The Stock Investor’s Pocket Calculator

A Quick Guide to All the Formulas and Ratios You Need to Invest Like a Pro

Author: Michael C. Thomsett
Pub Date: 2007
Your Price: $24.95
ISBN: 0814474608
Format: Hardcover

 

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Chapter 1

Rates of Return on Investment

What Goes In, What Comes Out

Even the most seemingly easy calculation can get quite involved. For example, what is your "return"? If you invest money in a stock or mutual fund, you need to be able to figure out and compare the outcome. But as the following explanation demonstrates, there are many different versions of "return," and you need to be sure that when comparing two different outcomes, you are making a like-kind study. Otherwise, you can be deceived into drawing an inaccurate conclusion. And accuracy is one of your goals in going to the trouble of drawing conclusions in the first place.

The "return" you earn on your investments can be calculated and expressed in many different ways. This is why comparisons are difficult. If you read the promotional literature from mutual funds and other investments, the return provided in the brochure could be one of many different outcomes.

This is why you need to be able to make distinctions between return on investment and return on capital. Your investment return is supposed to be calculated based on the amount of cash you put into a program, fund, or stock. Most investors use "return on investment" in some form to calculate and compare. The return on capital is usually different and is used by corporations to judge operations. To further complicate matters, capital is not the same as capitalization, so corporate return calculations can be difficult to compare. Return on capital normally means capital stock. Capitalization is the total funding of an organization, including stock and long-term debt.

 

Judging the Outcome—What Did You Expect?

All investment calculations are done in order to monitor and judge standards. You enter an investment with a basic assumption, an expectation about the return you will be able to earn.

In order to judge the quality or the investment and the reliability of your own decision-making capabilities, you will need to figure out how well the investment performed. In so doing, you need to be aware of some popular mistakes investors make, including the following primary points:

1. The purchase price is the assumed "starting point." It is an easy trap to believe that the point of entry to any investment is the price-based starting point. Thus, the assumption is that price must move upward from that point. No consideration is given to the realistic point of view that price at any given moment is part of a continuum of ever-evolving upward and downward price point movements. As a starting point, price does not always move upward. In other words, profitability is not the only possible outcome; the rate of return may also be negative.
2. There is no possibility of a loss of value. Investors also tend to overlook the possibility that they can lose money in an investment. But there is an unavoidable relationship between opportunity and risk. The greater the opportunity for profit, the higher the risk; this is inescapable. So picking the "best" investment is a matter of identifying how much risk you are willing and able to take.
3. A bail-out and/or profit goal is not specifically set. Too often, an investment is made with little or no idea about the individual's expectations. Do you plan to double your money? Triple it? Or would you settle for a 15% return in one year? Equally important is the question of possible loss. How much of your investment capital will you lose before you cut your losses and close it out? If you don't set goals and identify the point at which you will close the investment, then you cannot know what to expect.
4. The specific method of calculation is not understood. It is difficult to determine whether an investment is a success or a failure unless you also know how the return calculation is made. This includes making clear distinctions between different types of returns, the effect of taxes, and how the formula works. All these variables have to be made consistent between comparisons or they will not be valid.
5. The time factor is not considered. You need to take into account the reality that not all investments produce a return in the same amount of time. The longer the time required (thus, the longer your capital is tied up), the less effective the return. So the time element is crucial to the comparison of one investment to another.
6. The varying degrees of risk are not taken into account. Risk is not only an aspect of opportunity; it is really the reverse effect of it as well. Opportunity for profit and risk of loss are like two sides of the same coin. This relationship between the two attributes is shown in Figure 1.1.
   Even so, some investors focus only on the "heads" side and invest with the profitability potential in mind but have made no plans for the contingency of loss. How much could you lose? How much can you afford? What criteria do you use to judge risk? For example, investors who base their decisions on fundamental analysis look for revenue and earnings trends and compute working capital and capitalization ratios. Investors who prefer to trust in technical signals check price volatility and look at charts. Whatever method you use, a decision should be judged based on potential for both profit and loss.
7. Comparisons fail to include compound rates of return versus simple return. In calculating return, there are numerous methods in use, and these are explained in this chapter. However, in estimating future returns, it is important to know whether you will earn a simple return or a compound rate of return. For example, if you are buying shares of a mutual fund, will you take your dividends and other distributions in cash? If so, your annual returns will be simple. But if you instruct the fund to reinvest your earnings, your investment account balance will increase each time you earn; the result is a compound rate of return, and over many years it will be much higher. So without deciding in advance how your mutual fund or stock earnings are going to be treated, it is not possible to set profit goals for yourself.

