Textbook

Measuring a security’s performance is an important aspect of investing. An investor should be “in tune” with their portfolio and able to determine their best and worst investments based on their returns. Depending on the security, there may be multiple ways to measure performance. We’ll cover these common ways to do so 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

Not all returns are the same. For example, a 10% return on investment could be amazing or terrible depending on the security. A 10% return on a Treasury bill would be quite extraordinary given its lack of risk, while a 10% return on a high risk hedge fund may be considered an underperformance. That’s why some investors prefer to adjust their returns for risk to determine if they’re getting “bang for their buck.”

American economist William Sharpe developed a method for determining **risk-adjusted return** in 1966. Nowadays known as the **Sharpe ratio**, Mr. Sharpe created this formula to determine a security or portfolio’s return while factoring risk out:

$Sharpe ratio=Standard deviationActual return - Risk free rate $

As we learned in the discounted cash flow chapter, the **risk-free rate of return** is equal to the 91-day Treasury bill rate. **Standard deviation** measures how far a security deviates from its average price. The higher the standard deviation, the more volatility a portfolio is subject to. Some investors refer to standard deviation as a measurement of “pure risk” (as opposed to beta, which measures volatility as compared to the market).

The numerator (top part) of the formula measures the security or portfolio’s **risk premium**. When investors expose themselves to the potential for loss, they should be compensated accordingly. The risk premium demonstrates compensated returns for the risk encountered.

The higher the Sharpe ratio, the more efficient the security or portfolio. The more efficient an investment, the higher its return in comparison to its risk profile. And, vice versa - the lower the Sharpe ratio, the less efficient the security or portfolio, and the lower its return in comparison to its risk profile. It’s unlikely you’ll be asked to perform a Sharpe ratio calculation on the exam, but you could encounter questions on the components of the formula or the concept behind it.

Investors in mutual funds typically utilize two different measures of returns when evaluating performance. One of them is **time-weighted return**, which analyzes mutual fund performance over specific periods of time while assuming a **buy and hold strategy**. This strategy is exactly what it sounds like - buy a security and hold without making any adjustments for a specified period of time.

Investors can typically find numerous versions of time-weighted returns on mutual funds they research. For example, you can find several time-weighted returns related to the JP Morgan Large Cap Growth Fund (or any other mutual fund) on **Morningstar**. Under the ‘Trailing Returns’ section, you’ll find 1-day, 1-week, 1-month, 3-month, year-to-date (YTD), 1-year, 3-year, 5-year, 10-year, 15-year, and lifetime (since inception) returns. These are all time-weighted returns, which assume a single investment was made at a point in the past and held over that time period. Additionally, it’s assumed all dividends and capital gain distributions are reinvested. For instance, the 3-year return assumes an investment was made 3 years ago, and no sale or additional purchases occurred.

Time-weighted returns are especially helpful for assessing a mutual fund manager’s performance. Every mutual fund has a team of financial professionals managing the fund, with a fund manager appointed as the leader. Some fund managers consistently perform well and are kept in their position for lengthy periods of time. For example, Will Danoff has been managing Fidelity’s Contrafund since 1990. He wouldn’t be in his position as a fund manager overseeing over $100 billion of assets if he wasn’t good at his job. On the other hand, some fund managers don’t even make it a few years before being fired from their position for underperformance.

When analyzing a mutual fund’s performance from a time-weighted perspective, it truly measures the fund’s achievements without the bias of making multiple investments or timing the market at the wrong or perfect moment. For example, let’s assume an investor buys a mutual fund on a day the market was up significantly, and subsequently sells the mutual fund on a day there was a significant decline. If they experience a loss, does that necessarily reflect on the fund manager? Probably not, as at least part of the loss could be attributed to bad timing on behalf of the investor.

**Dollar-weighted return** measures a mutual fund investor’s personal return, based on the mutual fund’s performance plus the investor’s transactions. Instead of measuring returns only over a specified period of time (like time-weighted return does), it additionally considers the timing and amount of additional purchases and/or withdrawals. In plain terms, dollar-weighted return is very investor-specific. If an investor times their transactions at opportune moments (buying shares when the NAV is low or selling shares when the NAV is high), their dollar-weighted return may be higher than the time-weighted return over the same period of time (and vice versa).

