Putting the D in the DCF: The Cost of Capital

If there were a contest for the most measured number in finance, the winner would be the cost of capital. Corporate finance departments around the world compute it as an integral part of investment analysis. Appraisers estimate it as a step towards estimating intrinsic or discounted cash flow value. Analysts spend disproportionate amounts of their time working on it, though not always for the right reasons or with the right inputs. Since I have spent a significant portion of my life, writing and talking about cost of capital, it stands to reason that it is one of the numbers that I compute for all the companies in my data base at the start of every year.

Defining the cost of capital

There are three different ways to frame the cost of capital and each has its use. Much of the confusion about measuring and using cost of capital stem from mixing up the different definitions:

1. For businesses, the cost of capital is a cost of raising financing: The first is to read the cost of capital literally as the cost of raising funding to run a business and thus build up to it by estimating the costs of raising different types of financing and the proportions used of each. This is what we do when we estimate a cost of equity, based on a beta, betas or some other risk proxy, a cost of debt, based upon what the business can borrow money at and adjusting for any tax advantages that might accrue from borrowing.
2. For businesses, the cost of capital is an opportunity cost for investing in projects: The cost of capital is also an opportunity cost, i.e., the rate of return that the business can expect to make on other investments, of equivalent risk. The logic is simple. If you are considering investing in a new asset or security, you have to earn more than you could make by investing the money elsewhere. There are two subparts to this statement. The first is that it is the choices that you have today that should determine this opportunity cost, not choices that you might have had in the past. The second is that it has to be on investments of equivalent risk. Thus, the cost of capital should be higher for riskier investments than safe ones.
3. For investors, the cost of capital is a discount rate to value a business: Investors looking at buying into a business are effectively buying a portfolio of investments, current and future, and to value the business, they have to make an assessment of the collective risk in the portfolio and how it may change over time. 

A good measure of cost of capital will find a way to bridge the differences between the three definitions and I believe that we can do so, with a little common sense and some data.

For this process to yield a number to meet all three requirements for cost of capital, i.e., that it be a cost of raising funding, an opportunity cost and a required return for investors, here are the requirements:

1. Investors price companies based upon a reasonable assessment of the company’s business mix (and country risk exposure) and what they can generate as expected returns on alternative choices of equivalent risk. The former requires companies to provide information on their business mixes and the latter generally is easier to do in a liquid, public market.
2. A company that operates in multiple businesses and many countries cannot use a single, “company-wide” cost of capital as its hurdle rate in investments. It has to adjust the cost of capital for both the riskiness of the business in which the investment is being planned and the part of the world that it is going to be located in.
3. The overall company’s cost of capital has to be a weighted average of the costs of capitals of the businesses that it operates in, and as the business mix changes, the cost of capital will, as well.

Estimating the Cost of Capital

Having laid the groundwork, let’s get down to specifics. If you, as an investor, are given the task of estimating the cost of capital for a company, here is the sequence of steps. First, you have to estimate the business risk in the company by taking a weighted average of the risks of the businesses that the company operates. Second, you have to adjust that risk measure for the effects of debt, which effectively magnifies your business risk exposure, and use the consolidated risk measure to estimate a cost of equity. Third, you have to bring in the cost of borrowing, net of any tax benefit, which will reflect the default risk in the company. Finally, taking a weighted average of the cost of equity and after-tax cost of debt yields a cost of capital. If you are approaching the same task as a CFO, you have to follow the same sequence to get a cost of capital for the company but you have to go further and estimate the costs of capital for the individual businesses that the company is invested in.

As someone who teaches corporate finance and valuation, I am equally interested in both sides of this estimation process and one of my objectives in providing data is to help both sides. To help companies in investment analysis, I try to estimate costs of capital by sector, in the hope that a multi-business company will be able to find the information here to build up business-specific costs of capital. While investors may also find this information useful in valuation/investment analysis, I also estimate costs of capital for individual companies, and while my data providers no longer allow me to share these company-specific costs of capital, I can still provide information on the distribution of costs of capital across companies that can be useful to investors.

