The surest way to become wealthy is to save money and invest it in the stock market. The stock market has been the greatest wealth generator of the past century.

Here are two tools you should be familiar with in order to reduce risk and increase your returns through diversification and portfolio theory.

Beta and the Capital Asset Pricing Model are also used to calculate the cost of equity. This is a method to derive a meaningful discount rate for discounting the future cash flows and valuing income-producing assets.

Attention Entrepreneurs

These tools can be used to create a rational valuation for a startup seeking early stage equity financing

Let’s take a look.

Beta and CAPM

Every company has different products and services, customers and competitors, technologies, and employees. These unique circumstances and situations mean that every company listed on the stock market has a different risk profile.

How can we measure and compare the relative risk of different stocks?

The equity risk premium is the excess return that investors in the stock market require above and beyond the interest rate provided by U.S treasury bonds. U.S. treasury bonds are the de facto risk-free alternative because they are backed by the government’s ability to pay.

Investors think in terms of a risk-reward tradeoff. The additional anticipated return compensates investors for taking on the higher risk of investing in stocks.

The stock risk premium is a theoretical estimate. It can’t be known precisely. No one knows how stocks will perform going forward.

We can estimate the risk premium by measuring past stock market performance.

Markets compensate investors for taking on the higher risk of investing in stocks.

Estimates of the equity premium vary. A reasonable estimate of the equity premium is around 5.5%. That premium compensates us for putting our money in the stock market instead of a treasury bond.

But what if we invest in the stock of an individual company? What if we put our money in shares of Apple, or Goldman Sachs, or Tesla? What rate of a return should we expect to invest our hard-earned money in the stock of a single company?

Individual stocks are riskier, potentially than investing in the overall stock market. That is why mutual funds and ETFs are so popular. They mirror the entire market or sectors of it.

We need to find out what the premium is to compensate us for taking on the additional risk. We need to measure individual stock risk and price that risk.

Our estimate for the annual average overall stock market return is 5.5%. We need a way to think about and measure the risk of individual stocks so we can calculate the risk premium required for investing in that stock.

How much risk premium should we expect to compensate us for investing in a specific stock? How do we measure

how risky that stock is?

Let’s consider what makes a stock risky. Stocks are volatile. Volatility is another way of saying that their price fluctuates up and down a lot. We can’t predict the future. We never know if a stock is going to go up or down in the short term.

The short term movement of a stock is a random walk. Maybe it jumps around more than the average share. One day it’s up 15% and the next it goes down 25%.

We can evaluate a stock’s past performance to get a sense of the stock-specific risk. We can see if the shares have varied a lot in their prior performance.

We aren’t limited to investing in only one specific stock. We can invest in a bunch of different stocks with different risk profiles. Holding a bunch of different commodities is called a portfolio. Some of the various stocks go up when others go down, and vice versa.

Think of investing in a suntan lotion company and an umbrella company. When the sun is shining, people buy suntan lotion, and that stock performs well. But few people are buying umbrellas and that stock languishes. When it is raining, the umbrella company is making sales and that stock soars. But the suntan lotion company is quiet.

The two companies perform the opposite. Each offsets some of the risks of the other.

Umbrellas and suntan lotion is a simplified example that illustrates the concept of diversification. Investing in different stocks creates diversification that reduces portfolio risk.

I might require a 20% return to hold a risky stock. Some other investors might be willing to accept less than a 20% return because they are going to place the stock in a diversified portfolio. The company will raise money from the investor with the cheaper required rate of return. From the company’s perspective, that is a less expensive cost of capital.

We want to quantify how diversification impacts the risk of an individual stock on our portfolio holdings.

Let’s look at an example using the historical returns for five years on three stocks, companies A, B, and C.

Imagine we are looking at the graphs of these three stocks. You know those squiggly lines that chart the movement of a stock over time. You can see them when you look up a company on Google Finance.

Company A goes up the most at 21% a year, plus or minus 27%. That’s a lot of volatility.

B is the middle stock and goes up, on average, 15% a year over five years, plus or minus around 19%. It goes up less and is less volatile.

