Defining Risk: The Dispersion of Returns

Defining Risk: The Dispersion of Returns

Risk is a most slippery and elusive concept. It’s hard for investors – let alone economists – to agree on a precise definition. The American Heritage Dictionary defines risk as the possibility of suffering harm or loss. If I buy one-year Treasury bills to yield 8 percent and hold them until they mature, I am virtually certain of earning an 8 percent monetary return, before incoming taxes. The possibility of loss is so small as to be considered nonexistent. If I hold common stock in my local power and light company for one year on the basis of an anticipated 9 percent dividend form, the possibility of loss is greater. The dividend of the company may be cut, and, more important, the market price at the end of the year may be much lower, causing me to suffer a serious net loss. Risk is the chance that expected security returns will not materialize and, in particular, that the securities you hold will fall in price.

Once academics accepted the idea that risk for investors is related to the chance of disappointment in achieving expected security returns, a natural measure suggested itself – the probable variability or dispersion of future returns. Thus, financial risk has generally been defined as the variance or standard deviation of returns. Being long-winded, we use the accompanying exhibit to illustrate what we mean. A security whose returns are not likely to depart much, if at all, from its average (or expected) return is said to carry little or no risk. A security whose returns from year to year are likely to be quite volatile (and for which sharp losses are typical in some years) is said to be risky.

Bloor street, Yorkville. Photo by Elena

Exhibit

Expected Return and Variance: Measures of Reward and Risk

This simple example will illustrate the concept of expected return and variance and how they are measured. Suppose you buy a stock from which you expect the following overall returns (including both dividends and price changes) under different economic conditions:

Normal economic conditions - Probability of occurrence - 1 chance in 3 – Expected return – 10 percent

Rapid real growth – 1 chance in 3 – 30 percent

Recession with inflation (stagflation) – 1chance in 3 - -10 percent.

If, on average, a third of past year have been “normal,” another third characterized by rapid growth, and the remaining third characterized by “stagflation,” it might be reasonable to take these relative frequencies of past events and treat them as our best guesses (probabilities) of the likelihood of future business conditions. We could then say that an investor’s expected return is 10 percent. A third of the time the investor gets 30 percent, another third 10 percent, and the rest of time he suffers a 10 percent loss. This means that, on average, his yearly return will turn out to be 10 percent.

Expected Return = 1/3 (0.30) + 1/3 (0.10) + 1/3 (-0.10) = 0.10.

The yearly returns will be quite variable, however, ranging from a 30 percent gain to a 10 percent loss. The “variance” is a measure squared deviation of each possible return from its average (or expected) value, which we just saw was 10 percent.

Variance = 1/3 (.30 - 0.10)2 + 1/3 (0.10 - 0.10)2 + 1/3 (-0.10 – 0.10)2 = 1/3 (0.20)2 + 1/3 (0.00)2 + 1/3 (-0.20)2 = 0.0267.

The square root of the variance is called the standard deviation. In this example, the standard deviation equals 0.1634.

Dispersion measures of risk such as variance and standard deviation have failed to satisfy everyone. “Surely riskiness is not related to variance itself,” the critics say. “If the dispersion results from happy surprises – that is, from outcomes turning out better than expected – no investors in their right minds would call that risk.”

It is, of course, quite true that only the possibility of downward disappointments constitutes risk. Nevertheless, as a practical matter, as long as the distribution of returns is symmetric – that is, as long as the chances of extraordinary gain are roughly the same as the probabilities for disappointing return and losses – a dispersion or variance measure will suffice as a risk measure. The greater the dispersion or variance, the greater the possibilities for disappointment.

While the pattern of historical returns from individual securities has not usually been symmetric, the returns from well-diversified portfolios of stocks do seem to be distributed approximately symmetrically. The following chart shows a twenty-five-year distribution of monthly security returns for a portfolio consisting of equal dollar amounts invested in 100 stocks. It was constructed by dividing the range of returns into equal intervals (of approximately 1 ¼ percent) and then noting the frequency (the number of months or 10.7 percent per year. In periods when the market declined sharply, however, the portfolio also plunged, losing as much as 13 percent in a single month.

