Investors can use many tools and resources to analyze their portfolios and the economy. The topics here connect closely, so we’ll cover them together:
Total return measures an investment’s overall gain or loss as a percentage of its original cost. In other words, it’s the investment’s overall rate of return.
A security can generate returns (or losses) in three main ways:
Preferred stocks and some common stocks pay cash dividends as income. Debt securities pay interest as income. Any security can also produce a capital gain or loss.
Total return adds up all gains and losses and compares them to the original cost. Here’s the formula:
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?
Answer = 14%
Let’s start with the formula:
You can calculate total return using total dollars or on a per-share basis. Either approach works. We’ll use per-share values to keep the math simple.
Now plug into the formula:
After-tax return is total return after accounting for taxes. This can get tricky because different types of returns may be taxed at different rates.
As you learned in the taxes unit, dividends and capital gains may be taxed differently. Here’s an example:
An investor in the 24% tax bracket purchases 100 shares of ABC Equity Fund at $80 per share. Over the course of a year, they receive $2 quarterly dividends (per share). The investor redeems the fund at $90 per share exactly one year after purchase. What is the after-tax return?
First, identify the two types of return:
The investor receives qualified* cash dividends, which 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.) The investor also realizes a short-term capital gain because the holding period is one year or less. Short-term capital gains are taxed at the investor’s tax bracket, which is 24%.
*You can assume all dividend income paid from equity securities and funds is considered qualified and subject to 15% or 20% taxation unless otherwise specified. If a test question identifies a dividend as non-qualified, it is taxable at the investor’s marginal income tax bracket (up to 37%).
Even though the investor bought 100 shares, we can work per share:
Here are the returns and their tax rates:
To convert each return to an after-tax amount, multiply by (100% − tax rate). This reflects the portion the investor keeps after taxes.
Now calculate after-tax return using the same structure as total return, but with after-tax dollars in the numerator:
Here’s a video that further breaks down after-tax return:
After you calculate the return on a portfolio or security, you’ll often compare it 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 outperforming (“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 prices of 500 of the largest US-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 securities differently. For example, changes in Amazon’s market price affect the S&P 500 more than changes in Alaska Airlines stock, because Amazon’s market capitalization is roughly 200 times larger. The larger the company, the more impact it typically has on a cap-weighted index.
Indexes typically fall into one of two camps when it comes to weighting securities: price-weighted or cap-weighted. Price-weighted indexes give more weight to higher-priced stocks, while cap-weighted indexes give more weight to stocks with higher market capitalizations.
These are the relevant indexes to be known for the exam:
The capital asset pricing model (CAPM) estimates a security’s expected return using only factors related to systematic risk. CAPM uses this formula:
Each input ties back to market-related (systematic) risk:
Here’s an example:
An investor is analyzing a large-cap stock fund prior to making a potential purchase. The expected return of the S&P 500 is 12%, while the security reflects a beta of 1.5 and a standard deviation of 22. Additionally, the 3-month T-bill rate is 2%. Assuming the investor is utilizing the capital asset pricing model, what is the expected return of the large-cap stock fund?
Can you figure it out?
Answer = 17%
First, identify the inputs:
Now apply the formula:
The standard deviation is not necessary to perform this calculation.
Notice what CAPM does (and doesn’t) include. The inputs are market-based, so CAPM focuses on systematic risk. Non-systematic risks such as business risk, financial risk, and liquidity risk are not part of the model. Bottom line: CAPM estimates expected return based on market dynamics and market-related risk.
If this formula looks familiar, that’s because it connects to alpha. Alpha compares a security’s actual return to its CAPM expected return. CAPM gives the expected return; alpha measures whether the actual return was above or below that expectation.
In 1952, economist Harry Markowitz published an essay on investing often viewed as the foundation of modern portfolio theory (MPT). The essay, titled “Portfolio Selection,” laid out rules and protocols for building an efficient portfolio.
An efficient portfolio is one with the highest return potential for the lowest risk exposure.
To develop these protocols, Markowitz made several assumptions about investors, including:
With those assumptions, investors face a tradeoff: higher potential returns generally require taking on more risk. Earning only the risk-free rate avoids much of that risk, but it may not meet an investor’s return goals. One of MPT’s key solutions to this problem is diversification.
An investor might pursue higher returns by holding a volatile (risky) security. That risk can be balanced by holding other securities whose returns don’t move the same way at the same time. For example, losses in luxury cruise line stock during an economic downturn might be offset by returns in a defensive investment like pharmaceutical company stock.
When a portfolio is properly diversified, the risk/return profile of any one security becomes less important. The focus shifts to the risk/return profile of the overall portfolio. This is why a conservative, risk-averse investor might still allocate a small portion of assets to a high-risk security and maintain a suitable overall portfolio.
To evaluate diversification benefits, investors use the correlation coefficient, which measures how two securities or portfolios have moved relative to each other. Correlation ranges from -1 to +1:
All other correlations fall between -1 and 1:
A key test point combines diversification and correlation: to further diversify a portfolio, you generally look for securities with negative correlations to the existing portfolio. Adding negatively correlated holdings introduces components that tend to move in the opposite direction (on average). When the overall portfolio declines, those negatively correlated holdings may rise, helping reduce overall losses.
Beyond diversification across securities, asset allocation also matters. Strategic asset allocation builds on MPT by emphasizing a suitable long-term allocation, avoiding market timing, and periodically rebalancing. When applied consistently, this helps keep the portfolio’s overall risk/return profile aligned with the investor’s goals.
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