- How do we measure the risk of an investment or a portfolio? What is the relationship between risk and return and is it possible to reduce our risk without sacrificing any return? Well, these are the questions that I'm going to explore today in my lecture on How to Measure and Manage Risk. This is the fourth in my Gresham College lecture series on the Principles of Finance, which is on basic financial literacy. Now maybe a good place to start is to define, well, what do we mean by risk? And you might think, well, I didn't need to come to a Gresham College lecture to do that. I could have just looked this up on Wikipedia. And what Wikipedia says is that risk is the possibility of something bad happening. Seems pretty uncontroversial, right? Let's say I've got 10 pounds in my pocket. And because I'm scatterbrained, there's a 50% chance of me losing it. That is risk. But in fact, that is not what I'm going to refer to as risk in today's lecture. So why is that? Because let's say there was a 50% chance of me losing my money. What that means is my expected money falls from 10 to five, right? I've got a 50% chance of keeping my 10, 50% chance of losing it, getting zero. So overall, my average amount of money is going to be five. Now, everybody dislikes this. Everybody is worse off, not so much because of risk, but because my amount of money has fallen from 10 to five. So instead, when I speak about risk today, what I'm going to be speaking about is how we are going to look at risk holding constant the same expected cash flow. So, I'm going to be comparing two situations. Number one, I'm going to be looking at a 50-50 chance between zero and 10, and I'm going to compare that versus five pounds, for sure. So why is that what I mean by risk? In both situations, my expected value is five. The average return is five. The difference is in one case that five is for certain, and the other case that five is uncertain. We might get zero, or we might be at 10, but still, on average, it's the same. And so why does this make this a much more interesting and less obvious problem? Because it's not actually clear that people will dislike risk. Well, you have some people who are risk-averse, right? They would prefer five pounds, for sure, rather than a 50-50 split. Why? Let's say they need the money to go and buy some dinner. Now, if you have nothing in your pocket, you go hungry. So to go from nothing to five pounds is great. Like you can now buy two sandwiches. Now, if you go from five pounds to 10 pounds, that's even better, you can now buy four sandwiches, but you are probably happy with two sandwiches, you'd rather have five pound for sure And so this is the idea of diminishing marginal utility, which is a fancy way of saying that you have diminishing returns, the happiness you get from going from zero to five is greater than the extra happiness from going from five to 10. So if you are that sort of a person, you are somebody who dislikes risk. You are risk-averse. But there might be other people who don't really mind that risk. You are risk-neutral. You are indifferent to risk. You are not harmed by it. Why? Let's say, in addition to that 10 pounds in your pocket, you have a credit card. And that credit card means that you are always going to be able to buy dinner. So it doesn't really matter whether you are careless and you lose your money, you are just as happy with a 50-50 chance of 10, as five for sure. Okay, so what we're going to look at today is how does risk change people's financial decisions? And so why might risk change financial decisions? Well, let's go back to my last lecture, which was called how to make financial decisions. And what we said is that a financial decision involve an investment. And what an investment means is we're going to spend some money today, and we're going to get some money in return in the future. For example, if you are a company, and you're building a new factory that costs us money today, but in the future that factory produces some clothes and we can sell those clothes. Or let's say you are a person and you might buy some shares. That costs me money today, in the future, I'm going to get some dividends, and those dividends will hopefully recoup my expenditure. Now, last lecture, we said there was two reasons why you can't just simply sum up the cash flows, take all the future money you are receiving and net it against today's costs. Why can't we do that simple sum? Well, last time, we highlighted that one pound today is worth more than one pound tomorrow. So we are spending money today. Yes, we're getting money in the future, but that money in the future is not so valuable because of the key idea of the time value of money. That was what we focused on entirely last time. Today, we're going to look at the second reason why these cash flows are not apples to apples, and that second reason is indeed risk. When you make an investment decision, you are spending money for sure. When I build my factory, it is definitely costing me 1 million pounds. When I buy a share, it's definitely costing me 10 pounds, if that's the share price, but I have no idea what the dividends will be in the future. I have some sense, but it's risky. It depends on the state of the economy. And similarly, I don't know how many clothes my factory is going to be producing or what I'm going to sell them for. Again, it depends on economic conditions. So because the future cash flows are risky, what we'll need to do is we will need to apply a risk discount for the fact that they are uncertain rather than safe. But then you might think, well, there's kind of a problem here because how much will that risk discount be? It might be perfectly subjective because my first slide told you that there were some people who really dislike risk, they're risk-averse, and other people who don't mind it, they're risk-neutral. And I could just call these by some animal analogies. Let's call people who are risk-averse chickens, right? That's not supposed to be pejorative. There are people who are risk-averse, right, because they just don't like risk. Maybe they don't have much money. So whatever they have, they want to make sure they don't lose it. And on the other hand, you