耶鲁大学金融市场英文文本Financial-MarketsLecture-05-Transcript.doc

Financial Markets: Lecture 5 Transcript Professor Robert Shiller: I wanted to talk today about insurance, which is another risk management device thats traditionally separate from securities, which we talked about last time, but the underlying principles are the same. Before I begin, I want to just give some more thoughts about the diversification through securities and that will lead us into insurance. Let me just review the preceding lecture briefly for that purpose. What we did-the core theoretical framework that we had-was the mean variance theory, which led us to the capital asset pricing model. But the basic thing was that we had to-in order to use the framework-we had to start by producing estimates of the expected returns on each asset, we called those r, and the standard deviation of the return on each asset and the covariance between the returns of each pair of assets. Then, once we did that we could plug that into the formula that I gave you last time and get the standard deviation of the portfolio and the expected return on the portfolio. From then on, if you accept the analysis and the assumptions or the estimates that underlie it, then we pretty much know how to construct portfolios. The underlying estimates may not accord with your belief or your intuitive sense of common sense. The other thing that I mentioned last time was that there seems to be a really big difference between the expected return on the stock market and the expected return on short-term debt. We found an equity premium-or actually Jeremy Siegels book gave an equity premium of 4% a year. Some people find that hard to believe. How can it be that one asset does 4% a year better than another? Some people say, well if thats the case I want to invest in nothing more than that one asset. Why should I take something that is underperforming? Jeremy Siegel goes on further to say that since the mid-nineteenth century weve never had a thirty-year period when stocks under performed bonds, so stocks are really-if anyone who has an investment horizon of thirty years-youd think, why should I ever holds bonds. The numbers that Jeremy Siegel produces seem implausibly high for the stock market. What we call this is the-I want to emphasize it, Ill write this again-the equity premium puzzle. That term was actually coined by economists, Prescott and Mehra; its now in general use. That is, it just seems that stocks so much outperform other investments. For Jeremy Siegel, in the latest edition of his book, the equity premium is 4% a year since 1802. Thats almost-no thats more than 100-thats 206 years. Why would that be and can you believe that? One question that comes up is that maybe-this is for the U.S. data-and some people say, well, maybe, why are we looking at the U.S.? Because the U.S. is an arguably very successful country, so we have, potentially, a bias in-its called a selection bias. If you pick as the country you study one of the most successful countries in the world, that doesnt inform you very well about what it is for a random country or for the U.S. going forward, theres something wrong. The U.S. has been successful in financial markets and its being imitated by lots of countries. Financial markets similar to ours are being set up in many places. You wonder, you know, maybe theyre over imitating; maybe we were just lucky or maybe it was because the U.S. was the first, in some ways, to develop some of these financial institutions-or one of the first. But now, when more and more countries start doing it, maybe it wont work so well. One way of investigating this is-to get around the selection bias-is to try to look at all countries. Lets not just look at the United States; lets look at every country of the world and lets see if they have an equity premium. Theres a problem with that and the problem is that countries that are less successful dont keep data-thats a problem. Or they-sometimes they just shut down their stock markets at some point. This is since 1802-now how many countries do you think have uninterrupted stock market data since 1802? What do you think? Name another country that probably has it. Whats that? England, UK? If you go onto the continent, though, they tended to be interrupted by World War I and World War II. What about Japan, do they have-do you think they have uninterrupted? They had a little bit of a problem around World War II and you can try to bridge the gap, but-anyway, there are people who have tried to sort this out. Theres one, its a book by Dimson, Marsh, & Staunton that-called Triumph of the Optimists-that Jeremy Siegel quotes. He has a table in the new, fourth edition of his book. Dimson, Marsh and Staunton look at the following countries: Belgium, Italy, Germany, France, Spain, Japan, Switzerland, Ireland, Denmark, Netherlands, UK, Canada, U.S., South Africa, Australia, and Sweden. Every one of them has a positive equity premium; although the U.S. is on the high side of them all, its not the best. The country that has the highest equity premium-and thats for the whole twentieth century, they couldnt go back to 1802-the most successful country is Sweden and after that Australia. U.S. is not the most successful stock market although its high on the list. Jeremy Siegel concludes that theres-that the equity-he said that these-that this book by Dimson, Marsh and Staunton puts to bed any concerns about selection bias and he claims that so many countries have shown an equity premium that we can be confident. His book is really very strong on the conclusions. The title of the book, Stocks for the Long Run-stocks always outperform other investments for the long run and he says its not due to selection bias. You know, I kind of wonder, the list of countries that I just read to you, that Dimson, Marsh and Staunton studied, excludes some important countries, doesnt it? Who does