The measurement of an investment’s total gain or losses as a percentage of its original investment is **total return**. Essentially, total return measures the overall rate of return on an investment. There are three ways to make a return or lose capital (money) on a security:

- Dividends
- Interest
- Capital gains and/or losses

Preferred stocks and some common stocks pay cash dividends to investors as a form of income. Debt securities pay interest to investors as a form of income. Any security can obtain a capital gain or loss. Capital gains occur when an investment’s market value grows above its cost. Capital gains can be realized or unrealized; realized gains occur when an investment is sold and its gain is “locked in,” while unrealized gains occur when an investment is not yet sold. Capital losses occur when an investment’s market value falls below its cost. Like capital gains, capital losses can also be realized or unrealized.

Total return considers all possible forms of returns or losses related to an investment and compares it to the investment’s cost. Here’s the formula:

$Total return=Original costAll gains and/or losses $

Although calculations are few and far between on the Series 66, total return is a common calculation test takers encounter on the exam. The following video shows how to approach a total return question:

Now, let’s see if you can do it 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?

(spoiler)

Answer = **14%**

Let’s establish the total return formula:

$Total return=Original costAll gains and/or losses $

You can calculate the total return using the total numbers, or on a per-share basis. Either will work. For ease, let’s calculate it on a per-share basis.

The investor made $2 in dividends per share ($1 quarterly dividend per share x 2 quarters), plus realized a $5 capital gain (bought at $50, sold at $55). Therefore, the overall return is $7 per share ($2 dividend + $5 capital gain). The original cost was $50 per share. We now have all the necessary components:

$Total return=$50 original cost$2 dividend + $ 5 capital gain $

$Total return=$50 original cost$7 overall return $

$Total return=14%$

The rate of return on an investment over a specified period of time is known as **holding period return**. It’s basically a security’s total return over a specific time period. Both the six-month holding period return and the total return of the security in the example question above is 14%.

When total return is converted to measure annual (return), it is an **annualized return**. Using the same example question above, let’s explore this measure of return:

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?

As we discovered above, the total return was 14%. If the investor made a 14% in a six-month period, then their annualized return would be twice that amount given there are two six-month periods in a year. Therefore, the annualized return would be 28%. To find the annualized return on a security held for less than a year, multiply its total return by the number of those periods in one year. If the 14% return was instead obtained in a 4-month period, the annualized return would be 42%. There are three 4-month periods in a year, so the total return would be multiplied by 3 to arrive at the annualized return (14% x 3 periods = 42%).

What if the holding period was longer than a year? For example, what if the holding period return over two years was 14%? To find the annualized return, divide the total return by the number of years the holding period covers. A 14% return over two years would therefore be annualized to 7% (14% / 2 years).

The **inflation-adjusted return**, also known as the **real rate of return**, is the total return minus the inflation rate. The US government measures inflation primarily by the **consumer price index (CPI)**, which analyzes the price changes of a number of goods and services. As we learned in the fixed income unit, inflation negatively impacts securities with fixed rates of returns. To accurately depict the overall return while factoring out inflation, an investor can use this formula:

$Inflation-adjusted return=Total return - inflation rate (CPI)$

Let’s see if you can make your way through a 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?

(spoiler)

Answer = **4.5%**

First, we’ll need to determine the total return using this formula:

$Total return=Original costAll gains and/or losses $

The bond paid $50 in interest over the year (5% x $1,000 par). The investor purchased the bond for $940 (94*), and sold the bond for $970 (97*), therefore realizing a $30 capital gain.

**Both 94 and 97 are percentage of par quotes. 94% of par ($1,000) is $940, while 97% of par ($1,000) is $970. If you need a refresher on this topic, follow this link to revisit the chapter it was covered in.*

We can now calculate the bond’s total return:

$Total return=$940$50 interest + $30 capital gain $

$Total return=$940$80 overall return $

$Total return=8.5%$

Now that we have the total return, we can calculate the real rate of return:

$Real rate of return=Total return - inflation rate (CPI)$

$Real rate of return=8.5% - 4.0%$

$Real rate of return=4.5%$

When taxes are factored out of total return, the **after-tax return** has been calculated. This could be a tricky calculation depending on the tax status of different returns. As we learned in the tax considerations chapter, different forms of return are subject to different tax rates. Let’s go through a quick example together:

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, we must acknowledge the two types of returns the investor obtains. They received cash dividends and realized a short-term capital gain (remember, a holding period of one year or less is a short-term capital gain). Qualified* cash dividends for this investor are taxable at 15%; only those at the two highest tax brackets (35% and 37%) are subject to the 20% dividend tax rate. Short-term capital gains are taxable at the investor’s 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.*

Although the investor purchased 100 shares, we can again approach this question on a per-share basis. A total of $8 per share in dividends ($2 quarterly dividend x 4 payments) were received, while the investor realized a $10 capital gain (bought at $80, sold at $90). Let’s summarize the returns and applicable tax rates:

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

To find the after-tax returns, we must factor out taxes. The easiest way is to multiply the return by 100% minus the applicable tax rate. For example, the dividends would be multiplied by 85%, which is 100 minus the 15% tax rate. If the government receives 15% of the return via taxes, then the investor keeps 85% of the return. Let’s do those calculations:

- $8 in dividends x 85% (100% - 15%) =
**$6.80 after-tax** - $10 in capital gains x 76% (100% - 24%) =
**$7.60 after-tax**

Now, we can calculate the answer by doing the total return calculation with the overall returns adjusted for taxes:

$After-tax return=Original costAfter-tax returns $

$After-tax return=$80.00 original cost$6.80 dividends + $7.60 capital gain $

$After-tax return=$80.00 original cost$14.40 overal after-tax return $

$After-tax return=18%$

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

Back in the late 15th century, an Italian mathematician named Luca Pacioli created a simplistic method to determine the length of time it takes an investor to make a 100% return* on an investment. Known as the **Rule of 72**, this math technique does not produce absolutely accurate results (complex calculations are needed for this), but it provides a quick and easy way to determine how quickly one can double their money.

**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 to be aware of:

$Time needed to 2x money=Annual rate of return*72 $

**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.’*

Let’s see if you can utilize the calculation:

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?

(spoiler)

Answer = **8 years**

With an expected rate of return of 9%, we can utilize the Rule of 72 calculation:

$Time needed to 2x money=972 $

$Time needed to 2x money=8 years$

The Rule of 72 can also be used to determine the annualized rate of return needed to double an investment within a specified period of time. The formula changes slightly to determine this:

$Annual return to 2x money=Time period (in years)72 $

Let’s see if you can utilize the calculation:

A customer of yours has $50,000 to invest in 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?

(spoiler)

Answer = **12%**

The child is currently age 12 and the customer wants the funds to double by the time they’re age 18. Therefore, we have a time period of 6 years. We can now utilize the Rule of 72 calculation:

$Annual return to 2x money=6 years72 $

$Annual return to 2x money=12%$

While the questions listed above are fairly simple if you understand the underlying concept, be aware Rule of 72 questions can be more challenging. For example:

An investor recently received a $50,000 bonus from their employer and planned 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?

(spoiler)

Answer = **18%**

The investor wants to double their money twice in an 8-year period ($50k --> $100k --> $200k). Therefore, it can be simplified to assume the investor needs to double their money every 4 years. Now, the calculation can be performed:

$Annual return to 2x money=4 years72 $

$Annual return to 2x money=18%$

When the return on a portfolio or security is calculated, it’s often compared to a relevant **benchmark index**. For example, stocks from large companies would likely be compared to the S&P 500 index to determine over or underperformance. If a stock was up 15% on the year while the S&P 500 was up 10%, the stock would be considered “beating the market” by 5%.

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

In a general sense, an index tracks the average change in market prices of a basket of securities. However, they can weigh certain investments differently. For example, changes in Amazon’s market price are more heavily factored into changes in the S&P 500 than the price changes of Alaska Airlines stock (Amazon’s market capitalization is roughly 200 times the size of Alaska Airlines). This should make sense - the larger the stock, the bigger the impact it should have on an index.

Indexes typically fall into one of two camps when it comes to weighting securities: price-weighted or cap-weighted. **Price-weighted indexes** provide heavier weighting to stocks with higher prices, while **cap-weighted indexes** provide heavier weighting to stocks with higher market capitalizations.

These are the relevant indexes to be known 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 utility 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

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