[MUSIC] Investors and analysts are constantly looking at financial markets to see whether there are opportunities to buy and sell, and take advantage of the mispricing and inefficiencies we discussed in the last video segment. Suppose you want an overview of economic performance of the largest firms in the world during the past 25 years, you'd likely look at the US S&P 500 Index. The S&P is the Standard and Poor's equity market index which includes stocks of 500 prominent, large companies listed in the New York and NASDAQ stock exchanges. Why would you look at the S&P? One reason to do so is that the index includes a representative sample of leading firms including companies like Apple, Exxon, GE and IBM. Another reason is that due to the careful selection process, and large number of stocks it tracks, the S&P is considered a bellwether indicator of business cycles and market performance in the United States. Here's the S&P index value for the past 25 years. What do you see? Charts help to bring out patterns, and humans are amazing pattern recognition machines. But it's smart to be wary. Looking at this chart, it's tempting to interpret several patterns, some of which may appear to be conclusive which would imply some concrete actionable steps. Take, for example, the twin peaks on the chart. As mentioned in Course 2, Markets, Video, and Turbulence, you may have already deduced that the first peak reflects the dot-com bubble collapse in 2000. And that the second peak corresponds to the housing bubble and the subprime mortgage crash eight years later. Here we are today, in 2016, eight years hence, there is an even more spectacular increase in the market. If there is a pattern to be learned from the first two peaks, you might conclude that we take steps to prepare for the next big correction. But before we jump down that rabbit hole, let's say you come across another related graph that includes data on margin debt, which involves borrowed money to invest, which is that red line. As with the first graph, you might see some very familiar shapes. You see the impressive increases in borrowing when the market was on the rise, followed by sharp reductions in borrowing that coincide with the market crash. This trend or tendency can be explained in that borrowing to invest is associated with speculation, which typically accelerates and artificially increases prices. Or the reverse, speculation precipitates price decreases during a market correction. Speculators, which we discussed in the derivative sections of course 2 on markets, bet on price movements and are often driven by the kind of herd mentality explained in the Ascent of Money video which we included in our curation corner. But back to the issue at hand. Seeking patterns in our second graph, do you believe that this chart reinforces our earlier intuition that a market correction is imminent? If you find these patterns disconcerting, you might find yourself pondering whether you can identify any other signs that indicate a market correction is coming. Actually, earlier in this specialization, we discussed the proliferation of conditions and danger signals that raise alarm about market corrections. Some of these signals include desperate central bank actions, over-indebtedness in every economic sector, households, firms and governments and issues like inequity that bear on political factors. Each of these types of situations have been happening with unprecedented frequency and exacerbating this frightening state of affairs, the event of one situation fueling the fire on the other. Central banks are now stuck with zero or negative interest rates. All sectors of the economy are indebted at dangerously unsustainable levels. And extreme political candidates are poised to win elections, all of this exaggerating uncertainty. How are you feeling now? Is this information enough to make you feel even more certain that we're headed for a market correction? Before you decide, let's tackle this question first with conventional wisdom, and then with common sense. Conventional wisdom comes from expertise, some of which is influenced by academic findings, but mostly, it comes from industry analysts and portfolio managers. Keep in mind that practitioners generally promote their own interests, because most of them sell financial products and want to earn fees. Because of this, they have a very poor track records in advising us when to buy or when to sell. This is why we must continue to explore several hypothesis and viewpoints so that by the time you've completed the Capstone course in Finance for Everyone, you will be in a better position with more confidence to make your own decisions. Back to our issue at hand. What would conventional wisdom suggest? For one thing, you can expect to hear the refrain, don't do anything drastic and the suggestion that two graphs are not enough to make a case for a catastrophic event and a spectacular correction. Convention would repeat the points made in the previous video about efficient financial markets, where prices move in a random walk, where the markets self-correct. And where it is very, very hard to profit by timing market exits and entries since share prices already reflect all available information. The academic conventional wisdom view would back this