have some investors. I'm going to call them lions, right? They don't mind risk at all, perhaps because they're wealthy, they don't mind losing anything. And so the challenge for a company is that a company is owned by many, many shareholders, right? And some of those shareholders might be chickens, and they might not want the company to take risk. And other shareholders might be lions, and they might want the company to take loads of risk. So maybe if you are a drug company, maybe the lions will say, let's develop a cure for cancer. Yes, it's risky, but the reward could be high. And maybe the chicken will say, let's just keep making aspirin. That's something where the return is low, but I know there's always going to be demand for aspirin, and we know that there's always going to be certainty, that you'll be able to produce it. So that's the big problem here. If you are running a company, you are facing these risky investment decisions of spending money now, to get something uncertain in the future. You have some sense that you need to apply a risk discount for the fact that these things are uncertain, but how much should that risk discount be? And is it subjective? Would you have to ask every single shareholder how risk-averse or risk-neutral you are But what it turns out, and this is the punchline of today's lecture is there will be a single objective way to calculate the risk discount, which all shareholders will agree on, regardless of whether you are a chicken or a lion. And that makes financial decisions much more objective rather than purely based on references. So let me start to show you how this is. So let me start again with the big picture. What our goal is, is to calculate the risk discount. We know that a certain pound is worth more than a risky pound. How much more that is the risk discount, that's what we're going to look at. And intuitively based on common sense, how much should a risk discount be if cash is risky, how much should we haircut it by? It should depend on two things. Number one, the amount of risk, how risky it is. And number two the price of risk. How much compensation do you deserve for bearing a little unit of risk? And so what I'm going to focus on is how do we calculate the amount of risk. The first thing here, and so this is why my slide is going to be called, How Do We Measure Risk, we care about the amount of risk. And then you might think, I didn't need to come to a Gresham College lecture to learn this because I would remember my GCSE maths, right? Because in GCSE maths, we remember the way that you measure the amount of risk is something called the standard deviation, right? That shows you how variable a distribution is. So let's take three different companies where on average, all of them will make a profit of 50 pounds, but the blue company is pretty safe, right? You're pretty sure you're going to get 50, give or take five. And the green company is very risky. There's a big chance you'll get over 75, but are also a chance that you're going to get below 25. You might even get zero. And so what standard deviation measures is how spread out the distribution is where the green has the highest standard deviation. It is the most risky. Now that's what we learn in GCSE maths. And that seems to make sense. But actually, it turns out that that is not the way to measure risk in finance. Why not? It's best shown by going through an example. So let's take these two hypothetical companies. So one of them is called Izy's Ice Cream, sells ice cream. And as we know, the demand for ice cream is risky. It's going to depend on the weather. So when it's sunny, Izy's Ice Cream makes 14. And when it's rainy, then it's only going to be making six. So on average, it's getting 10, that's halfway in between, but there was some risk there, that standard deviation because you are dependent on the weather. Now let's take another company which I'm going to call Corollas Coffee. Here, you are independent of the weather because caffeine addicts. They need that caffeine hit, regardless of whether it's sunny or rainy. So with Corolla's Coffee, you are always getting nine. Your average is nine, and there's no risk at all. Now the question is, well, which of these companies would you prefer as an investment? One has a higher expected return, but the other has no risk? And you might think, well, it depends on whether you are a chicken or a lion, right? The chicken would prefer this one, no risk. The lion would prefer the first one, is these ice cream. Yes, there's the risk of the weather, but you are willing to bear that risk because of the higher return. But that actually turns out to be the wrong answer. Why? Because what we are now going to do is we're now going to introduce a third company. And that third company is called Ursula's Umbrellas. So this is umbrella shop, and it's dependent on the weather. But notice it's affected by the weather in the opposite direction to the ice cream company, right? You do really well in the rain. You do badly in the sun. So you have a high return, but you also bear some risk. But you might think, well, that doesn't change the equation. It's still the case that the chicken will prefer the coffee company because it has no standard deviation, the other two companies are risky. But why is that the wrong answer? Because of one of the most fundamental concepts in finance, which is diversification. So I'm sure you've heard this word before, but let me be precise about what it means. Diversification means when we hold stocks, we are not constrained to holding just one company or another, we can hold a portfolio. And what is a portfolio? It's a mixture of different stocks. So the idea is that if I was to hold this portfolio, which is one-third of Izy and two-thirds of Ursula, I'm going to be able to diversify away the vulnerability to the weather. Why? Because when it's sunny, yes, it's the case that Ursula is really badly, but I'm offset by the fact that I have the ice cream company and therefore, I'm still doing well. And in contrast, when it's rainy, nobody's buying my ice cream, but they are buying my umbrellas, so again, I'm immune. So the big punchline here is this is why the standard deviation, the most