Saturday, February 21, 2009

Fama-French and the Proxy Wars

A turning point in the debate on risk and return occurred in the early 1990s, when Gene Fama and Ken French wrote one of the most-quoted and influential papers on the topic. In it, they began with a simple premise. If our objective in risk and return models is to come up with expected returns on investments, should we not judge the quality of these models by looking at how well they explained actual returns over very long time periods? They began by looking at the CAPM: in it, all return differences across investments should be explained by differences in betas. Looking at actual stock returns from 1962 to 1990, Fama and French found that betas cannot explain a very large portion of the differences in returns across stocks.

This finding was not knew and reflected what other researchers had concluded in earlier papers. Fama and French, however, decided to turn the problem on its head. Rather than build an alternative risk and return model, which is what others had tried to do with the arbitrage pricing and multi factor models, with all their baggage, they decided to start with the data on returns and work backwards. In other words, they went looking for other company characteristics that would do a better job of explaining differences in returns across stocks, than betas did. Their search led them to two variables - the market capitalization of the company and it's price to book ratio- that together explained a large portion of the differences in returns. Small market cap companies and low price to book value companies consistently earned higher returns than large market cap companies and high price to book value companies. Rather than view this as an inefficiency (which other papers had in the past), Fama and French considered these variables as proxies (stand ins) for risk. In effect, they concluded that small companies must be riskier than large companies and low price to book companies must be riskier than high price to book companies.

While the logic of the Fama-French approach is impeccable, it has one significant weakness. Since it is data driven, any proxy, no matter how outlandish, that explains differences in returns could be used in the model. At the risk of pushing this argument to absurd limits, if companies with fatter CEOs have higher returns than companies with thinner CEOs, the weight of the CEO should be used as a risk proxy. Not surprisingly, as the data we look at gets richer and deeper, other variables have been added to the list of good risk proxies - return momentum, earnings revisions, insider buying etc.

Models that test the CAPM against proxy models by looking at how much of past returns are explained by each are almost certainly going to find the CAPM wanting. After all, the proxies were not picked at random but because they had been correlated with returns in the past.

I think that the question of whether to stick with the CAPM or go with a proxy model depends in large part on what you are using the model for. If your job is performance evaluation, say of mutual funds, I think that proxy models make sense, because you are looking at the past and examining whether individual mutual funds beat the market. If you are trying to forecast expected returns in the future, which is what you are doing when estimating cost of equity in corporate finance or valuation, I prefer to stick with the CAPM, with bottom up betas and adjustments for financial and operating leverage.

Tuesday, February 17, 2009

Can betas be negative? (and other well used interview questions)

Here is a favorite question among corporate finance interviewers: " Can betas be negative? And if so, what exactly do they tell us?" The reason negative betas pose a conundrum to many finance students is that they seem to go against intuition. After all, if a beta of one is average risk and a beta of zero is riskless, how can an investment have negative risk?

Here is the answer. Yes, betas can be negative. To see how and why, consider what betas measure: the risk added by an investment to a well diversified portfoli0. By that definition, any investment that when added to a portfolio, makes the overall risk of the portfolio go down, has a negative beta. A more intuitive way of thinking about this is that a negative beta investment represents insurance against some macro economic risk that affects the rest of your portfolio adversely. A standard example that is offered for a negative beta investment is gold, which acts as a hedge against higher inflation (which devastates financial investments such as stocks and bonds). It is also true that puts on stocks and selling forward contracts against indices will have negative betas.

What are the consequences of a negative beta? The expected return on that investment will be less than the riskfree rate; the nominal returns on gold over the last 40 years have been 2% less,on average annually, than the riskfree rate. However, that makes complete sense if you think of it as buying insurance. You are paying for the insurance by settling for a very low or even negative return.

Are there actual investments out there that have negative betas? I know that there are stocks with negative regression betas, but those are the mostly the result of something strange happening during the period of the regression - an extended lawsuit or acquisition battle throwing off the correlation with the market- rather the true betas. In fact, in my fifteen years of updating betas by sector, I have still not found a sector with a negative beta. Furthermore, even assets that, in theory, could have negative betas (gold, for instance) seem to have positive betas when securitized (gold shares, gold ETF). There seems to be something about the securitization process that makes real assets behave more like financial assets.

Sunday, February 15, 2009

Alternatives to Regression Betas

In my prior post, I explain why I am averse to regression betas - the high standard errors of the estimates, the backward-looking nature of the estimates and the loss of intuitive feel for risk. In this post, I would like to look at alternatives that are offered to regression betas, with an eye towards making better estimates:

1. Relative standard deviations: The beta is a function of the standard deviation of the stock, the standard deviation of the market and the correlation of the stock with the market:
Beta = (Correlation between stock and market) (Std dev of stock)/Std dev of mkt
The primary culprit behind the high standard error of betas is the shifting correlation number. Hence, there are some who suggest using an alternative measure of relative risk:
Relative Std dev = (Std dev of stock)/Average std dev across all stocks
Note that the denominator has to the average standard deviation across all stocks, not the standard deviation for the market, since you want the relative risk number to average out to one across all stocks (and it will not if you use the standard deviation of the market).
Pros: This number, like beta, should average out to one across stocks and should have lower standard error; even in a period like the last quarter, the standard deviations rose across the board and the relative standard deviation was fairly stable.
Cons: You are looking at total risk (not just market risk), which may not be appropriate for a diversified investor. You are also still backward looking and dependent on stock prices.