C has been lackluster over the last five years. C hasn’t had high returns. It has gone up, on average 5% over the previous five years, plus or minus around 17%.

By analyzing the individual returns and volatility, in terms of risk premium, I should charge A the most, I should charge B the middle, and C the lowest risk premium.

But what if I put all three together in a diversified portfolio? Together on average, what risk premium would I require that for the collection?

The three stocks together average out to a smoother line. Let’s say that the total curve goes up at around 12% plus or minus 10%. The aggregate line is smoother than any of the three individual lines.

By owning those stocks together into one portfolio, the wiggles in the lines tend to cancel each other out. This phenomenon is due to the diversification of the portfolio.

Let’s return to the umbrella company and a suntan lotion company to reinforce the concept of diversification. When it’s raining, the umbrella company does well, and the suntan company is slow. When it is sunny, the suntan lotion company is selling, and the umbrella company is stagnant. Each cancels out the other, and the two together are less volatile than either by itself. That is the risk hedging impact of diversification.

In our case, sometimes A goes up a lot when B goes down. Sometimes stock C goes up when B and A go down. The mutual cancellation of each independent variation creates a smoother group price line.

That’s what we seek as investors. We want to earn a smooth return and not be concerned about the market’s rollercoaster ups and downs.

Through diversification, the variations in individual stock price movements cancel each other out. That helps us be more comfortable about putting our hard-earned money into risky securities like stocks.

The more those variations cancel each other out, the lower the return we require for an individual stock.

What we want is a quantitative measure of how each stock contributes to the portfolio variation.

Does a stock make the overall portfolio more or less volatile? It doesn’t depend on the individual stock wiggles, but how much it varies with the other stocks in our portfolio.

That’s a key concept. The risk of a stock comes from how much it impacts the other stocks in our portfolio. Holding multiple equities can reduce overall risk.

Why not hold lots of stocks? Why not invest in a portfolio representing the whole market? That is what mutual funds and ETFs are. They are baskets of stocks that represent an industry sector or the entire market.

Let’s examine how to measure the risk of an individual stock. Volatile variations and jumps could be useful if that stock wiggles and jumps independently of all the other stocks in our portfolio. We are looking for stocks that zig when our other stocks zag.

We want to measure how a particular stock changes the risk of our portfolio. How does the stock’s price movements make the portfolio price movements vary? Does the stock make our collection more or less volatile?

That measurement is called Beta.

Remember, volatility is our measure of risk.

Beta tells us how much the stock moves up and down with the market.

We’re going to measure the variance of the stock, and we’re also going to calculate covariance. Covariance is how two things vary together.

If two stocks tend to move together, they’ve got high covariance. If two stocks vary independently, they don’t matter to each other; then, there’s no covariance between them.

The more they move together, the more covariance there is.

Covariance is the measure of how things move together. Variance is a measure of how something moves by itself.

Now I am going to introduce the risk measurement called Beta and how to calculate it.

Beta measures an individual stock’s risk contribution to a portfolio.

Beta is a ratio of covariance and variance. We divide one by the other. Beta is covariance divided by variance.

Beta measures an individual stock’s volatility relative to the volatility of the market. A stock with a beta of precisely 1.0 means it moves in lockstep with the market. If the stock’s Beta is less than 1.0, it moves less than the market. If a stock moves more than the market, the stock’s Beta is greater than 1.0.

Investing is all about risk vs. return. Having a quantitative way of assessing risk gives us a tool to evaluate the returns we require or can expect.

High-beta stocks are considered riskier but provide higher returns. Low-beta stocks pose less risk but also have lower yields.

How much does a stock move with the market? Here is the formula for calculating Beta.

Beta coefficient(β) = Covariance(Re​,Rm​)​ / Variance(Rm​)

where:

Re​=the return on an individual stock

Rm=the return on the overall market

Covariance=how changes in a stock’s returns relate to changes in the stock market’s returns

Variance=how far the market’s data points spread out from their average value​

The covariance between our stock Re, and the market, Rm, is the numerator. Covariance measures how much the individual stock we are interested in moves relative to the overall market.