The important determination of an investment's success has two components. First is the decision as to how much profit you expect (or how much loss you will accept). Second is deciding how to compute the outcome.

Setting goals involves identifying the profit you hope to earn and, if you do not plan to hold your investments indefinitely, the point when you will sell. It also involves identifying when you will sell if the investment falls in value. At what point will you bail out and take a small loss to avoid a larger loss later on?

The second part—deciding how to compute profits and losses—is equally important because you need a consistent, reliable, and accurate method in order to assess your investing success and make valid comparisons between different investments.

 

The Basic Equation: Return on Cash Invested

Calculating return is perceived in many instances as rather simple. And it is, as long as the amount of money placed into the investment is the entire amount invested. In some cases, though, you deposit only a portion of the investment's total value, deferring payment of the remainder. Anyone who has ever purchased a home knows that the down payment is only a small portion of the property's total value; the remainder is financed and paid over many years.

The same thing happens with investments. For example, if you use a margin account, you are allowed to buy stock and pay for only one-half of the current market value. The balance is held in margin, and interest is charged. The concept here is that when a stock's price moves upward, margin investors make twice the profit (less interest) because they can afford to own twice as much stock. It's a great concept, unless your investments lose value or take too long to become profitable.

Another example involves the use of options, which is explained in greater detail later in this chapter. As one form of leverage, you can control shares of stock with the use of options for a fraction of their market value. So calculating return will be more complicated when options are used.

The most basic calculation is return on purchase price, which is simply the return you earn or expect to earn when you put the entire amount of capital into the investment. For example, if you buy 100 shares of stock and pay $2,587 in cash, you have paid the entire purchase price in cash. If you later sell for a net of $2,934, your profit is $347.

Return on purchase price is calculated by dividing the profit by the original basis:

Return on purchase price is the calculation most investors are describing when discussing or thinking about their investments. It is the standard by which success is defined, and by which one investment is most likely to be compared to another. But what happens to the return calculation when you do not put the entire amount into the investment?

Return on purchase price may continue to be used as a common standard for the sake of ensuring consistency. But if you use a brokerage margin account to leverage your capital, you can expect two differences in the return. First, profitable returns are going to be much greater when you isolate the cash amount only; second, risk is also considerably higher. So the higher return is accompanied by far greater risks. Thus, it is not realistic to prefer using margin for all investing just because returns are greater. You also must accept greater risk levels.

For example, if your cost for 100 shares of stock is $2,587 but you deposit only one-half using your margin account, you may continue to calculate return on purchase. But you will also want to figure out your return on invested capital. In this case, only the actual amount invested is involved in the final outcome. The "gross" return on invested capital (before deducting margin costs) will involve a 50% investment, or $1,294. The formula for this calculation is:

This calculation is a theoretical outcome only. It is not realistic to count this triple-digit return as typical because not all investments are going to be profitable; it does not take into account the higher risk levels; and it ignores the fact that you continue to be obligated for the margin debt.

The advantage to using margin is that your capital can be leveraged. However, if a particular position loses money and you sell at a loss, you are still obligated for the amount borrowed. The return on invested capital formula is important in fixing the outcome, but only for a specific purpose: judging overall margin-based investing. So if you buy stocks only with cash, your outcome will be reviewed on the basis of the common formula, return on purchase price. If you use margin and invest only one-half, you double your opportunity and your exposure. A review of all outcomes on the basis of calculated return on invested capital will enable you to decide whether margin investing is more profitable or not. If your losses offset or surpass your gains, the added exposure to risk will not be worth the advantage (and greater risk) in leverage.