2. Option based approaches: A few years ago, there was a hue an a cry, arising from a paper published in the Harvard Business Review, which claimed to have come up with a forward looking estimate for risk. In the approach, the implied standard deviation of stocks is backed out of traded options issued by the company and compared to the standard deviation of bonds issued by the same company.
Cost of equity = Cost of debt *(Imp std dev of equity/ Std dev of bonds)
Pros: Forward looking, becauase you use option prices to back out standard deviation.
Cons: Works only for companies that have traded options and bonds... and it mixes up total risk and market risk. Does not strike me as a general approach that will work with most companies.

3. Accounting betas: Rather than regressing stock returns against market returns, we could regress changes in accounting earnings at a company against changes in accounting earnings for the entire market, and the slope would be the accounting beta.
Pros: Not dependent upon stock prices and can be estimated even for private businesses. For those who do not trust markets, accounting earnings offer a more stable alternative (assuming that you trust accountants).
Cons: Accounting earnings are often smoothed out and lag true earnings. Furthermore, the number of observations in your regression is restricted. With quarterly statements, you will have 20 observations over 5 years and the resulting standard error will be huge.

4. Bottom-up Betas: In this approach, we start with the businesses that a firm operates in, estimate the betas of these businesses (by looking at the average regression betas of publicly traded firms in each of the businesses) and clean up for differences in financial leverage.
Pros: The average across many regression betas will be more precise than any individual company's regression beta. It can be computed based upon the current or even a future business mix of a company and for private businesses.
Cons: You do need to find publicly traded companies that operate predominantly or only in each individual business and you the average regression beta does reflect the past. For instance, the average beta across all banks over the last 5 years may understate the true beta for banks for the future.

I am a firm believer in the last approach. Since there are lots of mechanical details that can trip you up, I do have a link on my site where I examine these:
More in my next post!

Wednesday, February 11, 2009

The problem with regression betas

I must confess that I find the practices used to estimate betas to be both sloppy and counter intuitive. The standard approach, offered in every finance text book, is to regress returns on the stock against returns on a market index, with the slope yielding the beta. I have five problems with this approach:

1. Statistically, the slope coefficient in a simple regression comes with a standard error. The beta estimate for a typical US company has a standard error that is about 0.20. One way to read this number, is when you are told that the beta for a company (from a regression) is 1.10, the true beta could be anywhere from 0.70 to 1.50 (plus or minus two standard errors).

2. Outside the US, regression betas often look much more precise but only because the indices used tend to be narrow local indices (DAX, Bovespa, Sensex). As anyone who has toyed with the parameters of the beta regression (2 vs 5 years, daily vs weekly, different market indices) knows, you can arrive at very different betas for the same company, based on your choices. None of them is the right beta, and they may all be coming from the same distribution, but it is a wide one.

3. By definition, a regression beta has to be backward looking, since you need past returns. To the extent that companies change their business mixes  (by expanding, divesting and acquiring businesses) or their financial leverage (debt ratios) over time, the regression beta may not be a good measure of the beta for the future.

4. If the only way you can estimate betas is with a regression, you will be stymied right from the start, if you are analyzing the division of a company, a private business or a company that went public recently.

5. By making beta a statistical number, we are missing the fundamentals that drive beta. Every company has an intrinsic or true beta that comes from choices it has made and understanding how these choices can cause your beta to change is central to a better beta estimate.

So, I would take any beta reported for a company by a service or an analyst with a grain of salt. It probably came from a regression and should not define your thinking about the firm's risk. In my next two posts, I will offer my analysis of the determinants of betas and an alternative to regression betas.

Saturday, February 7, 2009

What betas can... and cannot do...

There is no concept that is more abused, and more misinterpreted, than beta in corporate finance. I have heard betas blamed for everything from global warming to the market collapse. "Warren Buffet does not use beta", the refrain goes, "so why should I?"

I think the biggest mistake that people make is to wrap betas up with the assumptions of the capital asset pricing model (CAPM). Does the CAPM make unrealistic assumptions about no transactions costs and no private information to get to its final conclusion (that all exposure to market risk can be captured in a beta, which should then be the sole determinant of the differences in expected returns)? Absolutely. However, just because you don't like the CAPM's rigidity does not mean that you throw the baby out with the bathwater and abandon beta as a measure of risk, or worse, use no measure of risk at all.