it exclude? Well, it doesnt have India, Russia, and China in it, for example. At least Russia and China-do you know anything about their history? They have any stock market disruptions in the last one hundred years? Thats kind of obvious. They had a communist revolution in both places, right? Russia and China are not mentioned by-or not studied by Dimson, Marsh and Staunton. Why not? Well, they cant get data, there wasnt a stock market. Well there actually was a stock market in Russia before 1918 and in China before 1949, so what happened to investors? If you were a Chinese investor in Chinese stocks in 1949, what happened? We know what happened. It went-thats that famous minus 100% return, right, which dominates everything. I think-what would Siegel say? Hes really saying that this equity premium is enduring and we should believe it. I dont know, I think that-I think what Jeremy would say is, well youre looking-if you look at Russia and China, youre looking at political factors and Im only looking at politically stable countries, so this whole thing is irrelevant. Really, were not going to have a communist revolution in any of these advanced countries now. So Jeremy would say, forget that, it looks pretty sound that we have an equity premium so we can trust that. Well, hes a good friend of mine, but I think he may be overstating it a little bit; we have some disagreements. The thing that comes to my mind is that-I want to say before concluding this review of the last lecture-that is that the stock market is inherently political in any country. Politics have tremendous effects on the values in the stock market and thats because of-even if the government doesnt nationalize the stock market or confiscate assets, they tax them. Do you know we have, in the U.S., a corporate profits tax? Well, its not just in the U.S., essentially every-I dont know if theres any exception. There may not be an exception, but essentially every country has a corporate profits tax and then we also have a personal income tax. The corporate profits tax goes after the profits that corporations make. The personal-its taken from corporations before they pay out their dividends. The personal income tax is levied on individuals and these individuals have to pay it. The personal income tax is not simple; its not just a flat rate on your income, it depends on the type of income. Dividend income or capital gains income in the stock market is taxed differently. The interesting thing is that through time, as political winds change, these taxes have changed and theyve gone up to some very high levels in the past in the United States and other countries. Im going to give some U.S. tax rates. The personal tax on dividends-of course it depends also on your tax bracket and your income; Im going to talk about the highest tax bracket. In the U.S., it went over 90% in World War II and the succeeding years. The government was taking 90% of your dividend income. What is it today? Does anyone know? Whats the tax rate of dividends today? It might be zero for some people, but its actually-it is-the standard rate for people who have not negligible income is 15%. Its gone down from over 90% to 15%. Why did it do that? Well, its some kind of political change and the corporateincidentally, at the beginning of the twentieth century you were right. Who said zero? We didnt even have income tax until 1913 when the Supreme Court allowed it, so it was zero, then it went up to 90%-or actually it was 94% at the peak-and it came down to 15%. Thats a pretty big hit on the stock market. So, it wasnt just China that took the stock market. When we were taking 90% of dividends that was 90% of the stock market being taken by the government; but thats not all because we were also taxing the corporations. In the early post-war period, the corporate-now Im going to talk-theres a distinction between the rate that they charge and the actual amount that they take. Most advanced countries of the world today have a corporate profits tax rate for large corporations of about a third. So they-a typical advanced country takes a third of the profits, the government takes a third of the profits. Thats not the actual amount that they pay because the tax law is so complicated and there are so many loopholes. What I looked at-and I have this on the website, I have a chart showing corporate profits taxes paid, as a fraction of corporate profits for the United States since 1929. That has moved around a lot, but it got almost up to 60% in the post-World War II period and now its down to less than a third. Why is it down? Its because theyre changing enforcement of the taxes and changing amounts of loopholes, so most countries have a tax rate of about a third, but corporations are paying less than a third of their profits to taxes. If we want to look going forward at the equity premium, we have to know how much-whats the politics? And whats the government going to do in the future? Theyve moved these tax rates around a lot, so I think that its very hard to be sure that we know going forward what are , the expected return, the standard deviation of returns and the covariance of returns-are really. We have a nice theoretical framework, but the application of the framework to the real data is hard and it ends up with politics underneath it all; thats just the real world. I want to say one more thing about the diversification and the mutual fund. Ideally, mutual funds are calculating r and and 12 and plugging in and finding what the optimal portfolio that you should hold is, then offering that to you in their mutual fund. Firms that do that are, in practice, however, the minority and most mutual funds have some gimmick or some special-they claim to be beating the market not forming the optimal portfolio. I also have up on the website some questions that I asked investors about what they think about picking stocks. Picking