The University of Chicago’s Gene Fama has a new blog with frequent coauthor, Dartmouth financial economist Ken French at the following address: http://www.dimensional.com/famafrench. This blog will be well worth following for those interested in finance!
Category Archives: Finance
Are ‘Quant’ Kings Free of Blame?
Page C18 of today’s Wall Street Journal has a very interesting article entitled “Absolving the Quants, a Bit” concerning the financial market consequences of so-called quantitative hedge funds. This article notes, among other things, that there has been a proliferation over time of hedge funds implementing similar “LTCM-style” quantitative strategies. With so many arbitragers chasing similar (transitory) profit opportunities all at the same time, these investors are finding that earning excess returns is becoming increasingly more difficult. As the article notes, “To boost the raw returns achievable this year to those seen in 1998, a fund would have to borrow much more, with a consequent increase in risk. If funds are borrowing more, there is a bigger chance that a move to cut debt could trigger sharp and correlated market moves. Such an effect would likely be much broader than the "quantagion" caused when different computer-driven trading models work in similar ways.”
Are 'Quant' Kings Free of Blame?
Page C18 of today’s Wall Street Journal has a very interesting article entitled “Absolving the Quants, a Bit” concerning the financial market consequences of so-called quantitative hedge funds. This article notes, among other things, that there has been a proliferation over time of hedge funds implementing similar “LTCM-style” quantitative strategies. With so many arbitragers chasing similar (transitory) profit opportunities all at the same time, these investors are finding that earning excess returns is becoming increasingly more difficult. As the article notes, “To boost the raw returns achievable this year to those seen in 1998, a fund would have to borrow much more, with a consequent increase in risk. If funds are borrowing more, there is a bigger chance that a move to cut debt could trigger sharp and correlated market moves. Such an effect would likely be much broader than the "quantagion" caused when different computer-driven trading models work in similar ways.”
Actively versus passively managed investment accounts
A long-standing debate in the financial services industry concerns whether investors are better off in the long run with actively versus passively managed investment accounts. Active management is simply an attempt to “beat” the market as measured by a particular benchmark or index such as the S&P 500. One of the more famous active fund managers is Legg Mason’s Bill Miller, who until 2006 had managed to outperform the S&P 500 for 15 years in a row. In 2006, Mr. Miller significantly underperformed the S&P 500. Going forward, no one (including Mr. Miller) really has any way of predicting with any degree of certainty whether Mr. Miller will be able to revert back to systematically beating the market over time.
Notwithstanding Mr. Miller’s impressive historical performance record, it is important to note that typically only 10-20% of actively managed funds outperform the S&P 500 in any given year. Furthermore, the funds belonging to this elite group tend not to consistently replicate this performance in subsequent years; if anything, “winners” in any one period tend on average to subsequently be “losers”. Interestingly, to the extent that there is any persistence, it tends to be among funds which underperform the S&P 500 (e.g., see “Performance Persistence”).
I have worked out a simple numerical example (shown in the Addendum below) which shows that on average, active portfolio management can be expected to result in significantly worse investment performance than a passive (indexed) strategy, based upon the 10-20% odds mentioned above. In order to make money (on an after-transaction cost, risk-adjusted basis) with an active management strategy, over time one has to be significantly better than average in order to have any hope of outperforming an indexed strategy. The numerical example shown below implies that an investor would need to pick winners nearly 50% of the time in order to make active portfolio management worthwhile. Furthermore, I have implicitly assumed that each period represents a completely independent lottery; thus the analysis does not consider the possibility of persistence in one’s investment performance. In order to model persistency, one would need to make the probability of beating the market in any given year (notated below as “p”) a function of previous p’s; I will leave this to the reader as an exercise.
