Archive for April 5th, 2009
The starting point for the Standard Model is risk aversion and the tradeoff between risk and return. Most market participants are risk averse, and savers have good reasons to be especially risk averse. In the aggregate, the people who supply savings to the markets are more risk averse than the would-be users of other people’s savings. This mismatch has been a prime mover for financial innovation and is a major part of the raison d’etre for financial intermediation. Intermediaries work to remedy the mismatch and earn profits when they succeed.
Savers put their money in bank accounts, and they also buy bonds and common stocks. They hold a mix of assets, and they vary the mix of assets according to how optimistic or pessimistic they feel about future economic conditions, according to how much risk they can afford to take, and according to how old they are. For them to buy a risky security, they have to believe its future returns will be high enough to compensate them for the risk they are taking.
Finance experts have known those points for centuries. The new discovery came in 1952, and it gives a way of calibrating how risky a security is. The discoverer, Harry Markowitz, noticed that professional portfolio managers do not invest 100 percent of a portfolio in the security they think will go up the most. Instead, they invest in many different securities, diversifying the holdings among a wide range of different securities.
The breakthrough was that Markowitz computed a measure that nobody had computed before. He measured the amount of risk reduction this strategy of diversifying the portfolio achieved. He did this with a mathematical technique that is quite simple and easy to illustrate.
To see Markowitz’s method, consider a risky security. In this example we use the common stock of an oil company. This company operates in a country with the necessary institutional infrastructure, so the shareholders will get the benefit if the company does well. The company has oil wells, so if the price of oil rises, its revenues and profits will rise. The company will pay some of the higher profits to the shareholders, so if the price of oil goes up, the stock price will rise. If the price of oil goes down, the stock price will fall, but not by very much. It will fall only a small amount because the company will survive and will probably continue to pay dividends, and the oil price might rise during some later time period.
To continue with the example, let us suppose the oil stock is selling at $20 a share at the beginning, before the oil price goes up or down. Let us suppose that if the oil price rises, one year later the stock will have gone up to $28 a share; and if the oil price falls, one year later the stock will have fallen to $18 a share. Assume these price fluctuations include the cash dividends the oil company pays, so, for example, if the company paid a dividend of $0.50 during the year, the ending stock prices would have been $27.50 and $17.50.
This oil stock is a risky security because its price can go down and also because the range of outcomes is wide for such a short time horizon as one year. A risk-averse investor would not buy this stock, or would buy only a very small amount, so that the stock’s fluctuations would not destabilize the entire portfolio.
Now consider another risky security. This second one is the common stock of an airline. This particular airline is more stable than most, and is not facing much risk of bankruptcy, but its operating results are very vulnerable to fluctuations in the price of jet fuel. Its profits rise and fall with the price of oil. If the price of oil falls, jet fuel will be less expensive, and the airline will do well. If the price of oil rises, the airline will not do as well. Suppose that at the beginning, before the price of oil falls or rises, the airline stock price is $40. If the price of oil falls, the airline stock price will rise to $56 after one year, and if the price of oil rises, the airline stock price will fall to $36 after one year. Again, these ending prices include dividends the airline pays to its shareholders. For example, if the dividend per share were $1, the ending stock prices would have been $55 and $35.
This second security is also quite risky, and a risk-averse investor would not buy it. It is exactly as risky as the oil stock. It can deliver a return of 40 percent or a loss of 10 percent.
Markowitz measured the risk of each security by computing a statistical measure of dispersion called the standard deviation. This was a big advance, because earlier writers had not used such a precise, easy-to-compute indicator of risk.
The real breakthrough that Markowitz made, however, was to point out that these securities are much less risky if they are combined in a portfolio. He developed a method of computing how much risk the diversified portfolio has, and contrasted the risk of the portfolio with the risk of each individual security in the portfolio.
To see the effect that diversification has on reducing the risk of owning securities, consider a portfolio that has shares of the oil company stock and the airline stock in it, and no other securities.
The portfolio is
½ invested in shares of the oil company; and
½ invested in shares of the airline.
Each of these stocks is quite risky by itself, but when they are in this simple portfolio, they are much less risky. In fact, in this example, the portfolio’s value after one year comes out the same, whether the price of oil rises or falls. To verify this, let us compute the value of the portfolio after one year. Suppose the investor began with $200,000 and at the beginning put $100,000 into each of the two common stocks. The investor would buy 5,000 shares of the oil company stock and 2,500 shares of the airline stock. So the portfolio would consist of
5,000 shares of oil company stock; and
2,500 shares of airline stock.
One year later the portfolio would be worth $230,000, regardless of whether the price of oil rose or fell. The value of each individual stock in the portfolio would have risen or fallen, but the total value of the portfolio would come out to be worth $230,000 in both cases.
If the price of oil rose, the oil stock would have risen to $28, so that portion of the portfolio would be worth $140,000, including the dividend the oil stock paid during the year. The airline stock would have fallen to $36, so that portion of the portfolio would be worth $90,000, including the dividend the airline stock paid during the year. The total value of the two holdings would be $230,000.
If the price of oil fell, the oil stock would be worth $90,000, and the airline stock would be worth $140,000. Both figures include the dividends the stocks paid during the year. As before, the total value of the two holdings would be $230,000.
In this idealized example, the strategy of diversifying the portfolio works so well because the two stocks respond in exactly opposite ways to the oil price. Their returns are perfectly negatively correlated.
Several caveats are in order. First, the portfolio is still vulnerable to other macroeconomic events, so it is not completely risk-free. Second, finding two stocks whose returns are perfectly negatively correlated is difficult in real life.
This first breakthrough had many implications and had a profound effect on financial management. It explained why portfolio investors were willing to buy risky common stocks, despite being quite averse to risk. It explained why some risks did not scare them away and why other risks, which did not look any greater by themselves, were red flags.
Corporate treasurers gradually learned how to design securities so that portfolio investors would consider the securities attractive. Treasurers revised their view of shareholders. In the centuries before 1950, the dominant view was that shareholders were like business partners. They understood the characteristics of the businesses they invested in and tolerated the ups and downs of those businesses. If an entire industry sector had a slump because of overcapacity, shareholders understood the situation and rode through the slump, looking forward to better times. They did not blame the managers of the companies and did not sell the shares.
After Markowitz, corporate treasurers came to understand that shareholders are not business partners. They buy common stocks because they expect the shares will deliver returns and offset the risks of other shares in their portfolios. They hold the shares as long as the shares perform those roles in the investors’ portfolios. When the shares cease to perform, or when shares that can perform better become available, the investors sell the shares. They do not feel any sense of shared destiny with the companies or loyalty to the managers of the companies.
There were many implications, and soon specific techniques appeared for calculating whether a security would be attractive to buyers. Portfolio managers used these techniques, and corporate treasurers soon had to master the techniques and apply them to tailor the securities they sought to issue. The ones who did this successfully got more capital for their companies, and they got it more cheaply. The ones who did not adopt the new view were still able to get capital for their companies, but they got less of it, and their companies had to pay more for it.
