Question

Discuss the basics of risk return analysis in the financial context and the statistical tools we use to analyze risk and return.

Discuss how we can use this data to structure a portfolio and

how we compute both portfolio return and portfolio risk and how diversification reduces overall portfolio risk

Answer 1

basics of risk return analysis in the financial context

In investing, risk and return are highly correlated. Increased potential returns on investment usually go hand-in-hand with increased risk. Different types of risks include project-specific risk, industry-specific risk, competitive risk, international risk, and market risk. Return refers to either gains and losses made from trading a security.

The return on an investment is expressed as a percentage and considered a random variable that takes any value within a given range. Several factors influence the type of returns that investors can expect from trading in the markets.

standard deviation,value at risk(var)and  beta are the two well-known statistical tools that are used for risk analysis

Standard Deviation

Standard deviation measures the dispersion of data from its expected value. The standard deviation is used in making an investment decision to measure the amount of historical volatility associated with an investment relative to its annual rate of return. It indicates how much the current return is deviating from its expected historical normal returns. For example, a stock that has high standard deviation experiences higher volatility, and therefore, a higher level of risk is associated with the stock

Beta

Beta is another common measure of risk. Beta measures the amount of systematic risk an individual security or an industrial sector has relative to the whole stock market. The market has a beta of 1, and it can be used to gauge the risk of a security. If a security's beta is equal to 1, the security's price moves in time step with the market. A security with a beta greater than 1 indicates that it is more volatile than the market.Conversely, if a security's beta is less than 1, it indicates that the security is less volatile than the market. For example, suppose a security's beta is 1.5. In theory, the security is 50 percent more volatile than the market.

Value at Risk (VaR)

Value at Risk (VaR) is a statistical measure used to assess the level of risk associated with a portfolio or company. The VaR measures the maximum potential loss with a degree of confidence for a specified period. For example, suppose a portfolio of investments has a one-year 10 percent VaR of $5 million. Therefore, the portfolio has a 10 percent chance of losing more than $5 million over a one-year period.

During the process of constructing the optimal portfolio, several factors and investment characteristics are considered. The most important of those factors are risk and return of the individual assets under consideration. Correlations among individual assets along with risk and return are important determinants of portfolio risk. Creating a portfolio for an investor requires an understanding of the risk profile of the investor

how to compute portfolio risk and return

i. Portfolio Return:

The expected return of a portfolio represents weighted average of the expected returns on the securities comprising that portfolio with weights being the proportion of total funds invested in each security (the total of weights must be 100).

The following formula can be used to determine expected return of a portfolio:

Applying formula (5.5) to possible returns for two securities with funds equally invested in a portfolio, we can find the expected return of the portfolio as below:

ii. Portfolio Risk:

Unlike the expected return on a portfolio which is simply the weighted average of the expected returns on the individual assets in the portfolio, the portfolio risk, σp is not the simple, weighted average of the standard deviations of the individual assets in the portfolios.

how diversification reduces overall portfolio risk

Diversification is a technique that reduces riskby allocating investments among various financial instruments, industries, and other categories. It aims to maximize returns by investing in different areas that would each react differently to the same event.

Most investment professionals agree that, although it does not guarantee against loss, diversification is the most important component of reaching long-range financial goals while minimizing risk. Here, we look at why this is true and how to accomplish diversification in your portfolio.