Series 66 Study Guide Navigation

We start our Series 66 exam preparation by looking first at various analytical methods that securities professionals should know about. 

A. Analytical methods 

These analytical methods involve mathematical concepts that will help you to make the best investment decisions possible for your customers. 

Time value of money

The time value of money is one of the tools available to quantitative analysts to help them make better investment decisions. 

But what is it?

Well, the concept of time is money is something that you can certainly link to investments, that’s for sure. 

Let’s look at it this way.

If an investor invests their money in something that will pay out a certain amount 10 years down the line, how does that compare to if they kept the money and instead used it during the next 10 years instead of waiting on it to make a return. 

So if they had $38.55 today, and made 10% on the money, in 10 years, after we allow for the figure being compounded annually, they will have $100.

We call this the present value of a future sum.

But there is another way to look at the time value of money. 

This uses an assumed rate of return and looks at the amount that someone should invest at this moment to reach a specific return at some point in the future. 

This is known as computing future value. 

Future value (FV)

Now that we understand what future value is, what does it depend on?

Well, there are two things:

  • The rate of return it will earn (r)
  • The time (in number of years) that it will be invested (n)

Therefore to work out FV, you can use the following equation:

  • FV = Present Value (PV) x (1xr)n

Present value (PV)

When calculating PV, we use the following equation:

  • PV = FV / (1 + r)n

You should remember this about PV and FV.

  • If you know the FV you find the PV
  • If you know the PV you can find the FV

Rule of 72

This method, which is a shortcut, can help to work out how many years it will need for an investment to double.

This assumes that the investment will receive compounded earnings. 

So by dividing 72 by the interest rate paid by an investment, you can calculate how many years it will take to double. 

For example, if you invested $2,000 and it earns an interest rate of 6%, it will double in a period of 12 years because 72 divided by 6 is 12. 

This rule works in reverse as well, so if you know the period, the required earnings rate to double by can be calculated as well.

All you need to do is divide the time period you have into 72 to give you the earnings rate needed to double your money.

Net present value (NPV)

The difference between the present value of an investment and the cost thereof is known as its NPV. 

This can be used by an investment adviser as a way to take any investment vehicle with a projected stream and then evaluate a client’s investment in it. 

To do this, the investment cash flows will be projected by the advisor while taking into account the required rate of return the investor wants while discounting them to their present value. 

Anything that shows a positive NPV is worth adding to an investment portfolio. 

Internal rate of return (IRR)

What is IRR?

Well, it’s linked to the NPV of an investment and it’s the discount rate (r) that makes it equal to zero.

In present PV and FV value calculations, IRR can be thought of as the (r) but you should note that calculating it directly is difficult. 

To work it out uses a process called iteration, which is very much trial and error.

You should also note the time value of money is always taken into consideration with IRR. 

IRR is used mostly when it comes to common stock on companies that deliver stable dividends but it can be used for pretty much any investment. 

Central tendency measures

Several other numerical tools that don’t relate to time value can appear on the exam and we are going to cover the most important of them now. 

Mean/Arithmetic mean

Mean, average, it’s all pretty much the same thing.

When measuring central tendency, however, this is one of the ways that it is commonly carried out. 

It’s easy to do.

Take the variables, add them up, divide by their number and you have the mean (average). 

A stock returning 4%, 5%, 3% and 4% has a mean of 4% (4+5+3+4 is 16 / 4 occurrences = 4).

When it comes to skewed distributions, however, the mean isn’t always the most appropriate way to measure them. 


When we talk about the midpoint of a distribution, this is referred to as the median. 

When you have a number of returns from an investment over a period, you can find the media by first listing them in order.

Once you have done that, look for the middle number.

For example, the median of 12, 8, 5, 14, and 9 is 9 (5, 8, 9, 12, 14 – 9 is the middle number).

If you have a set of even numbers and not odd as above, you will need to take the average of the middle two to find the median.

The mean and the median will never be the same number. 

When working out skewed distributions, the median is an appropriate way to do so, and certainly better than using the mean. 

It’s also excellent when outliers – variables that are outside of the normal range – are involved. 


In a distribution of numbers, mode will help measure the most common value. 

Consider these numbers: 3,3,3,7,8,8,10. 

Here the mode is 3, the most common value. 

Geometric mean

You will multiply everything to work out the geometric mean of a given set of numbers. 

Once you have done that, you take the nth root of them to get the geometric mean.

