Measuring a security’s performance is a core part of investing. You’ll want to be able to tell which holdings have performed best and worst based on their returns. Depending on the security, there may be more than one useful way to measure performance.

Here are the common measures covered in this chapter:

• Risk-adjusted return
• Time-weighted return
• Dollar-weighted return
• Total return
• Holding period return
• Annualized rate of return
• Inflation-adjusted return
• After-tax return
• Rule of 72
• Benchmark comparisons

Risk-adjusted return

Not all returns mean the same thing. A 10% return could be excellent or disappointing depending on how much risk you took to earn it. For example, a 10% return on a Treasury bill would be extraordinary given its low risk, while a 10% return on a high-risk hedge fund might be considered underperformance. That’s why some investors adjust returns for risk - to see how much return they’re getting per unit of risk.

American economist William Sharpe developed a method for measuring risk-adjusted return in 1966. Now known as the Sharpe ratio, it measures a security’s or portfolio’s return while accounting for risk:

$$\text{Sharpe ratio}=\frac{\text{Actual return - Risk free rate}}{\text{Standard deviation}}$$

The risk-free rate of return is the 91-day (3-month) Treasury bill rate. Standard deviation measures how far a security’s returns deviate from its average return. Higher standard deviation means more volatility. Some investors describe standard deviation as a measure of “pure risk” (as opposed to beta, which measures volatility relative to the market).

The numerator (the top of the fraction) is the security’s or portfolio’s risk premium:

• Actual return − risk-free rate = risk premium

The idea is straightforward: if you accept the possibility of loss, you should expect compensation for taking that risk.

Interpreting the Sharpe ratio:

• A higher Sharpe ratio suggests the investment is more efficient (more return for the amount of risk taken).
• A lower Sharpe ratio suggests the investment is less efficient (less return for the amount of risk taken).

It’s unlikely you’ll be asked to calculate a Sharpe ratio on the exam, but you may see questions about what the components mean or what the ratio is used for.

Time-weighted return

Investors in mutual funds commonly use two different return measures when evaluating performance. One is time-weighted return, which measures performance over a specific time period while assuming a buy and hold strategy.

A buy and hold strategy means you buy the investment and hold it for the entire period, with no additional purchases or sales during that time.

When you research a mutual fund, you’ll often see multiple time-weighted returns. For example, on Morningstar, a fund’s “Trailing Returns” might include 1-day, 1-week, 1-month, 3 months, year-to-date (YTD), 1-year, 3-year, 5-year, 10-year, 15-year, and lifetime (since inception) returns. These are time-weighted returns because they assume:

• A single investment was made at the start of the period
• The investment was held for the entire period
• Dividends and capital gain distributions were reinvested

For instance, a 3-year return assumes the investment was made three years ago and then held, with no additional purchases or sales.

Sidenote

Morningstar

Morningstar is a financial services company focused on investment research. It’s well known for mutual fund research and its rating system.

A Morningstar rating assigns mutual funds 1-5 stars based on recent performance. 5-star funds have the highest risk-adjusted returns compared with similar funds (funds with similar investment goals), while 1-star funds have the lowest risk-adjusted returns.

Time-weighted returns are especially useful for evaluating a mutual fund manager’s performance. Mutual funds are managed by teams of professionals, typically led by a fund manager. Some managers remain in place for long periods due to consistent performance. For example, Will Danoff has managed Fidelity’s Contrafund since 1990.

Time-weighted return helps isolate the fund’s performance from an investor’s timing decisions. For example, if an investor buys on a day the market rises sharply and sells on a day the market drops sharply, a loss may reflect poor timing rather than poor fund management.

Dollar-weighted return

Dollar-weighted return measures a mutual fund investor’s personal return based on:

• The fund’s performance, and
• The investor’s own cash flows (the timing and size of purchases and withdrawals)

Unlike time-weighted return, dollar-weighted return reflects what the investor actually experienced. If an investor buys more shares when the NAV is low or sells when the NAV is high, their dollar-weighted return may be higher than the time-weighted return over the same period (and vice versa).

Total return

Total return measures an investment’s overall gain or loss as a percentage of its original cost. It captures the full rate of return from all sources.

There are three ways an investor can earn a return (or lose money) on a security:

• Dividends
• Interest
• Capital gains and/or losses

Preferred stocks and some common stocks pay cash dividends. Debt securities pay interest.

