Investors can utilize numerous tools and resources to analyze their portfolios and the economy. We’ll discuss the following related topics:
Total return
After-tax return
Benchmark comparisons
Capital asset pricing model (CAPM)
Modern portfolio theory
Economic analysis
Total return
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
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%
After-tax return
When taxes are factored out of the 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 taxes unit, 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 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, 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%.
*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%).
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) was 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:
Benchmark comparisons
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:
The capital asset pricing model (CAPM) predicts a security’s expected return based solely on factors related to systematic risk. CAPM utilizes the following formula:
The three components of the formula - the risk-free return, beta, and market return - all relate to a security or portfolio’s systematic risk. The risk free rate of return refers to the rate of return on the 3 month (or 91 day) Treasury bill. While technically not free of all risk, Treasury bills are considered to have the lowest level of risk in the securities markets, and therefore provide insight into the returns that can be expected with little-to-no systematic risk. Beta refers to a security or portfolio’s volatility as compared to the general market. The market return provides insights into expected volatility in the market.
Let’s take a look at an example of a CAPM question:
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?
(spoiler)
Answer = 17%
Let’s first determine the necessary components of the expected return formula:
Risk free rate = 2%
Beta = 1.5
Market return = 12%
Now, let’s establish the expected return formula:
ER=RF + (Beta x (MR - RF))
ER=2% + (1.5 x (12% - 2%))
ER=2% + (1.5 x 10%)
ER=2% + 15%
ER=17%
The standard deviation is not necessary to perform this calculation.
All components of the expected return formula relate to the market and have little to do with the actual security itself. Non-systematic risks like business risk, financial risk, and liquidity risk are not factored into this model. Bottom line - the calculation above only determines the expected return based on market dynamics and risks.
If the expected return formula above seems similar, it is. When you learned how to calculate alpha, we utilized all the components of this formula. The only difference between the two is the alpha calculation involves subtracting the expected return (what we’re calculating above) from the actual return of the security or portfolio. CAPM only determines the expected return, while alpha compares that expected return to the actual return to determine if the portfolio or security is over or underperforming expectations.
Modern portfolio theory (MPT)
In 1952, economist Harry Markowitz published an essay on investing that still remains relevant in the financial industry today and is often referred to as the birth of modern portfolio theory (MPT). Aptly named ‘Portfolio Selection,’ this essay established a number of rules and protocols for attaining an efficient portfolio. The most efficient portfolio is one with the highest return potential for the lowest risk exposure.
In order to set forth protocols for creating an efficient portfolio, Markowitz made several assumptions about investors, including:
Investors share the same assumptions
Investors can borrow at the risk-free rate
Investors seek the highest return but are also risk averse
With those assumptions in place, investors face a catch-22. They want the highest possible returns but also don’t want to expose themselves to risk. They want to avoid risk, but would not be content with obtaining the risk-free rate of return. As we’ve established throughout this material, with more risk potential comes more return potential. So, how does MPT recommend investors deal with this conundrum? One key component is diversification.
An investor may seek high returns with a highly volatile (risky) security. While a fair amount of risk may be present with any given investment, it can be balanced out with the potential returns of other securities. For example, a loss experienced on luxury cruise line stock due to an economic downturn may be offset by the returns on a defensive investment like pharmaceutical company stock.
When a portfolio is properly diversified, the risk/return profile of any one given security is not important. Instead, the risk/return profile of the overall portfolio should be the primary focus. This means a conservative, risk-averse investor may allocate a small portion of their assets to a high-risk security and still maintain a suitable portfolio.
An investor can utilize the correlation coefficient to determine the best security to add to a portfolio for further diversification. Correlation references the similarities in the market price fluctuations of two different securities or portfolios. It is measured on a scale of negative 1 to positive 1. Two securities or portfolios with a perfect correlation of 1 have market prices that have historically moved at the same speed and in the same direction. For example, the S&P 500 index and an S&P index fund should have maintain a correlation of 1. If the S&P 500 index is up 10% one day, then the index fund tracking its performance should also maintain a 10% return. The two have a perfect correlation.
On the other side, a security with a perfect negative correlation (-1) moves at the same speed, but in opposite directions. For example, the S&P 500 index should maintain a -1 correlation with an inverse S&P 500 exchange-traded fund (ETF). If the S&P 500 index is up 10% one day, the inverse S&P 500 ETF should be down approximately 10%. The two have a perfect negative correlation day-to-day. However, the correlation will decay in the long run due to the investors’ holdings effectively being adjusted daily.
All other correlations will fall between -1 and 1. A correlation of zero means there’s no relationship between the two securities or portfolios being compared. A correlation of 0.5 roughly translates to the two comparisons acting similarly 50% of the time. A correlation of -0.5 roughly translates to the two comparisons acting as inverses 50% of the time. And so forth.
A key test point integrates diversification and correlation. If an investor wants to further diversify their portfolio, they should invest in securities with negative correlations to the portfolio. By doing so, they’re introducing new components that act inversely to the rest of the investor’s securities (on average). When the overall portfolio is losing value, the new securities with negative correlations should increase in value, thereby reducing the investor’s losses.
Beyond diversifying a portfolio across a number of different securities, proper asset allocation also plays an important role. Strategic asset allocation builds upon the principles of MPT by encouraging the maintenance of a suitable long term asset allocation, avoiding market timing, and periodically rebalancing. When implemented correctly, an investor can ensure their portfolio retains an appropriate risk/return profile.
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