So we've discussed the flow of funds, price discovery, and the allocation of scarce resources. Now let's take a look at this important function of risk sharing, Risk Diversification. Let's start with an example from the commodity market, where Kellogg's needs to secure its raw materials, from farmers say in the midwest. Kellogg's could directly engage with individual farmers. But by instead bringing all supply and demand for corn together in a single market, Kellogg's and therefore the market, would be able to diminish the risk of default by a single farmer, with whom it might decide to contract. So while the individual farmer might still fail, the market then kind of covers the overall risk of Kellogg's not having a supply of corn. So commodity markets provide corporations like Kellogg's with the opportunity to secure supply with less risk of specific harvest outcomes. Very important for agricultural commodities. But risk management benefits of markets extend well beyond minimizing counter party risk of the nature we just described for the commodity market. By spreading investments over multiple investment opportunities, there is a raft of benefits. First and foremost, investors in those assets will be able to reduce their overall risk of investment. By reducing the risk, they will not require as large of a risk premium as before. So it reduces the required risk premium for the investors. That in turn, will make it cheaper for corporations to attract financing. Not having to pay as large a risk premium. And by being able to get cheaper financing, corporations will then be able to improve the net present value of investment projects and bring more of those investment projects to market. So economic growth depends crucially on innovation. So let's start at the beginning, biotechnology, e-commerce, advanced manufacturing are all promising to bring innovation to the market to lead to the next phase of economic growth. But we already know that many of those ventures will in fact, fail. So venture capital markets pool the risk of those failures. So rather than invest in a single biotechnology firm, a typical venture capital fund, a venture capital market would invest in a thousand biotechnology firms. And a small number of them will survive and handsomely deliver returns. Survivors of debt process will do, eventually an initial public offering. Once they are investment ready. But even when they are investment ready, they're typically still high growth, high risk investment opportunities for share investors. So what the investors will then do is to include some of these prospects in a properly diversified shared portfolio. There by making it feasible for them to provide financing to these high risk, high growth innovative firms. So just to illustrate how that works, and maybe hear an example for somewhat more mature firms than those ventures. Consider investing in a portfolio where you allocate a proportion WK to Kellogg's shares and a proportion 100% minus WK in Kraft shares. So those weights could be 50/50- .5/.5 for investments in Kellogg's, and it's competitor, Kraft. So the table here tells you that the standard deviation of returns, the typical variation in a particular year, per annum of returns on shares in Kellogg's, is about 25%. Kraft is less risky and has a typical variation of returns of only about 20%. So, if investors expect the same level of return for investing in Kellogg's shares as they expect a return for investing in Kraft firms, then they would opt for an investment in Kraft shares. Given that Kraft has got less risk attached to it. For Kellogg's investments, they would require a higher risk premium. But now consider the opportunity for this investor to not make a either fully invest in Kellogg's shares or fully invest in Kraft shares but actually splits the portfolio, say in 50/50. You would expect that then the risk of the portfolio's returns, half invested in Kellogg's shares, half invested in Kraft's shares would be somewhere between 20 and 25%. Obviously, not as risky as fully invested in Kellogg's shares, 25%, or as below the level of risk when the investor is fully invested in Kraft shares, which would be 20%. We can easily compute the risk, the standard deviation of that portfolio of Kraft and Kellogg's shares. According to the formula that you see there where the standard deviation of the portfolio invested in the two shares is the square root of the sum of the variances of the returns in Kraft and Kellogg's. And a term at the end, the covariance of the returns between Kraft and Kellogg's. And the crucial variable in the formula is the rho. The correlation between Kellogg’s and Kraft returns. That value could be perfectly correlated where whatever Kraft shares do Kellogg’s shares replicate. So the movement in share prices would be perfectly matched. Or, they would be totally unrelated whenever the Kellogg's share price goes up, the Kraft share price doesn't move at all. Or, they could exactly do the opposite. Kraft's fortunes are Kellogg's misfortunes. There's a variety of possible values of that correlation, rho. And that turns out to have a crucial impact on the overall portfolio risk. So to illustrate that graphically, consider this graph which provides three lines for different strengths of correlation. How closely the returns on Kraft match those returns of Kellogg's of 0.1, very weak correlation. They're almost unrelated to each other. To a correlation of 0.9, where they almost perfectly replicate each other, where they almost do exactly the same in turns of returns. So what you see in the graph on the horizontal axis is the portfolio weight invested in Kellogg's shares. If you go to Kellogg's portfolio weight of one, you see that the portfolio would still be fully invested in Kellogg's shares only because one minus that weight would be zero invested Kraft shares. If the portfolio weight in Kellogg's is one, you can see that the risk of that portfolio would obviously be the risk of Kellogg's shares of 25%. If we put the weight of Kellogg's shares to zero, which would mean that the weight in the portfolio of Kraft's shares would be one, we see that that risk is identical to the Kraft risk of 20%. But now consider the purple line where correlation is .1. So the shares returns in Kraft and Kellogg’s are almost unrelated to one another. We would call that independent from one another. You can see that the formula tells you that the portfolio risk, at about a weight of 0.4, minimizes at something slightly over 16%. How is that possible? How is it possible that by combining two shares in a small portfolio. Two shares Kellogg's and Kraft delivers a portfolio risk of about 16%, which is well below the minimum portfolio risk of an individual share investment, which would have been 20% for investing in Kraft shares. That is the power of diversification. Whenever the shares are less than perfectly correlated, it is possible for an investor to reduce the risk of the portfolio below its individual components. Now if we can do that for two assets combining our investments in Kraft and Kellogg's, we can do that for many assets. We could build a portfolio combining the 500 companies that are components of the Standard & Poor’s 500 on the New York stock exchange. Ultimately what we will get is a much reduced level of portfolio risk below smaller portfolios. What we will get will be what we ultimately label as the market risk. The risk which is the minimum level of combining all the shares listed on, say, the New York Stock Exchange in a single portfolio. And in fact in turns out, you actually don't have to combine 500 different companies in your portfolio. The risk drops down very quickly and the marginal improvements in risk reduction become smaller and smaller after about 50 different companies combined in a portfolio. That is the power of the New York Stock Exchange, the market for equity. And we can have a similar argument for debt markets, for commodity markets, and even for currency markets. So it's great we can reduce risk to much more acceptable levels for investors. Who therefore would require much lower risk premiums, reducing the cost of capital for firms. But it also gives us a pretty powerful argument why it pays to have an exchange that lists more than just a single company. So for example, why we do not see a Kellogg's Equity Exhange? It's simply would not be an optimal market because it would not provide investors in that market with the risk diversification benefits that a much more comprehensive market provides. But if that is the case, you could push the argument and say that, why just stop at a market of just equity? Why not also trade bonds on the New York Stock Exchange? Currencies or commodities? Surely, by including all these other assets that are very likely to offer correlations with equity that are less than perfect. Maybe we can get to our even lower levels of risk. Mutual funds are an example where that actually occurs. Where investors combine different asset classes, yet we do not see that translated as just a single market platform where you trade everything. So maybe, just maybe, there are still some specialization benefits. For a bond market to trade bonds, for an equity market to trade equity, and for a commodity market to focus on raw materials. Or maybe there are a set of regulation imperatives. It is really difficult to come up with a regular trade regime that covers both equity and bonds. Or maybe it is diminishing returns from diversification. So by combining more diverse assets into a single exchange, we're not actually making that much headway in further reducing the risk. Or maybe it is even market specific news events that need to be released to the public in a regular fashion. Maybe that is best done by a market that just focus on ownership and corporations or bonds or commodities. There might be a variety of reasons that we still see markets, specialization is a particular asset class.
