationship between interest on securities and their price. Price is generally equal to the total of net present value of cash inflows expected from the security discounted at the interest rate of securities. Thus any increase in price causes a decrease in interest rate and the same holds true vice versa. For eg: In case of bonds, there is a convex relationship. Thus for every 1% increase in interest, the price rises at a faster rate and for every 1% decrease therein, it falls at a slower rate. The following diagram illustrates the relationship:

(d) The purpose of building of portfolios is to diversify investments. By diversifying investments, the return of the portfolio can be increased. Also the overall risk can be reduced, provided the correlation between the two stocks is negative.

For example when we invest in a security with return=10%, our overall return will be 10% only. However if we invest in 2 stocks one with return 10% and another with 20% Then the overall return on the portfolio will be the weighted average of the 2 stocks, i.e. 15%.

Also risk of the portfolio is given by the following formula:

Thus we must appreciate that if the P₁₂ IS NEGATIVE THAT IS THE CORRELATION BETWEEN TWO STOCKS IS NEGATIVE, THE TOTAL RISK WILL BE LOWER THAN THE WEIGHTED AVERAGE OF THE TWO STOCKS.

-Firm specific risk refers to risk of downward fluctuation in the stock price arising out of an internal event of the firm which is specific to that particular firm in the industry and has no effect on the stock prices of other firms within the same industry.

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- Market risk on the other hand refers to risk of downward fluctuation in the stock price arising out of an external event of the firm which is not specific to that particular firm in the industry and has effect on the stock prices of every firm within the same industry. Market risk is MORE DIVERSIFIABLE.

-Unsystemtic risk can be reduced by forming a portfolio. For example if we have an ice cream company stock, it'll go higher in summers and lower in winters. Now if we make a portfolio by combining it with a sweater company share, the risk that is specific to the firm that is, the unsystematic risk can be reduced thereon. This is because the correlation between the ice cream stock and sweater company stock is nagative, it means that when the ice cream company stock goes up (in summers) the sweater company stock comes down and same happens vice versa. If we form a portfolio of 2 positively correlated stocks (the stocks that move in the same direction), say 2 ice cream company stocks, the risk will not be negated because the portfolio return will go high in summer and low in winter rather than being evenly distributed throughout the year.

Hence in case of NEGATIVELY CORRELATED STOCKS ONLY the overall portfolio risk can be reduced.