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What Is Considered a Good Return on Investment?

A good return on investment is generally considered to be about 7% per year, based on the average historic return of the S&P 500 index, and adjusting for inflation. But of course what one investor considers a good return might not be ideal for someone else.

And while getting a “good” return on your investments is important, it’s equally important to know that the average return of the U.S. stock market is just that: an average of the market’s performance, typically going back to the 1920s. On a year-by-year basis, investors can expect returns that might be higher or lower — and they also have to face the potential for outright losses.

In addition, the S&P 500 is a barometer of the equity markets, and it only reflects the performance of the 500 biggest companies in the U.S. Most investors will hold other types of securities in addition to equities, which can affect their overall portfolio return.

Key Points

•   A good return on investment is generally considered to be around 7% per year, based on the average historic return of the S&P 500 index, adjusted for inflation.

•   The average return of the U.S. stock market is around 10% per year, adjusted for inflation, dating back to the late 1920s.

•   Different investments, such as CDs, bonds, stocks, and real estate, offer varying rates of return and levels of risk.

•   It’s important to consider factors like diversification and time when investing long-term.

•   Investing in stocks carries higher potential returns but also higher risk, while investments like CDs offer lower returns but are considered safer.

What Is the Historical Average Stock Market Return?

Dating back to the late 1920s, the S&P 500 index has returned, on average, around 10% per year. Adjusted for inflation that’s roughly 7% per year.

Here’s how much a 7% return on investment can earn an individual after 10 years. If an individual starts out by putting in $1,000 into an investment with a 7% average annual return, they would see their money grow to $1,967 after a decade, assuming little or no volatility (which is unlikely in real life).

It’s important for investors to have realistic expectations about what type of return they’ll see.

For financial planning purposes however, investors interested in buying stocks should keep in mind that that doesn’t mean the stock market will consistently earn them 7% each year. In fact, S&P 500 share prices have swung violently throughout the years. For instance, the benchmark tumbled 38% in 2008, then completely reversed course the following March to end 2009 up 23%.

Factors such as economic growth, corporate performance, interest rates, and share valuations can affect stock returns. Thus, it can be difficult to say X% or Y% is a good return, as the investing climate varies from year to year.

A better approach is to think about your hoped-for portfolio return in light of a certain goal (e.g. retirement), and focus on the investment strategy that might help you achieve that return.

Line graph: 10 Year Model of S&P 500

Why Your Money Loses Value If You Don’t Invest it

It’s helpful to consider what happens to the value of your money if you simply hang on to cash.

Keeping cash can feel like a safer alternative to investing, so it may seem like a good idea to deposit your money into a savings account — the modern day equivalent of stuffing cash under your mattress. But cash slowly loses value over time due to inflation; that is, the cost of goods and services increases with time, meaning that cash has less purchasing power. Inflation can also impact your investments.

Interest rates are important, too. Putting money in a savings account that earns interest at a rate that is lower than the inflation rate guarantees that money will lose value over time.

This is why, despite the risks, investing money is often considered a better alternative to simply saving it. The inflation risk is lower.

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What Is a Good Rate of Return for Various Investments?

As noted above, determining a good rate of return will also depend on the specific investments you hold, and your asset allocation. You can always calculate the expected rate of return for various securities.

CDs

Certificates of deposit (CDs) may be considered a relatively safe investment because they offer a fixed rate of return in return for keeping your money on deposit for a specific period of time. That means there’s relatively little risk — but because investors also agree to tie their money up for a predetermined period of time CDs are also considered illiquid. There is generally a penalty for withdrawing your money before the CD matures.

Generally, the longer money is invested in a CD, the higher the return. Many CDs require a minimum deposit amount, and larger deposits (i.e. for jumbo CDs) tend to be associated with higher interest rates.

It’s the low-risk nature of CDs that also means that they earn a lower rate of return than other investments, usually only a few percentage points per year. But they can be a good choice for investors with short-term goals who need a relatively low-risk investment vehicle while saving for a short-term goal.

Here are the weekly national rates compiled by the Federal Deposit Insurance Corporation (FDIC) as of April 17, 2023:

Non-Jumbo Deposits National Avg. Annual Percentage Yield
1 month 0.24%
3 month 0.78%
6 month 1.03%
12 month 1.54%
24 month 1.43%
36 month 1.34%
48 month 1.29%
60 month 1.37%

Bonds

Purchasing a bond is basically the same as loaning your money to the bond-issuer, like a government or business. Similar to a CD, a bond is a way of locking up a certain amount of money for a fixed period of time.

Here’s how it works: A bond is purchased for a fixed period of time (the duration), investors receive interest payments over that time, and when the bond matures, the investor receives their initial investment back.

Generally, investors earn higher interest payments when bond issuers are riskier. An example may be a company that’s struggling to stay in business. But interest payments may be lower when the borrower is trustworthy, like the U.S. government, which has never defaulted on its Treasuries.

Stocks

Stocks can be purchased in a number of ways. But the important thing to know is that a stock’s potential return will depend on the specific stock, when it’s purchased, and the risk associated with it. Again, the general idea with stocks is that the riskier the stock, the higher the potential return.

This doesn’t necessarily mean you can put money into the market today and assume you’ll earn a large return on it in the next year. But based on historical precedent, your investment may bear fruit over the long-term. Because the market on average has gone up over time, bringing stock values up with it, but stock investors have to know how to handle a downturn.

As mentioned, the stock market averages a return of roughly 7% per year, adjusted for inflation.

Real Estate

Returns on real estate investing vary widely. It mostly depends on the type of real estate — if you’re purchasing a single house versus a real estate investment trust (REIT), for instance — and where the real estate is located.