Addendum
Suppose there are four time periods. Let u represent an “up” move where you beat the market,1 and d represent a “down” move where you underperform the market. Thus u > 1, and d < 1.2 Also suppose that you want to invest $1 at t=0. The following table lists all possible portfolio values across all dates and states for four periods:
t=0 |
t=1 |
t=2 |
t=3 |
t=4 |
|
|
|
|
u4 |
|
|
|
u3 |
|
|
|
u2 |
|
u3d |
|
u |
|
u2d |
|
1 |
|
ud |
|
u2d2 |
|
d |
|
ud2 |
|
|
|
d2 |
|
ud3 |
|
|
|
d3 |
|
|
|
|
|
d4 |
The probability of an up move is p, whereas the probability of a down move is (1-p). After 1 period, there are two possible outcomes; you either have an up move with probability p or a down move with probability p. After two periods, there are three possible outcomes; you either have two consecutive up moves with probability p2, two consecutive down moves with probability (1-p)2, or two moves involving up and down moves with probability 2p(1-p), etc. Taking this out to four periods yields the following set of probability distributions for 1, 2, 3, and 4 periods:
t=0 |
t=1 |
t=2 |
t=3 |
t=4 |
|
|
|
|
P4 |
|
|
|
p3 |
|
|
|
p2 |
|
4p3(1-p) |
|
p |
|
3p2(1-p) |
|
1 |
|
2p(1-p) |
|
6p2(1-p) |
|
1-p |
|
3p(1-p)2 |
|
|
|
(1-p)2 |
|
4p(1-p)3 |
|
|
|
(1-p)3 |
|
|
|
|
|
(1-p)4 |
Next, suppose that the odds of beating the market in any one year (p) is 20%, and that u = 1.1. Thus d = 1/1.1 = .91. The following table lists the portfolio values in each possible state occurring 1, 2, 3, and 4 periods from now combined with associated probabilities based upon the previous table:
t=0 |
t=1 |
t=2 |
t=3 |
t=4 |
|
|
|
|
$1.46 |
|
|
|
$1.33 |
0.160% |
|
|
$1.21 |
0.80% |
$1.21 |
|
$1.10 |
4.0% |
$1.10 |
2.560% |
$1.00 |
20% |
$1.00 |
9.60% |
$1.00 |
|
$0.91 |
32.0% |
$0.91 |
15.360% |
|
80% |
$0.83 |
38.40% |
$0.83 |
|
|
64.0% |
$0.83 |
40.960% |
|
|
|
51.20% |
$0.75 |
|
|
|
|
40.960% |
Note that the probabilities in each column sum to 100%. You can calculate the expected value of your actively managed portfolio relative to an indexed portfolio 1, 2, 3, and 4 periods from now by calculating the state contingent portfolio values by their probabilities; thus the expected values at each of these dates are:
Expected (relative) portfolio values |
|
t=1 |
$0.9473 |
t=2 |
$0.8973 |
t=3 |
$0.8885 |
t=4 |
$0.8332 |
In other words, by following an active management strategy, on average you can expect to be significantly worse off than you would be if you follow a passive strategy. Furthermore, your underperformance grows worse over time (note that the indexed strategy by definition produces an expected value of $1.00 at each of these future dates).
Here is a copy of the spreadsheet that I used in order to perform these calculations. The reader can perform further sensitivity testing by changing the values of p, u, and d.
Endnotes
[1] By beating the market, I mean that one earns excess returns on an after-transaction cost, risk-adjusted basis by following an active management strategy rather than a passive (indexed) strategy. For example, suppose you invest in an actively managed technology fund which has transactions costs of 200 basis points per year and a portfolio beta of 2. If such a portfolio earns 12% when the market returns 8%, then this is not beating the market; e.g., if the riskless rate of interest is 5%, then the after transactions cost, risk adjusted return on this portfolio is 12% (gross portfolio return) – 2% (transactions costs) – 6% (risk premium = b(E(rm)-rf) = 2(8-5)) = 4%, whereas the passive (indexed) strategy returns ~ 5% on a risk adjusted, after transactions cost basis.
[2] For simplicity, assume that ud = 1; i.e., if you outperform (underperform) the market during the course of the next time period and underperform (outperform) the market during the subsequent time period, this means that your performance over two time periods is in line with the market.
Finance to the Rescue
For what it’s worth, I am one of four people (along with Jeff Holland, Liongate Capital Management founder, John W. Howton Rockbrook Capital founder, and John C. Bogle, founder and former CEO of the Vanguard) interviewed in “Finance to the Rescue”, an article that appears in the Fall 2005 issue of Baylor Business Review. My interview is on the topic of cat bonds, which is a topic that I have previously blogged about.
Cat bonds
The very concept of insurance is based on risk. So it’s no surprise that important innovations in risk management and finance often come from the insurance industry. One such innovation that is growing in popularity is the so-called catastrophe bond, or “cat bond.”
