## The objective of portfolio theory

Diversification of risk is a process that captures the reduction of risk through the allocation of investment among diverse financial instruments or categories. A diversified portfolio is accompanied by high returns. Research by Besley and Brigham (2007) shows that diversification helps to reduce unsystematic risk. Lawsuits, loss of key personnel, and strikes are some of the diversifiable risks that could be reduced by diversification.

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Risk is the chance that an investor will receive an outcome that is different from the expected. It means that there exists variability in outcomes from an investment. A risk of an investment can thus be measured by the variability of all outcomes from an investment. In summary, a risk is viewed as the possibility of earning a particular return that is different from the expected one. When variability is high, risk will also be high. On the other hand, return is the weighted average of outcomes. The weight of each outcome is given by the probability of occurrence. Risk and return are related in the sense that when risk is high, there is a probability of getting higher return. Similarly, a lower risk has a low anticipated return.

Co- insurance entails the spreading of risk among different parties.

Portfolio return is measured by calculating change in portfolio value and adding income generated by an investment. If there were no additions or withdrawals from an investment portfolio, return on a portfolio would be determined through calculation of percentage change in value of a portfolio i.e.

Standard deviation of return is the most common instrument used to measure risk on a portfolio. Distribution of returns around the mean is the standard deviation. The other tool used to measure risk is beta, which gives stock price volatility compared with the general market. A portfolio with a beta that is higher than 1.0 is considered riskier and has higher potential return in the market. Conversely, a portfolio with a beta lower than 1.0 is less risky and yields lower returns. Thirdly, portfolio risk is measured using alpha, which gives the volatility of a stock with reference to a particular nature of a security. The final instrument for measuring risk is Sharpe ratio. It is the incremental reward that is realized from taking up more risk. When the Sharpe ratio is high, the portfolio has greater potential.

## Difference between volatility and beta

Volatility is a measure of dispersion of returns around the mean value (Dowd, 2007). In reality, volatility is the uncertainty surrounding change in value of a security. When volatility is high, the value of a security can occupy a wide range of values hence the price of a security can change drastically within a short period. From the definition above, it can be concluded that volatility is measured using standard deviation. Volatility is affected by several factors including economic uncertainty, trading activity, and government action or inaction.

Beta is a measure of how returns on a specific stock move with change in stock market (Cheng-Few and John, 2010). It measures volatility of an investment relative to the market as a whole. The tool is applied in CAPM model to find expected return i.e.

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*Expected return = risk free rate + market beta * equity risk premium*

In the equation, expected return depends on the value of beta. Beta is affected by the type of business as well as level of operating and financial leverage of a firm. Beta is the best estimator of risk because it measures volatility of stock relative to market.

## Reference List

Besley, S & Brigham, E 2007, *Essentials of Managerial Finance*, South-Western Cengage Learning, Mason, OH.

Cheng-Few, L & John, L 2010, *Handbook of Quantitative Finance and Risk Management*, Springer, New York.

Dowd, K 2007, *Measuring Market Risk*, John Wiley & Sons, Chichester.