January 2019 Data Update 5: Hurdle Rates and Costs of Financing

In the last post, I looked at how to measure risk from different perspectives, with the intent of bringing these risk measures into both corporate finance and valuation. In this post, I will close the circle by converting risk measures into hurdle rates, critical in corporate finance, since they drive whether companies should invest or not, and in valuation, because they determine the values of businesses. As with my other data posts, the focus will remain on what these hurdle rates look like for companies around the world at the start of 2019.

A Quick Introduction

The simplest way to introduce hurdle rates is to look at them from the perspectives of the capital providers to a business. Using a financial balance sheet as my construct, here is a big picture view of these costs:

Thus. the hurdle rate for equity investors, i.e., the cost of equity, is the rate that they need to make, to break even, given the risk that they perceive in their equity investments. Lenders, on the other hand, incorporate their concerns about default risk into the interest rates they set on leans, i.e., the cost of debt. From the perspective of a business that raises funds from both equity investors and lenders, it is a weighted average of what equity investors need to make and what lenders demand as interest rates on borrowing, that represents the overall cost of funding, i.e., the cost of capital.

I have described the cost of capital as the Swiss Army Knife of finance, used in many different contexts and with very different meanings. I have reproduced below the different uses in a picture:

Paper on cost of capital

It is precisely because the cost of capital is used in so many different places that it is also one of the most misunderstood and misused numbers in finance. The best way to reconcile the different perspectives is to remember that the cost of capital is ultimately determined by the risk of the enterprise raising the funding, and that all of the many risks that a firm faces have to find their way into it. I have always found it easiest to break the cost of capital into parts, and let each part convey a specific risk, since if I am careless, I end up missing or double counting risk. In this post, I will break the risks that a company faces into four groups: the business or businesses the company operates in (business risk), the geographies that it operates in (country risk), how much it has chosen to borrow (financial leverage risk) and the currencies its cash flows are in (currency effects). 

Note that each part of the cost of capital has a key risk embedded in it. Thus, when valuing a company, in US dollars, in a safe business in a risky country, with very little financial leverage, you will see the 10-year US treasury bond rate as my risk free rate, a low beta (reflecting the safety of the business and low debt), but a high equity risk premium (reflecting the risk of the country).  The rest of this post will look at each of the outlined risks.

I. Business Risk
In my last post, where I updated risk measures across the world, I also looked at how these measures varied across different industries/businesses. In particular, I highlighted the ten most risky and safest industries, based upon both price variability and earnings variability, and noted the overlap between the two measures. I also looked at how the perceived risk in a business can change, depending upon investor diversification, and captured this effect with the correlation with the overall market.  If you are diversified, I argued that you would measure the risk in an investment with the covariance of that investment with the market, or in its standardized form, its beta.

To get the beta for a company, then, you can adopt one of two approaches.

• The first, and the one that is taught in every finance class, is to run a regression of returns on the stock against a market index and to use the regression beta. 
• The second, and my preferred approach, is to estimate a beta by looking at the business or businesses a company operates in, and taking a weighted average of the betas of companies in that business. 

To use the second approach, you need betas by business, and each year, I estimate these numbers by averaging the betas of publicly traded companies in each business. These betas, in addition to reflecting the risk of the business, also reflect the financial leverage of companies in that business (with more debt pushing up betas) and their holdings in cash and marketable securities (which, being close to risk less, push down betas). Consequently, I adjust the average beta for both variables to estimate what is called a pure play or a business beta for each business. (Rather than bore you with the mechanics, please watch this video on how I make these adjustments). The resulting estimates are shown at this link, for US companies. (You can also download the spreadsheets that contain the estimates for other parts of the world, as well as global averages, by going to the end of this post).

To get from these business betas to the beta of a company, you need to first identify what businesses the company operates in, and then how much value it derives from each of the businesses. The first part is usually simple to do, though you may face the challenge of finding the right bucket to put a business into, but the second part is usually difficult, because the individual businesses do not trade. You can use revenues or operating income by business as approximations to estimate weights or apply multiples to each of these variables (by looking at what other companies in the business trade at) to arrive at value weights. 

II. Financial Leverage

You can run a company, without ever using debt financing, or you can choose to borrow money to finance operations. In some cases, your lack of access to new equity may force you to borrow money and, in others, you may borrow money because you believe it will lower your cost of capital. In general, the choice of whether you use debt or equity remains one of the key parts of corporate finance, and I will discuss it in one of my upcoming data posts. In this post, though, I will just posit that your cost of capital can be affected by how much you borrow, unless you live in a world where there are no taxes, default risk or agency problems, in which case your cost of capital will remain unchanged as your funding mix changes.  If you do borrow money to fund some or a significant portion of your operations, there are three numbers that you need to estimate for your cost of capital:

1. Debt Ratio: Th mix of debt and equity that you use represents the weights in your cost of capital.
2. Beta Effect: As you borrow money, your equity will become riskier, because it is a residual claim, and having more interest expenses will make that claim more volatile. If you use beta as your measure of risk, this will require you to adjust upwards the business (or unlettered) beta that you obtained in the last part, using the debt to equity ratio of the company. 
   
3. Cost of Debt: The cost of debt, which is set by lenders based upon how much default risk that they see in a company, will enter the cost of capital equation, with an added twist. To the extent that the tax law is tilted towards debt, the after-tax cost of borrowing will reflect that tax benefit. Since this cost of debt is a cost of borrowing money, long term and today, you cannot use a book interest rate or the interest rate on existing debt. Instead, you have to estimate a default spread for the company, based upon either its bond ratings or financial ratios, and add that spread on to the risk free rate:
   

I look at the debt effect on the cost of capital in each of the industries that I follow, with all three effects incorporated in this link, for US companies. The data, broken down, by other regional sub-groupings is available at the end of this post.