For symmetric distributions, such as this one, a helpful rule of thumb is that two-thirds of the monthly returns tend to fall within one standard deviation of the average return and 95 percent of the returns fall within two standard deviations. Recall that the average return for this distribution was just under 1 percent per month. The standard deviation (our measure of portfolio risk) turns out to be about 4 1/2 percent per month. Thus, in two-thirds of the months the returns from the portfolio were between 5 1/2 percent and -8 percent. Obviously, the higher the standard deviation (the more spread out are the returns), the more probable it is (the greater the risk) that at least in some periods you will take a real bath in the market. That's why a measure of variability such as standard deviation is so often used and justified as an indication of risk (standard deviation and its square, the variance, are used interchangeable as risk measures. They both do the same thing and it's purely a matter of convenience which one we use).

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc.

Documenting Risk: A Long-Run Study

Documenting Risk: A Long-Run Study

One of the best-documented propositions in the field of finance is that, on average, investors have received higher rates of return for bearing greater risk. The most thorough study has been done by Roger Ibbotson and Rex Sinquefield. Their data cover the period 1926 through 1988. Appearances notwithstanding, the table was not designed to show One Manhattan skyline and a series of Eiffel towers. What Ibbotson and Sinquefield did was to take several different investment forms – stocks, bonds and Treasury bills – as well as the consumer price index, and measure the percentage increase or decrease each year for each item. A rectangle was then erected on the baseline to indicate the number of years the return fell between 0 and 5 percent; another rectangle indicated the number of years the returns fell between 5 and 10 percent; and so on, for both positive and negative returns. The result is a chart which shows the dispersion of returns and from which the standard deviation can be calculated.

A quick glance shows that over long periods of time, common stock have, on average, provided relatively generous total rates of return. These returns, including dividends and capital gains, have exceeded by a substantial margin the returns from long-term corporate bonds. The stock returns have also tended to be well in excess of the inflation rate as measured by the annual rate of increase in consumer prices. Thus, stocks have also tended to provide positive “real” rates of return, that is, returns after washing out the effects of inflation. The data show, however, that common-stock returns are highly variable, as indicated by the standard deviation and the range of annual returns, shown in adjacent columns of the table. Returns from equities have ranged from a gain of over 50 percent (in 1933) to a loss of almost the same magnitude (en 1931). Clearly, the extra returns that have been available to investors from stocks have come at the expense of assuming considerably higher risk. Note that small company stocks have provided an even higher rate of return since 1926, but the dispersion (standard deviation) of those returns has been even larger than for equities in general. Again, we see that higher returns have been associated with higher risks.

A long-run study. Photo by Elena

There have been several periods of five years or longer when common stocks have actually produced negative rates of return. The early 1930s were extremely poor for stock-market investors. The early 1970s also produced negative returns. The one-third decline in he broad stock-market averages during October 1987 is the most dramatic change in stock prices during a brief period since 1930s. Still, over the long pull, investors have been rewarded with higher returns for taking on more risks.

The patterns evident in Ibbotson and Sinquefield’s table also appear when the returns and risks of individual stock portfolios are compared. Indeed, the differences that exist in the returns from different funds can be explained almost entirely by differences in the risk they have taken. However, given the rate of return they seek, there are ways in which investors can reduce the risks they take. This brings us to the subject of modern portfolio theory, which has revolutionized the investment thinking of professionals.

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc.

Navigating the Water of IRAs

Navigating the Water of IRAs

Here’s how to avoid a minefield of penalties

When tax laws limited the tax benefits of Individual Retirement Accounts in 1986, investors abandoned IRAs by the droves. Contributions tumbled from nearly $40 billion in 1986 to around $19 billion in 1994. Investors may have bailed out too soon, though. Even though some IRA contributions are not deductible, tax deferral on the account’s earnings still make IRAs a pretty good deal over the years.