a. Cost of capital by sector

In my data updates each year, I estimate the cost of capital, by sector, for companies both globally and classified by region (US, Europe, Japan, Emerging Markets). In making these estimates, I first begin by breaking my total sample of 41,410 companies down into 96 industry groups, some of which may be far broader than you would like to see. I prefer this broad categorization for two reasons. First, I estimate a beta for each industry group by averaging the betas of the individual companies in that group, and these estimates are more precise with larger sample sizes. Second, from a first principles perspective, I believe that since betas measure risk from a macro risk perspective, you are better served with broader categories than narrow ones. Thus, rather than estimate the beta for shrimp fishing as a business, I would rather estimate the beta for food processing businesses (assuming that the only reason that people buy shrimp is to eat them.). Once I have the industry groups, I estimate the cost of equity for each group (in US dollar terms, by using a US dollar risk free rate and a equity risk premium in US dollar terms, though the magnitude of the premium can vary across countries and regions) by using the average beta across companies in the sector. For the cost of debt, I do have a problem, since all I usually have at the industry level is a book interest rate (obtained by dividing the interest expense by the book value of debt) which is not very useful from a cost of capital perspective. I use the variance in stock prices as an indicator of the risk and use it to estimate a default spread in US dollar terms, which then allows me to compute a cost of debt. As the final step, I use the industry average debt to capital ratios (in market value terms) to compute a cost of capital; in keeping with my view that lease commitments are debt, I convert lease commitments to debt for all companies in my database:

The results from the start of 2015 are captured in the attached spreadsheet, which includes costs of capital by sector not only for global companies, but also includes my regional estimates.

b. Cost of Capital - By company

As part of my data analysis, I also try to estimate the cost of capital for each of the 42,410 companies in my database. Since it is impractical to analyze each company in detail, I do have to make some simplifying assumptions.

• First, I assign each company to one primary business in estimating business risk and use the unlevered beta for that business as the beta for the company. Optimally, I would compute the unlevered beta for each company, using the mix of businesses it is in, but with my sample size and data access, it is close to impossible to do. 
• Second, I assume that the company gets all its revenues in the country in which it is incorporated and assign it the equity risk premium of that country. Thus, a Russian company’s cost of equity is computed using the Russian ERP (see my earlier post on country risk) and a German company’s cost of equity is computed based on the German ERP. I know that this violates my earlier point of multinational companies, and I would never make this assumption in building up an individual company’s cost of capital but I am afraid I have no choice with the larger sample. 
• Third, I estimate a default spread for the company by using the variance in its stock prices. It is true that some of the companies (about 4000 or about 10% of my sample) have bond ratings available on them, but the bulk of my companies do not. In addition, if the company is incorporated in a country with sovereign default risk, I add the default spread for the country on to that of the company. I also use the marginal tax rate of the country that the company is incorporated in to estimate an after-tax cost of debt. 
• Finally, to keep the numbers comparable, I compute the costs of capital for all companies in US dollars.

While I cannot provide you with the company-level costs of capital, I can provide the cross sectional distribution of my estimates. As you look at companies, I hope that you can use this for perspective, i.e., in making judgments on what comprises a high, low and median cost of capital. With US companies, the cost of capital distribution across all companies is below:

Cost of capital in US dollars: US companies in January 2015

Thus, if you use a cost of capital of 10% in the United States, you would effectively be assuming that your company is in the 98th percentile of US companies, in terms of cost of capital. With global companies, the cost of capital distribution is as follows:

Cost of capital in US dollars: Global companies in January 2015

Note that I have used a larger equity risk premium and incorporated sovereign default spreads into the cost of debt, yielding a larger spread in the cost of capital. A cost of capital of 12.5% for a global company would put it in the 94th percentile of companies.

A Cost of Capital Computation Template

If you work in finance, you will run into the challenge of estimating the cost of capital for a company sometime during the course of the year. I hope that the datasets that I have created are useful to you in that endeavor and if you decide to use them, here is a simple template for arriving a company's cost of capital in the currency of your choice.

