Risk management in banking and my PhD topic

Hi all. I’m thinking I should write this post in English as well, to increase the range a bit. I got the idea for this article today, again in a Twitter discussion. It was about banking. As you might have heard, Dexia is exposed to the default of Detroit. Dexia is a sensitive topic in Belgium, since the government has granted guarantees for an enormous amount. If that stuff goes wrong, Belgian taxpayers are going to need a drink. But anyway, that’s not what I want to talk about here. Today I want to talk about risk management in banking, because I sense that people are very interested in this topic, yet cannot find enough material out there to understand how it all works. So let me tell you what comes to my mind when I hear risk management in banking. By the way, my PhD topic is about risk management in banking as well, but I’ll explain that later.

Bank risks

Okay, so everybody knows banks are exposed to all kinds of risks. Let’s talk about the main ones. But first, what is risk? Risk means that there’s a chance you’re going to lose money. It means you don’t know what is going to happen when you buy or sell something. Risk is about unexpected things. Things that you expect to happen are not risks. When you buy a stock, there’s the risk of a fall in value. When you loan money to somebody, there’s the risk of him or her not paying back. And so on.

Banks borrow from some people and lend it back out to others. A unique function of banks is that fact that they usually borrow money on shorter timeframes than they lend money out. Say I bring 100.000 EUR to the bank and buy a one year savings certificate (kasbon in Dutch) with an interest rate of 2%. The bank then takes my 100.000 EUR and lends it out to a company wanting to invest in new equipment, which they will pay back over a period of five years at a rate of 4%. This process is called maturity transformation. Notice that the bank earns a handsome 2% a year or 2.000 EUR as a compensation for this maturity transformation.

Immediately we can distinguish several types of risk. First, there’s credit risk. If the company goes bankrupt, the bank is not going to get all its money back, but still owes me my 100.000 EUR. Next, we have interest rate risk, also an important one. Say one year passes and my savings certificate matures. Obviously, the bank doesn’t have my money since they gave it to the company for five years. So they need to find somebody else who will lend money to the bank, just like I did a year ago. Say they find such a person but market conditions have changed and the relevant interest rate is now 3%. The bank borrows 100.000 from somebody else and pays them 3% a year. Note that the profit margin has gone down from 2% to 1%. The corporate loan stills pays 4% a year but the bank now needs to pay out 3% instead of 2% to the holder of the savings certificate. So interest rates changing is also a source of risk, since it has an impact on profits. Credit risk and interest rate risk are the most important risks banks face. There’s also liquidity risk, operational risk, reputational risk, strategic risk, and so on. But these are less important. Credit and interest rate risk make up the bulk of total risk for banks.

How do banks manage their risk?

So now that we know a bit about the risks banks are exposed to, we might ask ourselves how banks take care of these risks. You can basically do two things: you get rid of the risk (hedging) or you keep the risk but make sure it will not take you down in bad times (holding capital).

You can hedge all kinds of risks by buying products with a bad name, such as credit default swaps (CDS) or interest rate swaps (IRS). Assuming these instruments trade at fair prices, they actually are a wonderful invention because they allow people to share risks. Say I loan money to somebody but I don’t like interest rate risk. I buy an IRS and now I’m only exposed to the credit risk, which makes me feel better. The other person is now exposed to the interest rate risk, but that is exactly what he or she wanted. Everybody is happy. Remember that in financial markets, risk is rewarded by return. There’s no point in bearing risk if there’s not going to be a compensation. So markets will price products in such a way that risk will be rewarded, on average. Riskier products are cheaper than safer products. If you don’t bear risks, you’re going to earn the risk-free rate, which to the best of my knowledge is negative or zero today.

Now say you don’t want to get rid of the risk, because you want to make some money. Well, where there is risk, there should be capital (or equity). The more capital a bank has, the more trouble it can handle. Or in other words: the lower the leverage, the safer the bank. High leverage (little equity and a lot of debt) means that when you suffer some losses, your equity will get a serious blow. It might even become negative. Low leverage (a lot of equity and little debt) means that you can take a series of blows without the danger of going bankrupt. This is why banks should hold capital, in order to make sure that a small or large blow will not cause bankruptcy. It’s important to realize that capital is NOT money lying around doing nothing. No, capital is also invested in assets, but the difference with regular debt is that regular debt should be paid back in full at some point in time.

How much capital to hold?