III. Country Risk
It strikes me as common sense that operating in some countries will expose you to more risk than operating in others, and that the cost of capital (hurdle rate) you use should reflect that additional risk. While there are some who are resistant to this proposition, making the argument that country risk can be diversified by having a global portfolio, that argument is undercut by rising correlations across markets. Consequently, the question becomes not whether you should incorporate country risk, but how best to do it. There are three broad choices:

1. Sovereign Ratings and Default Spreads: The vast majority of countries have sovereign ratings, measuring their default risk, and since these ratings go with default spreads, there are many who use these default spreads as measures of country risk. 
2. Sovereign CDS spreads: The Credit Default Swap (CDS) market is one where you can buy insurance against sovereign default, and it offers a market-based estimate of sovereign risk. While the coverage is less than what you get from sovereign ratings, the number of countries where you can obtain these spreads has increased over time to reach 71 in 2019. 
3. Country Risk Premiums: I start with the default spreads, but I add a scaling factor to reflect the reality that equities are riskier than government bonds to come up with country risk premiums. The scaling factor that I use is obtained by dividing the volatility of an emerging market equity index by the volatility of emerging market bonds. 

To incorporate the country risk into my cost of capital calculations, I start with the implied equity risk premium that I estimated for the US (see my first data post for 2019) or 5.96% and add to it the country risk premium for each country. The full adjustment process is described in this picture:

I also bring in frontier markets, which have no sovereign ratings, using a country risk score estimated by Political Risk Services. The final estimates of equity risk premiums around the world can be seen in the picture below:

You can see these equity risk premiums as a list by clicking here, or download the entire spreadsheet here. If you prefer a picture of equity risk around the world, my map is below:

Download spreadsheet

I also report regional equity risk premiums, computed by taking GDP-weighted averages of the equity risk premiums of the countries int he region.

IV. Currency Risk
It is natural to mix up countries and currencies, when you do your analysis, because the countries with the most risk often have the most volatile currencies. That said, my suggestion is that you keep it simple, when it comes to currencies, recognizing that they are scaling or measurement variables rather than fundamental risk drivers. Put differently, you can choose to value a Brazilian companies in US dollars, but doing so does not make Brazilian country risk go away.

So, why do currencies matter? It is because each one has different expectations of inflation embedded in it, and when using a currency, you have to remain inflation-consistent. In other words, if you decide to do your analysis in a high inflation currency, your discount rate has to be higher, to incorporate the higher inflation, and so do your cash flows, for the same reason:

There are two ways in which you can bring inflation into discount rates.  The first is to use the risk free rate in that currency as your starting point for the calculation, since risk free rates will be higher for high inflation currencies. The challenge is finding a risk free investment in many emerging market currencies, since even the governments bonds, in those currencies, have default risk embedded in them. I attempt to overcome this problem by starting with the government bond but then netting the default spread for the government in question from that bond to arrive at risk free rates:

Download raw data

These rates are only as reliable as the government bond rates that you start with, and since more than two thirds of all currencies don't even have government bonds and even on those that do, the government bond rate does not come from liquid markets, there a second approach that you can use to adjust for currencies. In this approach, you estimate the cost of capital in a currency that you feel comfortable with (in terms of estimating risk free rates and risk premiums) and then add on or incorporate the differential inflation between that currency and the local currency that you want to convert the cost of capital to. Thus, to convert the cost of capital in US $ terms to a different currency, you would do the following:

To illustrate, assume that you have a US dollar cost of capital of 12% for an Egyptian company and that the inflation rates are 15% and 2% in Egyptian Pounds and US dollars respectively:

The Egyptian pound cost of capital is 26.27%. Note that there is an approximation that is often used, where the differential inflation is added to the US dollar cost of capital; in this case your answer would have been 25%. The key to this approach is getting estimates of expected inflation, and while every source will come with warts, you can find the IMF's estimates of expected inflation in different currencies at this link.

General Propositions
Every company, small or large, has a hurdle rate, though the origins of the number are murky at most companies. The approach laid out in this post has implications for how hurdle rates get calculated and used.

1. A hurdle rate for an investment should be more a reflection the risk in the investment, and less your cost of raising funding: I fault terminology for this, but most people, when asked what a cost of capital is, will respond with the answer that it is the cost of raising capital. In the context of its usage as a hurdle rate, that is not true. It is an opportunity cost, a rate of return that you (as a company or investor) can earn on other investments in the market of equivalent risk. That is why, when valuing a target firm in an acquisition, you should always use the risk characteristics of the target firm (its beta and debt capacity) to compute a cost of capital, rather than the cost of capital of the acquiring firm.
2. A company-wide hurdle rate can be misleading and dangerous: In corporate finance, the hurdle rate becomes the number to beat, when you do investment analysis. A project that earns more than the hurdle rate becomes an acceptable one, whether you use cash flows (and compute a positive net present value) or income (and generate a return greater than the hurdle rate). Most companies claim to have a corporate hurdle rate, a number that all projects that are assessed within the company get measured against. If your company operates in only one business and one country, this may work, but to the extent that companies operate in many businesses across multiple countries, you can already see that there can be no one hurdle rate. Even if you use only one currency in analysis, your cost of capital will be a function of which business a project is in, and what country it is aimed at. The consequences of not making these differential adjustments will be that your safe businesses will end up subsidizing your risky businesses, and over time, both will be hurt, in what I term the "curse of the lazy conglomerate".
3. Currency is a choice, but once chosen, should not change the outcome of your analysis: We spend far too much time, in my view, debating what currency to do an analysis in, and too little time working through the implications. If you follow the consistency rule on currency, incorporating inflation into both cash flows and discount rates, your analyses should be currency neutral. In other words, a project that looks like it is a bad project, when the analysis is done in US dollar terms, cannot become a good project, just because you decide to do the analysis in Indian rupees. I know that, in practice, you do get divergent answers with different currencies, but when you do, it is because there are inflation inconsistencies in your assessments of discount rates and cash flows.
4. You cannot (and should not) insulate your cost of capital from market forces: In both corporate finance and investing, there are many who remain wary of financial markets and their capacity to be irrational and volatile. Consequently, they try to generate hurdle rates that are unaffected by market movements, a futile and dangerous exercise, because we have to be price takers on at least some of the inputs into hurdle rates. Take the risk free rate, for instance. For the last decade, there are many analysts who have replaced the actual risk free rate (US 10-year T.Bond rate, for instance) with a "normalized' higher number, using the logic that interest rates are too low and will go up. Holding all else constant, this will push up hurdle rates and make it less likely that you will invest (either as an investor or as a company), but to what end? That uninvested money cannot be invested at the normalized rate, since it is fictional and exists only in the minds of those who created it, but is invested instead at the "too low" rate. 
5. Have perspective: In conjunction with the prior point, there seems to be a view in some companies and for some investors, that they can use whatever number they feel comfortable with as hurdle rates. To the extent that hurdle rates are opportunity costs in the market, this is not true. The cost of capital brings together all of the risks that we have listed in this section. If nothing else, to get perspective on what comprises high or low, when it comes to cost of capital, I have computed a histogram of global and US company costs of capital, in US $ terms.
   