Step	Input	Measure	Comments/ Data sets
1	Risk free rate	Use the prevailing 10-year US T.Bond rate as the risk free rate in US dollars, even if you plan to compute the cost of capital in another currency.	Fight the urge to normalize, tweak or otherwise mess with this rate. It is what you can make today on a risk less investment, no matter what your views on it being too low or high.
2	Business Risk (Unlevered beta)	Break the company down into businesses, using an operating metric (revenues work best) and compute the weighted unlevered beta across the businesses.	Company breakdown: In company’s annual report or financial filings Beta of businesses: My unlevered betas by business (broad groups) or you can create your own subgroups.
3	Financial Risk (Debt to equity and levered beta)	Lever the beta using the market debt to equity ratio for the company today. (If you prefer to use a target debt to equity ratio, make sure it is based on market values.	Market value of equity: Use the market capitalization as market value of equity.  Market value of debt: For debt, use book value as your proxy for market value, or better still convert book value to market value.  Add the present value of operating leases to debt.
4	Equity Risk Premium	Obtain the geographical breakdown of the company’s revenues (or other operating metric, if you don’t like revenues). Take a weighted average of the ERP of the countries/regions that the company operates in.	Geographical Breakdown:  The company’s revenues will be in its financial statements, though it is not always as clear and detailed as you would like it to be. ERP by country: My ERP by country.
5	Cost of debt	If you can find a corporate bond rating for your company, use it to get a default spread and a cost of debt. If you cannot find a bond rating, estimate a bond rating for the company and a default spread on that basis. If you are doing the latter, add a default spread for the country to get the pre-tax cost of debt.	Bond Rating: If available, you should be able to find it at S&P or online. Synthetic Rating: You can use this spreadsheet to get a synthetic rating for your company. Rating-based default spread: My lookup table of default spreads for ratings classes. Country default spreads: My estimates
6	Marginal tax rate	Multiply the pre-tax cost of debt by (1- marginal tax rate) to get the after-tax cost	Marginal tax rate by country: KPMG estimates of country tax rates
7	Debt Ratio	Use the market values of debt and equity (from step 3)	See step 3
8	Currency change	If you want to convert the US dollar cost of capital into another currency, add the differential inflation rate (between that currency and the US dollar) or better still, scale up the  US$ cost of capital for the difference in inflation.	The inflation rate in the US can be estimated as the difference between the US 10-year T.Bond Rate and the US TIPs rate. For other countries, you can use the actual inflation rate last year as a proxy for expected inflation.

If you are interested, I have a spreadsheet that has these steps incorporated into it. Give it a shot!

Implications
Looking at the costs of capital across sectors and companies, there are lessons that I take away for valuation and corporate finance:

1. A rising (falling) tide lifts (lowers) all boats: The first reaction that most analysts and CFOs will have to my estimates of the cost of capital is that they look too low, with a median value of 7.40% for US companies and 8.32% for global companies. In fact, the longer that you have been around in markets, the lower today's numbers will look like to you, because what you consider a normal cost of capital will reflect your experiences. The low costs of capital, though, are appropriate, given the level of risk free rates today.
2. The cost of capital does not (and should not) reflect all risk faced by a business: Even if you accept the proposition that the costs of capital are lower because of low risk free rates, you may still feel that the costs of capital don't look high enough for what you view as the riskiest companies in the market. You are right but that is because the cost of capital captures risk to a diversified investor in a going concern. Consequently, it will not reflect risks that are sector-specific but not market-wide, such as the risk to a biotechnology company that its newest drug will not be approved for production. Those risks are better reflected in the expected cash flows. The cost of capital also does not reflect truncation risk, i.e., that a firm may not survive the early stages of the life cycle or an overwhelming debt burden. That risk is better captured through decision trees and probabilistic approaches.
3. Don't sweat the small stuff: In my view, analysts spend too much time finessing and tweaking the cost of capital and not enough on the cash flows. After all, the cost of capital, even if you go with the global distribution, varies within a tight range (6% to 12%, if you use the 10th and 90th percentile) and your potential for making mistakes is therefore also restricted. In contrast, profit margins and returns on capital have a much wider distribution across companies and getting those numbers right has a much bigger pay off.

Dataset attachments

1. Cost of capital by sector (US, Emerging Markets, Europe, Japan, Global)
2. Tax rates by country
3. Ratings and default spreads 

Spreadsheet attachments

1. Cost of capital worksheet

Data update blog posts

1. An ERP Retrospective: Looking back (2014) and Looking forward (2015)
2. Country Risk, Return and Pricing: The Global Landscape in January 2015
3. The Tax Story (in January 2015): Myths, Misconceptions and Reality Checks
4. Putting the D in the DCF- The Cost of Capital
5. The X Factor in Business: Excess Returns and Value

The Tax Story in 2015: Myths, Misconceptions and Reality Checks

Each of us believes that we pay our fair share in taxes and that it is other people that do not, and not surprisingly, we find evidence to back up our priors. I find that the only way to at least partially offset my own biases is to look at the data. I have done it before, as in this post last year, but with the new data in hand, I thought it is worth an update.

Corporate Tax Rates across Countries

I believe that the US tax code is full of perverse incentives for corporations to borrow too much and to under invest domestically, and that change will be slow to come (and I hope that I am wrong). Since corporate behavior is affected by tax differences across countries, I start by look at differences in corporate tax rates across countries, with a helping hand from KPMG, below:

While there are numerous countries competing for the prize of having the lowest corporate tax rate, the battle for highest tax rate looks like no contest, with the US as the winner (with a marginal tax rate of 40%).