intuitive measure of risk, actually is not the correct measure, right? Both Izy and Ursula, they both have standard deviation, both of them are risky because ice cream demand and umbrella sales, they both depend upon the weather. But because we can diversify, we can construct a weatherproof portfolio, which actually has no standard deviation. And as we can see, this is actually preferred to Corolla, right? Because both of these have no risk, but the portfolio has higher return. And so that's a little insight as to why these decisions are not subjected. Even if you are a chicken, even if you absolutely hate risk, you will still never buy the coffee company. You'll always better off buying a portfolio of the ice cream company and the umbrella company. Because even though both the individually risky, when you combine them, risk goes away. So at this point in the lecture, you might think, well, if this just goes away, why shouldn't we just end the lecture here and go home? Because we can actually completely get rid of risk. But the answer is, unfortunately, no. Why? Because diversification, even though it's really powerful, you can get rid of risk, you can't get rid of all risk. Why? Let me take the same example with exact same numbers, but here, rather than having sun and rain being the risky factor, let's say it now depends on the state of the economy, whether you are in a recession or a boom. Now, the key difference here is that with the weather, the effect of the ice cream company and the umbrella company in different directions, but the state of the economy that affects both companies in the same direction. So, in a boom, people are buying more ice clean, more coffee and more umbrellas. And so this means that you can't diversify away your sensitivity to economic conditions. So let's say you started with the ice cream company. That's really sensitive. You get six only in a recession, but a massive 14 in a boom. Let's say that's too much risk, and we're going to do the same strategies before. Let's just have a third of the ice cream and two-thirds of the umbrella company. Yes, you've reduced your risk, but you can't reduce it all the way to zero. Why? Because there are some risks which are shared by every company in the economy. Regardless of what you sell, you're are always affected by economic conditions. And so the big punchline of the first half of my talk is that there's two types risk, right? Total risk is that standard deviation. That's what we study in GCSE math. That's all the risk that a company has. But what we've established is that some types of this risk are known as idiosyncratic or unique. They are specific to one company. So the risk of rainfall that is a risk that the ice cream company faces, but the coffee company doesn't care. And actually, the umbrella company is happy with it. So that is specific to one company. But there's a second type of risk, which is systematic risk. And that shared across all companies. And so why this matters is the first type of risk is diversifiable. We were able to get rid of the risk of the weather just by buying a portfolio. But the second type of risk is non-diversifiable, right? No matter how many companies we diversify away to, we are never going to get away from the fact that some risk is systematic. It is shared. So the punchline of this is that the title of this lecture is how to measure and manage risk. How we measure risk is we don't actually care about all the total risk here. The only thing we care about is the systematic component. What is the risk that you cannot diversify away? So this is the only thing we care about. We don't care about anything which is specific to one company. Okay, so the next step is, well, how do we measure the amount of non-diversifiable systematic risk? So what is systematic risk? This is the risk that all companies share. That is the risk that is shared by the rest of the market. Why? You diversify by holding the entire market. That might be all stocks on the London Stock Exchange. But even if you were to hold all stocks on the London Stock Exchange and have mass maximum diversification, there are still the fact that that will depend on the economy. So how do we measure risk that is shared with the market? Well, another way to say that is what is your risk that is correlated with the market. And that might ring another bell, back to GCSE maths, because remember the idea of the correlation coefficient and that is something which actually does apply to our current setting. So let me just give you a little bit of a refresher. What the correlation coefficient is, is a number between -1 and +1 which measures whether two things move in the same direction or in directions. And rather than going through these words, let me go you through a picture because a picture tells a thousand words. So let me start with the correlation of -1. So this row, this is the Greek letter. That's what we typically use to denote the correlation coefficient.- 1 means that these two things move perfect opposite directions to each other. When one does well, the other does badly, like the ice cream and the umbrella company. You might have the correlation being negative, but not as badly as one. And here, yes, when one does well, the other tends to do badly, but it's not as rigid as in the first case. You might have positive correlation here where when one does well, the other tends to do well, but again, it's not always the case. And then at the other extreme, you have perfect positive correlation where when one goes up, the other always goes up as well. And in one intermediate case is you could have no correlation where these two things are completely unrelated to each other. Okay, so what the correlation measures is do you move up with the market or do you move down with the market, or do you not move at all with the market? The market just doesn't matter for what you are doing. So the key to measuring this systematic risk, the risk that we care about, because it's not diversifiable is to look at how correlated you are with the market. But that's actually not the full picture, because what that shows is directionally, do you go up when the market goes up. What we care about is the