up. Relying on a few data points that show the twin peaks is probably coincidental. Patterns and correlations offer great explanations but only after the fact and have a poor track record to predict. And the margin debt data? That comes in from a two-month lag representing only 2% of the $19 trillion S&P index, and so the speculator theory is probably over-the-top. Conventional wisdom also invokes a measurement view. It looks at the lessons learned from modern efficient market theory and a large body of subsequent work on how prices reflect risk. A lot of investment courses focus on these ideas and at the risk of oversimplifying, I'm going to take the next few minutes to highlight the measurement aspects of conventional wisdom. And then, come back to the more intangible factors that will help us to bridge theory with practice. Recall from the last video that risk has many definitions to many people but the financial definition focuses on volatility because this notion is measurable. Let's now build on that idea. For as single asset, like a stock, the most common measure of risk is the dispersion of possible outcomes from its central tendency known in statistical jargon as the standard deviation. For example, say you're measuring the risk of earning an expected return on a stock that has an equal 15% chance to earn either a positive or a negative return of 20%, and the remaining 70% chance to earn a 10% return. Now you can calculate the expected return which will work out to 7% and a standard deviation of 11.9%, which I will illustrate to you in the following table. We begin by making some assumptions about scenarios. We have three scenarios here. Two extreme scenarios, one for extraordinarily optimistic Boom scenario. And then the opposite and extraordinarily pessimistic Bust scenario. And then the remainder, which we'll call a Normal scenario. In these three different states, what we do have of course are chances for each of these to occur. And those chances we can denote under probability of occurrence. So let's assign some probabilities as was given in this particular case. We had an equal chance of a Boom and a bBust scenario given to be 15%. And since all of these add up to 100%, the remainder is the expected Normal scenario of 75%. Now here is where we focus our expected returns for each of these. So our expected return for the boom scenario that was given to me 20% and then, for the pessimistic one -20%, and for the normal one 10%. So that's the data that we need to be able to calculate the expected return of these different scenarios. And we can come up with a standardized formula for that, which is to calculate the expected return. What we're going to do is take the sum of each of these individual probabilities and expected returns. So, we'll take each probability and then multiply it by the associated return to come up with the expected values. So if we do that right now, for this example we're going to have the product of these two, 0.03, 0.07. And then, of course, this is going to be -0.03. This will cancel out, and so we will be left with a 7% expected return. So one this gives us the return calculation what we still need to do is calculate our first measure of risk. Right, so we're going to use this expected return data to help us compute our first measure of risk and that measure of risk is going to be known as the standard deviation. And this standard deviation by the Greek symbol sigma is simply equal to the square root of the variance. And this variance is going to be the sum of each of these expected outcomes that we have minus the mean squared, multiplied by the associated probability. So, let's write that down. So, it's going to be the difference between each of these expected outcomes, minus the mean, squared, times the associated probability. Now why don't we plug the numbers in to see how this would work out in our example. We have the first expected outcome .20 minus the mean of .07 and we will square that, multiplied by the associated probability of 15. Then we'll go with the second one, 10 percent, minus the expected return squared times the associated probability. And finally our third outcome which is now -.20 percent minus the mean squared times the associated probability of 15. So if we compute the variances, the variance works out, in fact, to be 0.0141 you take the square root of that and we finally get our number standard deviation which is 11.87%. So what you have here are two measures, the mean and standard deviation that explains the dispersion of how far will each outcome is from the mean. So if we draw this on a graph, you can see here, this is going to be a mean, and this distance the standard deviation. In this example, this is the 7%, and this distance here is the 11.87%. So, risk is always relative to return, so we first calculated the expected return. And here, again, just to repeat and summarize. The 7% is nothing more than the sum of each of these expected outcomes with their associated probabilities. And that starts to look like a normal distribution if you have many, many data points. So what do I mean by many, many data points? Well think about it like this, suppose you are going to flip a coin 1,000 times. That distribution of results would be a two-tailed distribution