Risk and Return in Portfolio Management

In portfolio management risk and return plays a very vital role. With every increase, in return the risk also increases. The investor shall choose the portfolio, which yield a maximum return with the minimum amount of return. In order to reduce the risk from investment in shares, the investor invests in diversified portfolio to combat the risk. In the financial industry, risk measurement plays a vital role. A potential investor has to measure risk while he is investing in market portfolio. Irrespective of the investment in mutual funds, stocks, shares, bond, derivatives, it is important for the investors to determine the unexpected trend of the market or the risk return factor. The big investment firms and the analyst use any tools to measure risk but one of the significant tools is the Standard deviation. Standard deviation measures market volatility (Arnold, 2013).  The more return a portfolio gives the more the risk it carries. Standard deviation measures the risk. It is calculated as subtracting the mean from each value and then summing and squaring the differences to produce the differences.

Statistics, SD, Variance is a useful tool used and is used in finance and economics. In order to calculate the financial data and economic theories the application of probability and statistics is important (Viceira, 2012). In order to determine the investment risk and to find out the risk, which is potent on a particular security, it is important to have the understanding on the measurement of risk using the statistical tools. Correlation coefficient, coefficient of variation is statistical tool, which measures risk per unit of mean return (Baron et al., 2016)

When the person invests in a portfolio, the risk gets reduce even though the return with that respect does not decrease. The portfolio risk consists of both the systematic and unsystematic risk. When an investor buys shares of more than one company, it helps in the overall reduction of risk with a well-diversified portfolio (Hull, 2012). The risk and return from various portfolios depend n various factors such as corporate tax rate, inflation interest and market rate. Some shares are sensitive to the market change than the rest. If an investor invest in shares of different companies then he will be only be affected to the risk of the market that is systematic risk but he will not be affected by the individual sector risk that is the unsystematic risk. Investment in a single share makes the investor affected by both the systematic and the unsystematic risk. A well-diversified portfolio saves the investor from unsystematic risk.

Diversification: A Key to Risk Reduction

In case of efficient portfolio, we need to include the securities having lower risk with a higher return. The total risk measured by using the technique of standard deviation. In case of efficient portfolio we with choose the best portfolio having higher return (Brigham and Houston, 2012).The coefficient of variation is the calculated by dividing standard deviation with mean and multiplied by hundred. If we are to invest in one security out of the efficient portfolio, then we will take decision based on variation. The coefficient of variation indicates the risk per unit of return. Lower the coefficient of variation better is the investment.

The correlation of the two assets depends on the covariance of two assets and the standard deviation of the two securities. The key was not that two stocks provided twice as much diversification as one, but that by investing in securities with negative or low covariance among themselves, we could reduce the risk. Markowitz’s efficient diversification involves combining securities with less than positive correlation in order to reduce risk in the portfolio without sacrificing any of the portfolio’s return. In general, the lower the correlation of securities in the portfolio, the less risky the portfolio will be. In considering a two-security portfolio, portfolio risk is as per the equation defined as:

sp =√

Where,

sp = portfolio standard deviation

 W_A = percentage of total portfolio value in stock

W_B = percentage of total portfolio value in stock

s_A = standard deviation of stock

 s_B = standard deviation of stock

 r_AB = correlation coefficient of X and

When the assets include a riskless asset and another is a risky asset, the combination of two assets will give a linear relationship. A risk free asset is default free and without the inflation risk, that is treasury bills. The risk free asset means that the interest rates of the security or inflation free risk of the security (Brigham and Ehrhardt, 2013). The portfolio will have higher return. In a capital market line, the investor chooses an optimal risky portfolio. We can assume risky asset to be a mutual fund and the return on the assets is termed as R_m. The risk on return on risk free asset will be termed as R_f. The formula of mean and variance is used. The risk free asset is without risk. The return is the same and will be equal to mean. The formula for capital asset pricing model

Role of Statistical Tools in Risk Measurement

This CAPM Model describes a relationship between the beta and the return. Beta risk is that the risk of the market is not diversifiable. Beta is the measurement of systematic risk. In case of risk free security, it is better to lend than to invest. Portfolio of assets, which held by investor, will be same to the portfolio held of risky assets, which is held by other investor. If all investors hold the same risky portfolio, then, in equilibrium, it must be the market portfolio. The market portfolio consists of risky assets. Each of the assets held in the proportion, which the market value of the asset represents to the total market value of all risky assets. All investors thus hold combinations that are of two portfolios, one is the market portfolio and the other is riskless security or risk free security

As per Simon Hoyle, in case of price of baked beans does not change according to the change in price of the shares. If we consider two components such as a tin of baked beans and the share price of a Company. The price of the baked beans is fixed while the price of the shares of the company is volatile. To measure the risk of an asset or the volatility we take into account the standard deviation. Standard deviation is a method used by the analyst to determine the return from the asset.

To plot the standard deviation that is the risk and return on the graph of X-axis and Y-axis. The bell curve gives an explanation. The bell curve portrays the asset’s returns, which is clustered around the numbers. More the certainty for a asset more we can determine the return from the asset. The higher the standard deviation, which means more risky, is the share of the company, the less risky is the shares means the return is average. The share and price of the share will vary and fluctuate but the price of baked in will be same, the risk and return will not affect the price of the asset (Bodie, 2013).

There are two kind risk, systematic risk and unsystematic risk. Systematic risk refers to as the market risk whereas the unsystematic risk is referred o as the company specific risk. Firstly, in case of systematic risk it is not specific to a particular company, sector, but it is associated to the overall market whereas in case of unsystematic risk which is associated with any particular company and sector. Secondly, systematic risk is beyond the control of the management whereas unsystematic risk is within the control of the management. Thirdly, the systematic risk affects all the companies in the market; if one is in the market (Brealey et al., 2012). Unsystematic risk is within the control of the management and the risk affects the company or the particular sector only .Fourthly the systematic risk arises because of the political, economic situation. It arises due to fluctuation in the interest and inflation rates. In case of unsystematic risk arises because of competition in industrial dispute and management issue.

Beta measures systematic risk, it gives the relationship between change in the market index and change in the security prices. If beta is 1.5 then it means if the market changes by 1%, the security and stock prices change by 1.5% in the same direction (Brigham and Daves, 2012).

 References

Arnold, G. (2013). Corporate financial management. Pearson Higher Ed.

Baron, M. D., Brogaard, J., Hagströmer, B., & Kirilenko, A. A. (2016). Risk and return in high-frequency Bodie, Z. (2013). Investments. McGraw-Hill.trading.

Bodie, Z. (2013). Investments. McGraw-Hill.

Brealey, R. A., Myers, S. C., Allen, F., & Mohanty, P. (2012). Principles of corporate finance. Tata McGraw-Hill Education.

Brigham, E. F., & Ehrhardt, M. C. (2013). Financial management: Theory & practice. Cengage Learning.

Brigham, E. F., & Houston, J. F. (2012). Fundamentals of financial management. Cengage Learning.

Brigham, E., & Daves, P. (2012). Intermediate financial management. Nelson Education.

Viceira, L. M. (2012). Bond risk, bond return volatility, and the term structure of interest rates. International Journal of Forecasting, 28(1), 97-117.