A third calculation that will help you to ensure like-kind comparisons in different markets and employing different strategies is return on net investment. This is the same calculation as either of the two previous formulas, but all outcomes are expressed on a net basis. So if you use margin, the actual profit is decreased (or loss is increased) by the interest cost of using margin. The formula is:

An alternative method of computing this would assume that the margin cost should be added to the invested capital. The formula under this method is:

So rather than deducting interest costs from the sales price, they are simply added to the original basis. For example:

This outcome is not significantly different from the previous calculation. However, the longer the holding period, the higher the costs—and the more important this distinction becomes.

Two final versions of return involve calculations with the dividends earned. First is total return, which includes a calculation net of costs, but adds in any dividends earned during the holding period. The formula:

The involvement of dividends is somewhat complicated, for two reasons. First, you are able to reinvest dividends for most listed companies and buy additional fractional shares rather than taking dividends in cash. This creates a compound return and makes comparisons more elusive. Second, the holding period will also affect the total return. If you own stock up to a few days before the ex-dividend date, you will not earn the dividend for the last period, which also affects overall return.

VALUABLE RESOURCE:

To find out more about reinvesting dividends in DRIP accounts (Dividend Reinvestment Plans), check the Web site www.wall-street.com/directlist.html
 

The final calculation for return on cash invested is dividend yield, also called current yield. This is the rate you earn on dividends, calculated as a percentage of the stock's market value. However, a distinction has to be made. This yield is reported every day in the financial press and is based on the stock's closing price. But if you buy stock, your actual yield will always be based on the price you paid and not on what is reported later. So for anyone who already owns shares, the daily changes in yield are meaningless. The formula for dividend yield is:

The higher the stock's price moves, the lower the yield (as long as the dividend remains at the same amount per share), and the lower the price, the higher the yield. For example, if the market share price moved up to $55 per share, the $1.60 per share would represent a yield of 2.9% ($55 _ $1.60). And if share value fell to $40 per share, yield would increase to 4.0% ($40 _ $1.60). However, if you were to buy shares at the current price of $48.86 per share, your yield would remain at 3.3% for as long as you held those shares.

This calculation becomes more complicated when you reinvest dividends, creating a compound rate of return. Although the actual yield values may be quite small, an exact calculation would assume a continuing 3.3% yield on the original shares, plus an adjusted yield calculated at the time dividends were posted in additional fractional shares. For example, if you owned 100 shares and you received the next quarterly dividend of $0.40 per share, or $40; and at that time the share price was $42 per share, you would take the dividend in the form of shares, or an additional 0.95 share of stock. The yield on that 0.95 share would be 3.8% per year. (The $0.40 per share is a quarterly dividend, so it is multiplied by 4 to arrive at the annual $1.60. Divide this by the current share value of $42 per share to arrive at 3.8%.) The result:

100 shares earn 3.3% current yield

0.95 share earns 3.8% current yield

If this calculation were performed each quarter, you would arrive at a very accurate overall yield. However, with only 100 shares, the difference this makes would be minimal. For portfolios with many more shares, the calculation would be more significant because the dollar values would be higher as well.

 

Calculating Option Trading Returns

The calculations of stock return and dividend yield involve subtle variations. The key thing to remember is that comparisons should be made consistently between different stocks, funds, and other investments. The same level of calculation for options trading is far more complicated and involves many more variables.

An option is an intangible contract, a right. The owner of an option has the right to buy or to sell 100 shares of stock at a fixed price and for a very specific period of time. Once an option expires, it becomes worthless.