As with other investments, it all comes down to risk. The riskier the investment, the higher the chance of greater returns and greater losses. Investors often debate the merit of investing in real estate versus investing in the market.

Likely Return on Investment Assets

For investors who have a high risk tolerance (they’re willing to take big risks to potentially earn high returns), some investments are better than others. For example, investing in a CD isn’t going to reap a high return on investment. So for those who are looking for higher returns, riskier investments are the way to go.

Remember the Principles of Good Investing

Investors focused on seeing huge returns over the short-term may set themselves up for disappointment. Instead, remembering basic tenets of responsible investing can best prep an investor for long-term success.

First up: diversification. It can be a good idea to invest in a wide variety of assets — stocks, bonds, real estate, etc., and a wide variety of investments within those subgroups. That’s because each type of asset tends to react differently to world events and market forces. Due to that, a diverse portfolio can be a less risky portfolio.

Time is another important factor when investing. Investing early may result in larger returns in the long-term. That’s largely because of compound interest, which is when interest is earned on an initial investment, along with the returns already accumulated by that investment. Compound interest adds to your returns.

Investing with SoFi

While every investor wants a “good return” on their investments, there isn’t one way to achieve a good return — and different investments have different rates of return, and different risk levels. Investing in CDs tends to deliver lower returns, while stocks (which are more volatile) may deliver higher returns but at much greater risk.

Your own investing strategy and asset allocation will have an influence on the potential returns of your portfolio over time.

Ready to invest in your goals? It’s easy to get started when you open an Active Invest account with SoFi invest. You can invest in stocks, exchange-traded funds (ETFs), and more. SoFi doesn’t charge commissions, and other fees apply (full fee disclosure here). Members can access complimentary financial advice from a professional.

For a limited time, opening and funding an Active Invest account gives you the opportunity to get up to $1,000 in the stock of your choice.


SoFi Invest®
INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE
SoFi Invest encompasses two distinct companies, with various products and services offered to investors as described below: Individual customer accounts may be subject to the terms applicable to one or more of these platforms.
1) Automated Investing and advisory services are provided by SoFi Wealth LLC, an SEC-registered investment adviser (“SoFi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC.
2) Active Investing and brokerage services are provided by SoFi Securities LLC, Member FINRA (www.finra.org)/SIPC(www.sipc.org). Clearing and custody of all securities are provided by APEX Clearing Corporation.
For additional disclosures related to the SoFi Invest platforms described above please visit SoFi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform.

Financial Tips & Strategies: The tips provided on this website are of a general nature and do not take into account your specific objectives, financial situation, and needs. You should always consider their appropriateness given your own circumstances.

Investment Risk: Diversification can help reduce some investment risk. It cannot guarantee profit, or fully protect in a down market.

Claw Promotion: Customer must fund their Active Invest account with at least $25 within 30 days of opening the account. Probability of customer receiving $1,000 is 0.028%. See full terms and conditions.

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How to Calculate Expected Rate of Return

When investing, you often want to know how much money an investment is likely to earn you. That’s where the expected rate of return comes in; it’s calculated using the probabilities of investment returns for various potential outcomes. Investors can utilize the expected return formula to help project future returns.

Though it’s impossible to predict the future, having some idea of what to expect can be critical in setting expectations for a good return on investment.

Key Points

•   The expected rate of return is the profit or loss an investor expects from an investment based on historical rates of return and the probability of different outcomes.

•   The formula for calculating the expected rate of return involves multiplying the potential returns by their probabilities and summing them.

•   Historical data can be used to estimate the probability of different returns, but past performance is not a guarantee of future results.

•   The expected rate of return does not consider the risk involved in an investment and should be used in conjunction with other factors when making investment decisions.

•  

What Is the Expected Rate of Return?

The expected rate of return — also known as expected return — is the profit or loss an investor expects from an investment, given historical rates of return and the probability of certain returns under different scenarios. The expected return formula projects potential future returns.

Expected return is a speculative financial metric investors can use to determine where to invest their money. By calculating the expected rate of return on an investment, investors get an idea of how that investment may perform in the future.

This financial concept can be useful when there is a robust pool of historical data on the returns of a particular investment. Investors can use the historical data to determine the probability that an investment will perform similarly in the future.

However, it’s important to remember that past performance is far from a guarantee of future performance. Investors should be careful not to rely on expected returns alone when making investment decisions.

Recommended: Building An Investment Portfolio

How To Calculate Expected Return

To calculate the expected rate of return on a stock or other security, you need to think about the different scenarios in which the asset could see a gain or loss. For each scenario, multiply that amount of gain or loss (return) by its probability. Finally, add up the numbers you get from each scenario.

The formula for expected rate of return looks like this:

Expected Return = (R1 * P1) + (R2 * P2) + … + (Rn * Pn)

In this formula, R is the rate of return in a given scenario, P is the probability of that return, and n is the number of scenarios an investor may consider.

For example, say there is a 40% chance an investment will see a 20% return, a 50% chance that the investment will return 10%, and a 10% chance the investment will decline 10%. (Note: all the probabilities must add up to 100%)

The expected return on this investment would be calculated using the formula above:

Expected Return = (40% x 20%) + (50% x 10%) + (10% x -10%)

Expected Return = 8% + 5% – 1%

Expected Return = 12%

What Is Rate of Return?

The expected rate of return mentioned above looks at an investment’s potential profit and loss. In contrast, the rate of return looks at the past performance of an asset.

A rate of return is the percentage change in value of an investment from its initial cost. When calculating the rate of return, you look at the net gain or loss in an investment over a particular time period. The simple rate of return is also known as the return on investment (ROI).

Recommended: What Is the Average Stock Market Return?