stocks means trying to find a stock thats going to do really well. What I found-the question I asked is, do you agree-which of the following is a correct answer to this statement: Trying to time the market, to get out before it goes down and in before it goes up is (a) a smart thing to do, or (b) not a smart thing to do? Most people think that its not a smart thing to do-to try to time the market. Only 11% said yes to that. But then I asked another question, do you think trying to pick mutual funds, trying to find a mutual fund that will beat the market is a smart thing to do or not a smart thing to do? Most people think its a smart thing to do. What I think the mutual fund industry has turned into, largely, is a stock picking industry, not a portfolio diversification industry. What most people are doing when they go into a mutual fund is theyre trying to find smart people who will beat the market-who will pick those stocks that will do well. The mutual fund theory that we gave last time said, no the mutual fund is just supposed to be diversifying for you. In fact, the truth is somewhere in between. Most mutual funds are providing some diversification service and theyre also trying to beat the market. Finally, I just want to say that Ive been talking mainly about the U.S., but mutual funds have been growing in importance around the world. There was a recent paper by Khorana, Servaes, and Tufano, that looked at what it is that explains which countries have had rapidly growing mutual fund industries. They found, not surprisingly, that it tends to-mutual funds have been growing more rapidly in countries that have stronger securities laws and institutions, especially laws that protect individual shareholders rights. Also, mutual funds have been growing more in countries that have higher level of education and a higher level of wealth. They also grow more in countries that have institutional structures that encourage investing in mutual funds, such as pension plans. I think its a trend around the world that were going to see more and more mutual funds and I think its a good thing. I think they will help us to diversify our risks. Anyway, I want then to move on to the topic of todays lecture, which is insurance. Insurance is the other side of the risk management institutions that we have. Insurance evolves separately from securities. Its long been a different industry, but the principles are the same. The principles of insurance-the fundamental powerhouse-is the principle of risk pooling. Insurers, just like mutual funds, are providing risk pooling for you. Risk pooling means they put a lot of people with independent or low-correlated risk into a pool and reduce the risk for the whole pool. They have to contend with something called moral hazard, which is the risk that people will be affected by the fact that theyre insured and do something bad. The classic moral hazard problem is the problem that you give fire insurance on a house and someone burns down the house in order to collect the insurance. They also have to deal with selection bias. What this means in the insurance context is that if you offer insurance policies you will tend to attract people who are higher risk. If you offer life insurance, you have life tables which give you probabilities of dying at various ages, but thats for the general population. All the sick people will come to you to buy life insurance and they will turn out to have a higher death rate than the population at large. These are the problems of insurance that we have to deal with. I just want to review the mathematics of insurance. This is actually just, in part, just a review of what we talked about in the second lecture. In the ideal world, if you have independent risks, under the independence assumption, the probability distribution for the number of insurance contracts that you will have to pay on follows the binomial distribution. x is the number of accidents-lets say this is some accident insurance-the probability of having-n is the number of policies that youre writing. If youre going to have p as the probability of an accident, then the binomial distribution gives you the probability of having x accidents out of your n policies. We had that before, that is px(1- p)(n-x) n!/(x! (n - x)!) That is the binomial distribution and it allows you to calculate the probability of any number of accidents. The mean proportion-The mean of x/n, is equal to p. If x is the number of accidents, the mean number of accidents divided by your number of policies is given just by the probability, but the standard deviation of x/n is equal to the square root of p(1 p)/n. That is the-that gives you the mean and standard deviation of the proportion. To actually apply this it helps to go to something called the normal approximation to the binomial, because its kind of difficult to compute this formula. Theres an easier formula and you assume that the binomial distribution is really a normal distribution with a meanIm sorry, the proportion of accidents x/n follows a normal distribution with mean p and standard deviation given by this. Thats the whole theory that I have here; its simple. Maybe I should make a bigger-let me do it here, I can fit it in here I think. Im going to draw an example. Ive got it plotted out and its on the website, but its a very simple example. I have the case where p = .2, so the probability of an accident is 20%. This is a significantly high probability of accidents. Can you see this? Lets do this from 0 to .4. If you wrote only one policy, whats the probability distribution of x/n? Well, it has two possible values. It could be the one person doesnt have the accident or does have the accident. So, if n = 1 we have an 80% chance of no accident and-lets make this 1 not .4-then a 20% chance of x/n = 1. Im plotting-this is the probability of various values of x/n. If n = 1, x/n can take on only two value