There are two types of options. A call grants its owner the right but not the obligation to buy 100 shares of a stock at a fixed price. A put is the opposite, granting the right to sell 100 shares of stock. Every option is tied to one stock, called the underlying security; and it cannot be transferred to other stocks. The strike price is the fixed price at which the owner of an option can exercise. When a call owner exercises that call, it means 100 shares of the stock can be bought at the strike price, even when the stock price is substantially higher. If and when a put owner exercises a put, he or she sells 100 shares of stock at the fixed strike price even though the stock's current market price is far lower.

In a nutshell, that is how options work. But because option values change as stock prices changes, not all options are exercised. In fact, about three out of every four options expire worthless. For the owner of an option, one of three things can happen: First, you can simply let it expire, in which case you lose the entire amount invested. Second, you can exercise the option and buy (with a call) or sell (with a put) 100 shares of stock. And third, you can sell the call or put and take a profit or loss on the transaction.

You can also act as seller rather than as buyer. In other words, instead of going through the sequence of buy-hold-sell, it is reversed to sell-hold-buy. Going short on options is far riskier than buying in most situations because you may lose more money than you can afford. One exception to this is the covered call, a strategy in which you sell one call while also owning 100 shares of the underlying security. If the call is exercised by its buyer, you have 100 shares to deliver; so even if the stock price moves far higher, you do not lose on the option transaction. (You do lose the increased market value of the shares, however.) You keep the money paid to you when you go short, called the option premium. The covered call is very conservative, and there are several possible outcomes. Analyzing these outcomes helps you to decide whether a particular position is worth the risks or should be avoided.

The calculation of profit or loss for buyers is simple. You buy an option, and later you sell it. The difference is either profit or loss. (If you allow the option to expire worthless, your loss is 100%.) Even though three-fourths of options expire worthless, they remain popular as side-bets in the market. This is true partly because the options market holds a certain allure for the more speculative investor or trader. However, options are also cheap. They can be bought for one-tenth or less of the price of stock. So rather than investing $4,000 in 100 shares of stock, you can spend $400 or less and own an option.

A comparative outcome is useful in identifying the attraction of options. For example, if you were to buy 100 shares of stock and the price rose four points, your profit upon sale (before calculating trading costs) would be $400, or 10%. However, if you bought a call option and spent $400 and the stock rose four points, you would double your money and sell for $800, or a 100% gain.

IN-THE-MONEY AND OUT-OF-THE-MONEY.

The illustration of an option's value matching the stock price point for point does not always occur. This is true only when the option is in-the-money. This means the stock price is higher than a call's strike price, or lower than a put's strike price. An in-the-money call will change in value point for point with the stock; as the price of the stock rises, so does the call's value. An in-the-money put does the opposite; as the stock's price falls, an in-the-money put rises one point for each point the stock loses.

The comparison between a stock's profit and an option's demonstrates the power of leverage. For $400, the call buyer controls 100 shares of stock, but without carrying the risk of investing $4,000 in shares. The maximum loss is limited to the price of the option. For example, if your $4,000 investment in stock falls to $3,800, your paper loss is $200 or 5%. However, you are not required to take that loss, and you can hold onto shares indefinitely. The option buyer, however, has to be concerned with expiration. The two-point loss represents 50% of the premium value. So while profit and loss can be far more substantial for options, their primary advantage is the lower dollar amount at risk. And the primary disadvantage is expiration.

The calculation of profit or loss for long positions is not complex. In comparison, when you go short with a covered call, your profit or loss is more complicated, for several reasons. First, there are three possible outcomes (expiration, exercise, or closing of the position). Second, because you also own shares of stock, exercise means that your stock will be sold; so you need to structure a covered call with the related capital gain on stock in mind.

The first calculation involving options involves selling covered calls and the sale of stock. Without options, the return on purchase price is easily calculated, because that price does not change. But when you sell covered calls, the outcome changes because the net basis in stock is reduced.