How to Calculate Rate of Return

The formula to calculate the rate of return is:

Rate of return = [(Current value − Initial value) ÷ Initial Value ] × 100

Let’s say you own a share that started at $100 in value and rose to $110 in value. Now, you want to find its rate of return.

In our example, the calculation would be [($110 – $100) ÷ $100] x 100 = 10

A rate of return is typically expressed as a percentage of the investment’s initial cost. So, if you were to sell your share, this investment would have a 10% rate of return.

Recommended: What Is Considered a Good Return on Investment?

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Different Ways to Calculate Expected Rate of Return

How to Calculate Expected Return Using Historical Data

To calculate the expected return of a single investment using historical data, you’ll want to take an average rate of returns in certain years to determine the probability of those returns. Here’s an example of what that would look like:

Annual Returns of a Share of Company XYZ

Year

Return

2011 16%
2012 22%
2013 1%
2014 -4%
2015 8%
2016 -11%
2017 31%
2018 7%
2019 13%
2020 22%

For Company XYZ, the stock generated a 21% average rate of return in five of the ten years (2011, 2012, 2017, 2019, and 2020), a 5% average return in three of the years (2013, 2015, 2018), and a -8% average return in two of the years (2014 and 2016).

Using this data, you may assume there is a 50% probability that the stock will have a 21% rate of return, a 30% probability of a 5% return, and a 20% probability of a -8% return.

The expected return on a share of Company XYZ would then be calculated as follows:

Expected return = (50% x 21%) + (30% x 5%) + (20% x -8%)

Expected return = 10% + 2% – 2%

Expected return = 10%

Based on the historical data, the expected rate of return for this investment would be 10%.

However, when using historical data to determine expected returns, you may want to consider if you are using all of the data available or only data from a select period. The sample size of the historical data could skew the results of the expected rate of return on the investment.

How to Calculate Expected Return Based on Probable Returns

When using probable rates of return, you’ll need the data point of the expected probability of an outcome in a given scenario. This probability can be calculated, or you can make assumptions for the probability of a return. Remember, the probability column must add up to 100%. Here’s an example of how this would look.

Expected Rate of Return for a Stock of Company ABC

Scenario

Return

Probability

Outcome (Return * Probability)

1 14% 30% 4.2%
2 2% 10% 0.2%
3 22% 30% 6.6%
4 -18% 10% -1.8%
5 -21% 10% -2.1%
Total 100% 7.1%

Using the expected return formula above, in this hypothetical example, the expected rate of return is 7.1%.

Calculate Expected Rate of Return on a Stock in Excel

Follow these steps to calculate a stock’s expected rate of return in Excel:

1. In the first row, enter column labels:

•   A1: Investment

•   B1: Gain A

•   C1: Probability of Gain A

•   D1: Gain B

•   E1: Probability of Gain B

•   F1: Expected Rate of Return

2. In the second row, enter your investment name in B2, followed by its potential gains and the probability of each gain in columns C2 – E2

•   Note that the probabilities in C2 and E2 must add up to 100%

3. In F2, enter the formula = (B2*C2)+(D2*E2)

4. Press enter, and your expected rate of return should now be in F2

If you’re working with more than two probabilities, extend your columns to include Gain C, Probability of Gain C, Gain D, Probability of Gain D, etc.

If there’s a possibility for loss, that would be negative gain, represented as a negative number in cells B2 or D2.

Limitations of the Expected Rate of Return Formula

Historical data can be a good place to start in understanding how an investment behaves. That said, investors may want to be leery of extrapolating past returns for the future. Historical data is a guide; it’s not necessarily predictive.

Another limitation to the expected returns formula is that it does not consider the risk involved by investing in a particular stock or other asset class. The risk involved in an investment is not represented by its expected rate of return.

In this historical return example above, 10% is the expected rate of return. What that number doesn’t reveal is the risk taken in order to achieve that rate of return. The investment experienced negative returns in the years 2014 and 2016. The variability of returns is often called volatility.

Recommended: A Guide to Historical Volatility

Standard Deviation

To understand the volatility of an investment, you may consider looking at its standard deviation. Standard deviation measures volatility by calculating a dataset’s dispersion (values’ range) relative to its mean. The larger the standard deviation, the larger the range of returns.

Consider two different investments: Investment A has an average annual return of 10%, and Investment B has an average annual return of 6%. But when you look at the year-by-year performance, you’ll notice that Investment A experienced significantly more volatility. There are years when returns are much higher and lower than with Investment B.

Year

Annual Return of Investment A

Annual Return of Investment B

2011 16% 8%
2012 22% 4%
2013 1% 3%
2014 -6% 0%
2015 8% 6%
2016 -11% -2%
2017 31% 9%
2018 7% 5%
2019 13% 15%
2020 22% 14%
Average Annual Return 10% 6%
Standard Deviation 13% 5%

Investment A has a standard deviation of 13%, while Investment B has a standard deviation of 5%. Although Investment A has a higher rate of return, there is more risk. Investment B has a lower rate of return, but there is less risk. Investment B is not nearly as volatile as Investment A.

Systematic and Unsystematic Risk

All investments are subject to pressures in the market. These pressures, or sources of risk, can come from systematic and unsystematic risks. Systematic risk affects an entire investment type. Investors may struggle to reduce the risk through diversification within that asset class.

Because of systematic risk, you may consider building an investment strategy that includes different asset types. For example, a sweeping stock market crash could affect all or most stocks and is, therefore, a systematic risk. However, if your portfolio includes bonds, commodities, and real estate, you may limit the impact of the equities crash.

In the stock market, unsystematic risk is specific to one company, country, or industry. For example, technology companies will face different risks than healthcare and energy companies. This type of risk can be mitigated with portfolio diversification, the process of purchasing different types of investments.

