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# Measures of risk

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Measuring risk is only helpful for a portfolio of stocks rather than for an individual stock, and this is so because investing in a diversified portfolio reduces the overall risk of the individual stocks in the portfolio. As pointed out earlier in this chapter, a diversified portfolio of greater than 20 to 40 stocks reduces the unsystematic portion of risk in the portfolio, leaving only the systematic risk in the portfolio. Reducing some of the risk should reduce the variability of the returns in that portfolio. However, market risk is not reduced by diversification, but having a long time horizon can lessen a portion of this risk. If the market declines with a short time horizon, you would have to sell your stocks at lower prices, whereas with a long time horizon you are able to liquidate your stocks when they have appreciated in value.

## Standard Deviation

The standard deviation measures the amount by which a stock’s or portfolio’s returns vary around its average return, which provides a measure of volatility. Measuring the standard deviation of stocks can show you which stocks are the least volatile. For example, consider Table 4–7, which presents the monthly returns for Citigroup and Amgen over a one-year period.

The first step in determining the relative volatility of the two stocks, Citigroup and Amgen, is to find the average monthly returns for each stock. This is based on the closing price at the end of every month. The monthly return is calculated as follows:

Monthly return = [(ending price - beginning price) + dividend]/beginning price

For example, the following is the return for Citigroup for the first month:

Return = [(52.84 - 51.25) + 0]/51.25 = 3.1%

The standard deviation is a quantitative measure of the stock’s risk. The lower the standard deviation, the lower is the variability or risk of the investment.

In a normal distribution of data, two-thirds of the monthly returns in the distribution fall within plus or minus one standard deviation from the mean. For example, Citigroup has a mean of -0.99 percent and a standard deviation of 7.86 percent, so two-thirds of the monthly returns should fall between 6.87 and -8.85 percent. Amgen has a mean of -2.39 percent and a standard deviation of 8.6 percent, so two-thirds of the monthly returns should fall between 6.21 and -10.99 percent.

Another indication of volatility and risk is the range of a stock’s high and low returns. Citigroup has a high return of 12.39 percent and a low of -12.56 percent. Amgen has a high return of 16.91 percent and a low of -15.03 percent. Within the 12-month period, Citigroup had five months of negative returns, and Amgen had seven.

So which of these two stocks is less volatile? Citigroup stock is less volatile than Amgen stock on all three indications of volatility. Table 4–8 illustrates how to use Excel software to determine the mean and standard deviation for the returns of a stock. Excel calculates the mean and standard deviation for the entered data field.

The disadvantage of the standard deviation as a measure of risk is the assumption that returns will be normally distributed as in a bell-shaped curve. Stock markets can have crashes that would not be predicted in the normal distribution of data. However, the standard deviation is a useful measure to compare the volatility of different stocks and portfolios.

Table 4-7
Determination of Risk and Return ## Beta

The beta coefficient is a measure of the sensitivity of the rate of return on a stock in relation to the movement of the market. In other words, it measures the stock’s systematic risk.

To determine the beta coefficient, you plot or graph the monthly returns for a stock in relation to the monthly returns for the market (the S&P 500 Index or any other measurement of the market). This shows the average movements in the price of the stock relative to the price movements in the market index. The slope of the line is the beta coefficient, which determines how the stock will react to the movement in the market.

The market always has a beta coefficient of 1, so a stock with a beta coefficient of 1 has systematic risk equal to that of the market. If a stock’s beta coefficient is 1.2, for example, this means that the stock is 20 percent more volatile than the market. A stock with a beta coefficient of 0 has no systematic risk; a stock with a beta coefficient of less than 1 is less volatile to changes in the price movements of the market. Beta coefficients for stocks generally range between 0.6 and 1.6, but this does not mean that beta coefficients cannot be more or less. At one point in time, Johnson & Johnson, for example, had a beta coefficient of 0.07, which indicated a miniscule amount of market risk. Table 4–9 shows how to use the Internet to obtain beta coefficients for listed stocks.

