# 7.4: Risk pooling and diversification


## Silicon Valley: from angel investors to public corporation

Risky firms frequently succeed in attracting investment through the capital market in the modern economy. A typical start-up firm in the modern economy originates in the form of an idea. The developers of Uber got the idea of simplifying and streamlining the ride sharing business (sometimes called the taxi business). In its simplest form the inventors developed an App that would link users to drivers. The developers of Airbnb got the idea that spare accommodations in individual homes could be used to satisfy the needs of travellers. The founders developed an efficient means of putting potential renters/guests in communication with suppliers of rooms, houses and condominiums. WeWork was founded on the belief that workers and small corporations, particularly those in the technology sector, have immediate and changing space needs. The result is that WeWork provides flexible work space on a 'just in time' basis, frequently on a shared overhead basis. Each of these corporations acts as an intermediary, and sells intermediation services.

Typically the initial funding for new ideas comes from a couple of founding partners who develop a model or prototype of their software or their business. Following trials, the founders may approach potential investors for 'small' amounts that will fund expansion. Such investors are frequently 'angel' investors because they are a source of funding that makes the difference between expansion and death for the venture in question. If the venture shows promise the founders seek 'round A' funding, and this funding may come from venture capitalists who specialize in new ventures. Further evidence of possible success may result in 'round B' funding, and this frequently amounts to hundreds of millions of dollars.

Venture funds are managed by partners, or capitalists, with reputations for being better able than most to predict which start-ups will ultimately see profitability. These venture capitalists invest both their own funds and the funds of individuals who entrust their accumulated savings to the investing partnership.

But extremely high risk is associated with most start-ups. Funding frequently takes place in an environment where the venture has no revenue; merely a product in the course of development. Winners in the new economy are recognized and celebrated. Bill Gates' Microsoft, Jeff Bezos' Amazon, Steve Jobs Apple, and Larry Page and Sergey Brin's Google are corporate giants with valuations approach one trillion dollars. But Elizabeth Holmes' Theranos, once with an implicit valuation of several billion dollars has expired. Theranos hired several hundred employees with the aim of developing blood tests for scores of purposes using just a pin-prick of blood. But it was a failure, despite attracting hundreds of millions of dollars in investment. In the year 2019 Canada had dozens of cannabis-based firms listed on the Canadian Securities Exchange. None of these is earning a profit in 2020, some have negligible earnings, yet several have a value in excess of one billion dollars. It is highly improbable that all will survive.

Capital market: a set of financial institutions that funnels financing from investors into bonds and stocks.

Venture capital: investment in a business venture, where the ultimate outcome is highly unpredictable.

How can we reconcile the fact that, while these firms carry extraordinary uncertainty, investors are still willing to part with large sums of money to fund development? And the investors are not only billionaires with a good sense of the marketplace; private individuals who save for their retirement also invest in risky firms on the advice of their financial manager. Let us explore how and why.

## Dealing with risk

Most (sensible) investors hold a portfolio of investments, which is a combination of different stocks and bonds. By investing in different stocks and bonds rather than concentrating in one single investment or type of investment, an individual diversifies her portfolio, which is to say she engages in risk pooling. Venture capital partnerships act in the same way. They recognize that their investments in start-ups will yield both complete failures and some roaring successes; the variation in their outcomes will exceed the variation in the outcomes of an investor who invests in 'mature' corporations.

Portfolio: a combination of assets that is designed to secure an income from investing and to reduce risk.

Risk pooling: Combining individual risks in such a way that the aggregate risk is reduced.

A rigorous theory underlies this "don't put all of your eggs in the one basket" philosophy. The essentials of diversification or pooling are illustrated in the example given in Table 7.2 below.1 There are two risky stocks here: Natural Gas (NG) and technology (Tech). Each stock is priced at $100, and over time it is observed that each yields a$10 return in good times and $0 in bad times. The investor has$200 to invest, and each sector independently has a 50% probability (p=0.5) of good or bad times. This means that each stock should yield a $5 return on average: half of all outcomes will yield$10 and half will yield zero. The challenge here is to develop an investment strategy that minimizes the risk for the investor.