Expected Rate of Return vs Required Rate of Return

Expected return is just one financial metric that investors can use to make investment decisions. Similarly, investors may use the required rate of return (RRR) to determine the amount of money an investment needs to generate to be worth it for the investor. The required rate of return incorporates the risk of an investment.

What is the Dividend Discount Model?

Investors may use the dividend discount model to determine an investment’s required rate of return. The dividend discount model can be used for stocks with high dividends and steady growth. Investors use a stock’s price, dividend payment per share, and projected dividend growth rate to calculate the required rate of return.

The formula for the required rate of return using the dividend discount model is:

RRR = (Expected dividend payment / Share price) + Projected dividend growth rate

So, if you have a stock paying $2 in dividends per year and is worth $20 and the dividends are growing at 5% a year, you have a required rate of return of:

RRR = ($2 / $20) + 0.5
RRR = .10 + .05
RRR = .15, or 15%

What is the Capital Asset Pricing Model?

The other way of calculating the required rate of return is using a more complex model known as the capital asset pricing model.

In this model, the required rate of return is equal to the risk-free rate of return, plus what’s known as beta (the stock’s volatility compared to the market), which is then multiplied by the market rate of return minus the risk-free rate. For the risk-free rate, investors usually use the yield of a short-term U.S. Treasury.

The formula is:

RRR = Risk-free rate of return + Beta x (Market rate of return – Risk-free rate of return)

For example, let’s say an investment has a beta of 1.5, the market rate of return is 5%, and a risk-free rate of 1%. Using the formula, the required rate of return would be:

RRR = .01 + 1.5 x (.05 – .01)
RRR = .01 + 1.5 x (.04)
RRR = .01 + .06
RRR = .07, or 7%

The Takeaway

There’s no way to predict the future performance of an investment or portfolio. However, by looking at historical data and using the expected rate of return formula, investors can get a better sense of an investment’s potential profit or loss.

There’s no guarantee that the actual performance of a stock, fund, or other assets will match the expected return. Nor does expected return consider the risk and volatility of assets. It’s just one factor an investor should consider when deciding on investments and building a portfolio.

If you’re ready to build your portfolio, SoFi Invest® can help. With a SoFi Invest investment account, you can trade stocks and exchange-traded funds (ETFs) with no commission for as little as $5. And if you would like help creating an investment portfolio, SoFi automated investing uses a portfolio of ETFs based on your goals, risk tolerance, and projected timeline.

For a limited time, opening and funding an Active Invest account gives you the opportunity to get up to $1,000 in the stock of your choice.

FAQ

How do you find the expected rate of return?

An investment’s expected rate of return is the average rate of return that an investor can expect to receive over the life of the investment. Investors can calculate the expected return by multiplying the potential return of an investment by the chances of it occurring and then totaling the results.

How do you calculate the expected rate of return on a portfolio?

The expected rate of return on a portfolio is the weighted average of the expected rates of return on the individual assets in the portfolio. You first need to calculate the expected return for each investment in a portfolio, then weigh those returns by how much each investment makes up in the portfolio.

What is a good rate of return?

A good rate of return varies from person to person. Some investors may be satisfied with a lower rate of return if its performance is consistent, while others may be more aggressive and aim for a higher rate of return even if it is more volatile. Ultimately, it is up to the individual to decide what is considered a good rate of return.


SoFi Invest®
INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE
SoFi Invest encompasses two distinct companies, with various products and services offered to investors as described below: Individual customer accounts may be subject to the terms applicable to one or more of these platforms.
1) Automated Investing and advisory services are provided by SoFi Wealth LLC, an SEC-registered investment adviser (“SoFi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC.
2) Active Investing and brokerage services are provided by SoFi Securities LLC, Member FINRA (www.finra.org)/SIPC(www.sipc.org). Clearing and custody of all securities are provided by APEX Clearing Corporation.
For additional disclosures related to the SoFi Invest platforms described above please visit SoFi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform.

Claw Promotion: Customer must fund their Active Invest account with at least $25 within 30 days of opening the account. Probability of customer receiving $1,000 is 0.028%. See full terms and conditions.

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The Black Scholes Model, Explained

The Black-Scholes Model, Explained

The Black-Scholes option pricing model is a mathematical formula used to calculate the theoretical price of an option. It’s a commonly-used formula for determining the price of contracts, and as such, can be useful for investors in the options market to know and have in their pocket for use.

But there are some important things to know about it, such as the fact that the model only applies to European options, and more.

Key Points

•   The Black-Scholes model is a mathematical formula used to calculate the theoretical price of an option.

•   It is commonly used for pricing options contracts and helps investors determine the value of options they’re considering trading.

•   The model takes into account factors like the option’s strike price, time until expiration, underlying stock price, interest rates, and volatility.

•   The Black-Scholes model was created by Myron Scholes and Fischer Black in 1973 and is also known as the Black-Scholes-Merton model.

•   While the model has some assumptions and limitations, it is considered an important tool for European options traders.

What Is the Black-Scholes Model?

As mentioned, the Black-Scholes model is one of the most commonly used formulas for pricing options contracts. The model, also known as the Black-Scholes formula, allows investors to determine the value of options they’re considering trading.

The formula takes into account several important factors affecting options in an attempt to arrive at a fair market price for the derivative. The Black-Scholes options pricing model only applies to European options.


💡 Quick Tip: How do you decide if a certain trading platform or app is right for you? Ideally, the investment platform you choose offers the features that you need for your investment goals or strategy, e.g., an easy-to-use interface, data analysis, educational tools.

The History of the Black-Scholes Model

The Black-Scholes model gets its name from Myron Scholes and Fischer Black, who created the model in 1973. The model is sometimes called the Black-Scholes-Merton model, as Robert Merton also contributed to the model’s development. These three men were professors at the Massachusetts Institute of Technology (MIT) and University of Chicago.

