Generating Risk

People dislike uncertainty and view risk is something to be avoided. True, we often must take some risk to achieve our goals, but many of us try to take as little risk as possible. But sometimes risk is a good thing. Generally, risk and reward tend to be roughly correlated (you get paid for taking risk) so ideas which are high risk can also be high reward. This tends to make high risk ideas attractive to many people and thus oversubscribed. The result is that high risk ideas have a worse reward/risk ratio than low risk ideas. In theory, one could leverage low risk ideas to the appropriate risk/reward point to get better results. When possible, this is generally better than investing in inherently high risk ideas (but leverage has its own dangers and always needs to be considered carefully). In the following, I explore these ideas in more depth.

In the financial markets as well as in many other areas of life, we are faced with large uncertainties and hopefully large opportunities as well. A common way to measure an opportunity is with the Sharpe ratio or information ratio¹ (IR). This is basically the expected return divided by the standard deviation, volatility, risk, etc. For example, over a long period of time the US stock market has had an expected return above cash of about 5% and a volatility of about 15% for an IR of about 1/3. That is, for every dollar you invest you expect to earn about 5 cents more than a savings account but the range of returns is typically in the range of -$0.10 to +$0.20. Long term (e.g., 10-year) bonds in the US have had a comparable return/risk ratio but with lower return (about 2% above cash) and lower risk (about 6%).

The first thing to notice here is that the risk is much larger than the expected return. Since risk scales as the square root of time while returns scale linearly with time, this effect is amplified on finer time scales. So on a monthly basis, the stock market expected return/risk is about (5%/12)/(15%/√12) = 0.096. So on a monthly basis, the risk is about 10 times larger than the expected return. On short time scales, the risk dominates everything.

The second thing to notice here is that the reward/risk ratio is roughly constant across stocks and bonds. In fact, the reward/risk ratio tends to be roughly similar across many assets. The basic reason for this is that nobody likes risk. So all other things being equal, people generally tend to invest their money in the best reward/risk assets they can find. This drives down the rewards on the best assets until everything has a roughly equal IR.

Proponents of the efficient market hypothesis (EMH) would have you believe that basically every investment idea has a reward/risk ratio proportional to its correlation with the market or with other undiversifiable risk factors. This loading on the market risk is summarized with the coefficient "beta" that you often see quoted along with other information about a stock. Roughly speaking, higher beta stocks tend to move more with the market. So a stock with a beta of 2 may have twice the market risk and twice the market return.

Personally, I think it's best to view the EMH as a rough approximation to reality as opposed to gospel truth. One may be able to do clever (or stupid) things to increase (or decrease) the reward/risk ratio in various settings. This is certainly worthwhile, but to a large extent many things have roughly similar reward/risk ratios. It is difficult (but not impossible) to find an investment which makes sense on fundamental grounds and has a information ratio much less than 1/3 or much greater than 1 (as measured on an annual basis). A further complicating factor is that our estimates of the information ratio are themselves noisy and so it is generally hard to have much faith in the information ratio estimate. Consequently, even if we are given an investment with an expected IR of .5 and another with an expected IR of .7, prudence generally forces us to consider them to be quite similar.

Now we arrive at the key point of this article: generating risk. Imagine that you want to achieve a certain target return. For example, you may decide that if you want to buy your dream house then you need to earn 10% per year on your current assets. Or you may decide that if you want to live comfortable in retirement, you need at least 2.5% per year more than what a savings account would yield. This generally dictates the kind of investments you can make.

You may find that a savings account or a short term bank certificate of deposit offers a fantastic reward/risk ratio of say 1%/1% = 1.0. This may be the best risk/return trade-off you can find anywhere. But the return is only 1%/year. Thus despite the attractive IR, if you want to earn 2.5% a year more than a savings account for your retirement, you may be forced to invest a good portion of your money in the stock market with a much lower IR of about 1/3 in order to generate enough risk. For example, you might invest half your assets in the stock market and the other half in cash. Alternatively, you might invest essentially all your assets in long term bonds. In that case, some of your investments would need to be in bonds with maturity greater than 10 years since you would need the increased return (and increased risk) to achieve your goal of 2.5%/year above cash.

This phenomenon which we can call "generating risk" plays out across many markets as well as non-market areas. The basic effect is:

1. People need to achieve a certain level of return
2. Most options have roughly similar reward/risk ratios
3. People choose options with higher inherent risk in order to achieve the target return.