   
   You can convert this table into any currency you want. The bottom line is that, at least at the start of 2019, a dollar cost of capital of 14% or 15% is an extremely high number for any publicly traded company. You can see the costs of capital, in dollar terms, for US companies at this link, and as with betas, you can download the cost of capital, by industry, for other parts of the world in the data links below this post.

In short, if you work at a company, and you are given a hurdle rate to use, it behooves you to ask questions about its origins and logic. Often, you will find that no one really seems to know and/or the logic is questionable.

YouTube Video


Data Sets

1. Betas by Business: US, Global, Emerging Markets, Europe, Japan, India, China, Aus & Canada
2. Sovereign Ratings and CDS Spreads by Country in January 2019
3. Equity Risk Premiums by Country in January 2019
4. Risk free Rates by Currency: Government bond based
5. Cost of Capital in US $ (with conversion equation for other currencies): US, Global, Emerging Markets, Europe, Japan, India, China, Aus & Canada

January 2019 Data Updates

1. Data Update 1: A Reminder that equities are risky, in case you forgot!
2. Data Update 2: The Message from Bond Markets
3. Data Update 3: Playing the Numbers Game
4. Data Update 4: The Many Faces of Risk
5. Data Update 5: Of Hurdle Rates and Funding Costs!
6. Data Update 6: Profitability and Value Creation!
7. Data Update 7: Debt, neither poison nor nectar!
8. Data Update 8: Dividends and Buybacks - Fact and Fiction!
9. Data Update 9: Playing the Pricing Game!

January 2019 Data Update 4: The Many Faces of Risk!

I think that all investors would buy into the precept that investing in equities comes with risk, but that is where the consensus seems to end. Everything else about risk is contested, starting with whether it is a good or a bad, whether it should be sought out or avoided, and how it should be measured. It is therefore with trepidation that I approach this post, knowing fully well that I will be saying things about risk that you strongly disagree with, but it is worth the debate.

Risk: Basic Propositions

I. Risk falls on a continuum: Risk is not an on-off switch, where some assets are risky and others are not. Instead, it is better to think of it on a continuum, with investments with very little or close to no risk at one extreme (riskless) to extraordinarily risky investments at the other.

In fact, while most risk and return models start off with the presumption that there exists a riskless asset, one in which you can invest for a guaranteed return and no loss of principal, I think that a reasonable argument can be made that there are no such investments. In abstract settings, we often evade the question by using government bond rates (like the US treasury) as risk free rates, but that assumes:

1. That governments don't default, an assumption that conflicts with the empirical evidence that they do, on both local currency and foreign currency borrowings
2. That if the government delivers it's promised coupon we are made whole again, also not true since inflation can be a wild card, rendering the real return on a government bond negative, in some periods. A nominal risk free rate is not a real risk free rate, which is one reason that I track the inflation indexed treasury bond (TIPs) in conjunction with the conventional US treasury bond; the yield on the former is closer to a real risk free rate, if you assume the US treasury has no default risk.

If there is one lesson that emerged from the 2008 crisis, it is that there are some periods in market history where there are truly no absolutely safe havens left and investors have to settle for the least stomach churning alternative that they can find, during these crises.

II. For a company, risk has many sources: Following up on the proposition that investing in the equity of a business can expose you to risk, it is worth noting that this risk can come from multiple sources. While a risk profile for a company can have a laundry list of potential risks,  I break these risks into broad categories:

Note that some of these risks are more difficult to estimate and deal with than others, but that does not mean that you can avoid them or not deal with them. In fact, as I have argued repeatedly, your best investment opportunities may be where it is darkest.

III. For investors, risk standing alone can be different from risk added to a portfolio: This is perhaps the most controversial divide in finance, but I will dive right in. The risk of an investment can be different, if it is assessed as a stand-alone investment, as opposed to being part of a portfolio of investments and the reason is simple. Some of the risks that we listed in the table above, to the extent that they are specific to the firm, and can cut in either direction (be positive or negative surprises) will average out across a portfolio. It is simply the law of large numbers at work. In the graph below, I present a simplistic version of diversification at play, by looking at how the standard deviation of returns in a portfolio changes, as the number of investments in it goes up, in a world where the typical investment has a standard deviation of 40%, and for varying correlations across investments.

Download diversification benefits spreadsheet

If the assets are uncorrelated, the standard deviation of the portfolio drops to just above 5%, but note that the benefits persist as long as the assets in your portfolio are not perfectly positively correlated, which is good news since stocks are usually positively correlated with each other. Furthermore, the greatest savings occur with the first few stocks that are added on, with about 80% of the benefits accruing by the time you get to a dozen stocks, if they are not all in the same sector or share the same characteristics (in which case the correlation across those stocks will be higher, and the benefit lower).