Common sense as well as theory suggests that proper diversification of any risk involving a remote possibility of enormous loss (such as a natural or man-made catastrophe) makes such a risk more manageable. Traditionally, catastrophe, or “cat” risk was transferred and shared through the insurance and reinsurance markets. However, in spite of the dramatic growth in the magnitude of human and economic losses from natural and man-made catastrophes in recent years, it is surprising how little cat risk transfer actually occurs. Property owners fail to adequately insure catastrophe risk, and even when they purchase insurance, their insurers tend to retain most (as much as 70 percent) of this risk rather than distribute it more broadly through the reinsurance market. The reason why cat reinsurance is so limited is due to inadequate global capacity and correspondingly high reinsurance premiums.
Cat bonds came into existence due to this lack of capacity in the reinsurance market. Although they have been used primarily as an alternative to cat reinsurance, there are examples of corporations and other non-insurance entities issuing cat bonds. For example, during the summer of 1999, Tokyo Disneyland issued cat bonds because management found at the time that it was cheaper to have the capital markets insure its earthquake exposure than the insurance markets. More recently, the Fédération Internationale de Football Association (FIFA) issued a $260 million cat bond to protect itself against (a terrorism-related) cancellation of the 2006 World Cup in Germany.
Cat bonds represent a form of insurance securitization in which risk is transferred to investors rather than insurers or reinsurers. Typically, an insurer or reinsurer will issue a cat bond to investors such as life insurers, hedge funds and pension funds. The bonds are structured similarly to traditional bonds, with an important exception: if a pre-specified event such as a terrorist attack or hurricane occurs prior to the maturity of the bonds, then investors risk losing accrued interest and/or the principal value of the bonds.
Although the cat bond market is still relatively small compared with the traditional insurance and reinsurance markets, it is already having a particularly important effect on reinsurers. Since the cat bond market provides insureds with a credible alternative to traditional reinsurance, the cat bond market has forced reinsurers in particular to become more competitive in their pricing and underwriting practices. Furthermore, investors value cat bonds in part because returns on these securities tend not to be very highly correlated with returns on other asset classes such as stocks, conventional bonds, commodities and real estate.
Given the benefits that cat bonds offer both insureds and investors, the market for cat bonds is expected to continue to grow and exert an important check and balance upon pricing and underwriting practices in conventional insurance and reinsurance markets. Ironically, as documented by a recent Wall Street Journal article, the growth of the cat bond market is in turn fueling the growth prospects of the reinsurance industry, as a number of hedge funds that were early cat bond investors are now starting to launch their own reinsurance firms.
Tax compliance costs and related issues
It is well known that the U.S. income tax system has enormous compliance costs. Economists generally view compliance costs as the sum of direct payments made to tax lawyers and tax accountants for tax-related services plus the opportunity cost of time spent by everyone else. Everyone else basically includes firms and individuals who complete their own tax forms and deal directly with the IRS with respect to tax audits and litigation (rather than employ tax professionals to do the “dirty work” for them). A cursory survey of the tax compliance literature yields estimates (based upon this specific compliance definition) ranging from $200 to $300 billion, or approximately 1.7 to 2.5% of GDP.
In 2002, it is estimated that individuals, businesses and non-profits spent 5.8 billion man-hours complying with the federal income tax code, which is the financial equivalent of imposing a 20.4-cent surcharge for every dollar that the income tax system collects. Apparently it is quite expensive to figure out what taxable income actually is. This is not surprising in light of the substantial and growing complexity of the Internal Revenue Code. The number of words in the Internal Revenue Code that specifically address the topic of income taxation has grown from 172,000 words in 1955 to 982,000 by 2000, an increase of 472 percent. Income tax regulations, which provide taxpayers with the “guidance” they need to calculate their taxable income, have grown at an even faster pace from 572,000 words in 1955 to 5,947,000 words by 2000, an increase of 939 percent. Combined, the federal income tax code and regulations grew from 744,000 words in 1955 to 6,929,000 by 2000—an increase of 831 percent. (Source: “The Cost of Tax Compliance”).
Interestingly, the CNNMoney website published an article yesterday that points out another yet another important cost related to the current U.S. income tax system that is of a similar order of magnitude as the cost of compliance. This relates to the cost of noncompliance. Preliminary findings from a recently published IRS study show that the gap between what’s owed and what’s actually paid is between $257 billion and $298 billion (see the article entitled “Taxpayers stiff IRS by nearly $300B”). So let’s summarize. The current U.S. income tax system has substantial transactions costs (1.7 to 2.5% of GDP) and at the same time produces a net shortfall of tax revenues to the government of a similar order of magnitude (i.e., an additional 2.1 to 2.5 percent of GDP). Relative to the amount of money actually collected by the IRS, these costs total around 40%.