representing the 50/50 outcomes. Which we know is the probability of how many values occurred close to the mean, or the average. The volatility is the measure by the variance of the average dispergence of each outcome from the middle known as the mean or expected value as I have explained. The variance is calculated as I showed to you again as the sum of the squared differences of each outcome and the expected return. And by standardizing the variance, we take the square root, we get this 11.9%, our first measure of risk. Now, let's add another stock so we have a portfolio consisting of two stocks. We could now calculate the portfolio expected return and the portfolio standard deviation. This would be very useful, because investors own portfolios of assets and not single stocks or single assets. Let's also assume that the second stock has an expected return of 13%, so our first one here we have an expected return of 7, let's assume the second one has an expected return of 13%. Now if I put half of my money here, and I put half of my money in here? Well we can see that my weighted average return is going to be the sum of these two which will work out to 10%, that's easy to do. Whether I have two assets or one hundred assets, I just take a weighted average, and I can calculate my portfolio return. But it's not such a simple matter when we try and calculate the portfolio standard deviation. This is because, we not only have the different variances which we have to weight. But we also have a third term known as core variance and that has to do with the relationship of the individuals stock returns. These relationships have to do with how well they are correlated. Okay, and the idea of correlation is really key to understanding the very powerful idea of diversification. So imagine this. If I had these two assets that are correlating like this, you can see that the correlation, if this is time, right, and these are the returns. You can see there is almost a perfect positive correlation between the first and the second asset. But supposed I had a correlation that looks something like this, now you can see the correlation between one and three is actually negative because when one is moving up. The other is moving down, now this implies that if I put some of my money in one and some of my money in the second one. What I could do is that I could smoothen out the variations that you see here. So when one is going down, it's compensated by the other one going up. So this idea of correlation is extremely important in calculating the portfolio diversification effect. So think of this covariance term. The third term that I was mentioning as a way in which we can spead our risk or that old saying we don't put all of our eggs in one basket. As long as these additional stocks in the portfolio spread and reduce our overall risk without sacrificing returns, we should of course keep adding stocks to our portfolio. And generally we can show that by the time we have about 20 to 30 stocks in our portfolio, then it is considered fully diversified. So note that the diversification is not going to eliminate risk. But instead what it does is it spreads the risk across the stocks so that losses of some are compensated by gains from others. Harry Markowitz is the father of modern portfolio theory and was recognized in 1990 with a Nobel prize in economics for in fact looking at exactly this kind of stuff. At the affects of risk, return, correlation and diversification on investment portfolio returns. Building on Harry's fantastic work is another gentleman by the name of William Sharp, a joint Nobel recipient. And he's credited for his contributions to the famous capital asset pricing model, commonly refered to as the CAPM or the CAPM. Again, without getting into the math, the CAPM model uses a number of efficient market assumptions that we discussed earlier to arrive at a very elegant result that can be measured in a simple equation that uses a risk index to compute the expected return. The following graph which I'm going to sketch for you shows the main result of the CAPM model and applies it to the 13% that we would expect, anticipating from buying that second stock. So let's assume, if I look at this model here, that I'm going to measure return on this axis. And risk on this axis. And the risk is going to be measured by something known as beta. The relationship actually is linear and straightforward. The CAPM suggests that the relationship looks like this. And here I'm going to throw some numbers in. Let's assume this is a point where there is no risk but some return, and let's give this a value of 3%. Let's also assume that the entire market has a risk index of 1, and that corresponds to a return that is commensurate with a rate of 8%. And then of course if we have a stock like ours, which has a risk index of 2, well, that would suggest a much higher return which would correspond according to this model to be 13%. So how do we get that 13% value by looking at this risk index of 2? Well we'll look at the famous CAPM equation. And the equation is simply suggesting that the expected return, these values that we're forecasting, that you saw over here and then of course this particular one is equal to this first component here which is the risk free component, so this is the risk free rate plus we're adding to this part here a premium. This is the premium of risk that we're going to add for the additional risk that we are taking. And that premium is the function of the difference between the return on a market portfolio. This is the return on a market portfolio with the risk index of 1 minus the risk free rate. That gives us this distance over here, Rm- Rf. And then, we adjust that with beta and that gives us the additional risk premium and takes us all the way up to 13%. So if we apply the numbers here, it's easy to see that the risk free rate of 3 plus the return on the market of 8- 3, that's 5 times 2. 