The model functions as a differential equation that requires five inputs:

•   The option’s strike price

•   The amount of time until the option expires

•   The price of its underlying stock

•   Interest rates

•   Volatility

Modern computing power has made it easier to use this formula and made it more popular among those interested in stock options trading.

The model only works for European options, since American options allow contract holders to exercise at any time between the time of purchase and the expiration date. By contrast, European options come at cheaper prices and only allow the owner to exercise the option on the expiration date. So, while European options only offer a single opportunity to earn profits, American options offer multiple opportunities.

Recommended: American vs European Options: What’s the Difference?

What Does the Black-Scholes Model Tell?

The main goal of the Black-Scholes Formula is to determine the chances that an option will expire in the money. To this end, the model goes deeper than simply looking at the fact that a call option will increase when its underlying stock price rises and incorporates the impact of stock volatility.

The model looks at several variables, each of which impact the value of that option. Greater volatility, for example, could increase the odds the options will wind up being in the money before its expiration. The more time the investor has to exercise the option also increases the likelihood of it winding up in the money and lowers the present value of the exercise price. Interest rates also influence the price of the option, as higher rates make the option more expensive by decreasing the present value of the exercise price.

The Black-Scholes Formula

The Black-Scholes formula expresses the value of a call option by taking the current stock prices multiplied by a probability factor (D1) and subtracting the discounted exercise payment times a second probability factor (D2).

Explaining in exact detail what D1 and D2 represent can be difficult because the original research papers by Black and Scholes didn’t explain or interpret D1 and D2, and neither did the papers published by Merton. Entire research papers have been written on the subject of D1 and D2 alone.


💡 Quick Tip: If you’re an experienced investor and bullish about a stock, buying call options (rather than the stock itself) can allow you to take the same position, with less cash outlay. It is possible to lose money trading options, if the price moves against you.

Why Is the Black-Scholes Model Important?

The Black-Scholes option pricing model is so important that it once won the Nobel Prize in economics. Some even claim that this model is among the most important ideas in financial history.

Some traders consider the Black-Scholes Model one of the best methods for figuring out fair prices of European call options. Since its creation, many scholars have elaborated on and improved this formula. In this sense, Black and Scholes made a significant contribution to the academic world when it comes to math and finance.

Some claim that the Black-Scholes model has made a significant contribution to the efficiency of the options and stock markets. While designed for European options, the Black-Scholes Model can still help investors understand how an option’s price might react to its underlying stock price movements and improve their overall options trading strategies.

This allows investors to optimize their portfolios by hedging accordingly, making the overall markets more efficient. However, others assert that the model has increased volatility in the markets, as more investors constantly try to fine tune their trades according to the formula.

How Accurate Is the Black-Scholes Model?

Some studies have shown the Black-Scholes model to be highly predictive of options prices. This doesn’t mean the formula has no flaws, though.

The model tends to undervalue calls that are deeply in the money and overvalue calls that are deeply out of the money.

That means the model might assign an artificially low value to options that are much higher than the price of their underlying stock, while it may overvalue options that are far beneath the stock’s current value. Options that deal with stocks yielding a high dividend also tend to get mispriced by the model.

Assumptions of the Black-Scholes Model

There are also a few assumptions made by the model that can lead to less-than-perfect predictions. Some of these include:

•   The assumption that volatility and the risk- free rate within a stock remain constant

•   The assumption that stock prices are stable and large price swings don’t happen

•   The assumption that a stock doesn’t pay dividends until after an option expires

Recommended: How Do Dividends Work?

Such assumptions are necessary, even if they may negatively impact results. Relying on assumptions like these make the task possible, as only so many variables can reasonably be calculated.

Over the years, math scholars have elaborated on the work of Black and Scholes and made efforts to compensate for some of the gaps created by the original assumptions.

This leads to another flaw of the Black-Scholes model, unlike other inputs in the model, volatility must be an estimate rather than an objective fact. Interest rates and the amount of time left until the option expires are concrete numbers, while volatility has no direct numerical value.

The best a financial analyst can do is calculate an estimation of volatility by using something like the formula for variance. Variance is a measurement of the variability of an asset, or how much prices change from time to time. One common measurement of volatility is the standard deviation, which is equivalent to the square root of variance.

The Takeaway

The Black-Scholes option-pricing model is among the most influential mathematical formulas in modern financial history, and it may be the most accurate way to determine the value of a European call option. It’s a complicated formula that has some drawbacks that traders must understand, but it’s a useful tool for European options traders.

Given the Black-Scholes model’s complexity, it’s likely that many investors will never use it. That doesn’t mean it isn’t important to know or understand, of course, but many investors may not get much practical use out of it unless they delve deeper into the world of options trading.

Ready to invest in your goals? It’s easy to get started when you open an investment account with SoFi Invest. You can invest in stocks, exchange-traded funds (ETFs), mutual funds, alternative funds, and more. SoFi doesn’t charge commissions, but other fees apply (full fee disclosure here).

For a limited time, opening and funding an Active Invest account gives you the opportunity to get up to $1,000 in the stock of your choice.


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SoFi Invest®
INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE
SoFi Invest encompasses two distinct companies, with various products and services offered to investors as described below: Individual customer accounts may be subject to the terms applicable to one or more of these platforms.
1) Automated Investing and advisory services are provided by SoFi Wealth LLC, an SEC-registered investment adviser (“SoFi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC.
2) Active Investing and brokerage services are provided by SoFi Securities LLC, Member FINRA (www.finra.org)/SIPC(www.sipc.org). Clearing and custody of all securities are provided by APEX Clearing Corporation.
For additional disclosures related to the SoFi Invest platforms described above please visit SoFi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform.

