Measures of risk
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.
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
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
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
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.
Determination of Risk and Return
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).
How to Compute a Mean and Standard Deviation Using
Use Excel to calculate these statistical measures by entering the monthly returns in
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.”
How to Use the Internet to Obtain Stock Beta Coefficients
1. Go to Yahoo (www.yahoo.com).
2. Click the “Finance” link.
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.
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.
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
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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