Introduction
In this article I will examine the effect that risk has on the investment choices of investors, the return the investors will require on their investment and how securities are priced in the stock market or how to value shares of a particular company listed in the stock exchange.
If a person is a financial manager of a company an understanding of the above mentioned concepts is necessary when investing in securities. As well, it is also necessary because the return required by investors affects a companies cost of capital which in turn affects decision concerning capital structure, capital budgeting and working capital management.
Return on Investment
Rate of return comprises two elements. They are dividends or interest received by investors and increase or decrease in the market price of the security.
To calculate the return on investment the total return is divided by the market price at the beginning of the year.
If R= rate of return in investment
P1= Market price of security end of year
P0= Market price of security at the beginning of the year
C= cash flow of dividend or interest income
Then R= P1-P0+C/P0
Say a company A declared a dividend of 17 cents per share during the year. Its share price at the beginning of the year was 1.60 and at the end of year was 1.67 then one can calculate the return on investment. Applying the formula as above the rate of return on investment is (1.67-1.60+0.17)/1.60=0.15 or 15%.
In situations where return on investment is calculated for a period less than a year and it is required to express the return as a nominal annual rate it is necessary to vary the return on investment by multiplying the above equation for the rate of return on investment by the number of periods within a year. Say the number of periods is N then the rate of return on investment R= (P1-P0+C)*N/P0.
Say company A declared dividends in June and December 15 cents and 10 cents respectively. The quarterly stock prices are 1.25, 1.28, 1.27, 1.24 and 1.30. Then applying the adjusted formula in can calculate nominal annualized rate of return on investment for the four quarters as follows.
- 1st Quarter return on investment R= (1.28-1.25+0)*4/1.25 = 0.096 or 9.6%
- 2nd Quarter return on investment R= (1.27-1.28+0.15)*4/1.28=0.4375 or 43.75%
- 3rd Quarter return on investment R=(1.24-1.27+0)*4/1.27=-0.94 or -9.4%
- 4th quarter return on investment R= (1.30-1.20+0.10)*4/1.24=0.516 or 51.6%
Risk
Return on all investments is uncertain. As a result investors are exposed to a degree of risk. Risk will have the effect of lowering the price of a company's shares because investors expect higher returns on investment to compensate for exposure to risk. Risk is measured by standard deviation of the expected return. Say a company has the following returns and the possibility of such returns measured by probability Say the possible returns are .02, .07, .12, .27 and .22 and the respective probabilities of such returns are 0.10, 0.25, 0.30, 0.25 and 0.10. For this company the expected return is the mean of the above distribution of returns. It can be calculated by calculating the sum of the product of probability and the returns. In this instant, the expected return is equal to (0.12*0.10+0.07*0.25+0.12*0.30+0.17*0.25+0.22*0.20). That is the expected return is 0.12 or 12%. The standard deviation of the possible returns is calculated by the square root of deviations of the respective returns from the mean times the probability. In this
Instant, the standard deviation is equal to [(0.02-.12)2*0.10+ (0.07-0.12)2*0.25+ (0.12-0.12)2*0.30+ (0.17-0.12)2*0.25+ (0.22-0.12)2*0.10]. There fore the standard deviation of the expected return for this company is 0.057 or 5.7%. If any investor wants to reduce risk then the investor can invest in unrelated securities so that it is likely that the returns from different investments will move to a smaller or greater extent in opposite direction and this can have an effect of smoothing out the returns of the port folio. This will reduce the standard deviation and therefore risk compared to investing in only one type of security. That is the diversification will reduce the unsystematic or the risk inherent to the securities by the smoothing effect. That is a financial manager must invest in shares which are unrelated and choose the number of shares and the proportion so that it can eliminate all the unsystematic risk closer to zero. This called an optimal portfolio given the risk preference of the investor.