Any security can produce a capital gain or loss:

• A capital gain occurs when market value rises above cost.
  • Realized gains occur when the investment is sold.
  • Unrealized gains occur when the investment hasn’t been sold yet.
• A capital loss occurs when market value falls below cost.
  • Like gains, losses can be realized or unrealized.

Total return adds up all gains and losses and compares them to the original cost:

$$\text{Total return}=\frac{\text{All gains and/or losses}}{\text{Original cost}}$$

Although calculations are relatively limited on the Series 65, total return is a common calculation test takers encounter. The following video shows how to approach a total return question:

Now, try one on your own:

An investor purchases 100 shares of stock at $50 per share. The investor receives two quarterly dividends of $1 per share after holding the security for six months, then sells the security for $55 per share. What is the total return?

Can you figure it out?

Holding period return

Holding period return is the rate of return earned over a specific holding period. In other words, it’s the total return for a defined time span.

In the example above, the investor held the stock for six months, and the holding period return over that six-month period is 14%.

Annualized return

An annualized return expresses a total return as an annual rate.

Using the same example:

An investor purchases 100 shares of stock at $50 per share. The investor receives two quarterly dividends of $1 per share after holding the security for six months, then sells the security for $55 per share. What is the annualized return?

We already found the total return over six months was 14%. Since there are two six-month periods in a year, the annualized return is:

• 14% × 2 = 28%

For holding periods less than one year, multiply the total return by the number of those periods in a year:

• If 14% was earned in 4 months, annualized return = 14% × 3 = 42% (three 4-month periods in a year)

For holding periods longer than one year, divide the total return by the number of years:

• If the holding period return over two years is 14%, annualized return = 14% ÷ 2 = 7%

Inflation-adjusted return

The inflation-adjusted return, also called the real rate of return, is the total return minus the inflation rate.

In the U.S., inflation is commonly measured using the consumer price index (CPI), which tracks price changes across a basket of goods and services.

Sidenote

Personal Consumption Expenditure (PCE) Price Index

Technically, the Federal Reserve targets inflation based on the Personal Consumption Expenditure (PCE) Price Index, which is similar to CPI but differs in weighting and measurement.

If you want the details, this article is a helpful reference: PCE vs. CPI: What’s the difference and why it matters right now

As covered in the fixed income unit, inflation is especially harmful to securities with fixed rates of return. To show the return after removing inflation’s effect, use:

$$\text{Inflation-adjusted return}=\text{Total return - inflation rate (CPI)}$$

Try this practice question:

An investor buys a $1,000 par, 5% bond at 94 in the market. After holding the bond for exactly one year, the investor sells the bond at 97. Assuming CPI is reported at 4% for the year, what is the real rate of return?

Can you figure it out?

After-tax return

After-tax return is the total return after accounting for taxes.

This can get tricky because different types of returns may be taxed at different rates. As covered in the tax considerations chapter, dividends and capital gains don’t always receive the same tax treatment.

Let’s work through an example:

An investor in the 24% tax bracket purchases 100 shares of stock at $80 per share. Over the course of a year, they receive $2 quarterly dividends (per share). The investor sells the stock at $90 per share exactly one year after it was purchased. What is the after-tax return?

First, identify the two sources of return:

• Cash dividends
• A short-term capital gain (a holding period of one year or less is short-term)

Qualified* cash dividends for this investor are taxed at 15%; only investors in the two highest tax brackets (35% and 37%) are subject to the 20% dividend tax rate. Short-term capital gains are taxed at the investor’s ordinary income tax bracket, which is 24%.

*Nearly all income paid from equity securities is considered qualified and subject to 15% or 20% taxation. There’s one exception - real estate investment trusts (REITs) pay non-qualified dividends, which are taxable at the investor’s income tax bracket. Again, you can revisit the tax considerations chapter if a refresher is necessary.

Even though the investor bought 100 shares, it’s easiest to compute on a per-share basis:

• Dividends: $2 quarterly dividend × 4 payments = $8 per share
• Capital gain: $90 − $80 = $10 per share

Applicable tax rates:

• $8 in dividends, taxed at 15%
• $10 in capital gains, taxed at 24%

To convert each return to an after-tax amount, multiply by (100% − tax rate):

• $8 dividends × 85% (100% − 15%) = $6.80 after-tax
• $10 capital gain × 76% (100% − 24%) = $7.60 after-tax

Now compute after-tax return using the same structure as total return:

$$\text{After-tax return}=\frac{\text{After-tax returns}}{\text{Original cost}}$$

$$\text{After-tax return}=\frac{\text{\$6.80 dividends + \$7.60 capital gain}}{\text{\$80.00 original cost}}$$

$$\text{After-tax return}=\frac{\text{\$14.40 overal after-tax return}}{\text{\$80.00 original cost}}$$

$$\text{After-tax return}=\text{18\%}$$

Here’s a video further breaking down after-tax returns:

Rule of 72

In the late 15th century, Italian mathematician Luca Pacioli introduced a simple way to estimate how long it takes to earn a 100% return* on an investment. This shortcut is called the Rule of 72.