Banks need to be able to survive a lot of worst-case scenarios. They won’t be able to do that if they don’t hold too much capital. So the amount of capital they hold should ensure that the bank is able to survive a lot of potential future scenarios. For example, a bank that strives for an A-rating (defined as a 0.07% probability of default within the year) would need to be able to survive 99.93% of all possible scenarios that can occur within the next year. So the amount of capital they need to hold should be enough so that the bank is able to survive those 99.93% of all scenarios. This amount of capital is also called economic capital.

So, how do we compute economic capital for the entire bank? Well, in practice, banks first calculate economic capital for separate risk types. They calculate how much capital they need to hold in order to cover their credit risk, then how much capital they need to hold in order to cover their interest rate risk, and so on. Then, when all these numbers are available, they add them together using a correlation matrix or something like that. You can’t just take the sum, since there is diversification. Interest rate risk and credit risk are correlated: usually not all bad things happen at the same point in time. It’s the same principle when you’re investing in stocks. Not all stocks go down at the same time, there is diversification. Holding more stocks means your position becomes less risky. So adding everything together as a sum would overstate your risk. Therefore, something like a correlation matrix is used, which is not very sound. You could view it as a “shredder”. You worked hard to get reliable estimates of economic capital for separate risk types, but then you must add them together using some dubious method. For example, what are those correlations? How would you be able to verify they are correct? And aren’t these correlations unique for each bank? Indeed, it’s not the best method.

My PhD topic

This is where my PhD topic comes in, on the idea of integrating risk. We no longer calculate economic capital for each risk type separately. Instead, we calculate it in one go, for all risks at the same time. The main difficulty is that now you need to define the relationships between different risks. For example: what happens to default probabilities when interest rates change? Does economic growth impact defaults and interest rates, and if so: in what way? This area of financial economics is not very well developed yet. So, first we define how all these risk drivers act together in a unified framework. Then, we calculate economic capital based on this framework, so that you get an estimate which is based on a sound and reliable method. Correlations between risk drivers are the same for all banks. It’s just the banks’ exposure to different risks that might differ. So it makes the job of the regulator a bit easier. Also, we can now verify if our numbers make any sense or if they correspond to reality, since everything can be traced back to basic observable economic variables.

So in a nutshell, this is what I’m working on. I hope that I could give some people a better idea of what risk management is about (although I must emphasize that I really am only scratching the surface) and a better idea of what I’m working on. Feel free to ask questions.

Advertenties

Some thoughts on efficient markets, return predictability and bubbles

Hi all. Let me first say that I’m going to write this post in English since I’d like to refer this post to some people that don’t speak Dutch. This post is going to be mixture of ideas on important topics in finance. These ideas are not mine, obviously. They are a mix of what other people have to say about these topics. I’m warning you, this is a long post. Read it all in once, in parts, or not at all, it’s up to you.

Efficient markets

Whenever I talk to people about markets, people have strong opinions. In an article in the Financial Times, John Kay writes “In the past decade, the efficient market hypothesis has been mugged by reality”. Kay also refers to another article by John Plender, who writes: “the financial crisis put paid to [the efficient markets hypothesis]. The credit bubble before 2007 clearly pushed the price of most financial assets far from fundamental value”. In my view, these articles take inefficiency as a given instead of showing that markets are inefficient. It’s as if there is already a scientific consensus that markets are not efficient.

Let’s be clear: there is no such consensus. For example, let’s see what John Cochrane has to say. He’s a respected Chicago economist who wrote “the bible” on asset pricing. Consider this quote from a 2011 paper where he discusses the current state of affairs in asset pricing: “Informational efficiency is not wrong or disproved. Efficiency basically won, and we moved on. When we see information, it is quickly incorporated into asset prices. There is a lot of asset-price movement not related to visible information, but Hayek (1945) told us that would happen, and we learned that a lot of such price variation corresponds to expected returns”. In my opinion, one important reason why so many people are convinced that markets are inefficient is because they are not careful about definitions. Another one is that they are not careful about what type of market behavior could explain the things we observe. They see strange things and instantly attribute them to irrational markets. If only matters were that easy. When we’re talking about efficient markets, we need to be very clear about what we mean.