Marginal corporate tax rate in 2014

It is worth noting that two decades ago, there would have been lots of competition for the US at the top of the table, but much of it has faded, not because the US has raised its tax rate (it has not) but because the rest of the world has moved on. Just as an aside, and this was the main focus of my post in August, the US is one of six countries that tries to tax foreign income at the US corporate tax rate, which leads to predictable consequences (trapped cash, inversion etc.)

Effective Tax Rates across Countries

According to the tax scolds, US companies are tax cheats and don’t pay their fair share in taxes, thus rendering the corporate tax rates moot. That claim can be easily checked by looking at the effective tax rates paid by companies in different countries in 2014 and they are captured in the picture below:

While US companies clearly don’t pay 40% of their income in taxes, they paid 28.09% of their taxable income in taxes, higher than the 26.84% paid by European companies and 21.56% by emerging market companies. Only Japanese firms pay more in taxes that US firms:

Effective tax rates by Global Regions: January 2015 (based on trailing 12 months)

In my post on taxes last year, I developed a measure of tax efficiency obtained by comparing the effective tax rate paid by companies to the marginal tax rate. Updating that measure to reflect the 2014 effective tax rates, here is the list of the least efficient tax systems in the world (eliminating pure tax havens and city/states):

The US remains in the top ten list, a dubious distinction given the company it is keeping on this list.

Effective Tax Rates across sectors and size classes

Are some sectors more likely to hold back on paying taxes than others? Given that the tax code has been used as a mechanism by the legislature for the dubious purpose of encouraging “good” behavior (job creation and green energy come to mind), I would not be surprised if this were not the case. As part of my data update, I do compute different measures of taxes paid, by sector. In the table below, I list the dozen industries that pay the highest effective tax rates and the ones that pay the lowest:

Effective Tax Rates in January 2015: Trailing 12-month numbers

The list of the lowest tax paying sectors includes some of the usual suspects, such as real estate investment trusts (since the tax code explicitly relieves them of the tax burden). It is also interesting that investment and asset management shows up on the list, perhaps reflecting the advantageous treatment of income, at least to some portfolio managers. The list of the highest tax paying sectors is tilted towards the retail sector and transportation companies. Oil and gas offers an interesting contrast, with oil/gas distribution companies in the lowest tax paying list and integrated and production companies showing up on the highest tax paying list.

I was also interested is looking at the tax burdens at large versus small companies, again with the intent of examining another widely disseminated view that the largest companies are the ones that pay the least in taxes. In the table below, I look at different measures of taxes paid by U.S. companies, classified by market capitalization into ten classes:

Based on taxable income & taxes in trailing 12 months: January 2015

The critics of large companies must be looking at very different numbers than I am, because at least based on taxes paid in 2014, it is the largest companies that paid the highest taxes, not the smallest. So much for extrapolating from the GE pays no taxes story!

A New Corporate Tax Code

There is talk in the US Congress of fixing the corporate tax code, to make it simpler, fairer and more effective. I may be revealing my ignorance of tax economics but I have a very simple rewrite of the tax code that will deliver (in my view):

1. Lower the corporate tax rate to 28% on income made by corporations on sales in the United States and compute that income based upon the proportion of sales that corporations get in the United States. Why 28%? That is roughly what US companies are paying in the aggregate right now, though with state and local taxes, the new rate will be higher than 28% in some states. The income allocation based on revenues, rather than reported earnings, will put a lot of transfer pricing specialists out of business, but I am sure that they will land on their feet.
2. Move to a territorial tax system, where income on foreign operations are taxed at the foreign tax rate. That will eliminate not only the problem of existing trapped cash but will stop the game playing on foreign income.
3. Eliminate all tax credits and sector-focused tax deductions, no matter how good they sound. I am including tax credits for R&D, green energy and job creation on this list.

If you don't like my suggestions, don't worry! I don't think that there is much chance that my tax code rewrite will become law.