Financial Tips & Strategies: The tips provided on this website are of a general nature and do not take into account your specific objectives, financial situation, and needs. You should always consider their appropriateness given your own circumstances.

Options involve risks, including substantial risk of loss and the possibility an investor may lose the entire amount invested in a short period of time. Before an investor begins trading options they should familiarize themselves with the Characteristics and Risks of Standardized Options . Tax considerations with options transactions are unique, investors should consult with their tax advisor to understand the impact to their taxes.
Claw Promotion: Customer must fund their Active Invest account with at least $25 within 30 days of opening the account. Probability of customer receiving $1,000 is 0.028%. See full terms and conditions.

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What Are Collateralized Debt Obligations (CDO)?

What Are Collateralized Debt Obligations (CDO)?

Collateralized debt obligations are complex financial products that bundle multiple bonds and loans into single securities.

These packaged securities are then sold in the market, typically to institutional investors. CDOs became more widely known to the general public due to their role in the 2008-2009 financial crisis.

Individual investors cannot easily buy CDOs. However, the 2008 financial crisis and subsequent recession revealed the interconnected nature of markets, as well as how losses on Wall Street can have ripple effects on the broader economy.

Therefore, it can be important for everyday individuals to grasp the role that complex financial instruments like collateralized debt obligations have in markets.

Key Points

•   Collateralized debt obligations (CDOs) are complex financial products that bundle multiple bonds and loans into single securities.

•   CDOs are sold in the market to institutional investors and became more widely known due to their role in the 2008-2009 financial crisis.

•   CDOs work by using the payments from underlying loans, bonds, and other types of debt as collateral.

•   CDOs are typically sliced into tranches that hold varying degrees of risk and are sold to investors.

•   Synthetic CDOs invest in derivatives, while regular CDOs invest in bonds, mortgages, and loans. CLOs are a subset of CDOs that gather debt from different companies.

How Do CDOs Work?

“Collateral” in finance is a term that refers to the security that lenders may require in return for lending money. In collateralized debt obligations, the collateral are the payments from the underlying loans, bonds, and other types of debt.

CDOs are considered derivatives since their prices are derived from the performance of the underlying bonds and loans. The institutional investors who tend to hold CDOs may collect the repayments from the original borrowers in the securities.

The returns of CDOs depend on the performance of the underlying debt. CDOs are popular because they allow lenders, usually banks, to turn a relatively illiquid security — like a bond or loan — into a more liquid asset.


💡 Quick Tip: Before opening any investment account, consider what level of risk you are comfortable with. If you’re not sure, start with more conservative investments, and then adjust your portfolio as you learn more.

Tranches in CDOs

CDOs are typically sliced into so-called tranches that hold varying degrees of risk and then these slices are sold to investors.

The most senior tranche is the highest rated by credit rating firms like S&P and Moody’s. The highest credit rating possible is AAA. Holders of the most senior or highest-rated tranche generally receive the lowest yield but are the last group to absorb losses in cases of default.

The most junior tranche in CDOs is sometimes unrated. Investors of this layer earn the highest yields but are the first to absorb credit losses. The middle tranche is usually rated between BB to AA.

Recommended: How Do Derivatives Work?

What Are Synthetic CDOs?

Regular, plain-vanilla CDOs invest in bonds, mortgages, and loans. In contrast, synthetic collateralized debt obligations invest in derivatives.

So instead of bundling corporate bonds or home mortgages, synthetic CDOs bundle derivatives like credit default swaps, options contracts, or other types of contracts. Keep in mind, these derivatives are themselves tied to another asset, such as loans or bonds.

Investors of regular CDOs get returns from the payments made on corporate debt or mortgage loans. Holders of synthetic CDOs get returns from the premiums associated with the derivatives.

CDOs vs CLOs

Collateralized loan obligations are a subset of CDOs. Instead of bundling up an array of different types of debt, CLOs more specifically gather together debt from hundreds of different companies, often this debt is considered below investment grade.

CLOs are considered by some market observers to be safer than CDOs, but both are risky debt products. CLOs do however tend to be more diversified across firms and sectors, while CDOs run the risk of being concentrated in a single debt type, such as mortgage loans during the 2008 financial crisis.

According to S&P, no U.S. AAA-rated CLO has ever defaulted. Also, CDOs can have a higher percentage of lower-rated debt. According to the ratings firm Moody’s, CDOs are allowed to hold up to 17.5% of their portfolio in Caa-rated assets and below (e.g. very high credit risk). That compares to the 7.5% in CLOs.

Collateralized Debt Obligations and the 2008-09 Housing Crisis

CDOs of mortgage-backed securities became notorious during the subprime housing crisis of 2008 and 2009. A selloff in the CDO market was said to amplify broader economic weakness in the economy.

Banks had been weakening lending standards when it came to home mortgages, allowing individuals to buy home that may have been too expensive for them.

Meanwhile, Wall Street banks were packaging home loans — some risky and subprime — into CDOs in the years leading up to the financial crisis. Ratings firms labeled these mortgage-backed CDOs as safe, on the premise that homeowners were a group of creditors less likely to default.

A mortgage-backed CDO holds many individual mortgage bonds. The mortgage bonds, in turn, packaged thousands of individual mortgages. These mortgage CDOs were considered to be of limited risk because of how they were diversified across many mortgage bonds.

But homeowners started to become unable to make their monthly payments, and defaults and foreclosures started piling up, leading to a domino effect of losses spread across the financial system.

Recommended: What Is Active Investing?

CDO Comeback

Around 2020, CDOs had a resurgence, with primarily corporate loans rather than home loans being packaged into securities.

