Category: Calculating expected returns

Once you’ve done your research on the risk and return characteristics of the different asset classes, you may feel ready to start investing.

If your goal is to build an investment portfolio, you may want to consider diversifying. Diversification is the process of buying assets that are hopefully non-correlated; the performance of one is not necessarily related to the performance of the other. For example, you could build a portfolio of stocks and bonds, two non-correlated asset classes.

To do this, you can buy stocks and bonds directly, or you can buy them within funds. Funds can provide a way to achieve a diversified portfolio because they bundle many different investments together.

One fund could hold hundreds or even thousands of stocks, bonds, or other investments. For example, an S&P 500 index fund invests in the 500 leading companies in the United States. But the variety of funds doesn’t stop there. There are funds that invest in countries and industries all over the globe.

With SoFi Invest®, you can keep costs such as transaction costs and account fees low in order to build out your portfolio—whether you want to buy stocks or exchange-traded funds (ETFs). 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.

If the real rate of return is a way to compare the value of an investment from when purchased to a given point of time, the compound annual growth rate is a way of measuring how much the investment has grown on average per year.

This can be useful because it’s a way of comparing investments over annual timespans. This is useful because typically investments are thought of as being held over a given time period and you want to compare which investment is most appropriate or will generate the biggest gains.

The compound annual growth rate does not tell you how much an investment’s value has grown in a given year, but it does give you a basis of comparison. Another assumption of the compound annual growth rate is that any profits from the investment are re-invested.

The formula for the compound annual growth rate is:

CAGR = (present or final value/starting or initial value)^1/n – 1, where n is the number of years.

So let’s look at a stock which you purchased for $50 in 2008 and has now grown to $200 in 2020. The simple rate of return for this stock would be 300%, which sounds impressive. But let’s look at its compound annual rate of return.

CAGR = (200/50)^1/12 – 1
CAGR = 4^.0833 – 1
CAGR= 12.25%

This 12.25% seems more modest than the 300% rate of return, but it’s useful to compare to other annual rates of returns, like from the market as a whole, from treasury bonds, dividend-stocks and more.

What we calculated above was the “simple” or “nominal rate of return,” a measure of how much the value of something has grown over time compared to when it was purchased.

Another way of thinking of rates of return is on assets that generate interest or yield. A certificate of deposit that pays 3% has a 3% simple or nominal rate of return. But then there’s inflation.

This formula is (1 + the nominal rate)/(1 + inflation rate) -1

So in our example of a 3% yielding CD and a 2% inflation rate, the real rate of return would be

(1+.03)/(1+.02) – 1
.0098
.98% = real rate of return

Another important formula to know is the “real rate of return.” What makes the real rate of return distinct from other formulas is how it takes into account inflation. This matters because the reason to invest in assets like stocks, bonds, property and so on is to generate money to buy things — and if the cost of things is going up faster than the rate of return on your investment, then the “real” rate of return is actually negative.

This is especially important for low risk investments in things like money market mutual funds or bonds, which are supposed to pay out steadily and provide cash flow, as opposed to stocks which typically are valuable for how the stocks themselves go up in price.

The rate of return is the conversion between the present value of something from its original value converted into a percentage. The formula is simple: It’s the current or present value minus the original value divided by the initial value, times 100. This expresses the rate of return as a percentage.

To understand the real rate of return, we must first understand what the simple or nominal rate of return is. You have to first be able calculate this before moving on to the real rate of return.

The required rate of return is a concept in corporate finance. It’s the amount of money, or the proportion of money received back from the money invested, that a project needs to generate in order to be worth it for the investor or company doing it.

This matters for investors because it’s a way of thinking about the relationship between the risk of an investment and the potential profitability or return that can be garnered from it. For the investor, the required rate of return can be applied to stocks.

What is the Dividend-Discount Model?

There are different ways of calculating the required rate of return for stocks.