amount, how much you go up when the market goes up. Here, there's perfect positive correlation, but that line is pretty flat. So really, the market doesn't really matter because there's not that much from an effect. So what we're doing is we're going to go again, back to our GCSE maths, when you learned about correlation, you would've also learned about something called covariance. So what that does is it takes correlation and multiplies it by the risk of the two individual securities, which is here one particular stock, stock one and the market. Let me repeat this. What we're trying to look at is what is the systematic risk of stock one, a hypothetical stock, how risky it is. It depends on how correlated that stock is with the market. Its individual risk, and the market's individual risk, and that's something which is known as covariance, how sensitive that stock is to the overall market. And so, what is the measure of risk that we're going to be using today? It is one of the most famous variables in finance. It is called the beta. What the beta is, is what you take, what you get, when you take this covariance and you divide it by the variance. So when we have measuring how risky a stock or a company is, what we care about is not the total risk, but we care about systematic risk. How do we measure systematic risk? We first find the covariance, how much you move up and down with the market, and then divide it by the variance of the market, and this is our measure of risk here, it's called beta. It's one of the most famous variables in finance. Now, before I proceed, let's just step back from the equations. And let me just talk about what we've done in terms of common sense. Right, where did I start? I said people don't like risk and because people don't like risk, any investment which is risky, they're going to be applying a risk discount to. That seems to make sense. But then we said, well, actually, there are certain types of risk that should not be discounted because you don't really care about them, right? If I were to buy an umbrella factory, yes, there's the risk of weather, but I don't care about this. So I'm actually not going to be applying a risk discount. The only reason I should apply a risk discount is if the risks of my investment are shared with the rest of the market, how do I measure the extent to which a company has risks shared with the market? I use this beta thing here. This is the measure of risk that is what's used throughout finance. So another way not looking at this is not through with the equations, but what it actually means. So you might think, well, I understand why there's a covariance here that measures correlation, but why do I divide by variance? Let me make my final reference, I promise, to your GCSE maths. You would've remember that this is the slope of a best line. Well, what is the best fit line? Well, what you can do is that let's take two things. The return on the market and the return on an individual stock. And what we can do is we can plot a scatter diagram of how one depends on the other. So let's say in one month, the market went up by 2.4% and the stock went up by three. We're going to do this dot, let's say there's another month where the market was unchanged, and the stock went down by one. And what we can do is we can plot a lot of these scattered plots of individual months. We can look at how the stock did and how the market did. And overall, we can look at the general sensitivity of the stock to the market, and we can draw a best fit line, which shows how sensitive the stock is to the market. So here, the beta is 1.21. This means that, on average, every time the market moves up by one, the company will move up by 1.21. So remember, what I said was important. It's not just the general direction of movement, but how much, right? How much risk do you have? What is the amount of risk? The amount of risk is measured by what is the effect of a market movement on the overall stocks movement. And just continuing this idea further, let's look at how beta changes the best fit line. If a company has a beta of a half, that means that changes in the market have relatively little effect on the company. If the beta is two, this means that changes in the market have a massive effect on the company. So what the beta measures is how sensitive the company is to the market movements. And importantly, this is not something between -1 and 1, unlike the correlation coefficient, this can take any variable which is realistic because there are some stocks which are really sensitive to the market. Let's take a luxury company like Rolex Watches, right? When the market does well, people can keep going out and buying Rolex watches. But when the market does badly, that's something that you are going to be cutting back on because it's a luxury, it's not something that's needed. And this is going to be linked to my next question, which is, let's again, step back from the numbers and let's think about common sense. What determines beta? What determines the amount of risk that a company has, which depends on the market? There's two things that it depends on. The first thing it depends is business risk. That's how risky your business happens to be in just due to whether you are in something which is luxury or something which is more every day. So if you are in luxury goods, let's say watches or jewelry, or expensive holidays, or cruises, then your beta will be really high. You are very sensitive to the market because when the market does badly, you are going to be cut back on. Now there are other companies which might have a small beta, but you do depend on the economy, but not by much. So let's take a shoelace company, right? So if indeed the economy has a slowdown, you're probably still going to be buying some shoelaces. Those are things which are pretty much every day. When a banker gets a huge bonus, she spends it and celebrates it, maybe buying a new car, not by buying more shoelaces. So this is not something sensitive to economic conditions. And importantly, there could be cases where beta is negative. There are some odd companies which actually do well when the market does badly. And what might be an example of that? Well, one