In the risk management literature, it is well known that the asymmetric nature of the corporate income tax creates incentives for firms to prefer hedging over retaining risk. Tax asymmetries derive from two important features of the corporate income tax; specifically, tax rate progressivity and incomplete tax loss offsets. Thus the incentives conveyed by the manner in which the tax system is structured creates yet another cost; specifically, firms and individuals have a tendency to underinvest in risky (but potentially profitable) assets, which in turn limits the economy’s prospective growth potential. Thus the current U.S. income tax system gives rise to underinsvestment problems in the economy and is also very costly to administer.
Clearly, very powerful vested economic interests (with lots of money to “invest” in lobbyists) prefer the status quo, so it will be interesting to see whether Congress is able to reform the tax system such that administrative costs are substantially reduced and economic incentives with respect to risk bearing are less distorted. Most of the proposals (e.g., a “flat” income tax or a consumption tax) that are on the table presently have the potential (at least in theory) to accomplish both of these goals, which in turn would bode well for the future growth and competitiveness of the U.S. economy.
Effects of tax rules on dividend policy
Tyler Cowen asks some rather interesting questions concerning Microsoft’s decision to declare a $3 per share “special dividend” (since Microsoft has more than 10 billion shares outstanding, this translates into more than $32 billion in cash, thus representing the largest corporate dividend payment in history). Specifically, 1) would these dividends have happened without the Bush tax cuts, and 2) does Microsoft fear that Kerry will win and raise taxes on dividends? Professor Cowen’s answers to these questions are “maybe not” and “probably” respectively. The Wall Street Journal corroborates Professor Cowen by noting that “…the company was clearly concerned with the possibility that John Kerry might be elected President and carry out his promise to return dividends to their former status as ordinary income (thus raising the dividend tax back to the nearly 40% Clinton-era top rate from today’s 15%).
That dividend policy is sensitive to tax rules is empirically borne out by a new working paper authored by Raj Chetty and Emmanuel Saez entitled “Do Dividend Payments Respond to Taxes? Preliminary Evidence from the 2003 Dividend Tax Cut“. Chetty and Saez note “The individual income tax burden on dividends was lowered sharply in 2003 from a maximum rate of 35% to 15%, creating a unique opportunity to analyze the effects of dividend taxes on dividend payments by U.S. corporations.” They find, among other things, that 1) the fraction of publicly traded firms paying dividends began to increase in 2003 after having declined continuously for more than two decades, and 2) firms that were already paying dividends prior to 2003 raised their dividend payments significantly after the tax cut became law.
A long standing theorem in finance is that any time a firm’s shareholders can find more highly valued uses of capital than the firm, then excess cash should be returned to shareholders. Indeed, the Washington Post quotes Wharton finance professor Jeremy Siegel as saying that “Cash that’s just sitting around gets discounted”. However, this theorem implicitly assumes that there are no tax asymmetries. The most famous tax asymmetry in corporate finance is that debt related income is only taxed at the personal level, whereas equity related income is taxed at both the corporate and personal levels. At the margin, this tax asymmetry compels firms to be more highly leveraged than they otherwise might be, and also causes firms to avoid generating cash distributions for their shareholders. Another important tax asymmetry which existed until last year was that cash distributions through share buybacks were more tax-efficient transactions than cash distributions through dividend payments. While the 2003 dividend tax reform doesn’t address the double taxation issue, it does significantly reduce the tax penalty for cash distributions to shareholders. Furthermore, the tax code is now neutral about the form of equity-related cash distributions, whereas before it favored share buybacks over dividend payments.
On the impact of high fuel prices on airline profitability and the propensity to hedge risk
Lately, there have been a slew of articles concerning the impact of high fuel prices on airline profitability. A common statistic which is being bandied about in the news media is that for every $1 increase in fuel costs, airline industry costs increase by $425 million. Indeed, it has become fashionable lately for airline executives to not only blame high fuel prices for their lack of profitability, but also to argue for the “need” for government intervention. As a case in point, consider the following quotes (taken from a June 3, 2004 Washington Post article entitled “Airlines Find Fuel Prices Tough to Swallow”):
1. “‘The price of oil has taken our profitability hopes away from us,” said Gordon M. Bethune, Continental Airlines Inc.’s chairman and chief executive. “The government ought to recognize that this is pretty serious.'”