Data Attachments

1. Marginal Tax Rates by country (Courtesy of KPMG)
2. Effective Tax Rates, by country 
3. Effective Tax Rates by sector (US, Europe, Emerging Markets, Japan, Global)

Data update blog posts

1. An ERP Retrospective: Looking back (2014) and Looking forward (2015)
2. Country Risk, Return and Pricing: The Global Landscape in January 2015
3. The Tax Story (in January 2015): Myths, Misconceptions and Reality Checks
4. Putting the D in the DCF- The Cost of Capital
5. The X Factor in Business: Excess Returns and Value

Country Risk, Return and Pricing: The Global Landscape in January 2015

Advance warning: I apologize. I went a little over-the-top with heat maps in this post. They are neat, though, since you can hover over a country (with your mouse or clicker) and you should be able to see the data for that country. If you prefer your data in old-fashioned tables, they are available as links at the bottom of the post.

I am happy to say that I am done with my data updates for 2015. While I like analyzing data, I am glad that I will not have to work with really big and sluggish excel spreadsheets until next year. Following up on my last post on US equity risk premiums, I thought it would make sense in this one to go global and take a look at the numbers, as they stand in January 2015. I am well aware that the global landscape of pricing and risk can change at the drop of a hat, but knowing what they changed is always useful. 

Country Returns

The US market had a good year in 2014, with the S&P 500 delivering a total return of 13.48% for the year. However, it was not not the best performing market for the year, as quite a few emerging markets ranked higher. The table below lists the dozen best-performing and dozen worst-performing markets, in both local currency and US dollar terms, for 2014.

Stock Market Returns: Calendar Year 2014

As an investor, I am not sure how these numbers should affect my investment choices for the coming year. While the contrarian in me is telling me to avoid the winning markets and seek out the losing ones, I have learned through painful experiences to respect momentum enough not to be a blind contrarian. As a consequence, I will stick with my base plan of valuing individual companies, no matter what country they are incorporated or operate in, and looking for under valued companies. 

Country Risk

To estimate value for companies, though, I do have to wrestle with measuring risk globally, and variations in risk across countries. For the last two decades, I have been trying to measure country risk and have reported my estimates annually. While I am ultimately interested in measuring exposure to equity risk, I start with measures of default, because they are more easily available and are easier to connect to expected returns.

The most widely reported measure of sovereign default risk are sovereign ratings, with Moody’s, Standard and Poor’s and Fitch all providing this service. The attached spreadsheet uses the January 1, 2015, data from S&P and Moody’s to provide a comprehensive listing of the local currency sovereign ratings of all rated countries. The following picture captures the breakdown, at least in January 2015, of countries by broad ratings classes (using Moody's sovereign ratings where available and S&P's converted into Moody's ratings, for a few countries):

Sovereign Ratings: January 2015

One critique of sovereign ratings is that they often lag developments in the real world, with changes in ratings occurring well after investors have priced in the changes. The sovereign CDS market provides market-based estimates of sovereign default risk, though only 68 countries have sovereign CDS spreads (far fewer than the 142 countries that have sovereign ratings available on them). The table below lists the sovereign CDS spreads for all available markets in January 2015 (and is also available as a downloadable spreadsheet):

Sovereign 10-year CDS Spreads: January 2015

Both sovereign ratings and CDS spreads are measures of default risk and investors in search of a wider measure of country risk (which extends beyond default into political and legal risk) may want to take a look at the composite risk scores reported by the Political Risk Services (PRS) group. The PRS composite risk score, is scaled to 100, with higher numbers reflecting more risk. Using the most recent values for these scores, I have created a risk map:

The red spots in the map are the most risky countries in the world, at least according to the PRS measure in January 2015.

As I mentioned up front, my end game requires equity risk premiums by country. I started with the sovereign ratings (since they are available for more countries and then used the look up table below to estimate default spreads by country. 

After scaling up these default spreads to reflect the fact that equities collectively are riskier than bonds, I obtained country risk premiums for each country. I made a judgment that the equity risk premium  (5.78%, which I approximate to 5.75%) that I obtained for the S&P 500 was a good measure of the mature market risk premium and adding the country risk premium yields the total equity risk premium for each country). To complete the picture, I used the PRS scores for those frontier markets (such as Libya, Syria, Iran and Iraq) that are not rated by the rating agencies, found rated countries with similar scores and averaged out their equity risk premiums. While you can download the spreadsheet that contains my estimates of equity and country risk premiums by clicking here, the picture below captures the risk differences across the world.

Note that I have used 5.75% as the mature market premium not just for the US but for all countries rated Aaa by Moody's and that the equity risk premiums for non-Aaa rated countries reflects the additional country risk premium. Again, the red spots on the map represent the countries with the highest equity risk premiums. 

At this stage, if you are primarily an investor in US companies, you may be heaving a sigh of relief that you don’t have to deal with these country risk measures, but your relief should be short lived. Since a company’s risk exposure comes from where it operates and not from where it is incorporated, most US companies (including small ones) operate in multiple countries and it is the weighted average of the equity risk premiums across countries that should be used in valuing these companies.