According to Scudder, Stevens & Clark Inc., a global investment management firm, and investor who put $2,000 in an IRA from 1982 to 1986 would have savings worth $16,888 in five years. By comparison, another saver who continued to pump money into the IRA, would have a cache worth more than $32,000 in five years, even without the tax deduction.

Many mutual fund companies lure IRA funds by setting low minimum initial investments and by allowing free automatic withdrawals every month or so. But first, you need to get past the deduction requirements. Well-heeled taxpayers who are covered by an employer-sponsored pension plan or whose spouses are covered by one and can contribute to an IRA but cannot deduce the contributions from their taxes. If neither you nor your spouse is covered by a retirement plan at work and if you each earned a determined sum, you can contribute and deduct the same amount each. If only one of you works, you can contribute and deduct more.

If you or your spouse are covered by an employer’s pension plan, your IRA contribution is fully deductible, as long as your modified adjusted gross income corresponds to a limit established by the government or is less for a single taxpayer. You get a partial deduction if you are married and your joined income is between some established sums. You can calculate modified adjusted gross income by adding your salary and other taxable income and subtracting any adjustments made on your 1040 income tax forms. Then turn to the worksheet included in your form 1040 instructions to figure your modified adjusted gross income.

Once your money is in an IRA, you’ll have to tread gently to get it out without triggering huge penalties. Some rules to keep in mind:

Breaking out early: If you are younger than 59-and-a-half and want to pull out money for a non-medical reason, the IRS gets 10 percent off the top. There is an exception. You can make penalty-free withdrawals if they are part of a series of roughly equal annual payments linked to your life expectancy and expected rates of return. To take advantage of this exception, you must take withdrawals for at least five years or until you are 59-and-a-half, whichever comes first. You can then take out as much or as little as you like without paying a penalty.

The IRAs Maze. Photo by Elena

There’s some leeway in calculating your equal payment schedule. One method is to divide your account total by your life expectancy and estimate the expected return on your account. If you want to take out as much money as possible early, use the highest interest rate that the IRS will consider reasonable. Ths IRS has accepted rates not more than 120 percent of the long-term federal rate published monthly by the IRS. The faster your account is projected to grow, the more you can withdraw annually.

Switching IRA funds: You can move from one IRA to another without paying taxes with either a direct transfer or a rollover. In a direct transfer, your IRA holder transfers funds directly to the new custodian without releasing the money to you. You can make an unlimited number of transfers and don’t need to report the switch to the IRS, but you do face costly transaction fees.

In a rollover, your IRA holder sends you the funds, which you reinvest into an existing or new account. You are allowed one rollover every 12 months and must complete I within 60 days, or you’ll trigger taxes and the 10 percent early withdrawal penalty. You must report rollovers to the IRS. If you intend to switch the funds to a future employer’s retirement plan, don’t add more money to the IRA. Otherwise, the IRA will be tainted and you won’t be able to roll it over again.

Tapping too little too late: If you withdraw from your IRA after age 70-and-a-half and you take out too little based on your life expectancy, you face a 50 percent penalty. If you should have withdrawn $1,000 but you took out only $600, for example, you’ll pay $200 in penalty taxes.

Planning for your golden years

These books, pamphlets, and retirement kits can help you make wise decisions as you devise a retirement strategy. Many are free.

The Dreyfus Personal Retirement Planner (Dreyfus Investments)

Retirement Planning Guide (Fidelity Investments)

Can You Afford to Retire? (Insurance Marketing and Research Association)

Retirement Planning Guide Kit (Retirement Planning Software)

Shaping Your Financial Fitness (National Association of Life Underwriters)

A single’s person guide to retirement planning (American Association of Retired Persons)

Vanguard Retirement Planner (A software kit by Vanguard Group)

The Consumer’s Guide to Medicare Supplement Insurance and the Consumer’s Guide to Long-Term Care Insurance (The Health Insurance Association of America)

Understanding Social Security (Social Security Administration)

When to Take an HIV Test

When to Take an HIV Test

If you are in a high-risk group, get tested now

Below we explain the test that identifies  the HIV antibody that can lead to AIDS.