One is the “dividend-discount model,” which can be used for stocks that pay out high dividends and have steady growth. In this model you get the stock’s value by dividing annual expected dividends by the required rate of return minus the dividend growth rate. By moving around the terms, you can find the required rate of return by dividing the dividend payments by the stock price and adding the growth of dividends.

So, if you have a stock paying $2 in dividends per year and is worth $30 and the dividends are growing at 2% a year, you have a required rate of return of:

$2/30 + .05,
.066 + .05
For a required rate of return of 11.67%

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” plus what’s known as “beta” (the stock’s volatility, or its change in price, compared to the market) which is then multiplied by the market rate of return minus the risk free rate.

For the risk free rate, we can take the yield on 10-year Treasuries, which is about 1% or .01, a beta of 1.5, and the market rate of return of 5% or .05.

So 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%

All investments are subject to pressures in the market. These pressures, or sources of risk, can come in the form of systematic and unsystematic risk. Systematic risk affects an entire investment type. Within that investment category, it probably can’t be “diversified” away.

Because of systematic risk, you may want to 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.

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

To be a savvy investor, it’s helpful to understand the risks involved with each asset class you’re looking to invest in. One way is to consider the standard deviation of an investment. Standard deviation measures volatility by calculating the dispersion (values’ range) of a dataset relative to its mean. The larger the standard deviation, the larger the range of returns.

Consider two different investments. Investment A has an annual return of 9%, and Investment B has an 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 where returns are much higher and lower than with Investment B.

Year	Investment A	Investment B
2000	14%	11%
2001	2%	12%
2002	22%	12%
2003	34%	3%
2004	5%	8%
2005	-18%	-1%
2006	-21%	-5%
2007	29%	11%
2008	6%	1%
2009	16%	8%
2010	22%	4%
2011	1%	3%
2012	-4%	0%
2013	8%	7%
2014	-11%	-4%
2015	31%	9%
2016	7%	5%
2017	13%	15%
2018	22%	14%
Average	9%	6%
ST. DEV.	16%	6%

On Investment A, the standard deviation is 16%. On Investment B, the standard deviation is 6%. 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.

Having historical data can be a good place to start in your journey of 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 take into account the risk involved by investing in a particular asset class. After all, investing can be inherently risky.

And risk and return are often two sides of the same coin. In order to achieve a higher rate of return, you’ll most likely have to take more risk. The risk involved in an investment is not represented by its expected rate of return.

Look at the first example. In this example, which uses historical returns, 9% 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 2005, 2006, 2012, and 2014. The variability of returns is often called volatility.

Sometimes, investment risks and managing them come with the possibility of losing money. Knowing this, it might be misguided to assume that 9% annual returns were going to show up as positive 9% returns each and every year. To achieve 9% average returns, there must be some risk involved.

When using probable rates of return, you’ll need the additional data point of the expected probability of each outcome. Remember, the probability column must add up to 100%. Multiply the return by the probability and add the outcomes together to get the expected rate of return. Here’s an example of how this would look.

Scenario	Return	Probability	Outcome
1	14%	30%	0.042
2	2%	10%	0.0028
3	22%	30%	0.066
4	-18%	10%	-0.018
5	-21%	10%	0.00441
		100%	0.09721

Using the formula above, in this hypothetical example, the expected rate of return is 9.7%.

To calculate the expected return using historical data, you’ll want to take an average of each outcome. Here’s an example of what that would look like.

Year	Return
2000	14%
2001	2%
2002	22%
2003	34%
2004	5%
2005	-18%
2006	-21%
2007	29%
2008	6%
2009	16%
2010	22%
2011	1%
2012	-4%
2013	8%
2014	-11%
2015	31%
2016	7%
2017	13%
2018	22%
Average	9%

In this example, the average rate of return is 9%. When using historical data, you may want to consider your pool of data. Are you using all of the data available? Or only data from a select period? If you are only using some data and not others, why?

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 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, simply 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 and/or D2.