example could be an insolvency company. What you do is when companies go bankrupt, you make money by advising them through that bankruptcy process. And therefore, you actually do the opposite to what the market does. Now, when I was teaching at MIT, I had as my exam question, can you give me an example of a stock with a negative beta and what one student wrote was a baseball bat company? Why? Well, his argument was that, well, if you are somebody who lends out money, then in a downturn, people need to pay you back. And in order to force you to pay them back, you would go around with a baseball bat throw onto people's front door. Now that was not why I had in mind when I asked the question, but because the student had an unusually high sense of humor for an MIT undergraduate, I gave him a half full of credit for that. But again, this is just a show, there are certain stocks that do well when the company does badly. And so why does this all matter? So I'm going to tie all the feds together now. Let me go back to a slide I had maybe about 20 minutes ago. I said the big picture goal of it is we're trying to measure the risk discount. How much will we haircut the cash flow because it's risky? And I spent a lot of time saying that actually, we don't care about the total amount of risk. The only risk we care about is the risk shared by the market. And we have now said that that risk is measured by beta. Now, the other thing we need to look at is the price of risk. So the amount of pain, the cash flow causes due to being risky, that's given by beta. But how am I much compensation to demand for that pay? That's given by the price of risk, which is given by this other term here. And so what I'm now showing you is perhaps the most well-known equation in finance, which is the relationship between risk and return. So the question here is we have a stock, stock 1, and what we're trying to look at is how much return should I get from owning the stock? Now, what we've established is that you should get a return because that stock is risky. So if RF is the risk-free rate, that's the return you get by buying UK government bonds. If I choose to take some risk and not invest in government bonds, but invest in the risky stock, I should get a return for the risk I'm taking on. Now, how much extra return should I get by taking on this risk? It depends on the amount of risk which we've established depends on beta, only systematic risk. And then it depends on the price of risk. And the price of risk here is given by red term. What is that? That is the return on the overall market minus the risk-free rate. So how much extra return you get by taking on some risk depends on not only how much risk you are taking on, but the difference between markets return and the return on the risk-free rate. And this is something called the market risk premium. And again, this is something where it might actually be clearer rather than you staring at the equations for me to show you a graph to show you how this works. Okay, so what am I plotting? On the X-axis, I'm plotting beta. Your measure of systematic risk and on the Y-axis, I'm plotting the expected return. Now, if we were to invest in government bonds, we are taking no risk because government bonds will always pay you back and we're getting the risk-free rate. The risk-free rate is the rate of return on a risk-free asset, like a government bond. Now what the red line does is it plots that exact equation I had on the last slide. So the more risk you take given by beta the greater the return. So if your beta is one, what does that mean? It means you have the same sensitivity as the market. So if you are having the same sensitivity as the market, it makes sense that your return should be the market's return. If there's a stock which moves in lockstep with the overall London Stock Exchange, then the return on that stock should be the return that the London Stock Exchange gives you. Now, if you have a stock with a beta of half where it's only half is risky as the London Stock Exchange, then you should get a return halfway in between the risk-free rate and the market return. And if you have a stock, which is really risky, maybe the Rolex company, then this has a double for beta of the market, and it should offer you a much higher return to compensate for this. And so this famous equation that I mentioned earlier, this is known as the Capital Asset Pricing Model, and it won a Nobel prize a couple of decades ago. So what it says is there was one reason, and one reason only, why a company should give you a higher return than the risk-free rate. And that's because it is something which gives you systematic risk. Now again, let me just step back from the equation and let me just go through the intuition and the common sense behind it. So let's take a company with a high beta, systematic risk. Let's say it's a luxury car company. So why don't we like investing in a luxury car company? When does the luxury car company do well? When does it pay high profits? It pays high profits when the economy is doing well, but when the economy is doing well, all my other stocks are doing well already. And so I'm already rich. I'm already going on holidays. I'm already paying the rent. I don't really value the extra return from the luxury car company because I'm already doing well off in an economic upswing. What happens in a downturn. In a downturn, the rest of my portfolio is doing badly. I'm being threatened with being kicked out of my house because I can't pay my rent. I really want my stocks to pay me some dividends. But in fact, the luxury car company also does really badly in the downturn because it has high beta, it has high systematic risk. So what this stock is, is it's like negative insurance, right? It does badly when like the rest of my portfolio does badly. It does well when the rest of my portfolio does well, but I don't really need that return because I'm already rich. And therefore, because this gives me negative insurance, I'm not going to be willing to hold that luxury car company, unless it gives me a high return. So why do I demand high returns? I will only be willing to invest in the company, which gives me negative insurance if, indeed, that