Country Pricing

It is true that some markets are riskier than others, but a knee jerk avoidance of the riskiest markets may not always be a good strategy. After all, at the right price even the riskiest market can be a bargain. To get a measure of how global markets are being priced right now, I estimated a range of pricing multiples including price earnings ratios. EV/EBITDA and price to book value ratios for all of the countries in my sample. Note, as you look at these numbers, that some of the markets (especially in Africa) that I look at are very small with only a handful of listings and that the ratios computed for these markets have to be taken with a grain of salt. 

Starting with PE ratios, here is what I find, as I look across the globe at the start of 2015.

The countries with the lowest PE ratios are highlighted in red, though hovering over the spots will give you a quick measure of why they might not be bargains.

Moving on to EV/EBITDA multiples and looking for bargains, here is what the global picture looks like in 2015:

The countries that trade at the lowest multiples of EBITDA are in red.

Completing the story with price to book ratios, the visualization yields the following.

Again, it should come as no surprise that the countries that trade at well below book value (colored red) also happen to be countries that are in crises.

Looking across all three multiples and listing out the countries that have the lowest values for each one in aggregate:

Based on market values on 1/1/15 and trailing 12-month financials

It is true that most of the countries on this list are also risky ones but that does end the analysis. If the essence of investing is looking for mismatches, you are looking for countries that trade at low prices (relative to earnings, book value or sales), after adjusting for risk. Much as I would like to go into ways of doing this, I think I have outlived my welcome in this post. So, it has to be put off for another day.

So what now?

If you are an investor, there are very few places left to hide from globalization. Very few companies operate in domestic market vacuums and most are exposed, sometimes in good ways and sometimes in bad ones, to changes in the global market landscape. In 2014, it was Russia that was the game changer in the first part but oil prices played the bigger role in the second half of the year. I am not sure what will move global markets in 2015 but I am sure it will be an interesting year. 

Data Attachments

1. Sovereign Ratings for Countries: January 1, 2015
2. Sovereign CDS Spreads: January 1, 2015
3. Country and Equity Risk Premiums: January 1, 2015
4. PE, PBV and EV/EBITDA multiples by Country: January 1, 2015

Data update blog posts

1. An ERP Retrospective: Looking back (2014) and Looking forward (2015)
2. Country Risk, Return and Pricing: The Global Landscape in January 2015
3. The Tax Story (in January 2015): Myths, Misconceptions and Reality Checks
4. Putting the D in the DCF- The Cost of Capital
5. The X Factor in Business: Excess Returns and Value

An ERP Retrospective: Looking back (2014) and Looking forward (2015)

At the beginning of 2014, the expectation was that government bond rates that had been kept low, at least according to the market mythology, by central banks and quantitative easing, would rise and that this would put downward pressure on stocks, which were already richly priced. Perhaps to spite the forecasters, stocks continued to rise in 2014, delivering handsome returns to investors, and government bond rates continued to fall in the US and Europe, notwithstanding the slowing down of quantitative easing. Commodity prices dropped dramatically, with oil plunging by almost 50%, Europe remained the global economic weak link, scaling up growth became more difficult for China and the US economy showed signs of perking up. Now, the sages are back, telling us what is going to happen to markets in 2015 and we continue to give them megaphones, notwithstanding their  forecasting history. Rather than do a standard recap, I decided to use my favored device for assessing overall markets, the equity risk premium (ERP), to take a quick trip down memory lane and set up for the year to come.

The ERP: Setting the stage
The ERP is what investors demand over and above the risk free rate for investing in equities. as an asset class. At the risk of sounding over-the-top, if there is one number that captures investors' hopes, fears and expectations it is this number, and I have not only posted multiple times on it in the last few years but also updated it every month on my website. In making these updates, I have had to confront a key question of how best to measure the ERP. Many practitioners use a historical risk premium, estimated by looking at how much investors have earned on stocks, relative to the returns on something riskfree ( usually defined as government bills & bonds)). Due to the volatility in stock returns, you need very long time periods of data to estimate these premiums, with "long time period" defined as 50, 75 or even 100 years of data. At the start of each year, I estimate the historical risk premiums for the United States and my January 1, 2015 update is below:

Stocks: S&P 500; T.Bills: 3-mth Bills; T.Bonds: US 10-year
Geometric average is based on compounded returns

Based on this table, the historical equity risk premium for the US is between 2.73% to 8%, depending on the time period, risk free rate and averaging approach used. I will also cheerfully admit that I don't trust or use any of these numbers in my valuations, for three reasons. First, using a historical risk premium requires a belief in mean reversion, i.e., that things will always go back to the way they used to be, that I no longer have. Second, all of these estimates of risk premiums carry large standard errors, ranging from 8.65% for the 2005-2014 estimate (effectively making it pure noise) to 2.32% for the 86-year estimate. Third, it is a static number that changes little as the world changes around you, which you may view as a sign of stability, but I see as denial.