Who should consider getting test for HIV?

Anyone who has been or is sexually active, anyone who is sexually active and not in a monogamous relationship;; IV drug users and anyone who has received a blood transfusion before the year 1985. Additionally, any person who does not know their HIV antibody status and who feels that they have been at risk for infection with HIV should consider testing.

How is the test given?

The Centers for Disease Control and Prevention have set guidelines, but not all doctors and hospitals follow them. Those guidelines recommend some type of prevention counseling before the test is given. Less than a tube of blood is then drawn. The labwork is done. The patient comes back for results and post-test counseling. At Whitman Walker, if the test is negative, that's the end of it. But the results are positive, the test is repeated three times to make sure it's accurate before telling the patient. Once again, not all doctors and hospitals follow those guidelines; some just draw the blood and send it to the lab.

What is the cost?

There is no charge at Whitman Walker, but the test costs money.

Once someone is exposed to HIV, how long does it take to show up on a test? Should he or she be tested again periodically?

It can take up to six months after the HIV virus enters the body before antibodies are produced. By six months, 99 percent of those infected with the virus will develop antibodies. But 95 percent of those who are infected with the virus will develop antibodies within three months after infection. Because of this window period for antibody development, people who have had unsafe sex or have shared needles three to six months before the test should consider re-testing.

The Centers for Disease Control and Prevention estimates that millions of people in the United States are now infected with HIV. HIV infection/AIDS is on of the ten causes of death among people of all ages in the country.  Photo by Elena

Can people run into problems with their health or life insurance companies if they are tested and the results are positive?

Many life insurance companies require an HIV test as a coverage prerequisite. These companies often will not provide life insurance coverage to a person who has tested positive for HIV, Health insurance providers may drop a person from coverage or put a cap on benefits paid.

How confidential are the test results?

Many clinics that provide testing, including Whitman Walker, provide anonymous testing. This method provides no way of tracing who has tested positive. Some clinics provide testing that is only confidential and not anonymous.

What are the lates methods for self-adminstration of tests at home? Are these tests now available? If not, when will they be?

To date, no home testing method has been approved by the Food and Drug administration. Many home collection methods have been developed but are not yet available. Home collection kitrs will allow people to draw blood at home and mail the sample to a central testing center where results can be retrieved with a self-determined code. The conception of home testing has been criticized for many important reasons. In addition to inaccurate and misinterpreted results, home testing methods make it impossible to provide face-to-face counseling. Such counseling is critically important both before and after the test is taken and results are received.

Should newborn babies be tested?

Newborns should be teste if there is concern about the mother's risk of infection. However, because newborns have a quickly changing immune system, a baby with an HIV-positive result may later test negative.

If someone tests positive, what kind of care should he or she seek after the results come back?

Individual who test positive should seek medical attention for treatment as well as counseling as needed.  Individuals should also protect themselves from further infection and protect others from the virus. Precautions include following safe sex guidelines; never sharing needles or other drug works; reducing or stopping alcohol, cigarette, and drug use; eating well and getting plenty of rest and exercising; avoiding infections, especially those passed by sex;; and not donating blood, plasma, sperm, or organs.

Should more people be tested to help curtail the spread of the virus?

Testing is one of the best methods for early detection of HIV. People who are aware of their HIV status can significantly help reduce the spread of HIV/AIDS by not putting others at risk.

Buying Stock On the Cheap

Buying Stock On the Cheap

If you know what you know, there’s no need to pay full commission.

Discount brokers now account for about a third of individual stock trades. No wonder. While full-service brokerages provide customers with investments advice and other services, discount brokers stick to making trades and offer fewer services, passing the savings on to you. Cost-conscious investors can take a huge chunk out of the commissions they pay on stock trades by using a discount brokerage firm. But you have to know what you want and you have to be comfortable making your own investment decisions.