At this point we need a specific working definition of risk. We define it in terms of how much variation a stock might experience in its returns from year to year. Each of NG and Tech have returns of either $0 or$10, with equal probability. But what if the Tech returns were either or with equal probability; or or with equal probability? In each of these alternative scenarios the average outcome remains the same: A positive average return of $5. If the returns profile to NG remains unchanged we would say that Tech is a riskier stock (than NG) if its returns were defined by one of the alternatives here. Note that the average return is unchanged, and we are defining risk in terms of the greater spread in the possible returns around an unchanged average. The key to minimizing risk in the investor's portfolio lies in exploring how the variation in returns can be minimized by pooling risks. Risk measurement: A higher degree of risk is associated with increased variation in the possible returns around an unchanged mean return. Table 7.2 Investment strategies with risky assets  Strategy Expected returns with probabilities$200 in NG 220 (p=0.5) 200 (p=0.5) $200 in Tech 220 (p=0.5) 200 (p=0.5)$100 in each 220 (p=0.25) 210 (p=0.5) 200 (p=0.25)

The outcomes from three different investment strategies are illustrated in Table 7.2. By investing all of her $200 in either NG or Tech, she will obtain$220 half of the time and $200 half of the time, as indicated in the first two outcome rows. But by diversifying through buying one of each stock, as illustrated in the final row, she reduces the variability of her portfolio. To see why note that, since the performance of each stock is independent, there is now only a one chance in four that both stocks do well, and therefore there is a 25 percent probability of earning$220. By the same reasoning, there is a 25 percent probability of earning $200. But there is a 50 percent chance that one stock will perform well and the other poorly. When that happens, she gets a return of$210. In contrast to the outcomes defined in rows 1 and 2, the diversification strategy in row 3 yields fewer extreme potential outcomes and more potential outcomes that lie closer to the mean outcome.

Diversification reduces the total risk of a portfolio by pooling risks across several different assets whose individual returns behave independently.

Further diversification could reduce the variation in possible returns even further. To see this, imagine that, rather than having a choice between investing in one or two stocks, we could invest in four different stocks with the same returns profile as the two given in the table above. In such a case, the likelihood of getting extreme returns would be even lower than when investing in two stocks. This is because, if the returns to each stock are independent of the returns on the remaining stocks, it becomes increasingly improbable that all, or almost all, of the stocks will experience favorable (or unfavorable) returns in the same year. Now, imagine that we had 8 stocks, or 16, or 32, or 64, etc. The "magic" of diversification is that the same average return can be attained, yet variability can be reduced. If it can be reduced sufficiently by adding ever more stocks to the portfolio, then even a highly risk-averse individual can build a portfolio that is compatible with buying into risky firms.

We can conclude from this simple example that there need be no surprise over the fact that risk-averse individuals are willing, at the same time, to pay a high home-insurance premium to avoid risk, and simultaneously invest in risky ventures.

Application Box 7.2 The value of a financial advisor

The modern economy has thousands of highly-trained financial advisors. The successful ones earn huge salaries. But there is a puzzle: Why do such advisors exist? Can they predict the behaviour of the market any better than an uninformed advisor? Two insights help us answer the question.

First, Burton Malkiel wrote a best seller called A Random Walk down Wall Street. He provided ample evidence that a portfolio chosen on the basis of a monkey throwing darts at a list of stocks would do just as well as the average portfolio constructed by your friendly financial advisor.

Second, there are costs of transacting: An investor who builds a portfolio must devote time to the undertaking, and incur the associated financial trading cost. In recognizing this, investors may choose to invest in what they call mutual funds – a diversified collection of stocks – or may choose to employ a financial advisor who will essentially perform the same task of building a diversified portfolio. But, on average, financial advisors cannot beat the market, even though many individual investors would like to believe otherwise.