This probably won’t appear on the exam, however.


When viewing a sample, the difference between the highest and lowest returns is the range. 

Results generally are skewed in a certain direction when there are many values at one extreme of the range. 

The number found in the middle of the range is called the mid-range value. 

The easiest way to find this is to look at the dataset and reorder it, starting with the smallest number and then moving to the largest. 

After that, you subtract the first element from the last element. 

For example, in the numbers 4,7,8,11 and 13, the range is 9 (13-4) while the mid-range will be 8.5. 

Beta and Alpha coefficient

Next, we look at two coefficients that you will need to know for the Series 66 exam: alpha and beta. 


Beta looks at a movement of a stock or portfolio as well as that of the market and then measures the variability between them. 

So when compared to the risk of the market, if a stock has a beta of 1.00, the overall risk of that stock is similar. 

When beta is measured, the most common index that it is measured against is Standard and Poor’s 500. 

The higher the beta, the higher the overall risk of a stock, for example, a stock with a beta measuring 1.50 is, when compared to the market, more volatile.

A beta lower than 1.0, however, indicates a stock that is less volatile when compared to the market. 

Assets can have a negative beta as well and this isn’t a bad thing, as they are useful when a securities professional is looking to diversify a portfolio.

If there is a general decline in the overall market, a stock with a negative beta should show some positive returns. 

A stock with a lower positive beta is perfect for clients that don’t want to take on investments with too much risk.

The higher the positive beta, the more risk involved and that’s perfect for those clients that are more aggressive in their investment strategies. 


Generating a positive alpha is something that portfolio managers are looking to achieve. 

When this happens, the investment has performed much better than was originally projected and based on the risk taken in terms of overall volatility.

Alpha values can be zero, positive or negative.

  • An underperforming portfolio will have a negative alpha
  • An overperforming portfolio will have a positive alpha

Computing alpha uses this formula:

  • (total portfolio return – risk-free rate) – (portfolio beta x [market return – risk-free rate])

Here, after eliminating the risk free rate, the performance is being compared.  

Standard deviation

Using historical performance data, standard deviation measures an investment’s projected returns but specifically the overall volatility thereof. 

Essentially, it’s the amount of variability around the average that’s measured here, with that variability also called the dispersion. 

A security will have a greater risk associated with it the higher the standard deviation because this means the returns are expected to deviate more from the average return. 

It’s as a percentage that standard deviation is expressed. 

The general rule of thumb is that about two-thirds of the time, a security will vary within one standard deviation while about 95% of the time, within two standard deviations. 

Standard deviation is an excellent way for an investor to compare two investments that they might be considering and then decide on which is the better option. 

What about standard deviation versus beta?

Well, if we talk about beta, it measures systematic (market) risk.

In other words, it looks at the overall market and then compares the volatility of a security against it. 

Standard deviation is different because it includes both systematic and unsystematic risk and measures the volatility of the security against the performance expected of it.

In other words, the total risk of the security or the portfolio is measured by standard deviation. 

Correlation coefficient 

When securities are moving in the same direction, they are said to be in correlation. 

If they achieve a perfect correlation, the relationship between their prices is considered to be a perfect positive and linear. 

This movement can be both up and down, but it’s always the same between the two securities.

So what’s the correlation coefficient?

Well, it ranges between -1 to +1.

When it is at +1, the securities are perfectly correlated. 

When it is at 0, there are unrelated price movements between securities. 

When it is at -1, there is a perfect movement between two securities, but this time it is in the opposite direction. 

In the industry, securities with correlation coefficients of between 0.80 and higher are said to be very high correlation securities. 

Balance sheet ratios

Looking at a corporation’s financial statement is an excellent fundamental analysis tool.

The balance sheet is particularly useful, and there are some of the elements from it that you should know for the exam.

Working capital

This denotes a company’s liquid capital or cash that they have readily available and is an excellent measure of its overall liquidity as a way to meet short-term obligations.

There is a formula to work this out as well:

  • Working capital = current assets – current liabilities

Working capital can be increased by:

  • Issuing either long-term debt or equity securities
  • Business operating profits
  • Noncurrent asset sales 

Working capital can be decreased by:

  • The declaration of cash dividends
  • Long-term debt payment
  • Running at a loss

Current ratio

For an even better way to measure a company’s financial strength, you can pair working capital with current ratio.

When computing the current ratio, you would again look at the current liabilities and assets of the company. 