I know that I am now opening up an age old debate in investing as to whether it is better to have a concentrated portfolio or a diversified one. Rather than argue that one side is right and the other wrong, I will posit that it depends upon how certain you feel about your investment thesis, i.e., that your estimate of value is right and that the market price will correct to that value, with more certainty associated with less diversification. Speaking for myself, I am always uncertain about whether the value that I have estimated is right and even more so about whether the market will come around to my point of view, which also means that it is best for me to spread my bets. You can be a value investor and be diversified at the same time.

IV. Your risk measurement will depend on how and why you invest and your time horizon: Broadly speaking, there are three groups of metrics that you can use to measure the risk in an investment. 

1. Price Measures: If an asset/investment is traded,  the first set of metrics drawn on the price path  and what you can extract from that path as a measure of risk. There are many in investing who bemoan the Markowitz revolution and the rise of modern finance, but one of the byproducts of modern portfolio theory is that price-based measures of risk dominate the risk measurement landscape. 
2. Earnings/Cashflow Measures: There are many investors who believe that it is uncertainty about earnings and cash flows that are a true measure of risk. While their argument is that value is driven by earnings and cash flows, not stock price movements, their case is weakened by the fact that (a) earnings are measured by accountants, who tend to smooth out variations in earnings over time and (b) even when earnings are measured right, they are measured, at the most, four times a year, for companies that have quarterly reporting, and less often, for firms that report only annually or semi-annually.
3. Risk Proxies: Some investors measure the risk of an asset, by looking at the grouping it belongs to, arguing that some groupings are more risky than others. For instance, in the four decades since technology stocks became part of the market landscape, "tech" has become a stand in for both high growth and high risk. Similarly, there is the perception that small companies are riskier than larger companies, and that the market capitalization, or level of revenues, should be a good proxy for the risk of a company.

While I will report on each of these three groups of  risk measures in this post, you can decide which measure best fits you, as an investor, given your investment philosophy.

Price Risk Measures
The most widely accessible measures of risk come from the market, for publicly traded assets, where trading generate prices that change with each trade. That price data is then used to extract risk measures, ranging from intuitive ones (high to low ranges) to statistical measures (such as standard deviation and covariance). 

Price Range 
When looking at a stock's current price, it is natural to also look at where it stands relative to that stock's own history, which is one reason most stock tables report high and low prices over a period (the most recent 12 months, for instance). While technical analysts use these high/low prices to determine whether a stock is breaking out or breaking down,  these prices can also be used as a rough proxy for risk. Put simply, riskier stocks will trade with a wider range of prices than safer stocks.

HiLo Risk Measure
To compute a risk measure from high and low prices that is comparable across stocks, the range has to be scaled to the price level. Otherwise, highly priced stocks will look more risky,  because the range between the high and the low price will be greater for a $100 stock than for a $5 stock. One simple scalar is the sum of the high and the low prices, giving the following measure of risk:

HiLo Risk = (High Price - Low Price)/ (High Price + Low Price)

To illustrate, consider two stocks, A with a high of $50 and a low of $25 and B with a high of $12 and a low of $8. The risk measures computed will be:

• HiLo Risk of stock A = (50-25)/ (50+25) = 0.333
• HiLo Risk of stock B = (12-8)/ (12 +8) = 0.20

Based upon this measure, stock A is riskier than stock B.

Distribution
I compute the HiLo risk measure for all stocks in my data set, to get a sense of what would be high or low, and the results are captured in the distribution below (Q1: First Quartile, Q3: Third Quartile):

Data at country level 

Embedded in the distribution is the variation of this measure across regions, with some, at first sight, counterintuitive results. The US, Canada and Australia seem to be riskier than most emerging market regions, but that says more about the risk measure than it does about companies in these countries, as we will argue in the next section. If you want to see these risk measures on a country basis, try this link.

Pluses and Minuses
The high/low risk measure is simple to compute and requires minimal data, since all you need is the high price and the low price for the year. It is even intuitive, especially if you track market prices continuously. It does come with two problems. The first is the flip side of its minimal data usage, insofar as it throws away all data other than the high and the low price. The second is a more general problem with any price based risk measure, which is that for the price to move, there has to be trading, and markets that are liquid will therefore see more price movements, especially over shorter time period, than markets that are not. It is therefore not surprising that US stocks look riskier than African stocks, simply because liquidity is greater in the US. So, why bother? If you are comparing stocks within the same liquidity bucket, say the S&P 500, the high-low risk measure may correlate well with the true risk of the company. However, if your comparisons require you to look across stocks with different liquidity, and especially so if some are traded in small, emerging markets, you should use this or any other price-based measure with caution.

Standard Deviation/Variance
If you have data on stock prices over a period, it would be statistical malpractice not to compute a standard deviation in these prices over time. Those standard deviations are a measure, albeit incomplete and imperfect, of how much price volatility you would have faced as an investor, with the intuitive follow up that safer stocks should be less volatile.

Returns on Stocks
As with the HiLo risk measure, computing a standard deviation in stock prices, without adjusting for price levels, would yield the unsurprising conclusion that higher prices stocks have higher standard deviations. With this measure, the scaling adjustment becomes a simpler one, since using percentage price changes, instead of prices themselves, should level the playing field. In fact, if you wanted a fully integrated measure of returns, you should also include dividends in the periods where you receive them. However, since dividends get paid, at most, once every quarter, analysts who use daily or weekly returns often ignore them.

Distribution
To compute and compare standard deviations in stock returns across companies, I have to make some estimation judgments first, starting with the time period that I plan to look over to compute the standard deviation and the return intervals (daily, weekly, monthly) over that period. I use 2-year weekly standard deviations for all firms in my sample, using the time period available for companies that have listed less than 2 years, and the distribution of  annualized standard deviations is in the graph below.

Data at country level  

As with the HiLo risk measure, and for the same reasons, the US, Canada and Australia look riskier than most emerging markets. Again, I report on the regional differences in the table embedded in the graph, with country-level statistics available at this link.