A world of ultralow yields in the bond market pushed investors to seek higher-yielding markets. The average yield stands at just 2%, while trillions of dollars in debt trades at negative rates. In contrast, CDOs can yield up to 10%.

This time around hedge funds and private-equity firms, rather than banks, became the big players in the CDO market. Hedge funds are the new buyers–accounting for 70% of volume in the market. Banks were responsible for 10% of volumes in 2019, compared with 50% in the past.


💡 Quick Tip: Are self directed brokerage accounts cost efficient? They can be, because they offer the convenience of being able to buy stocks online without using a traditional full-service broker (and the typical broker fees).

The Takeaway

Collateralized debt obligations or CDOs are financial structures that bundle together different types of debt and sell shares of these bundled securities to investors.

The return investors might see from these debt-based, derivative securities depends on the ongoing payments from the debt holders. CDOs are typically purchased by institutional investors, not retail investors, but it can be useful to know about this market sector.

Ready to invest in your goals? It’s easy to get started when you open an investment account with SoFi Invest. You can invest in stocks, exchange-traded funds (ETFs), mutual funds, alternative funds, and more. SoFi doesn’t charge commissions, but other fees apply (full fee disclosure here).

For a limited time, opening and funding an Active Invest account gives you the opportunity to get up to $1,000 in the stock of your choice.


Photo credit: iStock/akinbostanci

SoFi Invest®
INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE
SoFi Invest encompasses two distinct companies, with various products and services offered to investors as described below: Individual customer accounts may be subject to the terms applicable to one or more of these platforms.
1) Automated Investing and advisory services are provided by SoFi Wealth LLC, an SEC-registered investment adviser (“SoFi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC.
2) Active Investing and brokerage services are provided by SoFi Securities LLC, Member FINRA (www.finra.org)/SIPC(www.sipc.org). Clearing and custody of all securities are provided by APEX Clearing Corporation.
For additional disclosures related to the SoFi Invest platforms described above please visit SoFi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform.

Claw Promotion: Customer must fund their Active Invest account with at least $25 within 30 days of opening the account. Probability of customer receiving $1,000 is 0.028%. See full terms and conditions.

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How taxes and fees impact return on investment

Taxes, Fees, Commissions, and Your Investments

Earning returns can be exhilarating. But it’s important to remember that they don’t necessarily represent the money that goes in the bank. Commissions, taxes, and other fees impact the returns any investor makes on their investment.

Just how big a bite these investment expenses take out of an investor’s assets isn’t always instantly clear. But by understanding the fees they pay, and the taxes they’re likely to owe, investors can better plan for the money they’ll actually receive from their investments. And they can also take concrete steps to minimize the effects of fees and taxes.

Investment Expenses 101

There are a few different types of investment expenses an investor may come across as they buy and sell assets. Here are the most common ones.

Fund Fees

Mutual funds are a very popular way for investors to get into the market. They’re the vehicles that most 401(k), 403(b), and IRAs offer investors to save for retirement. But these funds charge fees, starting with a management fee, which pays the fund’s staff to buy and trade investments.

Investors pay this fee as a portion of their assets, whether the investments go up or down. (With employer-sponsored retirement accounts, the employer may cover the fees as long as the account holder is employed by the company.) Management fees vary widely, with some index funds charging as little as .10% of an investor’s assets. But other mutual funds may charge more than 2%.

In addition to the management fee, the fund may also charge for advertising and promotion expenses, known as the 12b-1 fee. Plus, mutual fund investors may have to pay sales charges, especially if they buy funds through a financial planner, or an investment advisor. While the maximum legal sales charge for a mutual fund is 8.5%, the common range is between 3% and 6%.

One way to understand how much of a bite these mutual fund fees take out of an investment on an annual basis is to look at the expense ratio.

💡 Quick Tip: Look for an online brokerage with low trading commissions as well as no account minimum. Higher fees can cut into investment returns over time.

Advisor Fees

Investors may also face fees when they hire a professional to help manage their money. Some advisors charge a percentage of invested assets per year. More recently, some advisors have simplified the cost by simply charging an hourly fee.

Broker Fees and Commissions

Even investors who want to manage their own portfolios typically pay a broker for their services in the form of fees and commissions. These fees and commissions may be based on a percentage of the transaction’s value, or they may be rolled into a flat fee. Another factor that may influence the fee: whether an investor uses a full-service broker or a discount broker.

How to Minimize the Cost of Investing

No matter how an investor approaches the market, they can expect to pay some fees. It’s up to each individual to decide whether or not those fees are worth it. For some, paying a professional for hands-on advice is worth the extra annual 1% fee (or more) of their invested assets. For others, minimizing costs may be a priority. Among many options, there are a few investing opportunities that stand out as relatively low-cost.

Index Funds

When investing in mutual funds, one type of fund has established itself as the least expensive in terms of fees: Index funds. That’s because these funds track an index instead of paying analysts and managers to research and trade securities. When it comes to index funds vs. managed funds, proponents typically cite the lower fees.

Automated Investing Platforms

People seeking investing advice or guidance who don’t want to pay typical fees might want to explore automated investing platforms, also known as “robo-advisors.” Some of these platforms charge annual advisory fees as low as .25%. That said, these platforms often use mutual funds, which charge their own fees on top of the platform fees.

Discount Brokerage

Investors who manage their own portfolio may opt for a discount or online brokerage. These brokers tend to charge flat fees per trade as low as $5, with account maintenance fees also often as low as $0 to $50 per account.