company gives me a high return. So that company, let's step away from finance. That company's like a fair-weather friend. Well, you know, those friends that you have, where if you invite them to a party, a barbecue party, let's say, if the weather is really good, they will come along, but you don't really need them because there's loads of other people coming along. But then when the weather's bad and you want company because you've still bought the food, that fair-weather friend is going to ditch you. And that friend is not as valuable as the loyal friend who will be at your party, regardless of the weather. And so that's why the fair-weather friend is less valuable. Similarly, the luxury car company is not valuable because of that fair-weather nature. Only does well when the economy is doing well. In contrast, let's take a company with a low beta or a negative beta. The let's take that baseball bat company, right? So that baseball bat company, when the economy's doing really well, the baseball bat company is not doing well at all because nobody needs baseball bats to go around and force repayments of loans. But you don't really care that the baseball bat company is paying you nothing because the rest of your portfolio is doing well. But where is that baseball bat company really helpful? It's helpful in the downturn when the rest of your portfolio is doing badly because the economy is so bad. That's when the baseball company comes through and therefore, it provides you with insurance. And because it provides you with insurance, then you're going to be willing to accept a low return for investing in the baseball bat company. So the higher the beta, the worth the insurance a company provides, and therefore, the higher the return you demand for investing in this. And so, this is the key to everything we've done today. This is the relationship between the risk and return. The greater the beta, the greater the sensitivity of the market, the worth the insurance, and therefore, the higher the expected return that you demand. So let me just close this off by actually showing you how to use this practically with some real numbers, and then we get to the questions. So let's take an example where we're going to use this to try to find out the expected return for a company, Vodafone. Right, so I'm going to take the same equation, but rather than the imaginative name of stock 1, the stock is Vodafone, so I'm going to put V here. Via return that Vodafone gives me above the risk-free rate, depends on the beta of Vodafone and the market risk premium. So let's see how you would calculate the elements of this equation in real life. So let me first start with beta because we spent a long time deriving it. So remember what the beta was. It's the covariance divided by the variance. And how would you calculate this? Well, what you would do is you would take data. So what I'm taking is data on Vodafone's shares, how they did in April 2021, that's when I wrote this lecture, and I'm going to compare that to the FTSE All-Share Index, that's the market. Okay, so what this tells me is on every day, what the stock price of Vodafone is and what the level of the FTSE was. But what we care about is not the price, we care about the return. And we know that return is just the change in price, right? On the 30th, Vodafone went up from 135 to 136, that was a 1% return. So just with our Excel, I can calculate the returns on Vodafone and on the FTSE All-Share on each day. And then with Excel, I can use the function, which is known as the slope function. And what that tells me is the slope. Remember beta was the slope the best fit line of these two things. This will tell me, on average, when Vodafone does well, does the market do well and vice versa. And what I come up with is this number of 0.468. So what this tells me is that on average, when the market goes up by one, then Vodafone is going to go up by 0.468. So Vodafone is not that sensitive to the market. And that makes a lot of sense for everybody needs their mobile phone. So even if the market is doing badly, people are still going to be keeping their mobile phone subscription. So this line here is relatively flat. Okay, so I've done the first thing, which is I've calculated beta. Notice there's other ways that you could do that. You might not even need to do the calculation. You could look it up. So you could look it up on Yahoo finance. So Yahoo finance here has the beta. They've got a different beta for me. They have a beta of 0.88, why, they looked at five years of data when I only looked at one month of data. So they have a slightly different number. You could also look at something like Bloomberg. What happens if you want to calculate the beta of a company which doesn't have shares because it's not public traded. Let's say you have your own business, right? You have your own restaurant business, and you want to calculate risk because you are thinking or expanding and having another restaurant chain. Now, what you could do is you could look at comparable companies, which are traded like the restaurant group, look at how their shares trade or there's a famous professor at NYU called Aswath Damodaran, and what he does is he calculates beta for each industry. So you can look at the average beta for an industry, even if the company that you are concerned about, isn't publicly traded. Okay, so lots of ways to calculate the amount of risk beta, either calculates it yourself in Excel, look it up here, or look at some comparables. The second thing we do is we want to look at the risk-free rate. Why? Because the return that we deserve by buying Vodafone, that's always the return above and beyond what you would get by buying UK government bonds. So how do we find the risky rate? Well, that is the rate for buying UK government bonds. And we can easily look this up. We can look at the Financial Times and the Financial Times tells me that the rate that you get is 0.897% per year, at least at the time in which I took this screenshot. Okay, so we've got that. We've got the current risk rate. We've got the beta, the final thing that we need to get is the risk premium on the market. How much extra return does the market give