Pluses and Minuses
It is Statistics 101! After all, when presented with raw data, one of the first measures that we compute to detect how much spread there is in the data is the standard deviation. Furthermore, the standard deviation can be computed for returns in any asset class, thus allowing us to compare it across stocks, high yield bonds, corporate bonds, real estate or crypto currencies. To the extent that we can also compute historical returns on these same assets, it allows us to relate those returns to the standard deviations and compute the payoff to taking risk in the form of Sharpe ratios or information ratios.

Sharpe Ratio = (Return on Risky Asset - Risk free Rate)/ Standard Deviation of Risky Asset

That said, the flaws in using just standard deviation as a measure of risk in investing have been pointed out by legions of practitioners and researchers.

1. Not Normal: The only statistical distribution which is completely characterized by the expected return and standard deviation is a normal distribution, and very little in the investment world is normally distributed. To the extent that investment return distributions are skewed (often with long positive tails and sometimes with long negative tails) and have fat tails, there is information in the other moments in the distribution that is relevant to investors.
2. Upside versus Downside Variance: One of the intuitive stumbling blocks that investors have with standard deviation is that it will higher if you have outsized returns, whether they are higher or lower than the average. Since we tend to think of downside movements as risk, not upside, the fact that stocks that have moved up strongly and dropped precipitously can both have high standard deviations makes some investors queasy about using them as measures of risk.
3. Liquidity effects: As with the high low risk measure, liquidity plays a role in how volatile a stock is, with more liquid stocks being characterized with higher standard deviations in stock prices than less liquid ones.
4. Total Risk, rather than risk added to a portfolio: The standard deviation in stock prices measures the total risk in a stock, rather than how much risk it adds to a portfolio, which may make it a poor measure of risk for diversified investors. Put differently, adding a very risky stock, with a high standard deviation, to a portfolio may not add much risk to the portfolio if it does not move with the rest of the investments in the portfolio.

In summary, the combination of richer pricing data and access to statistical tools has made it easier than ever to compute standard deviation in prices, but using it as your sole measure of risk can lead you to make bad investment decisions.

Covariance/Beta
In the graph on the effect of diversification on portfolio risk, I noted that the key variable that determines how much benefit there is to adding a stock to portfolio is its correlation with the rest of the portfolio, with higher and more positive correlations associated with less diversification benefit. Building on that theme, you can measure the risk added by an investment to a diversified portfolio by looking at how it moves in relation to the rest of the portfolio with its covariance, a measure that incorporates both the volatility in the investment and its correlation with the portfolio.

This equation for added risk holds only if the investment added is a small proportion of the diversified portfolio, but if that is the case, you can have a risky investment (with a high standard deviation) that adds very little risk to a portfolio, if the correlation is low enough.

Standardized Measure (Beta)
The covariance measure of risk added to a portfolio, left as is, yields values that are not standardized. Thus, if you were told that the covariance of a stock with a well diversified portfolio is 25%, you may have no sense of whether that is high, low or average. It is to obtain a scaled measure of covariance that we divide the covariance of every investment by the variance of the portfolio that we are measuring it against:

If you are willing to add on whole layers of assumptions about no transactions costs, well functioning markets and complete information, the diversified portfolio that we will all hold will include every traded asset, in proportion to its market value, the capital asset pricing model will unfold and the betas for investments will be computed against this market portfolio. Note though, that even if you are unwilling to go the distance and accept the assumptions of the CAPM, the covariance and correlation remain measures of the risk added by an investment to a portfolio.

Distribution
If you already are well versed in financial theory, and find the lead in to beta in this section simplistic and unnecessary, I apologize, but I think that any discussion of the CAPM and betas very quickly veers off topic into heated debates about efficient markets and the limitations of modern finance. I think it is good to revisit the basics of the model, and even if you disagree with the model's precepts (and I do not think that there is anyone who fully buys into all of its assumptions), decide what parts of the model you want to keep and which ones you want to abandon. Since the key number that drives the covariance and beta of an investment is its correlation with, I report on the global distribution of this statistics:

Data at country level 

Unlike the high low risk measure and the standard deviation, where my estimation choices were limited to time period and return interval, the correlation coefficient is also a function of the index or market that is used to compute it. That said, the distribution yields some interesting numbers that you can use, even as a non-believer in the CAPM. The median correlation for a US stock with the market is about 20%, and if you check the graph for savings, that would imply that having a portfolio of ten, twenty or thirty stocks yield substantial benefits. As you move to emerging markets, where the correlations are even lower, especially if you are a global investor, the benefits become even larger. Again, if you want to see this statistic on a country-by-country basis, try this link.

Pluses and Minuses
If you have bought into the benefits of diversification and have your wealth spread out across multiple investments, there is a strong argument to be made that you should be looking at covariance-based measures of risk, when investing. If you use a beta or betas to measure risk in an investment, you get an added bonus, since the number is self standing and gives you all the information you need to make judgments about relative risk. A beta higher (lower) than one is a stock that is riskier (safer) than average, but only if you define risk as risk added to a portfolio.

I use covariance based measures of risk in valuation but I recognize that these measures come with limitations. In addition to all of the caveats that we noted about liquidity's effect on price based measures, the most critical ingredient into covariance is the correlation coefficient and that statistic is both unstable and varies over time. Thus, the covariance (and beta) of the stock of a company that is going through a merger or is in distress will often decrease, since the stock price will move for reasons unrelated to the market. As a result, the covariance measures (and this includes the beta) have substantial estimation error in them, which is one reason that I have long argued against using the beta that you get for one company with one pass of history (a regression beta) in financial analysis.  What can you do instead? Since covariance and beta are measures of risk added to a portfolio, they should be more reflective of the businesses (or industries) a company operates in than of company-specific characteristics. Using an industry average beta for steel companies, when valuing US Steel or Nucor, or an industry average beta for software companies, when valuing Adobe, is more prudent than using the regression betas for any of these companies. I will build on this theme in my next post.