The end result is that many very high risk investments tend to have worse information ratios than "normal" while many very low risk investments tend to have better information ratios than "normal". This is best illustrated by some extremes. One good example is venture capital or startup companies. By investing or joining a startup, you have a (tiny) chance the be the next Bill Gates or Jeff Bezos and make billions. But you also have the chance to lose your entire investment. If you analyze the risk vs reward of venture capital across the market, you will find that it is significantly less than what you can earn in the public stock market². Why? Because venture capital can generate a lot of risk. So if you decide you want to be a billionaire, you just can't get there working a 9-to-5 job or investing in public equities. Those investments don't generate enough risk.

There are many examples of this effect in the financial markets besides venture capital. Some well known cases include duration in bonds. Short duration bonds tend to have better information ratios than longer maturity bonds. But short duration bonds don't generate enough risk so many people invest in long term bonds anyway. Another example is beta in stocks. High beta stocks like Las Vegas Sands Corp have higher risk and return than boring low beta stocks like public utilities. Growth stocks with high price/earnings ratios and exciting growth prospects tend to have higher risk and higher return than more reasonably priced value stocks. In all these cases, the high risk asset tends to have a worse information ratio than the low risk asset.

You may object that "generating risk" is the wrong terminology since investors really want to "generate return" not risk. This is true, but estimating future returns is generally much more difficult than estimating risks. That and the observation that risk and return tend to be roughly correlated often lead to thinking of the world in terms of risk. Of course, it's important not to lose sight of the fact that the ultimate goal is return not risk, but since risk is often the main variable under the control of the investor, thinking in terms of "generating risk" is sometimes useful.

How should one use this information? There are two key ideas to keep in mind:

1. When all else is equal, be suspicious of the high risk asset as it will probably have a worse risk/reward ratio. This isn't necessarily bad if you need the risk, but know what you are paying for.
2. If you can, try to leverage low risk assets to generate the desired returns.

The second point is worth some elaboration. If lower risk assets tend to have better return/risk ratios, you can generate the desired return/risk via leverage. For example, if you want to get returns of 2%/year over cash, you could either invest in long term bonds or you could borrow $1 for every dollar you invest (i.e., a leverage ratio of 2) and invest in short term bonds. If the short term bonds have a better return/risk ratio (which is true historically), you will end up with a higher information ratio. In a sense, one of the things private equity, hedge funds, real estate, and many other alternative assets provide is a way to leverage low return ideas to generate enough risk to be interesting.

Why don't individuals use leverage more? In some cases, they do via futures or real estate investments, but leverage is generally either costly or dangerous for many people. Leverage can be relatively inexpensive (especially when interest rates are low) in the futures markets, but most individuals are not familiar with futures. In general, most individuals will need to pay something for the leverage in terms of high borrowing rates due to credit risk, monitoring, or transaction costs. More importantly, leverage can make you lose either your entire investment or even more than your entire investment if you are wrong or unlucky. An excellent example of this is the recent real estate collapse. Many home owners made down payments of 10% or even 5% of the total house price and now that homes have gone down in price, the owners owe more on the mortgage than the house is worth. Leverage gives you the opportunity to ruin your life in a very short period. In contrast, assets which inherently generate plenty of risk without leverage are attractive because even if they go bust, you never lose more than your initial investment.

To summarize, assets or ideas which generate lots of risk (and hopefully return as well) are attractive because the provide inherent leverage. This generally means they have a worse return/risk ratio. Leveraging lower risk assets may provide better return/risk but may or may not be worthwhile due to financing costs or the danger of blowing up.

End notes:

1. The Sharpe ratio is generally defined as the return of an asset over the risk-free alternative (e.g., cash, a savings account, or very short term government bonds) divided by the risk. The information ratio is generally defined as the "active return" of an asset divided by the risk-free alternative divided by the risk. Sometimes they are used interchangeably, but at other times the information ratio is more like pure reward/risk without deducting the return of a risk-free alternative. For the purposes of our discussion, the main point to keep in mind is that both of these refer to reward/risk.

2. For example, see page 77 in Swenson's book Pioneering Portfolio Management, which shows median returns of 18.3% and 12.4% for public equity vs. venture capital. This is for the period ending in 1997 so the returns are generally very high for all assets. Alternatively see Swenson's other book, Unconventional Success, which on page 142 quotes venture capital returns of 19.6% and public equity returns of 20.2% for the US stock market.

Acknowledgments:

I am grateful to Ramesh Johari for discussions which spurred this article.

