The Risk Premium Factor

A New Model for Understanding the Volatile Forces that Drive Stock Prices

Stephen D. Hassett

• Publisher: Wiley
• Year: 2011
• Print ISBN: 9781118099056
• eBook ISBN: 9781118118610
• Edition: 1
• Topic: Business
• Subtopic: Finance
• Index: Business

A radical, definitive explanation of the link between loss aversion theory, the equity risk premium and stock price, and how to profit from it

The Risk Premium Factor presents and proves a radical new theory that explains the stock market, offering a quantitative explanation for all the booms, busts, bubbles, and multiple expansions and contractions of the market we have experienced over the past half-century.

Written by Stephen D. Hassett, a corporate development executive, author and specialist in value management, mergers and acquisitions, new venture strategy, development, and execution for high technology, SaaS, web, and mobile businesses, the book convincingly demonstrates that the equity risk premium is proportional to long-term Treasury yields, establishing a connection to loss aversion theory.

• Explains stock prices from 1960 through the present including the 2008/09 "market meltdown"
• Shows how the S&P 500 has consistently reverted to values predicted by the model
• Solves the equity premium puzzle by showing that it is consistent with findings on loss aversion
• Demonstrates that three factors drive valuation and stock price: earnings, long term growth, and interest rates

Understanding the stock market is simple. By grasping the simplicity, business leaders, corporate decision makers, private equity, venture capital, professional, and individual investors will fully understand the system under which they operate, and find themselves empowered to make better decisions managing their businesses and investment portfolios.

Chapter 1

Understanding the Simplicity of Valuation

The constant growth equation is a simple model for valuing a stream of cash flows in perpetuity based on cost of capital and long-term growth. By using earnings as a proxy for cash flow, this simple model can estimate fair value of the stock market. Understanding how lower cost of capital and higher growth rates translate to higher price-to-earnings (P/E) ratios, thus higher valuation, and that even small changes make a big difference is one of the most important lessons from the Risk Premium Factor (RPF) Model. The Capital Asset Pricing Model (CAPM) is used to determine cost of equity capital where the equity risk premium (ERP) is a key component. Despite its importance in valuation, most methods for estimating the ERP have been unsatisfactory.

Understanding the drivers of value requires familiarity with a few basic financial concepts. The first is the time value of money. This term refers to the idea that money promised at some future date is less valuable than money in hand today. Would you rather have $100 today or in one year? Of course, you'd rather have the $100 today to spend, invest, or pay down debt. At a 5 percent annual interest rate, $100 invested today is worth $105 in a year. We call this the future value (FV).

Conversely, assuming the same rate of return, $105 in a year is worth $100 today. This is referred to as discounted value. Discounting a stream of cash flows over several periods is discounted cash flow (DCF) analysis. This discount rate is the amount by which we discount future payments or cash flow to find their equivalent value today. It is also called the cost of capital—a term that will be used throughout this book and abbreviated by “C.”

How much is the promise to pay $100 in a year with C of 5 percent worth today? We call this the present value (PV). If you think it is $95, you are close, but wrong. A simple test is to take the estimated PV and use the discount rate to get the FV. In this case, if you invested $95 at 5 percent, you would have only $99.75 at the end of a year. In order to calculate present value, you need to divide by the discount rate (C). The math is simple. The future value in one year equals the present value (our original amount) plus the present value times the interest rate. Think of it this way, if you deposit $100 (PV) in the bank at 5 percent (C) at the end of one year, you have your initial $100 plus $100 times 5 percent.

FV = PV + PV × C, which is usually simplified to:

In our first example, that would be:

Therefore, we can just rearrange the equation to solve for PV:

FV/(1 + C) = PV, so to find the future value of $100 at 5 percent:

In other words, $95.24 invested for one year at 5 percent is $100.

Next, let's look at values over longer periods. What is the value of $100 at 5% in five years with interest paid at the end of each year and reinvested? At the end of year one, we have $105. The $105 is reinvested at 5 percent to return $110.25 at the end of year 2. At the end of year 3, $115.76. And at the end of year 5, $127.63. This is simply taking the PV and multiplying by (1 + C) once for each year.

This can also be expressed as:

In our example, that is:

This is another way of saying we multiply by 1.05, five times. The formula for PV is:

In words, we just divide by 1 + C once for each year.