The beta coefficient seems like a simple and easy way to measure market risk. When you invest in stocks with beta coefficients higher than the market (>1), the returns in rising markets should be greater than the market returns. Similarly, when you invest in stocks with beta coefficients lower than the market (<1), your potential losses in a declining market should be less than the market losses. Unfortunately, the beta coefficient does not provide a foolproof way to measure market risk because of the following four factors:

1. The beta coefficient for a company’s stock varies if you use different measures of the market (for example, the Value Line Index instead of the S&P 500 Index).
2. The beta coefficient for a company’s stock varies if you use different time frames (12, 24, 36, 48, or 60 months).
3. The risk-return relationship may differ from that predicted by the theory. Low-risk stocks have earned higher returns than expected, and high-risk stocks have earned lower returns than expected.
4. Relationships between stock prices and market prices change and do not always reflect past relationships (Malkiel, 1990, pp. 243–255).

Table 4-8
How to Compute a Mean and Standard Deviation Using Excel Software

Use Excel to calculate these statistical measures by entering the monthly returns in a column.
1. Click on “f*” in the toolbar near the top of the screen.
2. In the left box, highlight “Statistical.”
3. In the right box, highlight “Average” for the mean and “STDEVPA” for the standard deviation for a population of data.
4. Enter the data field for your column. For example, if the monthly returns are in the C1 through C12 columns, you would type “C1: C12.”

Table 4-9
How to Use the Internet to Obtain Stock Beta Coefficients

1. Go to Yahoo (www.yahoo.com).
3. Type the stock symbols (separate each with a comma) of the companies you are interested in, and then click on each individual symbol for more information.
4. Click the “Profile” link, which appears beneath the detailed information, and then click “Key Statistics,” where you find the beta measure for that particular stock.

## Portfolio Beta

Even though a perfect measurement of market risk does not exist, you can use the beta coefficient to determine whether the risk for a portfolio of stocks is greater or less than the risk of the market. The beta coefficient of a portfolio of stocks is the weighted average of the beta coefficients of the individual stocks. For example, a portfolio consisting of 32 stocks in which 8 stocks each have a beta of 1.2, 16 stocks each have a beta of 1.1, and 8 stocks each have a beta of 0.8 has a portfolio beta of 1.05. This calculation appears below: A portfolio beta of 1.05 means that if the market rises or falls by 1 percent, the portfolio rises or falls by 1.05 percent. The portfolio has slightly more risk than the market. Although individual beta coefficients may not accurately predict price movements relative to the market, they do provide an attempt for assessing the market risk of a portfolio.

## Sharpe Ratio

The Sharpe ratio is a measure of a risk-adjusted return of a portfolio. The risk-free rate is measured by the 90-day Treasury bill rate, and this rate is deducted from the portfolio’s return, which is then divided by the standard deviation of the portfolio. When comparing the Sharpe ratio of different portfolios, the larger the Sharpe ratio, the better are the returns per unit of comparable risk. In other words, by holding the risk of different portfolios constant, you can use the Sharpe ratio to find the portfolio that provides the higher return.

You can analyze the risk of your stocks and portfolio by using the Web site www.riskgrades.com.

## WHAT YOU CAN DO ABOUT RISK

An analysis of and an awareness of risk are important for two major reasons. First, you can determine how much risk you can tolerate through asset allocation (how much of your portfolio to allocate to stocks, bonds, and money market securities). Second, you need to have a diversified portfolio of stocks, which reduces the individual risk of specific stocks, and a long time horizon (holding period) for your portfolio of stocks.

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Planning plays a key role in the success or failure of any endeavor

Using too much Leverage

Failure to control Risk
Refusing to employ effective risk control measures can ensure your long-term failure

Lack of Discipline
A lack of discipline can destroy even the most talented and best prepared trader