In pursuit of a forward-looking, less noisy and dynamic equity risk premium, I drew on a standard metric in the bond market, the yield to maturity:

As bond price rises (falls), yield to maturity falls (rises)

In the equity market analogue, the bond price is replaced with stock index level, the bond coupons with expected cashflows from stocks, with the twist that the cash flows can continue in perpetuity:

There are both estimation questions (Are cashflows on stocks just dividends, inclusive of buybacks or a broader measure of residual free cashflows to equity?) and challenges (Do you use last year's cash flow or a normalized value? How do you estimate future growth? How do you deal with a perpetuity?), but they are not insurmountable. In my monthly estimates for the ERP for the S&P 500, here are my default assumptions:

This estimate is forward-looking, because it is based on expected future cashflows, dynamic, because it changes as stock prices, expected cash flows and interest rates change, and it is surprisingly robust to alternative assumptions about cash flows and growth. The spreadsheet that I use allows you to replace my default assumptions with yours and check the effects in the ERP. 

The ERP in 2014

Using the framework described in the last section, I estimated an equity risk premium of 4.96% for the S&P 500 on January 1, 2014:

During 2014, the S&P 500 climbed 11.39% during the year but also allowing for changes in cash flows, growth and the risk free rate, my update from January 1, 2015, yields an implied equity risk premium of 5.78%:

At the start of each month in 2014, I posted my estimate of the ERP for the S&P 500 on my website. The figure below graphs out the paths followed by the S&P 500 and the ERP through 2014:

The ERP moved within a fairly narrow band for most of the year, ranging from just under 5% to about 5.5%, with the jump to 5.78% at the end of the year, reflecting the updating of the growth rate.

The Drivers of ERP in 2014

To understand the meandering of the ERP during 2014, note that it is determined by four variables:  the level of the index, the base year cash flow, the expected growth and the government bond rate, and is a reflection of the risk that investors perceive in equities. In the figure below, I chronicle the changes in these variables during 2014, at least in my ERP estimates.

A confession is in order. While I update the index levels and government bond rates in real time, I update cashflows once every quarter and the growth rates materially only once a year (at the start of each year). One reason for the precipitous jump in the ERP in the January 1, 2015, update is the updating of the long term growth rate to 5.58% on that date. Updating the cashflow and growth estimates more frequently will smooth out the ERP but not change the starting and ending points.

Perspective: Against history and other markets

When I stated earlier in the post that the ERP was the one number that encapsulated investor hopes and fears, I was not exaggerating, since every statement about the overall market can be restated in terms of the ERP. Thus, if you believe that the ERP at the start of 2015 is around 5.78% (my estimate but you can replace with yours), your market views can be laid bare by how you answer the following question: Given what you perceive as risk in the market, do you think that 5.78% is a fair premium? If your answer is that it (5.78%) is too low (high), you are telling me that you think stock prices are too high (low). 

One reason that I posit that I am not a market timer is because I struggle with this question and there are two simple comparisons that I use for comfort. One is to compare the ERP today to implied quit risk premiums in previous years to see how it measures up to historic norms. The figure below summarizes implied equity risk premiums from 1960 to 2014:

My estimates of ERP at the end of every year from 1960 to 2014

Looking at the historical numbers, the current ERP looks high, not low; it is close to the norm if you use only the post-2008 time period. It is this argument that I used to contest the notion that the market was in a bubble in June 2014.

The other is to compare the equity risk premium to risk premiums in other asset markets. In the bond market, for instance, the default spread for corporate bonds is a measure of the risk premium and the figure below compares the equity risk premium to the Baa default spreads each year from 1960 to 2014:

Baa rates from the Federal Reserve data site (FRED) and Baa default spread computed relative to US 10-year T.Bond rate in that year.

Again, if history is any indication, equity risk premiums do not look inflated, relative to Baa default spread, though it is entirely possible that both spreads are too low. (You can download the data and check for yourself.)