For example, if you own 100 shares of stock originally purchased at $40 per share, and you sell a covered call for 4 ($400), that may be viewed as a reduction in your basis. Most calculations of option return separate stock and options because it is complicated to try and figure out the overall return. But if you treat the covered call strictly as a form of reduced basis, then this calculation—return if exercised—can be very useful, especially in comparing one stock investment with another. The formula:

If the covered call had not been included, the two sides of the transactions would be calculated apart from one another. Thus, the capital gain on stock would be 10% ($400 _ $4,000). And the gain on the covered call would be 100% (because you received $100 upon sale, and it is all profit). But this is unrealistic; upon exercise, the premium you receive for selling a covered call reduces the basis.

The outcome may also involve keeping the call open until it expires. In this situation, the option premium is 100% profit; but it may also be used to reduce the basis in stock on an ongoing basis. You can write an unlimited number of calls against 100 shares of stock and allow each to expire in turn. Until one is actually exercised, you keep your stock. So the true net basis in stock could be viewed as being discounted over a period of covered call writes.

Finally, a covered call may be closed and a profit taken. When you close a short position, it involves a closing purchase transaction. Your original order was a sell, so closing this requires a buy. For example, if you sell an option for $400 and later close it for $150, you have a $250 gain, or 62.5%. You may want to close the covered call for a number of reasons. For example, once it is closed, you are free to write another one with a higher strike price and more time until expiration. That extended time means the option premium will be higher, so it is profitable for you to sell. Remember, upon sale, you receive the premium, so the higher it is, the more profitable.

The discounting effect of covered call writing complicates the calculation of return on your investment. But it also discounts your basis in stock and provides a third way to gain (after capital gains and dividends) from investing in stock. Computing your investment return is also complicated by the effect of federal and state income taxes.

 

Taxes and Investment Return

There are two aspects to taxes that concern all investors: the effective tax rate and its impact on net returns, and the viability of tax-free investing (based on pretax and after-tax returns).

The effective tax rate is the rate that you pay on your taxable income. This is not the same as total income, gross income, or adjusted gross income. The formula for taxable income is:

This formula describes federal taxable income. The formula used by various states will vary considerably. The effective tax rate is the percentage that your total tax liability represents of your taxable income:

This formula applies to the federal tax rate. To find your overall tax rate (combining both federal and state and, where applicable, local income taxes), add together the computed tax liability and federal liability, and divide the total by the federal taxable income:

The state-based taxable income may not be identical to the federal figure, but based on the rationale that federal taxes are normally greater than those paid to the state or locality, using the federally computed taxable income is the most logical.

To compute after-tax income on any investment, you need to reduce the gross return by your effective tax rate:

By deducting your effective tax rate from 100, you arrive at the percentage of after-tax income you earn. This is divided by 100 to produce the decimal equivalent of the remaining portion of income. (For example, if your overall effective tax rate is 40%, you deduct 40 from 100 and arrive at 60. This is divided by 100 to find 0.60. This is the decimal equivalent of 60%, or your after-tax rate.)

There are many forms of investing free of income tax altogether, or with taxes deferred until the future. For example, municipal bonds are issued without a liability for federal or state taxes. But the interest rate is lower than you would earn from buying other bonds, so a comparison is necessary. By computing your effective tax rate, you can determine whether you would be better off one way or the other. The comparison would be to reduce the income on a taxable bond by your effective tax rate, resulting in your after-tax income. Is this higher or lower than the yield from a tax-free bond?

Another type of tax deferral is that earned in qualified accounts, such as individual retirement accounts. In these accounts, current income is not taxed until retirement or withdrawal, and, in some types of IRA accounts, you can withdraw your principal and leave earnings to accumulate without paying tax until later. In calculating a true and comparative return on investment, you have to consider the true net basis, the time the investment was held, and the tax consequences of profits. In the case of capital gains, a lower rate applies if the gain is long-term; this affects your effective tax rate as well.

Return on investment is far from simple or consistent, which is why you need to ensure that the methods you use are applied in the same manner in each instance. A much different method of calculations is used by corporations. When you invest in a company and examine the balance sheet, you discover that returns on capital are key indicators in picking the stock of one company over another. This is the topic of the next chapter.

© 2007 Michael Thomsett.
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