Book Review: Blink

Blink: The Power of Thinking Without Thinking by Malcom Gladwell is a thought provoking book. I have always found Gladwell controversial because he tends to tackle big ideas and ruthlessly simplify them. Some might say he over simplifies. But he is such a brilliant writer, weaving in fascinating anecdotes, that one cannot help but be drawn in. Ironically, because his books are so absorbing, I find myself reading closely to understand his ideas and evidence while carefully guarding my mind to draw it's own conclusions and not fall under the spell of his magical prose.

Blink is no exception. In fact, I think it is Gladwell's best book and a perfect example of his style and approach (both good and bad). Gladwell's basic point is that by simplifying the information we consider to be almost ridiculously small we can dramatically improve our decisions. As Gladwell puts it at the end of chapter one:

I believe -- and I hope that by the end of this book you will believe it as well -- that the task of making sense of ourselves and our behavior requires that we acknowledge there can be as much value in the blink of an eye as in months of rational analysis. "I always considered scientific opinion more objective than esthetic judgments," The Getty's curator of antiquities Marion True said when the truth about the kouros finally emerged. "Now I realize I was wrong".

Gladwell then goes through a number of wonderful anecdotes describing how people can distill the essential information for a decision into a tiny bit of data. He talks about a marital researcher who can observe a few minutes of husband and wife conversation and discover with extremely high accuracy whether they will stay married or divorce. He mentions another study about how dealers tend to price their cars based mainly on gender and race rather than appearance, education, evident ability to pay or other factors. One of my favorite examples, is his description of the heart attack protocol adopted by Cook County Hospital in Chicago as discussed on his web site:

One of the stories I tell in "Blink" is about the Emergency Room doctors at Cook County Hospital in Chicago. That's the big public hospital in Chicago, and a few years ago they changed the way they diagnosed heart attacks. They instructed their doctors to gather less information on their patients: they encouraged them to zero in on just a few critical pieces of information about patients suffering from chest pain--like blood pressure and the ECG--while ignoring everything else, like the patient's age and weight and medical history. And what happened? Cook County is now one of the best places in the United States at diagnosing chest pain.

I think this is Gladwell at his best. The point he makes is extremely valuable: sometimes adding more information reduces accuracy in decision making. Sometimes it's best to throw away information that you absolutely, positively, know is meaningful because it distracts you from the information that is most predictive. This is a point worth pasting on your wall and thinking about every day. Thinking scientifically, always measuring the value of a piece of information with evidence, and constantly trying to simplify our predictive models is one of the best ways to improve the human condition and make the world a better place.

So with a story about scientifically using the evidence dramatically improving outcomes, why does Gladwell start with a quote praising esthetic judgements over rational and scientific analysis? Gladwell seems enamored of mystery, flashes of brilliance, and other almost anti-intellectual ways of decision making. He points out (rightly I think) that sometimes our subconscious can make better decisions in the blink of an eye than a much more detailed, traditional analysis. This is probably true, but only for experts who have lots of practice making decisions over and over again and are already aware of the standard rational analysis methods. I think for many people, snap judgments are probably more likely to be wrong and rational, scientific, analysis is more likely to be write. The history of the world suggests that science and careful, rational analysis are the main source of progress.

Another caveat is that all of Gladwell's examples are drawn from high signal-to-noise ratio environments. That is, his examples come from areas where one can get very high accuracy (e.g., 90%). In those cases, one can identify important factors relatively easily and so it may make sense to focus on only a few key pieces of information. In some parts of the world, such as in financial markets), it is very difficult to have high accuracy. Simplifying information in these markets is still valuable (perhaps even more so since there is so much financial information to consider). But one should recognize that mindlessly translating ideas from a 90% accurate world to a 55% accurate world is dangerous.

Overall, the book is wonderful. I highly recommend reading it. But read it with a careful and open mind and think about what the stories and anecdotes imply without necessarily taking Gladwell's conclusions at face value.

Book Review: High-tech Startup

High Tech Start Up by John Nesheim is a great book about financing and other aspects of high technology startups. Having worked at a few tech startups myself and now being at what is basically a startup hedge fund, I have always wondered about some of the murkier details related to where the money comes from and where it goes. Usually, it's very difficult to learn these details even for an organization which you are part of let alone a broad cross section of venture backed companies.

This is where High Tech Start Up shines. Nesheim provides hard data about specific deals as well as broad summaries of things like how many companies make it to IPO, the median time to IPO, the amount that most founders make at IPO, etc. These numbers are by far the best part of the book and make it essential for potential or current entrepreneurs. Nesheim also provides some advice on business plans, legals details, etc. That is useful information but many entrepreneurs may already know this.