First of all, we’re talking about financial markets where financial assets are traded against market prices established by transactions between buyers and sellers. I’m not talking about the market for books or cans of Coca Cola. I’m talking about financial assets like stocks, bonds and options. Andreas jokingly made a comment about markets not being efficient since ScienceDirect (a giant database of academic papers) charges 39$ for a paper by Eugene Fama, which can also be found on Google for free. Other people involved in the discussion seemed to agree with the comment. Geert Janssens retweeted it, so can I assume he liked it a lot? Anyway, let’s for a minute act as if we were very serious people who took that comment very serious. First of all, a paper is not a financial asset. A book or a road map is also not a financial asset. The efficient markets hypothesis is about financial assets. Second, obtaining a paper using Google might not be legal (although I’m not 100% sure about this), meaning that you could compare it to stealing an apple. Or maybe to stealing an overripe lemon, if you don’t like Fama. Stealing is not really a transaction, is it? Lastly, and most importantly, the 39$ that ScienceDirect charges for the paper is not a market price. It’s an ask price. It’s is no more a market price as is the 450.000 EUR you would be willing to accept for your own house. A market price is established when a buyer and a seller agree on the price and a transaction takes place. However, I could imagine somebody buying the article for 39$, but again, it’s not a financial asset. It has nothing to do with efficient markets.

Secondly, let’s define clearly what efficient markets are. Efficient markets are markets in which all available information is immediately reflected into prices of financial assets. There is a weak, semi-strong and strong form of market efficiency. Each form uses a different definition of “available information”. The weak one says that all historical information is priced, so that you can’t earn abnormal returns by using technical analysis (charting, technical indicators like RSI, …). The semi-strong one says that all public information is priced, so that fundamental analysis (macroeconomic analysis, earnings forecasting, …) is useless as well: fundamentals are already reflected in the price, so don’t bother looking at them. The strong one says that private information (insider information) is also priced, so that even inside information cannot deliver abnormal returns. Forget about the strong form. It doesn’t hold in reality. Fama even admits this himself in his 1970 paper: “We would not, of course, expect this model to be an exact description of reality, and indeed, the preceding discussions have already indicated the existence of contradictory evidence”. The weak and semi-strong versions however, that’s a different story. They hold up quite well as has been shown up to this day.

Anyway, this is what academics mean when they’re talking about market efficiency. It is related to rationality in the sense that we expect information to be rationally reflected in asset prices. In other words, we don’t expect investors to multiply all numbers available to them by a random number between 0 and 2 before they start trading. We expect them to use information rationally, respecting probabilistic laws and such. Also note that rational markets and rational investors are not the same concept. Of course there’s a bunch of irrational investors out there! Kahneman and Tversky started that whole literature in their 1979 masterpiece on prospect theory. Kahneman got a Nobel Prize for that as well. But you see, just as in a poker game, there’s people all over the place trying to exploit mistakes by others. As long as there are enough rational traders with enough money, prices will reflect rational expectations. Because if prices deviate from fundamental values, arbitrageurs will come in and try to profit from mispricing, which will bring prices back to its correct level. So yes, there are irrational investors out there, but this is by no means proof for irrational markets.

Return predictability

We now move on to return predictability. Why? Well, because we also talked about that in our Twitter discussion. Jonas Deré (follow him as well!) asked me about predicting returns and compared it to the weather. You could predict that a day in January is going to be colder than a day in August. And you’d probably be right too if you live on the Northern hemisphere. But that’s because there is a trend in temperatures. We have seasons. There’s no such trend on the stock market. However, there is predictability. But first, let me distinguish two types of predictability. There is time-series predictability, which means that you can predict the evolution of returns over time. There also is cross-sectional predictability, which means that you can predict returns of individual assets or portfolios at one point in time, relative to each other. We don’t talk about predicting prices, since these just keep going up over time. We talk about predicting returns. The time-series and the cross-section are really interconnected, which is why financial economists often use large panel data sets: a bunch of assets over a large period of time. However, it’s good to understand the difference between the two dimensions.

Time series predictability

Let start with time-series predictability. Say that I found a method to predict returns of assets at future points in time. Tomorrow, next month, next year, whatever. Actually, there’s quite a lot of evidence out there that this is possible. Consider some results from the Cochrane paper mentioned earlier. A 1% increase in the dividend to price ratio of the aggregate US stock market increases future 1 year returns by 4% and future 5 year returns by about 20%. Or look at this graph plotting the dividend to price ratio of the aggregate US market in each year against the returns of the following 7 years. The conclusion is clear: dividend yields predict future returns.  And for that matter: there’s other variables that predict returns as well.

cohrane

People often associate efficient markets with returns that cannot be predicted. Random walks, and stuff like that. And clearly, there is predictability out there, so markets are not efficient? No, predictability is not a problem for market efficiency. The reason is simple: expected returns are time-varying. In the old days, people thought expected returns were constant. So if you would be able to predict them, there would be something wrong with market efficiency. But now, we know they are time-varying. Why are they time-varying? Well, there are a lot of possible explanations. We have rational theories involving consumption, investment, production and business cycles. We also have behavioral theories that focus on irrational expectations. We have theories about liquidity, and so on. We don’t really know that well why they move, but they move. We also know that expected returns tend to be high in bad times and low in good times, so that there’s a business cycle component tied to it. In any case, return predictability is not a problem for market efficiency, since it can exist in efficient and rational markets. Of course, it can also exist in irrational markets, which is what makes this discussion so hard but interesting. You should remember that return predictability over time is not necessary proof for irrational markets, as many people out there believe.