2. “United Airlines blamed high fuel costs for its operating loss in April. If prices had been lower, the airline would have reported a profit during the month, said Jake Brace, chief financial officer of UAL Corp., which owns United Airlines.”
After reading quotes such as these, one would think that the airline industry is powerless to do anything about fuel prices, and that the government may be their only “hope”. Of course, this is complete nonsense. Firms are in the business of taking and managing risk; after all, this is how they earn profit. Corporate risk management theory makes a compelling case for the notion that firms should hedge or insure “incidental” risks (which are risks that they cannot control, such as commodity prices), and retain “core” risks (which are risks that they are in a position to favorably influence). In the case of the airline industry, the price of jet fuel is clearly an “incidental” risk and therefore it represents the type of risk which ought to be transferred. On the other hand, passenger safety and security represent examples of “core” risks which the firm presumably has a comparative advantage in managing.
In light of these considerations, it is interesting to look under the hood at actual airline industry hedging practices. Casual empiricism reveals that the propensity to hedge tends to be positively related to profitability and inversely related to the risk of default. In other words, the more profitable, less financially troubled airlines (e.g., companies such as Southwest Airlines, Air Tran and Jet Blue) tend to aggressively hedge jet fuel prices, whereas the less profitable, more financially troubled airlines (e.g., Continental, Delta, Northwest, American and United) either do limited hedging or none whatsoever. Southwest Airlines is 80 percent hedged for the remainder of 2004 with prices capped below $24 per barrel, 80 percent hedged for 2005 with prices capped at $25 per barrel and 45 percent hedged for 2006 with prices capped at $28 per barrel. Compare Southwest’s policy with the policies followed by Northwest Airlines (only 7% of its 2004 fuel needs are hedged at $37 per barrel and none of its 2005 fuel needs), American Airlines (no hedging), and United Airlines (no hedging). During the second quarter of 2004, Southwest Airlines’ net income for the second quarter of 2004 was $113 million, $90 million of which was attributable to the lower jet fuel prices afforded by their hedging program. In contrast, American and United are expected to pay $700 million and $750 million respectively in additional fuel costs during 2004.
These data beg an obvious question; specifically why is there such a glaring disparity in terms of the risk management strategies of these companies? Digging a bit deeper, it is important to note the risk bearing incentive effects related to corporate limited liability, and how this affects corporate investment decision making. Finance theory suggests that when firms are financially distressed (as is the case with many airline companies), limited liability gives rise to various moral hazard problems. Among other things, firms that are close to going bankrupt often fall prey to perverse risk bearing and investment incentives; specifically, they tend to underinvest as well as take on too much risk. Since limited liability creates an asymmetry in terms of the impact of risk bearing on shareholders; i.e., shareholders are shielded from downside risk and exposed to upside risk, this will often compel financially distressed firms to adopt risk management strategies which wouldn’t be considered by financially sound firms. Basically, if you find yourself up against the wall, you may prefer not to hedge risk. If you lose, your losses are limited, but if you win, your gains are unlimited. The prospect of a government bailout further exacerbates this moral hazard and makes it even less likely that a financially troubled airline will be inclined to hedge.
In the case of the airline industry, the unprofitable and financially troubled firms consequently have greater incentive to take on incidental risks than profitable companies. Fuel price risk is clearly symmetric; while an increase in price reduces profitability, a price decrease enhances profitability. By rolling the dice and remaining largely unhedged, companies like Northwest, American, and United will benefit if fuel prices fall (indeed, as investments these companies’ stocks basically represent highly speculative, leveraged plays on future fuel prices). However, if prices rise, these companies have other risk management mechanisms at their disposal; specifically, bankruptcy protection and the possibility of government loan guarantees. Since these companies do not have to put much of their own money at risk, the costs of hedging likely outweigh the benefits. The reverse is true for profitable companies that are not likely to go bankrupt (such as Southwest Airlines). For these companies, the “option to default” is deeply out of the money, as is the prospect of a government bailout. Since their own money is at risk, they are more likely to adopt prudent business practices (including hedging incidental risks)
In closing, I would like to point out that there have been some academic studies done on this very topic; I would point the reader to a working paper by David Carter, Daniel Rogers and Betty Simkins entitled “Does Fuel Hedging Make Economic Sense? The Case of the U.S. Airline Industry“. These same authors have also recently written an interesting case study of Southwest Airlines entitled “Fuel Hedging in the Airline Industry: The Case of Southwest Airlines“.