If you're in or considering a startup, definitely take a look at the appendix to get a sense of how financing for past deals worked out.

The Burst-Delay Problem

One of my interests is communication in the presence of hard delay constraints. My favorite problem in this area is what I call "The Burst-Delay Problem" (or perhaps "The Single Burst-Delay Problem" to distinguish it from some other variants). Before discussing the problem in detail, I will describe an example which illustrates the main idea.

Imagine that each day you have a message to send to a friend who lives far away. You would like to send your messages through the mail, but the postmaster is unreliable and every once in a while he goes on vacation and for B days and loses all letters sent during that time. He is always embarrassed when this happens so he never tells anyone that he lost he letters. Your original message for day t fits on K pieces of paper, but you can fit N > K pieces of paper in each envelope. Your plan is to use the extra N-K pieces to send redundant information from previous letters in case they got lost in the past.

The two main questions to answer are:

1. How should you encode your letters and how should your friend decode them?
2. What is the smallest delay, T, for which you can guarantee your friend will be able to figure out what you sent despite possible losses due to the postmaster's vacations?

For example, if K=1, N=2, and B=3 you could just repeat your letter from three days ago each time you send a new letter. Then whenever the postmaster goes on vacation and fails to deliver the letter, your friend simply waits until he comes back and reads the redundant copies you sent. In this case, the minimum delay is T=B=3 and the encoding/decoding is very simple since you just repeat previous letters. Things get much more interesting for different values of K, N, and B.

I believe I solved this problem completely in my Ph.D. thesis (available at http://www.mit.edu/~emin/research/phd_thesis.pdf), generalized it to different kinds of channels, channels with multiple transmission paths, and also developed polynomial time encoding/decoding algorithms for some cases. Some of this work was done jointly with Carl-Erik Sundberg, Gregory Wornell, and Mitch Trott.

I find this problem interesting for two main reasons. First, it seems relevant for real-time applications like video-conferencing, voice over IP, online games, tele-surgery, etc. Second, the solutions that seem to arise involve matching error correcting codes to the dynamics of the channel in a way I have not seen in other problems. If you found this description interesting, you may enjoy reading more about it in my Ph.D. thesis or thinking about some of the (unsolved) generalizations discussed elsewhere on this blog.

Book Review: Stocks for the Long Run

Siegel's book Stocks for the Long Run is an investment classic. The book does a nice job of outlining the main ideas and facts about investing in stocks (and to some extent compares them to bonds). Some examples include the average (real and nominal) returns for stocks and bonds, tax advantages of equities, size premiums, mean reversion, and behavioral finance. I think the first edition of the book basically advocated buying a stock index fund and sticking with it through thick and thin. The recent version seems to lean toward a little market timing, and a little tilt toward value stocks (e.g., stocks with higher than average dividend yields). Overall, however, Siegel gives the impression that picking good stocks, market timing, or even finding good mutual fund mangers is impossible.

I think he is correct to a large extent. Most of the evidence and fairly reasonable theoretical arguments support him. It's actually quite depressing to think about how difficult successful investing really is. There are certainly exceptions (like Buffet, Lynch, Soros, Rogers, Paul Tudor Jones, etc.), but there are also plenty of managers who do well for decades and then come back to earth. For example, the Wall Street Journal recently had an article about Bill Miller and how he had a phenomenally successful career, beating the S&P500 since 1991 (17 years) until disaster struck in 2008 and he ended the year basically the same as the S&P over his career. If you can't count on a manager who has beaten the market for 17 years, it makes you wonder how you can possibly pick a good mutual fund manager.

One of the most amazing parts of the book is the discussion of dividend yield (D/P) based investing (chapter 9, outperforming the market in my version). According to Siegel's analysis, investing in the top quintile of US stocks based on D/P from 1957 to 2006 would have produced an annualized return of 14.22% versus 11.13% for the S&P500. That is an amazing difference which would result in $1 growing to $675,211 versus $176,134 for the S&P500.

This analysis ignores transaction costs, but those would probably not reduce performance by much since Siegel assumes you only trade once per year. Even assuming a 1% penalty for transaction costs produces almost a 2%/year benefit by using D/P. To put this into perspective, very few mutual funds outperform the market by 2%/year (after fees) for significant periods. This is despite the fact that dividends have been recognized as important at least since the days of Graham and Dodd's book in 1940. Furthermore, this "value premium" has been studied in various forms (dividend yield, earnings yield, book/market ratio, cash-flow/price, etc.) at least since the 1970s.