you? Because I'm going to get only 0.468 of that because my beta was not one, it was half that amount. So how much extra return is the market giving us? Well, what we can do is we can look at over the last six years, and we can find out what was the return on the overall market and what was the return on government bonds. And so this is what I've done in this table, and I've shown you my sources at the bottom. So this website here tells you the overall return that you would've got on the FTSE. You can see there were some years in which the market did really well. Others like 2020, because of the pandemic, the actual return was negative. You can compare that with government bonds and government bonds it's always positive in every year, because they're always going to give you a return. And so what we can do is for every year, we can look at the risk premium, how much extra return did the FTSE have over the market. So over the risk-free rate, which is this thing here, and sometimes the risk premium was negative, other times it was positive. So overall, what I get is a number which is 3.93%. And so now I have all of my inputs. What was the big picture? I'm trying to say, what return do you deserve by buying Vodafone, knowing that Vodafone is risky, unlike a government bond. And so, what is the answer? Well, if I was to buy government bonds, I would get the return of 0.897%, which I showed you two slides ago, given that Vodafone is riskier than government bonds. I should get more than that. Well, how much more should I get? I should get it depending on the beta. And here I'm taking the beta of 0.88, which was given by Yahoo Finance. And then I'm also taking the actual extra return on the market, which was that 3.93 that I've just shown. So again, how much extra return should I get? It depends on the riskiness. And because Vodafone is not as risky as the market, this is less than one, I'm not getting the full market risk premium of 3.93. I'm only getting 0.88 off that. And so overall what I am getting by investing in Vodafone, I should be deserving a return of 4.36% per year, not just the 0.897 I will be getting by buying government bonds. And so this takes me to my final slide because how I motivated this topic is we care not just about buying stock, but we care about making investment decisions. We care about building a factory. Maybe that would be something like buying a mobile phone factory. And so, let's take an investment, which has a simple payout. We are looking at an investment, which gives me 10 pounds next year, if the project is successful, but there's a 50% chance it's unsuccessful, and it gives me zero. That's the same example as I had at the start of the lecture with 10 pounds in my pocket. Now, what is this worth to you? Now, because there's a 50% chance of 10 pounds next year, that's five on average. But remember right at the start, I said, actually, there's a big difference between five for certain and a 50-50 split between 10 and zero because the latter is what is risky. So how much should the discount be because of that risk? Now, if that risk was completely idiosyncratic, right? We don't care about that risk because we can diversify it away. And if we can diversify away that risk, then we don't care about it. It's effectively risk-free. And so the only thing we would discount by is the risk-free rates of 0.897% because of the time value of money. So this cash flow, a 50% chance of 10, unexpected value of five is worth 4.96 to us, pretty close to five, slightly less because of the time value of money. But if that risk is systematic, the project succeeds in a boom, the project fails in a recession, then we use that beta of 0.88. We use that higher discount rate of 4.36 that we just arrived. And this gives us a lower valuation of the project. Why? Not only is it in the future and is there a discount for the time value of money, but second, there's a discount for the risk and there's a discount for the risk if the risk is systematic and it's not something that we can diversify away. Okay, so thank you very much to everybody for the attention. Let me invite (indistinct) Clare for any of the questions.(audience clapping)- So, the first couple of questions surrounded uncertainty. And is there a useful distinction to be made between risk and uncertainty?- There is. In the words of Donald Rumsfeld, right? So what you call risk is known unknowns, right? We know that these things are uncertain, but we have some idea of the probability. So let's say if you are to spin the roulette wheel, we don't know what it's going to land on, but we know that it under either red or black or green, we know what the probabilities are, uncertainty that's when there's unknown unknowns. Where we don't even know what the actual risks are. For example, then the start of 2020, we had no idea there might be a global pandemic. It's not that people sort of thought about it and said the chance is 1%, it was not even on our radar screen. So one potential limitation of my analysis is what this has shown is it's focused only on known unknowns. Things where we have some sort of idea of what the correlations are, but then the message to any practitioner is the goal is to try to find out what those unknown unknowns are and to try to quantify this. So this is why things sort of like diverse thinking, diversity of boards in terms of cognitive diversity is very useful because you have some people from outside the standard fields, they might be able to say, well, here are some other things which might be risk factors, which we should consider. And so the goal is to turn uncertainty, which we are not even considering to risk, which is still problematic, but we know how to deal with this. And hopefully, today's lectures shown how you can deal with a known unknown.- Great, thank you. And is there a difference between public and private sector risk or do the same principles apply?