RATES, COMPOUNDING, AND TIME VALUE

Interest rates have an obvious impact on time value. If instead of 5 percent you were able to invest at 10 percent per year, your annual return doubles. One hundred dollars at 10 percent is worth $110 in a year and $121 in two years. At the end of five years it is worth $161, compared to $127 at 5 percent. The calculation of reinvested interest plus principal over a number of years is called compounding. The compounding of interest results in ever growing returns over time with the impact of interest rates magnifying over time. While the difference between 5 percent and 10 percent for a year might not seem like much, over five years the initial investment would have grown just 27 percent at 5 percent, while growing 61 percent at a 10 percent annual rate. After 10 years at 5 percent the original $100 will have grown to just $163, while the investment of $100 at 10 percent will have grown to $259. Just as future value increases with the discount rate, present value decreases. The present value of $100 paid in five years at 5 percent is $78.35, while the present value at 10% is just $62.09. The higher the discount rate, the less that future dollar is worth.

We can see this in the equations. Since FV = PV × (1 + C)n, the larger the discount rate (C) and the longer it is invested in years (n), the more it grows. The opposite holds true for PV, since the equation for PV = FV/(1 + C)n, as C or n gets larger, the PV gets smaller. I am spending a lot of time on this point because, as we will see, the cost of capital (C) has a big influence on stock price.

WHY TIME VALUE MATTERS FOR THE STOCK MARKET

When you buy stock in a company, you are buying ownership. Just as an owner of 100 percent of a business owns 100 percent of the future cash flow, an owner of 0.01 percent of a company, owns 0.01 percent of its future cash flow. It is that cash flow that accounts for the value. If you own 100 percent of a business, you decide how that cash flow is invested—pay dividends or reinvest. If you own only a small part of the business—like a typical shareholder—you are entrusting management to decide how to dispose of its cash flow. They can pay dividends, reinvest, buy back shares, or acquire another business.

If we forecast future cash flows of a business, projecting out all revenue, expenses, and investment, the value of the business is equal to the present value of those cash flows. Valuation of companies reflects current earnings and future earnings—growth; but the more distant the earnings, the less value today.

How far in the future do we discount the earnings? In perpetuity—in other words, forever. Of course, the company could be sold in the next few years, but since the sale price is based on projected cash flow, the valuation at time of sale will still be based on perpetuity cash flows. As you will see, projecting future earnings into perpetuity does not require a spreadsheet with an infinite number of columns.

VALUING A PERPETUITY

If I promise to pay you $5 per year forever, what is that worth today? If we assume C is still 5 percent, then the payment at the end of the first year is worth $5/(1 + 0.05) and the second $5/(1 + 0.05)2 and so on. Table 1.1 shows the discount factors and present value for select future years. The PV in any year is the payment divided by the discount factor. The PV of the perpetuity is the sum of the PVs for each year out to infinity.

Table 1.1 PV of $5 at 5 Percent

Year	Discount Factor	PV
1	1.050	$4.76
2	1.103	$4.54
3	1.158	$4.32
4	1.216	$4.11
5	1.276	$3.92
10	1.629	$3.07
100	131.501	$0.04

The good news is that in order to calculate a perpetuity, you don't need to forecast cash flows forever. Assuming a constant discount rate and cash flow the value of a perpetuity is simply:

where E is the annual cash flow in each year. Notice that since E is divided by C, PV gets larger as C gets smaller—lower interest rates make values go up. Since in evaluating a company, E is not a constant we need to account for its growth.

CONSTANT GROWTH EQUATION: THE KEY TO UNDERSTANDING THE STOCK MARKET

Transforming the perpetuity equation to account for growth only requires subtracting the long-term growth rate (G) from C in the perpetuity formula, so PV = E/C becomes:

...

Table of contents

• Cover
• Series
• Title Page
• Copyright
• Dedication
• List of Figures
• List of Tables
• Preface
• Acknowledgments
• About the Author
• Chapter 1: Understanding the Simplicity of Valuation
• Part One: Exploring the Risk Premium Factor Valuation Model
• Part Two: Applying the Risk Premium Factor Valuation Model
• Appendix A: Mobile Apps: The Wave of the Past
• Appendix B: Technology on the Horizon: What if Moore's Law Continues for Another 40 Years?
• Appendix C: A Simple and Powerful Model Suggests the S&P 500 Is Greatly Underpriced
• Appendix D: S&P Index Still Undervalued
• Appendix E: 30 Percent Value Gap in S&P 500 Closed by Rise in Treasury Yields, Price
• Appendix F: Making a Case for Salesforce.com Valuation
• Glossary
• Notes
• About the Companion Web Site
• Index