At this point we may reasonably ask why individuals choose to invest any of their funds in a "safe" asset – perhaps cash or Canadian Government bonds. After all, if their return to bonds is lower on average than the return to stocks, and they can diversify away much of the risk associated with stocks, why not get the higher average returns associated with stocks and put little or nothing in the safer asset? The reason is that it is impossible to fully diversify. When a recession hits, for example, the whole stock market may take a dive, because profits fall across the whole economy. On account of this possibility, we cannot ever arrive at a portfolio where the returns to the different stocks are completely independent. As a consequence, the rational investor will decide to put some funds in bonds in order to reduce this systematic risk component that is associated with the whole market. This is not a completely risk-free strategy because such assets can depreciate in value with inflation.

To see how the whole market can change dramatically students can go to any publicly accessible financial data site – such as Yahoo Finance and attempt to plot the TSX for the period 2005 – present, or the NASDAQ index from the mid-nineties to the present. The year 2020 is a particularly appropriate year to examine. In that year the coronavirus pandemic struck with disastrous impacts on stock markets worldwide. Initially almost all stocks declined in value. But within a matter of days investors realized that some firms would perform better in this particular downturn: those specializing in home delivery and those specializing in home exercise equipment for example. The stock valuations of firms such as Shopify, Amazon and Peloton shot up, while the valuations of traditional auto makers languished.

## Efficiency and Allocation

We have now come full circle. We started this chapter by describing the key role in economic development and growth played by firms and capital markets. Capital markets channel the funds of individual investors to risk-taking firms. Such firms—whether they are Dutch spice importers in the seventeenth century, the Hudson's Bay Company in nineteenth-century Canada, communications corporations such as Airbnb or Expedia, or some high tech start-ups in Silicon Valley—are engines of growth and play a pivotal role in an economy's development. Capital markets are what make it possible for these firms to attract the savings of risk-averse individuals. By enabling individuals to diversify their portfolios, capital markets form the link between individuals and firms.

But capital markets fulfill another function, or at least they frequently do. They are a means of funnelling financial capital into ventures that appear to have a future return. It is not possible for each individual saver to perform the research necessary on a series of existing or new corporations, or 'ventures', in order to be able to invest in a knowledgeable manner. That is one reason we have financial intermediaries. When individuals deposit their savings with a bank, or with a financial manager, these individuals are anticipating that their savings will be protected and that a return will be forthcoming. A bank may promise a return of a fixed percent if an individual deposits her money in a guaranteed investment certificate. Alternatively, if the individual saver wishes to take on some risk she can place her savings with her financial manager, an equity fund, or even a venture capitalist. These intermediaries are better at assessing risks and returns than most private individuals. This in turn means that the return to the individual from entrusting their savings to one of them should on average exceed the returns that the individual would earn herself by following some investment strategy.

If the professional investor indeed invests in more profitable ventures than an amateur investor, then that intermediary is performing an efficiency function for the whole economy: He does better at directing the economy's savings to where it is more productive on a macro level. This in turn means that the economy should have a higher growth rate than if savings are allocated towards ventures that are less likely to grow and satisfy a need or a demand in the economy.

Consider the example of Airbnb that we cited earlier. The original intent of this corporation was to provide the owners of unused (home) space the opportunity to earn a return on that space. Airbnb was thus a transformative mechanism, in that it enabled unused resources to be more fully utilized - by linking potential buyers who were willing to pay for the product, with potential sellers who were willing to supply at a price buyers were willing to pay. Unused resources became utilized, created a surplus and contributed to growth in the macro economy.

While financial intermediaries perform a valuable service to both individual savers, and the economy at large, we should not expect that intermediaries always make optimal decisions. However, these analysts have research resources available, and thus they have a comparative advantage over individuals for whom investing is a part-time activity. By being more efficient than individuals, financial intermediaries perform their broader economic allocation function, even if that is an unintended by-product of their professional activity.

At times professional investors suffer from what has been called 'irrational exuberance'. Crowd psychology creeps into the investment world from time to time, sometimes with devastating consequences. In the late 1990s tech stocks were all the rage and the stock market that specialized in trading such stocks saw the capital value of these stocks rise to stratospheric heights. The NASDAQ index stood at about 5,000 in March 2,000 but crashed to 1,300 by January of 2003. The run-up in NASDAQ valuations in the late nineties turned out to be a bubble.

This page titled 7.4: Risk pooling and diversification is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Douglas Curtis and Ian Irvine (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.