- Yeah, so the same principles apply because both public and private projects are ones that depend on risk. So with any project, and regardless of whether the company is a publicly-traded or privately traded, you will have some components that depend on the market. And you have some components which depend on just your individual situation. Let's take one example of a private company. Let's take football clubs. Like most football clubs are still privately traded. What is a risk that a football club faces? Well, you face the risk that your star striker gets injured. That risk is idiosyncratic, right? Whether your star striker gets injured has nothing to do with the rest of the economy. And therefore, if your investors are diversified, you don't really care about that. But a second risk is the risk of an economic downturn, and that will affect the football club, just like it will affect all of your other stocks. So a private company faces similar risks. Some are idiosyncratic. some are systematic, but you can do exact same decomposition as you've done here for public companies.- [Participant] Sure, hi, thank you so much. That's fascinating. Talking about luxury goods because obviously it's correlated to the market performance. If you're doing well, you buy more, doing less, well, then stock tanks to a debris. But luxury cars are also a store of wealth, right? So sometimes, people with a certain wealth bracket will actually use it, as I said, a store of wealth. So think of Richmore, for example, they will lean into that, and they'll buy that as a proxy of diversification. And so the idea is what timeline are we talking about the risk in the future? So we saw the pandemic, everything went down, and then something like MS for example, it's done even better than before because the assumption is it's a time-old brand and the secondary market value goes up for those goods as well. So you're like, well, I don't mind if it goes down in the market, I know it's going to come back up at a higher rate than it was before the crash for the pandemic. So I just wonder what your thought was about luxury goods as a store of wealth, and also that timeline you're considering risk.- Well, that's a really good question. And I think here, what I should do is distinguish between consumption goods and investment goods. So if you're buying a luxury good for pure consumption purposes, so maybe a better example might have been that the cruise or the luxury holiday, that's something which is definitely going to be cyclical with the market. But if it's something which has an investment purpose, you might think art that is a luxury in some cases, but it's also an investment, or gold, or MS, then that's something where actually the beta might be smaller. So if indeed you have a company where you are selling MS products, some of that company might be... Some of the products might be bought for consumption purposes and some of investment purposes. And that investment demand will actually mitigate the cyclicality of the consumption demand. So out of the spectrum of luxury goods, if they are goods, which are used for investment purposes, as well as consumption purposes, that might indeed reduce their cyclicality. Thanks so much for that.- [Participant] Thank you for an interesting lecture. Both the beta and market value is, of course, based on historic data. What if you don't know the future beta, which you obviously don't, and future market return.- Yeah, this is, I think, the $64,000 question. So with finance, there's part art and part science. So the science is given some data like we know how to calculate these things. I've shown you those calculations, but the big question is, right, how do we know what the beta is going forward? So yes, maybe in the past, the beta of Vodafone was 0.88, maybe in the future, it could be high, or it could be lower because we might think that telecoms are going to be more or less cyclical. And so that's where some of the art will be. It could be that a financial analyst looks at the data and says, well, I actually think that going forward, it's going to be even higher. And somebody else will think it's going to be lower. So this is why different financial analysts will look at the same data, but somebody might rate Vodafone a buy, and the other, a sell. Let's go back to the football analogy. When you buy a striker, you know how many goals he's scored over the past three seasons, but some people might think he's going to get even better and do really well in the future. And others will say, no, I think he's past it. And so this is why there might be some still some disagreements. So part of the art of investing is to try to use past data, certainly as a guide, but try to think about, well, what other factors might have changed to mean that the future might be different from the past. And that's why we indeed get quite a lot of trade and a lot of differences of opinion, which I think makes finance interesting. It's not just the mechanical movement from Excel spreadsheets to decisions as I've highlighted here.- [Participant] Thank you. Would you put reputational risk under idiosyncratic or systematic risk?- Yeah, thank you. This is interesting because you might think that some things which are reputational risk are completely random. So whether you have a rogue trader or a London whale, that's something which is going to be occurring in any time. Or you might think it's positively systematic where when the market is booming, you want to get an even greater share of that booming market, so you might think it's positive. Or there might be arguments for it being negative, which is when the market is doing really badly. That's when we need to steal and steal some extra profits because things are doing poorly. So overall, I think there's different arguments for why it might be in positive, negative, or zero. The data seems to not suggest a clear way because there's just as many tendencies to do something bad in upswings as they all end downturn. So this is why I think it's mainly going to be something which idiosyncratic.- Great. Well, Professor Edmans, thank you so much for a wonderful lecture. I'd like to encourage you all to attend the next lecture in this series. How to Value a Stock, and that's on Tuesday the 17th of May. So we've got a little time in between, but please do keep it in mind, keep it in your calendars and join us then. And I'd like to take this opportunity to thank Professor Edmans. Please do join me.(audience clapping)- Thank you so much.