I think of betas as measures of relative risk, with the risk defined as exposure to macro economic variables (interest rates, overall economic growth, inflation). Thus, a stock with a beta of 1.2 is 1.2 times more exposed to macro economic risk than the average stock in the market. That proposition stands, whether one buys into the CAPM or not. Seen from that perspective, here are the things betas cannot do:
1. Explain changes in returns for the entire market. The betas for all stocks cannot go up at the same time, since they have to average out to one. (This is in response to those who have argued that the recent drop in equity prices can be explained by an increase in betas across the board.)
2. Capture emerging market risk. If we regress the returns on emerging market stock against emerging market indices, which is the standard practice for most estimation services, the average beta for Indonesian stocks will be one, as will the average beta of Swiss stocks. If we run regressions against a global index, the results are often unpredictable, with betas for emerging market companies often dropping simply because they are such as a small part of the index.
3. Capture firm specific risk: Betas cannot incorporate risks that affect only a firm or a few firms, even if these risks are huge. Thus, a tobacco company's beta cannot reflect litigation risk and a biotech firm's beta will not capture the uncertainty inherent in the FDA approval process.

Here is what betas can do. They can capture shifts in risk across the market. If a sector gets riskier, its beta should go up, but there has be another sector whose risk has to go down to compensate. Thus, banks will have higher betas today than they did a year ago but technology firms may have seen their betas decline, as they have held up fairly well in this downturn. They provide simple, intuitive and surprisingly effective snapshots of how risky an investment is, relative to the rest of the market, especially if you are an investor with multiple investments in your portfolio.

I do have to mention in closing that running a regression of stock returns against a market index is both a terrible way of estimating betas and of thinking about betas. However, this post is already way too long for me to suggest alternatives to regression betas. That will come in the next post.

Thursday, February 5, 2009

Executive Compensation Caps

The news of the day is the decision by the Obama administration to put caps on executive pay, at least at the companies that have lined up to received funds from the government. Not surprisingly, there are people with strong views lining up on both sides of the issue. So, I guess I will stick my toe into the water and hope not to get burned (since there is an obvious political component to this debate).

As a general rule, I don't think governments should have any role to play in setting compensation limits. The heavy hand of government intervention will not only create quirks in the labor market but have unintended consequences. For instance, the US government (in its last populist phase in the early 1990s) decided that executives were getting too much and decided to restrict the compensation that firms could deduct for tax purposes to $ 1 million (per executive)... Since compensation was defined in the legislation as pay and bonuses, and did not include options, it played a role in triggering the huge option packages that executives have received in the last two decades.

But here is why I am torn. The proposed executive pay cap is toothless for most companies and will have an impact only at those firms that have used the federal government as a piggy bank (Citi and BofA ). If we accept the proposition that there is no free lunch, these firms asked taxpayers for capital, were provided this capital and are in no position to deny taxpayers a say in how they make decisions or compensate employees. (As taxpayers, we are singularly unfortunate that we are represented in this process by legislators who have the attention spans of infants and the time horizons of riverboat gamblers...) Faustian bargains have a way of coming back to haunt you.... You lie down with dogs, you wake up with fleas!! (No more analogies, I promise!!!!)

I must close by noting that I think executive compensation is way out of hand at many companies but I think that just as voters in a democracy get the government that they deserve, stockholders are getting the treatment that they too deserve. If we want compensation to be reasonable, and by reasonable, I am not ruling out very large compensation for managers who truly deserve it (Steve Jobs at Apple should be given a few hundred million), we should not be looking to the government for solutions but to ourselves. Investors, and especially institutional investors, need to work to put in place rules that give them more say in compensation. I also like the British notion of putting top management compensation agreements up for stockholder approval routinely.

Monday, February 2, 2009

Low riskfree rates...

One of the many perils of valuing a company in the US or Europe right now is that the riskfree rates in US dollars and Euros are at unprecedented lows - about 2.3% in US $ and about 2.8% in Euros. Analysts, confronted with these riskfree rates, are faced with a quandary. If they use the low riskfree rates, they end up with low discount rates which then result in high valuations. To get around this problem, many are asking the question: Are riskfree rates too low and should we replace them with higher normalized rates (perhaps average rates over time)? Good question, but the wrong place to ask it...

Let me take a step back. It is true that riskfree rates are low but they are not the only numbers at unusual levels. Equity risk premiums and default spreads are at historical highs and the worry about global economic growth is deeper than at time in recent history. When we use low riskfree rates in valuation, we have to accompany them with much higher risk premiums than we would have used a few months ago, lower real growth and lower expected inflation. The net effect is that intrinsic values are lower now than they were a few months ago. 

What gets analysts into trouble is inconsistency. If we use today's riskfree rates and stick with risk premiums that we used to use in the past and growth rates and inflation rates that are also from the past, we will over value companies. The culprit is not the low riskfree rates but internal inconsistency. 

My advice is that you stay with today's riskfree rates but update the other numbers you use in valuation to reflect the environment we face right now. If you insist on replacing today's riskfree rate with your normalized number, you should then adjust all your other numbers to be consistent - not easy to do, in my view. 

Finally, I have a paper on riskfree rates that you may find useful (or not). You can find it by clicking on this link.
I hope you find it useful.