There’s no question you can save a bundle using a discount stockbroker to execute your trades. According to the 1995 Discount Brokerage Survey, published by Mercer, Inc. in New York, the average commission among the 10 cheapest discount brokers to trade 100 shares at $50 per share was $29.60. The big three regular discounters – Charles Schwab, Fidelity and Quick & Reilly – have an average commission of $52.70 for this trade, while full-service brokers typically charge $103.

It’s difficult to say which discount brokerage firm offers the best deal, because they set their prices differently. Rates often are based on the total dollar value of a transaction, the number of shares purchased or simply a flat fee for each type of transaction. Sometimes, small commissions and fees for non-routine trades are added on. Large dollar volume trades or trades ordered using a computer or touch-tone phone get further discounts at some firms.

What all this means is that some firms will be cheaper for some trades, and more expensive for others. The American Association of Individual Investors, advises that you choose a broker by first comparing the commissions they charge for the kinds of trades you are most likely to make. Call several discounters directly, or use one of the annual surveys published by Mercer or AAII. Mercer’s is easier to use, because it lists the 30 cheapest discounters in descending order by cost for each of 22 typical trades, while the AAII lists them alphabetically , and for only tree sample trades. But AAII’s list is much more inclusive, covering all 88 discount brokerage firms. Mercer also ranks 110 bank brokers by state and all the independent brokers.

After you have chosen several candidate firms, AAII recommends that you ask for a commission schedule and description of services, fees and bonus discounts. Keep in mind that some firms charge a flat fee to open a new account and charge high fees to wire funds and for copies or reports and bounced checks.

Buying Stock On The Cheap. Image: Megan Jorgensen (Elena)

The Big Three Discounters, and some of the others, try to compete with the full-service firms by offering research information, investment recommendations, 24-hour touch-tone service, asset management accounts (with check-writing privileges and ATM Cards), and margin accounts for trading other instruments, such as options, bonds and certificates of deposit, as well as extensive branch networks.

That said, you shouldn’t expect a lot of hand holding. Andre Scheluchin, managing editor of Mercer’s survey, warns investors to keep in mind that discounters have set rates and offer little maintenance of your account. If you want more attention, and more control over the price you pay, then you’re better off with a full-service broker. And, Scheluchin notes, it is not impossible to negotiate a cut in commission with a full-service broker, so you may only pay a little more than with a discounter.

If you want to check out a brokerage before doing business, background information is available from the National Association of Securities Dealers, or from the Central Registration Depositary of your state security agency, listed in the blue pages of the phone book.

No Broker Required. If you make an initial purchase directly from the company offering the stock, you can do away with the brokerage commissions altogether. The American Association of Individual Investors, reports that 17 companies sell stock directly to investors, at commissions of only a few cents a share. Most of these are sold nationwide: Arrow Financial Corp.; Atlantic Energy Corp.; Barnett Banks Inc.; Central Vermont Public Service (not available to residents in certain states); COMSAT Corporation; Dial.Corp.; DQE Co.; Exxon Corp.; First Alabama Bankshares Inc.; Johnson Controls Inc.; Kellwood Co.; Kerr-McGee Corp.; Mobil Corp.; SCANA Corp.; Summit Bankcorp (N.J.) Texaco Inc.; U.S. West Inc.

The top ten deep discounters in 1994: Wall Street Equities; Brown & Company; K. Afhausen and Company; Lombard Institutional; National Discount Broker; R.J. Forbes Group; Pacific Brokerage Services; Kennedy, Cabot & Company; Recom Securities; Barry Murphy and Company.

SIPC: Securities Investor Protection Corp, insures securities and cash up to $500,000. Plus sign indicates coverage beyond $500,000 at no extra charge.

SWEEP: Automatically invests cash balances in interest bearing money market fund until these funds are reinvested. Money market funds usually offer better interests. Than cash balance accounts.

INT: Pays interest on customers’ cash balances. Amounts in parentheses, if any, indicate minimum amount above which interest is paid, if a discount firm offers a sweep account, we do not include information on cash balance interest.

NLMF: No-load mutual funds can be purchased through the firm. Charges may apply, and available funds vary.

IRA: Self-directed IRAs can be set up. Charges may vary.