##### An Overview of the Equity Risk Premium

Recently, I’ve been thinking a lot about the equity risk premium, and I thought it would be an interesting topic for a series of posts.

The equity risk premium is one of the most debated topics in finance, and there are a variety of opinions about how historical return data should be interpreted and about what level of stock market returns we should expect in the future.

This first post gives an overview of the equity risk premium and discusses some possible interpretations of market valuation data. My next post (**Part 2**) will take a closer look at the historical data on the equity risk premium. **Part 3** will look at the theory behind the equity risk premium and discuss the Equity Premium Puzzle, and **Part 4** will calculate some ex-ante estimates of the equity premium using several methods.

##### What is the Equity Risk Premium?

The equity risk premium is defined as the difference between the overall stock market’s expected return and the risk-free rate. This risk premium compensates investors for the extra risk associated with holding stocks instead of relatively safe government bonds.

When calculating the equity risk premium, not all authors use the same measure for the “risk-free rate”. Many authors use the t-bill rate as the risk free rate, but others argue that long-term government bonds are a better match for the duration of a company’s cash flows.

It is important to understand which measure of the risk-free rate is being used by a particular author. Since long-term bonds rates are generally higher than t-bill rates, authors using long-term bonds as the risk-free reference will generally give lower estimates of the equity risk premium. In this series of posts, I will use the t-bill rate as the risk-free rate.

##### Why is the Size of the Equity Risk Premium Important?

Views about the equity-risk premium are an important input for many investment decisions.

If individual investors believe that the equity premium is large, then they may choose to allocate a greater percentage of their portfolio to equities since the average compensation they receive for taking the additional risk is high. If they believe the equity premium is small, then they may choose to hold more bonds since the average compensation for taking the additional risk is low.

Corporate decision makers also need to have some estimate of the equity premium since it is closely related to the cost of capital. Corporations can create shareholder value if they invest in projects which earn a return which is higher than their cost of capital, and they will destroy shareholder value if they invest in projects which earn a return which is lower than their cost of capital. Therefore, in order to estimate whether or not a particular project will create shareholder value, corporate decision makers generally need to have some estimate of the equity premium.

**Can Valuation Tell us Anything Useful?**

There are many valuation measures which investors use to estimate future stock returns. Usually these valuation measures involve comparing current market prices to some accounting measure such as earnings (P/E ratio), dividends (P/D ratio), sales (P/S ratio), book value (B/M ratio), etc.

Some academics and practitioners adjust the accounting measures used in valuation ratios to account for inflation and the business cycle. For example, in my next post, I will look at Robert Shiller’s CAPE ratio which uses a 10-year average of inflation adjusted earnings.

Past data shows that high market valuations have typically preceded times of relatively low average returns (in the long run), and low market valuations have typically preceded times of relatively high average returns. Valuations have shown some weak (i.e. slow) tendency to mean-revert, but there are debates about the statistical significance of this mean-reversion. However, the historical relationship between valuation and return is not the only logical possibility for the future, and we can use the Gordon Growth Model to think about the various alternatives.

**Example:**

The Gordon Growth Model equation is shown here:

This equation can be used for estimating the price of an individual security or the market as a whole.

The variables in this equation are:

Dividing through by dividends gives us the P/D ratio:

This equation shows that we can get a higher P/D ratio by reducing our required return (**r**) or increasing the expected growth rate (**g**), and we can get a lower P/D ratio by increasing our required return or decreasing the expected growth rate. So, high valuations can mean high expected growth or lower required returns, and low valuations can mean low expected growth or high required returns.

Also, we often hear that valuations are mean-reverting. Mean-reversion implies that while **r** and **g** may fluctuate over time, the long run averages for these values are fairly constant (or at least the average difference is fairly constant). This is an important point to remember since many “tactical asset allocation” or “market-timing” strategies rely on adjusting asset allocation based on the idea that valuations are mean reverting.

If we can come up with some reasonable arguments that **r** or **g** could possibly be meaningfully different in the future, then arguments for mean-reverting valuation are suspect. I’ll consider this in more detail in my **Part 3** post on the Equity Premium Puzzle.

An especially timely series of posts given all the questions surrounding valuation with the yield on the S&P 500 exceeding the yield on the 10 year Treasury.

Re Equity Risk premium – and the risk-free rate. Since the CAPM (and Markowitz’s Portfolio Theory) are single period models, the risk free rate should be the rate that is certain over the investment period, so if one is using monthly returns it should be the expected one-month return i.e. one month TB rates. If one is using say ten-years of historical equity monthly returns, it would be better to work with the premium over the monthly risk-free rates since the average of the one-month returns would not necessarily be a good proxy for the expected risk-free returns each period.