However, this time, they are expressed as a ratio of one another with the current assets divided by the current liabilities to compute that ratio. 

A company that has a high ratio following this computation is more liquid than one with a lower ratio.

While on this subject let’s discuss the quick asset ratio also called the acid ratio test.

Meeting short-term obligations is something that’s extremely important for any corporation. 

This ratio doesn’t look at all the current assets of a company but instead quick assets.

This is what remains when inventory is taken away from the current assets. 

To compute the quick ratio, you simply need to take these quick assets and then divide them by current liabilities. 

Or you can take the current assets and once you’ve removed the inventory from them, divide them by current liabilities. 

A further balance sheet computation is debt-to-equity ratio which can help compute the company’s use of financial leverage. 

Let’s say a company has a total capitalization of $90 million and of that, $50 million of that is long-term debt.

Dividing the total capital by the total long-term debt will give the debt-to-equity ratio. 

Here, if we divide $90 million by $50 million, that works out to a debt-to-equity ratio of close to 56%. 

Let’s also consider book value per share.

This is essentially a  liquidation value of a company.

This considers the disposal of all assets, payment to all creditors, and distribution of the profits to stockholders.

Only tangible assets will be included when calculating this, so intangible assets must be taken from the total assets first to help determine the amount. 

The formula for book value per share:

  • Book value per share = tangible assets – liabilities – preferred stock par value / shares of common stock outstanding.

Income statement ratios

There are a number of important ratios that use the income statement of a company to help calculate them. 

Let’s look at a few you should know starting with earnings per share (EPS).

This looks at each common share and measures the value of the company earnings from them. 

The equation used for this is:

  • EPS = Earnings available to common / outstanding number of shares  

Looking at earnings available to common stock, once the preferred dividend has been paid, this is the value that remains and so, when calculating EPS, it’s only in relation to common stock. 

Preferred stockholders are not due any other earnings over and above their dividends.

We also must discuss earnings per share after dilution.

This deals with convertible securities but with the assumption that conversion has taken place and they are all now common stock. 

Because more stock participates in earnings, there is a reduction in EPS. 

These calculations won’t be tested because of the fact that tax adjustments make them complicated, but it’s worth understanding what EPS covers. 

Next, we look at how to calculate current/dividend yield.

The annual dividend payout expressed as a percentage of the current stock price helps determine current yield and for this, the following equation is used:

  • Annual dividends per common share / market value per common share = current yield.

Here’s an example

Common stock dividends of $0.50 per share each quarter are paid by a corporation. 

Let’s say that their stock has a common value of $80 per share.

This means that yearly dividends are $2.00 ($0.50×4)

Using the formula, we can calculate $2.00/$80 which is a current yield of 2.5% when expressed as a percentage.

The last thing to look at regarding income statement calculations is dividend payout ratio.

This deals with stockholders and the proportions of earnings they receive in the form of dividends.

The following equation is used to calculate it:

  • Annual dividends per common share / earnings per share (PS) = dividend payout ratio

Well-established companies ordinarily pay out larger percentages of earnings to stockholders in the form of dividends.

Those companies that are still growing will reinvest their earnings more than paying out dividends and when it comes to this ratio, it’s pretty low for them. 

But there are still benefits for stockholders instead of receiving dividends.

For example, they will see gains in the stock price. 

Market price related ratios

The first type used by analysts in this category is price-per-earnings ratio (P/E).

Two elements are taken into account here and specifically the relationship between them.

These elements are different common stock prices compared with the accrued earnings to one share of stock with the following equation used to determine the P/E ratio.

  • Current market price of common share / earnings per share (EPS) = P/E ratio

When compared to cyclical companies, the P/E ratio associated with growth companies will be higher. 

The lowest of all P/E ratios will be associated with industries that are in decline.  

You can calculate EPS once if you know the P/E ratio and the market price of the stock, you can calculate EPS using the following equation:

  • Current market price of a common stock / P/E ratio = EPS

Fundamental analysts see price-to-sales ratio as a better analytical tool than price-to-earnings ratio.

The reason is that different accounting methods affect earnings more than sales.

Finally, let’s talk about price-to-book ratio.

The ratio represents the market price of a common stock as a percentage of its book value (which itself is expressed as a dollar value per share). 

As a measure of value in the event of a liquidation, a company will provide this ratio to its shareholders. 

There is no real relationship between price-to-book ratio and the current value of a company’s stock, however.

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