The Rule of 72 isn’t perfectly precise (more complex math is needed for exact results), but it’s a quick way to estimate how fast an investment can double.

*Making a 100% return on an investment is the same as doubling the investment. For example, assume an investor makes a $10,000 investment. A 100% return would be an additional $10,000, increasing the investment’s value to $20,000 (2x the starting amount).

Here’s the first Rule of 72 formula:

$$\text{Time needed to 2x money}=\frac{\text{72}}{\text{Annual rate of return*}}$$

*When using this calculation, do not enter the rate of return on a typical decimal basis. For example, if the rate of return is 7%, you will enter ‘7’ into the denominator, not ‘0.07.’

Try it:

An investor believes they can attain an annual rate of return of 9% on an investment of $100,000. Assuming their goal is to grow the funds to $200,000 for a down payment on a home, how long will it take to reach the goal?

Can you figure it out?

The Rule of 72 can also estimate the annual return needed to double an investment within a given time period:

$$\text{Annual return to 2x money}=\frac{\text{72}}{\text{Time period (in years)}}$$

Try it:

A customer of yours has $50,000 to invest for their daughter’s college experience. Their goal is to grow the funds to $100,000 before the child turns 18. Assuming the daughter is currently age 12, what annualized rate of return must they attain to reach their goal?

Can you figure it out?

Rule of 72 questions can also involve multiple doublings. For example:

An investor recently received a $50,000 bonus from their employer and plans to invest the funds into the market. Their goal is to reach $200,000 within 8 years. What annualized rate of return is required to reach their goal?

Can you figure it out?

Benchmark comparisons

After you calculate a portfolio’s or security’s return, it’s often compared to a relevant benchmark index. For example, large-company stocks are commonly compared to the S&P 500 index. If a stock is up 15% for the year while the S&P 500 is up 10%, the stock is said to have outperformed the market by 5%.

An index tracks the market prices of a pre-determined group of investments. For example, the S&P 500 tracks 500 of the largest U.S.-based publicly traded companies, including Apple, JP Morgan Chase, and Amazon.

In general, an index reflects the average change in market prices for a basket of securities. However, indexes can weight holdings differently. For example, Amazon’s price changes affect the S&P 500 more than Alaska Airlines stock because Amazon’s market capitalization is much larger. The larger the company, the more influence it typically has in a cap-weighted index.

Indexes typically use one of two weighting methods:

• Price-weighted indexes weight more heavily the stocks with higher share prices.
• Cap-weighted indexes weight more heavily the stocks with higher market capitalizations.

These are the relevant indexes to know for the exam:

• S&P 500
  • Tracks 500 large-cap stocks
  • Cap-weighted index
• S&P 100
  • Tracks 100 large-cap stocks (a subset of the S&P 500)
  • Cap-weighted index
• S&P 400
  • Tracks 400 mid-cap stocks
  • Cap-weighted index
• Dow Jones Composite
  • Tracks 65 prominent stocks
  • Composite of DJIA, DJTA, and DJUA (see below)
  • Price-weighted index
• Dow Jones Industrial Average (DJIA)
  • Tracks 30 prominent stocks (various industries)
  • Price-weighted index
• Dow Jones Transportation Average (DJTA)
  • Tracks 20 prominent transportation stocks
  • Price-weighted index
• Dow Jones Utilities Average (DJUA)
  • Tracks 15 prominent utilities stocks
  • Price-weighted index
• Russell 2000
  • Tracks 2,000 small-cap stocks
  • Cap-weighted index
• NASDAQ Composite
  • Tracks all stocks on NASDAQ exchange
  • Cap-weighted index
• NASDAQ 100
  • Tracks 100 largest stocks on the NASDAQ exchange
  • Cap-weighted index
• Wilshire 5000
  • Tracks all actively traded stocks in the US
  • Considered the broadest domestic index
  • Cap-weighted index
• EAFE index
  • Tracks stocks in Europe, Australasia and Far East
  • Cap-weighted index