Why does this value premium still exist? Why don't mutual fund managers forget trying to pick winning stocks and simply tilt their portfolio toward high D/P stocks until the value premium is gone? To some extent they do. The value premium has been responsible for the growth of "quant equity" money managers. Also, Schroeder's biography of Warren Buffet mentions a fellow named Walter Schloss who seems to ride the value premium effectively for decades. In fact, today you can even buy an ETFs such as VYM or DVY that will implement the dividend yield strategy for you.

Will this result in dividend yields becoming fairly priced and the end of the value premium? I don't know. The historical performance of the DVY ETF from 11/2003 to 11/2008 shows it roughly even with the S&P 500 and the SPY ETF. Does this mean the value premium is gone? Probably not.

Imagine equities have a volatility of about 16%/year, that the D/P strategy should outperform by 2%/year, that returns are normally distributed, and that the correlation between the D/P strategy and the S&P500 is 90%. At first, you may be tempted to compute the chance that SPY outperforms DVY over N years as 1-Φ(0.02/0.16 * sqrt(N)) where Φ is the cumulative distribution function for a standard normal distribution. This would be incorrect since DVY and SPY are very similar. Instead, one should think of DVY as consisting of 0.9 units of SPY and 1 unit of a pure dividend yield strategy which has an expected return of 0.2 and a volatility of roughly sqrt[(1-.9*.9)]*16% or about 7%. So the correct probability that DVY underpreforms SPY despite having a 2%/year advantage is roughly 1-Φ(0.02/0.07 * sqrt(N)). Plugging in N=5, 10, 20, 30 yields the probabilities 26%, 18%, 10%, 6%.

So seeing DVY underpreform for 5 years is not actually that surprising as it would happen in roughly 1 in 4 independent 5 year periods. As these numbers show, the level of noise in market statistics makes it difficult to count on anomalies (even relatively strong ones like D/P). Consequently, people may believe that the value premium is gone or be unwilling to wait long enough for it to manifest itself.

Book Review: The Only Three Questions That Count

Ken Fisher's book, The Only Three Questions That Count is an interesting discussion of how to think about investing. The three questions are:

1. What do you believe that is actually false?
2. What can you fathom that others find unfathomable?
3. What the heck is my brain doing to blindside me now?

Basically, Fisher is an advocate of rational, scientific investing based on data. All his questions and most of his book repeatedly make the point that investing is very difficult and the only way to be successful is to scientifically analyze the data and only make bets when you think you know or understand something that others do not.

The book is well-written, easy to read, and appropriate for people with little prior investing background. Despite that, the book should also be interesting to experienced investors since Fisher does a nice job of pointing out various myths and misconceptions. Some of these myths included:

1. High P/E ratios signal poor future returns.
2. Large budget deficits and large national debts are bad.
3. Oil prices and stocks are negatively correlated.
4. Dollar cost averaging is a good idea.

I certainly believed (and still believe to some extent) these "myths". In fact, I continue to believe that some of these are true when properly applied (e.g., P/E ratios which are high relative to interest rates signal poor future returns). Fisher does a great job of getting back to the raw data and making his case that the naive interpretations of many of the above claims are in fact myths. In my opinion, the main thing to take away from Fisher's analysis is that you always have to do the work of understanding an idea yourself instead of simply relying on the conventional wisdom. This is a good lesson to take to heart.

Overall, I enthusiastically recommend Fisher's book and plan to make my own studies even more thoroughly quantitative and scientific. I think that a common temptation among modern investors (especially quants) is to try and search for exotic relationships or apply elegant mathematics in the belief that knowing high powered math will provide an edge. Instead, I think the right thing to do is to question everything and always take a scientific approach to analyzing investment ideas. Simply believing an idea and having a good story is not enough; you need to make a solid case for the idea based on the data (including trying to look for holes or fallacies in your own analysis).

Programming: Dia

I recently came across a wonderful open source drawing tool called Dia. In addition to providing the ability to create your own stencils as Visio does, Dia allows you to write python plug-ins. This creates a whole world of possibilities for interesting programmers. You can create your own shapes using Dia to draw them and then modify the XML to add extended attributes using the ext_attributes tag. Using a Dia plug in, you can then generate the desired output as a function of the attributes (e.g., as illustrated by the codegen.py plug-in). While I don't have nearly as much time for programming anymore, this is something I might make time for in a few years.