We are and will continue to be inundated by experts, sages and market prognosticators, each wielding their preferred market measures, trying to convince us that markets are under or over valued. In this New York Times article from December 31, 2014, looking at where the market stands going into 2015,  the writer pointed to two widely followed statistics, the Shiller PE, a measure of how stocks are priced relative to inflation-adjusted earnings, and the Buffett ratio, relating the market cap of US stocks to the US GDP, and suggested that both pointed to an over valued markets. Both Robert Shiller and Warren Buffett are illustrious figures, but I think that both statistics are flawed, the Shiller PE, because it does not control for low interest rates, and the Buffett ratio, because of its failure to factor in the globalization of US companies. On market timing, I prefer to set my own course and am not going to be swayed by celebrity name-power in making my judgments.

The Weakest Links

If you believe at this point that I am sanguine about what stocks will do next year, you would be wrong. The nature of equity investing is that it is always coupled with worries and that the best laid plans can be destroyed by events out of your control. The notion that stocks always win in the long term is misplaced and there is a reason why we earn a risk premium for investing in equities. Looking at 2015, these are the three biggest dangers that I see:

1. An Earnings Shock? While current stock prices can be justified based on current cash flows, the cash flows to equity investors in 2014, from dividends and buybacks, represented an unusually high percentage of earnings, which, in turn, were at a high watermark, relative to history.

Based on aggregate numbers for S&P 500

Note that US companies paid out 87.58% of earnings to investors, below the 2007 & 2008 levels, but still well above the historical average (73.68%), and the profit margin of 9.84% in 2014  is the highest in the 2001-2014 time period. Both aggregate earnings and the payout ratio will be tested in the year to come. With aggregate earnings, the first test will be in the near term as the dramatic drop in oil prices in 2014 will play havoc with earnings at oil companies. As I noted in my earlier post on oil prices, lower oil prices may create a net positive benefit for the economy, but the immediate earnings benefit to the rest of the market will be modest. The second test may come from slower economic growth. While the US economy looks like it is on the mend, earnings at US companies are increasingly global, and a slowing down of the Chinese economic machine coupled with more stagnation in Europe, may net out to lower earnings. With the payout ratio, the challenge will be to deliver the earnings growth that investors are expecting, while paying out the high percentage of earnings that they are right now.

2. Fear the Fed? I have made this point before in my posts, but it is worth making again. While the equity risk premium has gone up significantly since the pre-2008 crisis, all of the increase in the risk premium has come from the risk free rate dropping and not from expected returns on stocks increasing.

If the US 10-year T.Bond rate were at 4%, closer to pre-2008 levels, right now, the equity risk premium would be only 3.95%.

3. Crisis, contagion and collapse? If we learned nothing else from 2008, it should be this. We are all part of a global economy, connected at the hip, and while that can yield benefits, the contagion risk has increased, where a crisis in one part of the world spills over into the rest of it. Again drawing on my post on oil, one danger of the sudden collapse in oil prices is that it has not only increased uncertainty about economic growth in the next year but also increased the risk of large, levered oil companies defaulting and sending shockwaves through the rest of the economy.

The perfect storm, of course, would be for all three phenomenon to occur together: a drop in earnings and an increase in interest rates, with an overlay of a global crisis, with catastrophic consequences of stocks. I think that the odds of this happening are low, because the circumstances that cause an earnings collapse are the ones that would keep interest rates low, but I may be missing something. If you disagree, you could take the safe route and hold cash, but unless your probability assessments of a crash are high and a crash is imminent, that does not strike me as prudent. (I have reattached the spreadsheet that I developed for my post on bubbles that you can use to make your own assessment.) 

Bottom line

Like every other year in my investing memory, I start this year both hopeful and fearful, hopeful that financial markets will navigate through whatever the new year will throw at them and fearful that there will be something that will rock them. Given what I know now, I don't see any reason to dramatically alter my exposure to stocks, bonds or real assets, and I will continue to look for stocks that I think are under priced. I wish you the very best in your investment choices this year as well and I hope that no matter what happens to your portfolio, you are healthy and happy!

Attachments: Data Sets

1. Historical Returns for US stocks, T.Bonds and T.Bills: 1928-2014
2. Implied Equity Risk Premiums for S&P 500: 1960-2014
3. ERP, Baa Yields and Real Estate Cap Rates: 1960-2014

Spreadsheets

1. Implied ERP Spreadsheet: January 1, 2015

Data Update 2015 Posts

1. An ERP Retrospective: Looking back (2014) and Looking forward (2015)