Cross-sectional predictability

Let’s now move on the cross-sectional predictability. Let’s say I sort all firms on their book-to-market ratio, which is the ratio of book equity divided by market capitalization. I sort from low to high, and form five portfolios with an equal amount of stocks. It turns out that portfolios with high book-to-market stocks will outperform portfolios with low book-to-market stocks. In my own European dataset covering 7.861 stocks over 30 years, the returns of the low book-to-market portfolio is about 0.80% per month (10% per annum) while the return of the high book-to-market portfolio lies around 1.40% per month (18% per annum). So there is cross-sectional predictability: book-to-market ratios predict the cross-section of returns. As it turns out, there are a lot of variables that have the power to predict the cross-section of stock returns. The most important ones are size, book-to-market ratio and momentum. Size is just the market capitalization of the firm and momentum is a measure of how well the firm performed over the last year: higher returns equal higher momentum. What are the empirical findings? Small firms earn higher returns than large firms. High book-to-market firms (value firms) earn higher returns than low book-to-market firms (growth firms). Lastly, high momentum firms do better than low momentum firms.

Is this cross-sectional predictability a problem for efficient markets? Again: not necessarily. When the variables you use to predict are related to risk, it’s not a problem. Say a firm is in distress and the market learns about this. The first thing that will happen is a plunge in the stock price, which of course causes the market capitalization to drop (the firm becomes smaller) and causing the book-to-market ratio to increase. So now we have a distressed firm that is small and has a high book-to-market ratio. Suppose you’d consider investing in such a distressed firm. The price would have to be low enough to convince you that you would be getting a reward for all the risk you’re taking. Or in other words: expected returns SHOULD be high for small firms with high book-to-market ratios, since these firms are often in distress. That’s the risk story that Fama and French came up with in 1992 and 1993. This story is compelling, also because macroeconomic factors seem to capture the same variation that size and book-to-market factors capture.

But there’s another story as well. An irrational one, best described by the paper of Lakonishok, Shleifer and Vishny in 1994. This paper is also a work of art, if you ask me. They argue that the market is not rational but rather extrapolates past earnings growth too far into the future. Firms with high past earnings growth would be expected to continue this high growth, so that they would have a high stock price and therefore a low book-to-market ratio. Likewise, firms with low past earnings growth would be expected to continue on this path, so that they would have a low stock price and therefore a high book-to-market ratio. When eventually new earnings are made public, they will be higher than expected for high book-to-market firms, causing high returns, and lower than expected for low book-to-market firms, causing low returns. So this pattern would explain the book-to-market effect as well. Why don’t the arbitrageurs come in then to correct the mispricing? Well, they argue, to profit from this effect you would need to hold your portfolio for a long time, sometimes 5 years or more. There’s no arbitrageur or fund manager out there who can convince his financiers that he’s going to make a lot of money, if he has lost money for 5 years in a row. He’d be fired, which is why he won’t undertake such a strategy. Lastly, they also show that the higher returns of high book-to-market stocks have nothing to do with higher risk. This, of course, poses a threat to the efficient markets hypothesis. Others then criticized the way they measured risk. And so on. To this day, the jury’s still out. There’s no consensus. In any case, value investing has perhaps never been more popular as it is today.

What should you remember from this? First, returns are predictable. Second, that this does not disprove market efficiency at all, since a lot of the predictability can be linked to risk and time-varying expected returns. However, not all phenomena are so easy to explain. Fama himself admits that the momentum anomaly poses a threat to market efficiency. Then again, he also states that there’s about an equal amount of overreaction-anomalies and underreaction-anomalies, which is also something you’d expect in efficient markets. Do you remember from statistics that you’ll always have a 5% chance to reject a correct hypothesis? Well, it’s about the same story here. There’s always going to be extremes at either sides of the sample that could make you think that a correct hypothesis (e.g. market efficiency) is not true. If the extremes are on both sides, it’s not a terrible problem for market efficiency. Another rational-markets argument to explain momentum is that momentum might be a noisy proxy for expected returns. If expected returns are constant (we’re pretty sure they’re not) or they are time-varying but highly persistent (which is plausible), then the buy-and-hold return of the last year (momentum) is a proxy for expected returns. If momentum is high, expected returns are high, so these stocks have higher returns. Which is what we observe. You see, it’s not easy to pick a side. Both sides can explain anomalies.