10 + 3 gives us the 13%. [COUGH] So just to summarize again. Instead of using the standard deviation, this particular model uses a risk index known as beta. The model assumes the entire market which for example is represented by the Standard & Poor's market index to have a beta equal to 1. Beta is actually computed using regression analysis. It's a regression coefficient which is based on the changes of the entire market relative to the changes of that particular stock in question. Thus a beta of 2 means that a particular stock is twice as risky as the average stock. Or twice as responsive to changes to the market price as opposed to changes of the stock. So if the market goes up by 2%, the stock, because of the beta of 2, would go up by 4%. And vice versa. So this model also assumes that all risky assets on the minimum risk-free rate which in this example we assume to be at 3%. The risk-free rate is typically offered in a government security like a treasury bond. So we can see that the expected return is the sum of the risk-free rate plus the market risk premium adjusted by beta, that works out to 13% and that's how the CAPM uses a neat equation to quantify risk. Despite attracting a lot of criticism as an appropriate measure of risk that is beta, due to its multiple assumptions and low predictive value, the CAPM, nevertheless, continues to be used and taught as a good proxy of measuring risk. A good takeaway from this model is the validation of our intuition. That by taking on more risk in the long run, markets should be rewarding you with more return. [COUGH] But does history prove this to be the case? We've already considered this question during the earlier discussion in the second course of the specialization market. When we looked at the performance of another market index, the famous Dow Jones index. Looking at the performance of the Dow, the graph clearly shows in the long run equities provide much higher returns even though they're marked by bumps due to business cycles, recessions and market corrections. They can be long periods when returns however are quite flacked. But the overall trajectory is upwards as you can see. Now I've over-simplified a lot of the theoretical and empirical work behind the measurement of risk, but let me emphasize an important point. The challenge is not in sophisticated models and quantitive analysis. But rather in the assumptions behind the models that are used to explain the complex multidimensional nature of risk. Conventional wisdom, we tend to hold tightly to these assumptions, particularly today, as they appear to have contributed to the market upswing that so many people have enjoyed and find themselves in. However, holding on to conventional wisdom may be an outdated option for many of us. There are just too many danger signals which would give pause to anyone who wants to protect themselves against perhaps a catastrophic financial correction. Indeed the chance of a grand correction seems increasingly likely as each day passes, but of course the exact timing is going to be anybody's guess. Your opinion is likely to be better informed after you've completed the forth course on debt, as well as activities that will mark your capstone in finance for everyone. Meanwhile if you are wondering what do ordinary folk do who do not have access to expertise who can not just shock proof their own portfolios from an imminent correction. What are some of the first steps that you can take? Consider the following. First of all think cash. That is, convert as many of your assets in cash as possible. Cash can insulate you from downward swings in both financial securities such as stocks and bonds and anything related to financial products. If you believe that the financial industry, including domestic banks are vulnerable, perhaps you want to secure your cash in a debt free international bank, or if that's not possible, then simply in a non bank vault. Second, think about buying perhaps some commodities and precious metals. Cash in a safety deposit box earns 0%. But because commodities in metals do appreciate in value, they have proven to be a good hedge and a safe haven against problems in the financial industry. And more broadly with bankrupt governments. Take gold for example, which has a 5,000 year history of growing value, a longer standing than that of the oldest paper currency, which is the British Pound. Third, pay off your debt. This should probably be the first thing that you do. But as the last one mentioned, it is certainly a perfect segue for us to explore a lot more about debt in the fourth course, and I look forward to seeing you very soon.