How Taxes Eat into Investing Profits

There are typically two kinds of taxes that investors have to worry about. The first is income tax, and the second is capital gains tax. In general, income taxes apply to investment earnings in the form of interest payments, dividends, or bond yields. Capital gains, on the other hand, apply to the returns an investor realizes when they sell a stock, bond, or other investment. (The exception: The IRS taxes short-term investments, which an investor has held for less than a year, at that investor’s marginal income tax rate.)

By and large, capital gains tax rates are lower than income tax rates. Income tax rates for high-earners can be as high as 37%, plus a 3.8% net investment income tax (NIIT). That means the taxes on those quick gains can be as high as 40.8%—and that’s not including any state or local taxes.

The taxes on long-term capital gains are lower across the board. For tax year 2023, for investors who are married filing jointly and earning less than $89,250, the capital gains tax rate is 0%. It goes up depending on income, with couples making between $89,250 and $553,850 paying 15%, and those with income above that level paying 20%.

For tax year 2024, those who are married and filing jointly with taxable income up to $94,050 have a capital gains tax rate of 0%. Couples making between $94,050 and $583,750 have a rate of 15%, and those with income above that have a tax rate of 20%.

💡 Quick Tip: Automated investing can be a smart choice for those who want to invest but may not have the knowledge or time to do so. An automated investing platform can offer portfolio options that may suit your risk tolerance and goals (but investors have little or no say over the individual securities in the portfolio).

Strategies to Minimize Taxes

There are a few ways an investor can minimize the impact of taxes on their investments. One popular way to take advantage of the tax code is by investing through a retirement plan, such as a 401(k), 403(b), or IRA. All of these plans encourage people to save for retirement by offering attractive tax breaks.

For tax-deferred accounts like a 401(k) or traditional IRA, the tax break comes on the front end. Retirees will have to pay income taxes on their withdrawals in retirement. On the other hand, retirement accounts like a Roth 401(k) or Roth IRA are funded with after-tax dollars, and money is not taxed upon withdrawal in retirement.

Another approach some investors may want to consider is tax-loss harvesting. This strategy allows investors to take advantage of investments that lost money by selling them and taking a capital loss (as opposed to a capital gain). That capital loss can help investors reduce their annual tax bill. It may be used to offset as much as $3,000 in non-investment income.

The Takeaway

Fees and taxes typically do have an impact on an investor’s returns on investments. How much they eat into profit varies, and is largely dependent on what the investments are, how they are being managed, and how long an investor has had them. Other factors include the investor’s income level, and whether they’ve also lost money on other investments.

Ready to invest in your goals? It’s easy to get started when you open an investment account with SoFi Invest. You can invest in stocks, exchange-traded funds (ETFs), mutual funds, alternative funds, and more. SoFi doesn’t charge commissions, but other fees apply (full fee disclosure here).


Invest with as little as $5 with a SoFi Active Investing account.


Third-Party Brand Mentions: No brands, products, or companies mentioned are affiliated with SoFi, nor do they endorse or sponsor this article. Third-party trademarks referenced herein are property of their respective owners.

Tax Information: This article provides general background information only and is not intended to serve as legal or tax advice or as a substitute for legal counsel. You should consult your own attorney and/or tax advisor if you have a question requiring legal or tax advice.

Financial Tips & Strategies: The tips provided on this website are of a general nature and do not take into account your specific objectives, financial situation, and needs. You should always consider their appropriateness given your own circumstances.

SoFi Invest®
INVESTMENTS ARE NOT FDIC INSURED • ARE NOT BANK GUARANTEED • MAY LOSE VALUE
SoFi Invest encompasses two distinct companies, with various products and services offered to investors as described below: Individual customer accounts may be subject to the terms applicable to one or more of these platforms.
1) Automated Investing and advisory services are provided by SoFi Wealth LLC, an SEC-registered investment adviser (“SoFi Wealth“). Brokerage services are provided to SoFi Wealth LLC by SoFi Securities LLC.
2) Active Investing and brokerage services are provided by SoFi Securities LLC, Member FINRA (www.finra.org)/SIPC(www.sipc.org). Clearing and custody of all securities are provided by APEX Clearing Corporation.
For additional disclosures related to the SoFi Invest platforms described above please visit SoFi.com/legal.
Neither the Investment Advisor Representatives of SoFi Wealth, nor the Registered Representatives of SoFi Securities are compensated for the sale of any product or service sold through any SoFi Invest platform.

Investment Risk: Diversification can help reduce some investment risk. It cannot guarantee profit, or fully protect in a down market.

Exchange Traded Funds (ETFs): Investors should carefully consider the information contained in the prospectus, which contains the Fund’s investment objectives, risks, charges, expenses, and other relevant information. You may obtain a prospectus from the Fund company’s website or by email customer service at [email protected]. Please read the prospectus carefully prior to investing.
Shares of ETFs must be bought and sold at market price, which can vary significantly from the Fund’s net asset value (NAV). Investment returns are subject to market volatility and shares may be worth more or less their original value when redeemed. The diversification of an ETF will not protect against loss. An ETF may not achieve its stated investment objective. Rebalancing and other activities within the fund may be subject to tax consequences.


Fund Fees
If you invest in Exchange Traded Funds (ETFs) through SoFi Invest (either by buying them yourself or via investing in SoFi Invest’s automated investments, formerly SoFi Wealth), these funds will have their own management fees. These fees are not paid directly by you, but rather by the fund itself. these fees do reduce the fund’s returns. Check out each fund’s prospectus for details. SoFi Invest does not receive sales commissions, 12b-1 fees, or other fees from ETFs for investing such funds on behalf of advisory clients, though if SoFi Invest creates its own funds, it could earn management fees there.
SoFi Invest may waive all, or part of any of these fees, permanently or for a period of time, at its sole discretion for any reason. Fees are subject to change at any time. The current fee schedule will always be available in your Account Documents section of SoFi Invest.

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