Bubbles

Lastly, let’s talk about bubbles. Before we start, let’s define them. You’ll see in a minute why a clear definition is everything but redundant. In an e-mail exchange between Eugene Fama and Ivo Welch, Fama defined a bubble as special cases of market inefficiency where cumulative returns differ predictably from equilibrium expected returns for sustained periods. Or in other words, the price is too high for fundamentals to support. It also means bubbles should be predictable in advance! So you can’t just look up a graph of some stock price, look for a plunge and scream: “IT’S A BUBBLE!” No, this is wrong because you use the advantage of hindsight. A crucial condition for you to be able to scream those words is that the bubble should be predictable. An unpredictable bubble is not a bubble. The idea here is that asset prices are just expectations about future cash flows. When these expectations change, prices change as well. So you could have a stock that plunges because irrational investors drove up the price for months and months and now finally start to see their mistake, or you could have a plunge in price because bad news reaches the market and becomes rationally reflected in prices. Both events can cause giant drops in stock price. For example, Fama argues that the 2008 drop in stock prices was due to news that a very big recession would be coming.

An example might clarify the hindsight problem. Say you buy an asset that will return $100 in a year with a 90% probability and $10 with a 10% probability. Assume that the proper discount rate is 5%. The fair value of the asset equals its expected cash flow, $91, discounted at 5%, which gives us $86.67. That’s the fair price. Now suppose we’re 6 months later and terrible news reaches the market. Suddenly, you have a 10% chance to get $100 and a 90% chance to get 10$. The discount rate stays constant. Now, the fair value drops to $18.54. Or in other words, your asset just lost about 79% of its value. Now suppose you’re an outsider with no knowledge about expectations, fundamental values, probabilities, discount rates, and so on. This all sure looks like a bubble, wouldn’t you say? How could investors ever have paid $86.67 for an asset that is now only worth $18.54? Surely they must have made a mistake. Well, as you can see, expectations were different at the beginning, perfectly justifying a price of $86.67. There was nothing irrational about this. Events with extremely small probabilities do happen, and they justify massive drops in value.

Lastly, let’s take another look at The John Plender quote I mentioned earlier: “the financial crisis put paid to [the efficient markets hypothesis]. The credit bubble before 2007 clearly pushed the price of most financial assets far from fundamental value”. How is Mr. Plender able to draw such conclusions? Did he watch prices fall by about 40% and therefore conclude that it was an irrational bubble? Because that would be silly. Did he calculate fundamental values of assets in 2007 based on 2007 expectations and did he then compare those numbers to the 2007 historical prices? I’m sure he didn’t do that. How in Gods name would he be able to price a CDO when he himself is claiming that all those PhD’s in physics, mathematics and economics were not able to do it correctly? Here’s what he did: he used the benefit of hindsight, which is wrong. If the financial crisis in 2008 had a 70% probability of happening, then yes, prices would be irrational. But did it really have a 70% of happening? Of course not. This crisis was an extreme event, with a very low probability. If it’s probability would be high, we would have these crises all the time. The question that remains unanswered is: what is the probability of such a crisis? Because if you want to evaluate observed asset prices against their fundamental values, you need estimates of probabilities of extreme events. And getting those estimates is close to impossible. So no Mr. Plender, you’re not getting off that easy. You did not show markets are inefficient.

Conclusion

Anyway, these were some thoughts on these topics. If you ask my opinion on this subject, you’ll find that I largely lean towards efficient markets. Most people in asset pricing do. But I’m not a true believer. I believe markets are efficient most of the time and that it is very hard for people to beat the market. But I’m also not convinced that markets are efficient always and everywhere. I think there’s a proper chance that some people might be able to beat the market, but that these people are extremely rare and that I will probably not be able to find them. I think there’s also a proper chance that markets have irrational expectations now and then. The thing is, I’m not sure about any of this. And that’s okay, I’m not forced to take a position on this. I think an honest view on this matter is to be agnostic. Economic science has not yet reached a conclusion and I don’t like to believe in stuff based on beliefs and nothing more than that. However, I do think that the efficient markets idea is getting a lot of discredit where none is deserved. In fact, that’s an irrationality of which I’m sure. So I’ll often play the devil’s advocate in order to give the dead sure opponents of the efficient markets hypothesis a run for their money. I hope I was able to achieve that here.