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.

Say a person want to invest in A Ltd and B Ltd shares fully or 50% in shares of A Ltd and 50% in the shares of B Ltd. In the boom state of the economy A Ltd has a return of 0.30 with a probability of 0.30 and B Ltd with the same probability has a return of 0.10.

In a normal state of the economy A Ltd has a return of 0.15 with a probability of 0.40 and B Ltd has return of 0.12 with the same probability. In a recession of the economy A Ltd has return of -0.09 with the probability of 0.30 and B Ltd has a return of 0.09 with the same probability. By applying the same process as above one can calculate the expected return and standard deviation of A Ltd and B Ltd and for the portfolio of A Ltd and B Ltd together.

Applying the equation for expected return and standard deviation Expected return of A Ltd is equal to [ (0.30*0.30) + (0.4*0.15) + (0.3*-0.09)] =0.123. The standard deviation of A Ltd returns is equal to square root of [0.3*(0.3-0.123)2 + 0.4*(0.15-0.123)2+0.3*(-0.09-0.123)2]. That is the standard deviation of A Ltd returns is equal to 0.153.

In the same manner the expected return of B Ltd is equal to [(0.30*0.1) + (0.4*0.12) + (0.3*0.09)]. That is the expected return of B Ltd is 0.105. The standard deviation of B Ltd shares is equal to square toot of [0.3*(0.1-0.105)2+0.4*(0.12-0.105)2+0.3*(0.09-0.105)2]. That is the standard deviation of B Ltd shares is equal to 0.0128.

If one considers the portfolio of A Ltd and B Ltd shares the weighted average standard deviation is equal to (0.153*0.5) + (0.0128*0.5) = 0.0829. However if one calculates the expected return and standard deviation of the portfolio of A Ltd and B Ltd shares applying the original equation expected return will be equal to [ 0.3*0.5*(0.3+0.1) + 0.4*0.5*(0.15+0.12) + 0.3*0.5*(-0.09+0.09)]. That is the expected return of the portfolio is equal to 0.114. The standard deviation of the portfolio of A ltd and B Ltd in the proportion of 0.5 in A Ltd and 0.5 in B Ltd is equal to square root of [0.3*(0.2-0.114)2+0.4*(0.135-0.114)2+0.3*(0-0.114)2]. That is the standard deviation of the portfolio is equal to 0.0793. The above calculation shows that the standard deviation of the portfolio is less than the weighted average of the standard deviation of A Ltd and B Ltd calculated separately and weighted in proportion of 0.5 of A Ltd shares and 0.5 of B Ltd shares. This is because the returns on the shares do not increase or decrease at the same rate. That is they are not perfectly correlated. Therefore it can be said an investors risk can be reduced by investing in both companies rather than in just A Ltd or B Ltd.

This can be graphically represented if one draws a graph of time against the return on investment individually and in port folio of 0.5 of A Ltd and 0.5 of B Ltd shares. The graph is as follows.

Graph of separate returns of A Ltd shares and B Ltd shares

Graph of Returns from Investing Half In Shares A and Half in Shares B

From the above graph it is obvious by investing in a portfolio of shares an investor can minimize the risk. That is if an investor invest in different shares which are not perfectly correlated it has the effect of minimizing the unsystematic risk to zero. That by diversifying the investment in different shares in different proportion given the investors investment preferences can minimize risk and also can increase the returns.

Return on investment

A

B

Time

Return on investment

Time