Earnings Risk Measures
For many value investors, the biggest problem with using standard deviations or betas is that they come from stock prices. So what? In the value world, it is not markets that should drive our perception of risk, but the fundamentals of the company. Thus, using a price based risk measure when doing intrinsic value is viewed as inconsistent. In this section, I will look at proxies for risk that are built upon a company's performance over time.

Money Losing or Money Making

If we define success in a business in terms of making money, the simplest measure of whether a company is risky is whether it generates profits or not. Simplistic though it might be,  a money losing company, all held held constant, is riskier than a money making company. That said, investors take multiple cracks at measuring profitability, with some defining it as net profits (after taxes and interest expenses), some more expansively as operating income (to look at pre-debt earnings) and some even more broadly as EBITDA. In the table below, I break down the percentages of companies globally that report positive and negative values, using each measure:

Data at country level 

Not surprisingly, in every part of the world, the percentage of firms that have positive EBITDA exceeds the percentage with positive operating income or positive net income. Looking across regions, Japan has the highest percentage of money making firms, with 88.80% making positive net income, and Canada and Australia, with their preponderance of natural resource companies, have the highest percentage of money losers.

Earnings Variance
It is true that whether a company makes money is a very rough measure of risk and a more complete measure of earnings risk would look at earnings variability over time. This is more difficult than it sounds, for three reasons. First, unlike pricing data, earnings data is available only once every quarter in much of the world, and even more infrequently (semi annual or annual) in the rest. Second, unlike price data, which can never be negative, earnings can, and computing variance in earnings, when earnings are negative, are messy. Third, even if you can compute the variance or standard deviation in earnings, it is difficult to compare that number across companies, since companies with higher dollar earnings will have more variance in those earnings in dollar terms. It is for this reason that I compute a coefficient of variation in earnings for each firm, where I divide the standard deviation in earnings by the average earnings over the period of analysis:
Coefficient of variation in earnings = Standard Deviation in Earnings/ Average Earnings over estimation period
When the average earnings are negative, I use the absolute value in the denominator. I computed this measure of earnings variability in both operating and net income for companies that have data going back at least five years, and the distribution is captured below:

Download country level statistics

There are some surprises here. While Australia and Canada again score near the top of the risk table, with the highest variation in earnings, Latin American companies have the lowest volatility in operating and net income, if you compare medians. You can take this to mean that Latin American companies are not risky or that there are perils to trusting accountants to measure performance. Finally, the country level risk statistics are available at this link.

Pluses and Minuses

While I sympathize with the argument that value investors pose, i.e., that using price based risk measures in intrinsic valuation is inconsistent, I am very quickly brought back to earth by the recognition that computing risk from accounting earnings or financial statements comes with its own limitations, which in my view, quickly overwhelm its benefits. The accounting tendency to smooth things out shows up in earnings streams and if you add to that how the numerous discretionary accounting plays (from how to account for acquisitions to how to measure inventory) play out in stated earnings, I am not sure that I learn much about risk from looking at a time series of accounting earnings. You may find that there are other items in accounting statements that are less susceptible to accounting choices, such as revenues or cash flows, but, for the moment, I remain unconvinced that any of these beat price-based measures of risk.

Risk Proxies
The vast majority of investors never attach risk measures to stocks, choosing instead to proxies or stand-ins for risk. Thus, tech stocks are viewed as riskier than non-tech stocks, small cap stocks are perceived as more risky than large cap stocks and, in some value investing circles, stocks that trade at low PE ratios or have high dividend yields are viewed as safer than stocks with high PE ratios or do not pay dividends. In this section, I look at how the measures of risk that I have computed from price and accounting data correlate with these proxies.

Market Capitalization
It seems like common sense to argue that smaller companies must be riskier than larger companies. After all, they often operate in niche markets, have less access to capital and are often dependent on a few customers for success. That said, though, even these common sense arguments start to break down if you think about investing in portfolios of small cap stocks, as opposed to large ones, since many of these risks are firm specific and could be diversified away across stocks. To examine, whether risk varies across market capitalization classes, I looked at the risk measures that we have computed already in this post:

Download full market cap risk statistics

The market capitalization correlates remarkably well with measures of both price and earnings risk, with smaller companies exposed to far more risk than larger firms. The note of caution, though, comes in the correlation numbers, where the smallest companies have the lowest correlation with the market, suggesting that much of the added risk in these companies can be diversified away. Put simply, if you want to own only three or four stocks in your portfolio, it is perfectly appropriate to think of small companies as riskier than large ones, but if you choose to be diversified, company size may no longer be a good proxy for the risk added to your portfolio.

PE Ratios and Dividend Yields
For some value investors, it is an article of faith that the stocks that trade at low multiples of earnings  and pay large dividends are safer than stocks that trade at higher multiples and or pay low dividends. That is perhaps the reason why the Graham screens for cheap stocks include ones for low PE and high dividend yields. In the table below, we look at how stocks in different PE ratio classes vary on  price and earnings risk measures:

Download risk data for PE ratio classes

We follow up by looking at how stocks broken down into dividend yield classes diverge on price and earnings risk measures:

Download data for Dividend Yield classes

With both groups, we notice an interesting pattern. While there is no clear link between how low or high a stock's PE ratio is and its risk measures, money losing companies (where PE ratios are not computed or are not meaningful) are riskier than the rest of the market. Similarly, with dividend yields the link between dividend yields and risk measures is weak, but non-dividend paying companies are riskier than the rest of the market.

Industry Grouping
For decades, investors have used the industry groupings that companies belong to as the basis for risk judgments. Not only does this take the form of conventional investment advice, where risk averse investors are asked to invest in utility stocks, but it is also used to make broad brush statements about tech stocks being risky. Again, there is probably a good reason why these views came into being, at the time that they did, but economies and markets change, and it behooves us to look at the data to see if these rules of thumb still hold. Just as with the market capitalization classes, I have computed the risk statistics for the 94 industries that I categorize all companies into, and you can get the entire list by clicking here. The ten most risky and least risky industries, using price based  risk measures are listed below:

Download full industry list

The least risky firms, looking globally, on a price risk basis, are financial service firms (with banks an and insurance companies making the list) and the most risky firms include natural resource, technology and entertainment companies. Looking at earnings based risk measures, we get the following listing:

Download full industry list

There is significant overlap between the two measures, with the same industries, for the most part, showing up on both lists. The caveat I would add is that some of these sectors have thousands of companies in them, and that there are wide differences in risk across these companies.