We take our covariance measure and scale it by the variance of how much market moves overall.

That ratio measure of the variation of the individual stock relative to the variation of the stock market (covariance) divided (scaled) by the overall market variance, is called Beta, or the beta coefficient.

Beta quantifies the unsystematic risk of an individual stock in comparison to the systematic risk of the entire market.

Systematic risk refers to the risk built-in to the entire market. Systematic risk is known as undiversifiable risk. It can’t be diversified away.

Beta is a statistical measurement. We can also calculate Beta by plotting the returns over time of the individual stock against the performance of the market. Beta is the slope of the regression line through those data points.

The good news is that Beta is calculated for you and is available as part of the general information about any stock on Google or Yahoo finance or whatever is your favorite place to look up stocks.

All you need to know is that beta measures how much a stock moves relative to all stocks scaled by how much the market varies overall.

That is a stock’s Beta. It’s a measure of how much it moves with the market.

Beta measures how risky a stock is when we include it in a portfolio.

If I put a particular stock into my portfolio, does that make my collection vary more or less?

Betas are usually around one. They can go as low as 0.25 and as high as 2.5. That is the range.

Beta tells us how much market risk we are taking when we buy a stock.

Let’s look at an example.

If a stock has a beta of 2.0, that stock varies in price twice as much as the market. That stock is two times as risky as the market. We will require two times the market premium to buy that stock.

Two times the market risk should also produce much higher returns.

Let’s think about the cost of equity. The cost of equity capital is how much investors require, as a rate of return, to invest in the company stock.

The rate of return was the risk-free rate plus a risk premium.

Recall our estimate of the overall stock market risk premium was 5.5%.

Now we can think about and quantify the risk premium for individual stocks. That risk premium is Beta. The risk premium for a stock is: how much market risk I’m taking, Beta, times the equity premium, the 5.5% of market risk.

Beta is a measure of how many portions of market risk a stock represents. The equity premium is one portion of market risk.

CAPM

We can put it all together in the Capital Asset Pricing Model CAPM.

CAPM describes the relationship between systematic risk, the risk that can’t be diversified away, and expected return for individual stocks.

CAPM says the required or expected rate of return of any asset is equal to the risk-free rate, plus beta times the Equity Premium.

RRoR = Rrf + B * EP

Where:

EP is the Equity Premium (the expected rate of return from the market above the risk-free rate)

B is Beta (Covariance / Variance)

Rrf is the Risk-Free Rate (U.S. Treasury Bonds)

RRoR is the Required Rate of Return

CAPM is a formula for measuring the risk and the required return on any stock. Every stock has a unique beta. We can calculate that Beta or look it up on Yahoo.

We can say what the return is we require on that stock. Our required rate of return is the risk-free rate plus beta times the equity premium.

Let’s calculate an example for a stock that has a beta 1.7. The equity premium is around 5.5%, and the risk-free rate is 2%. How would we calculate the cost of equity for that stock?

It’s the risk-free rate, plus beta times the equity premium. In this case, that would be 2% + 1.7 times the 5.5% equity premium, which equals 11.35%.

So if we buy that stock, how much do we expect to earn for taking that much risk? We plan to receive over 11% for a stock with a beta of 1.7.

Now we have a number. We can use that as the discount rate to discount our estimates of the future cash flows to equity holders.

If we look at the balance sheet of the company, we see assets on the left-hand side. On the right-hand side of the balance sheet are debt and equity. We now have a discount rate that we can apply to discount the cash flows of the company.

That discount rate is calculated using the capital asset pricing model, the risk-free rate plus beta times the market premium.

Summary

Check out my article on Net Present Value to see how to use that discount rate to discount estimated future cash flows to present value.

Diversification changes risk. Market risk can’t be diversified away.

We use an estimate of 5.5% in these examples, but you can modify that to meet your risk profile. Beta measures a stock’s sensitivity to that market risk.

When we put those two things together, the risk-free rate plus beta times the equity premium, we’ve got a way to measure the risk of owning individual stocks.

I hope this comes in handy on your way to wealth!

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