Picking your Poison

This has become a far longer post than I intended and I want to wrap it up with three suggestions, when it comes to risk.

1. Risk avoidance is not a strategy: During periods of high volatility and market tumult, investors often obsess about risk. While that is natural, it is worth remembering that avoiding risk is not a risk strategy, but a desperation ploy. In investing, the objective is to earn the highest returns you can, with risk operating as a constraint. Unfortunately, in corporate finance, this lesson has been forgotten by risk managers, where the focus has been on products (hedging, derivatives) that companies can use to minimize risk exposure rather than on determining what risks to avoid, what risks to pass through to investors and what risks too seek out to maximize value. (See my book on risk management for an eraboration)
2. Disagree with models but don't abandon first principles: Finance, in both theory and practice, is full of models for and measures of risk. Since these models/measures are built on assumptions, some of which you may disagree with vehemently, you may find yourself unwilling to use them in your investing. That is not only understandable, but healthy, but please do not throw the baby out with the bathwater and abandon first principles. Thus, refusing to use betas to estimate discount rates is okay but leaping to the conclusion that risk should not be considered in investing is absurd.
3. Pick the risk measure that is right for you: We are lucky enough to be able to estimate or access different risk measures, price or earnings based, for companies that we might be interested in investing in. Rather than lecturing you on what I think is the best measure of risk, I would recommend that you look inwards, because you have to find a risk measure that works for you, not for me. Thus, if you are a value investor who buys companies for the long term, because you like their businesses, and you trust accountants, an earnings-based risk measure may appeal to you. In contrast, if you are more of a trader, buying stocks on the expectation that you can sell to someone else at a higher price, a price-based risk measure will fit you better. With both price and earnings measures, the question of whether you want to use individual company risk or risk added to a portfolio will depend upon whether you have a concentrated or diversified portfolio. Finally, the different risk measures that I have listed in this section often move together, as can be seen in this correlation matrix.
   
   Thus, while you may use market capitalization as your risk measure and I might use beta, our risk rankings may not be very different.  

In closing, whatever risk measure you pick to assess investments, I hope that you earn returns that justify the risk taking!

YouTube Video



Data Links

1. Country Risk Measures (January 2019)
2. Industry Risk Measures (January 2019)
3. Market Cap Risk Measures (January 2019)
4. PE Ratio Risk Measures (January 2019)
5. Dividend Yield Risk Measure (January 2019)

January 2019 Data Updates

1. Data Update 1: A Reminder that equities are risky, in case you forgot!
2. Data Update 2: The Message from Bond Markets
3. Data Update 3: Playing the Numbers Game
4. Data Update 4: The Many Faces of Risk
5. Data Update 5: Of Hurdle Rates and Funding Costs!
6. Data Update 6: Profitability and Value Creation!
7. Data Update 7: Debt, neither poison nor nectar!
8. Data Update 8: Dividends and Buybacks - Fact and Fiction!
9. Data Update 9: Playing the Pricing Game!

Back to Class: A Teaching Manifesto!

I am convinced that each of us is granted moments of grace, where, if we are open to the possibility, we find out what we are meant to do with our lives. For me, one of those moments occurred in the second year of my MBA program at UCLA, when, cash poor, I decided to be a teaching assistant for a quarter to earn some money. At the time I made that decision, my plans were typical of many of my MBA cohort, to get a job in consulting or investment banking, and to make my work up the corporate ladder, but the day that I walked in to teach my first session, I knew that I had found my calling. I was going to be a teacher, though I was not sure what I would be teaching, or to whom. As fate would have it, I found myself fascinated by finance, and I ended up as a finance professor at NYU's business school. I have never regretted that choice, but when asked to describe what I do, I still tell people that I am a teacher, not a professor, a researcher or an academic.

Back to the Classroom!

Starting in 1986, I have been teaching almost every semester at Stern, but I have had a break of almost a year and a half from my class room teaching, the first year representing a long-delayed sabbatical and the last half year reflecting a choice that I made to do all my teaching in one semester this academic year (2018-19). During that period, I continued to teach my short-term (2 to 3 day) classes in different parts of the globe, and while I have enjoyed these visits immensely, I have missed my regular classroom. I am therefore looking forward to a new semester and three new classes this spring, a corporate finance class that I teach, primarily to first year MBAs, a valuation class, an elective for mostly second year MBAs, and another valuation class for undergraduates in their sophomore, junior and senior years. If you are not at Stern, you will not be able to sit in the class  but through the wonders of technology, you can still take these classes. With no further ado, let me describe them and offer you the choices.

Corporate Finance (MBA)

If there is one class in finance that everyone, no matter what their paths in life or business may be, should take, it is corporate finance. Corporate finance is a class that covers the first principles that govern how a business should be run and its reach is complete. Every decision that a firm makes is ultimately a corporate finance decision, no matter which functional area (marketing, production, personnel) it originates from, and that is the perspective I take in the class. I teach the class around what I call my big picture page, where I classify business decisions into investing, finance and dividend groupings and frame how to make those decisions with an end objective of increasing the value of the business.

Class webpage

You will notice chapter numbers and sessions under each topic, with the chapters representing chapters in my Applied Corporate Finance book, a book that I loved writing but one that is so hopelessly over priced that I do not require it for my own class, and the sessions showing the sequence of the class through the 26 sessions that start on February 4, 2019 and end on May 13, 2019. The class meets every Monday and Wednesday during this period, barring the break week of May 16-23, and the syllabus for the class can be found at this link. If you cannot be in these classes in person, don't fret since the classes will be recorded and be available for you to watch, not in real time, but about 2-3 hours after each class is done. To follow along with the webcasts (each about 80 minutes long), you can also access the slides that I use for each class, as well as additional material. Finally, I demand a great deal of my class (weekly puzzles, add on videos, exams and a project) and if you want, you can also do the puzzles, take the exams and do the project, though you will have to grade yourself (with a template that I will put online). You can even read the emails I send my class, and I send about a hundred over the course of a semester, at this link. If you prefer your videos on YouTube, you can try the playlist for the class, and if your preference is for an iTunes U version, this link should take you to the site. The good news is that it will cost you nothing (other than your time and perhaps a few relationships) but the bad news is that you will not get any official certification, if that is what you are looking for.

Valuation (Undergraduate and MBA)

I have a fondness for this class, since I created and taught the first full-semester version of it, at any business school, in 1987.  I was told then that there was not enough "stuff" in valuation to fill a class, and while that might have been true at that time, I have found plenty to fill in the gaps since. As the title of the class indicates, this is a class about valuation. Valuing what, you might ask, and my answer would be "just about everything" from stocks to bitcoin to the Kardashians. The picture below captures the broad reach of the class:

Class webpage

As I teach it, this is a class that is not only about valuing assets but also pricing them (I am afraid that you have to sit in on the class to find out the difference) and it looks at valuation/pricing from a variety of perspectives (investors looking at a stock, managers using value to guide decision making and even accountants writing disclosure and accounting rules). As those of you who read my blog know, my fidelity is to intrinsic value, but I try to keep an open mind on different perspective and approaches in this class.

As with the corporate finance class, we will meet every Monday and Wednesday for 14 (15) weeks, starting February 4 (January 28) for my MBA (undergraduate) class. If you are wondering which version to follow, I will save you the trouble, since the classes are identical in content and delivery, since I don't believe that there is any reason why I should challenge a bright 21-year old less than a bright 28-year old; age and work experience can give the latter more perspective but this is often offset by the extra energy and curiosity that youth brings to the table. The links that you can use to follow the class are in the table below for both versions of the class:

	Webcast page	YouTube Playlist	iTunes U class	Starts	Ends	# Sessions
MBA Valuation	Link	Link	Link	4-Feb-19	13-May-19	26
Undergraduate Valuation	Link	Link	Link	28-Jan-19	13-May-19	28

With both versions of the valuation class, I will also be posting what I call my valuation of the week, a company that I will value, with links to the excel spreadsheet and the story behind the value. I encourage you, if you are taking the class, officially or unofficially, to take my valuation and make it your own, changing the story and the inputs, and then recording your valuation in a shared Google spreadsheet. In a world where crowds decide what movies are successes (Rotten Tomatoes) and which restaurants we eat at (Yelp reviews), we can create our version of crowd valuations. It is an optional exercise, but the more people who participate, the more fun that we can have.

Other Options
I am under no illusions that you are sitting around, wherever you are in the world, with nothing better to do than watching two long sessions each week from February through May. Watching long lecture videos on my tablet is not my idea of fun and while some of you will start with the objective of sitting in on the class, life will get in the way. There are three options that you can consider, depending upon your constraints:

1. If time is your constraint: One of the advantages of taking the class or classes online is that you do not have to do finish the class in May 2019. In fact, the webcasts for the class will stay on for at least another year after the class ends. So, if you like the long class format, you can stretch the class out for longer, if all you need is more time.
2. If format is your concern: If you find your attention lagging or your brain decomposing because the lectures are too long, I have created online versions of both classes (plus a third one on investment philosophies), where I have compressed my 80 minute sessions into 12-15 minutes each. Without giving away any trade secrets, and at the risk of discounting the value of an MBA, it was not difficult to do. As with the regular classes, these are still free, still come with slides and post class quizzes but offer no official certification.
3. If you want accreditation: Even if you take my classes online religiously, mastering every nook and cranny of the topic, and acing every quiz, I do not have the bandwidth or the authority to hand out accreditation or certificates. Three years ago, I remedied this, with the help of NYU, by creating certificate versions of the online classes (with shorter duration videos). The pluses are that the videos are more polished than the ones I created for the free version, there is more administrative support and an active message board where you can chat with others taking the class and you will get a certificate at the end of the class. I will also, at least for the foreseeable future, also do live hourly WebEx sessions once every two weeks and grade your  projects.  The minus is that NYU does not give away certificates for free and if you get sticker shock, please don't make me your target. The decision on whether the certificate is worth the fee is yours to make, and the links to both the free and the NYU certificate versions are below.

	Online class	NYU Certificate Online class
Corporate Finance	Link	Link
Valuation	Link	Link
Investment Philosophy	Link	Link

Finally, you are always welcome to pick the parts of each class that interest you and ignore the rest. The end game is learning, and what interests me may not interest you.

Bottom Line
I know that there are some who say that those who can, do, and those who cannot, teach, and I have been told that or variants of it multiple times. I don't mind the insult, since I have a thick skin, but I know that there is nothing else in the world I would rather do. I answer to no one (other than my wife), pick when or where I work (for the most part), get a chance to change how people think and make a decent living. If your desire is to manage other people's money, be an equity research analyst or investment banker, or to start and run your own company, I wish you the very best, but I am lucky to be doing what I love, and I would be foolish to trade it in for more money or prestige. At the risk of recycling a cliche, I have only one life to live!

YouTube Video


Class Links
a. Full Semester Classes (Spring 2019) (Free)

1. MBA Corporate Finance Class (Spring 2019) (Free)
2. MBA Valuation Class (Spring 2019) (Free)
3. Undergraduate Valuation Class (Spring 2019) (Free)

b. Online Classes (Free)

1. Online Corporate Finance Class (Free)
2. Online Valuation Class (Free)
3. Online Investment Philosophies Class (Free)

c. NYU Online Certificate Classes (Not free!)

1. NYU Online Corporate Finance Certificate Class
2. NYU Online Valuation Certificate Class