In describing a simplistic example of portfolio theory, some economists – such as Burton Malkiel in A Random Walk Down Wall Street – will refer to an example of a theoretical simple island economy. In this economy there are two companies, a resort hotel, and an umbrella manufacturer. Each business generates positive cash flows over the long run, but returns for each are dependent on the weather over the short run.[1]

Island Economies 1.jpg

Where’s the risk?

On the island, it rains 50% of the time. The resort has positive returns when the weather is nice, and negative returns when it is raining. The positive returns are greater than the negative returns. The umbrella manufacturer has the opposite profile.  The argument goes on that the portfolio consisting of both the umbrella manufacturer and the resort hotel company is less risky than simply holding only the resort hotel (or only the umbrella manufacturer). This, it is argued, is because returns are generally predictable and certainly positive in every period, and there is therefore very little uncertainty. There is also very little portfolio volatility – or risk.

The implication in this two‐security economy is that the hotel company is worth less without the umbrella company in existence. In other words, if the hotel company were the only security in the economy, the future cash flows for the investor would be more volatile and we would need higher expected returns in order to justify the risk. With the addition of the umbrella manufacturing company to the opportunity set (a negatively correlated asset to the hotel company), the idiosyncratic risk can be diversified away. Thus, again by implication, an investor should therefore be willing to pay more for the resort hotel company in a portfolio that includes the umbrella manufacturer than if it were the only investment opportunity on the island.

Another way to put this is this: We theoretically will pay more for an asset if we are able to hedge away the risks that are specific to an individual firm – the unsystematic risk. The systematic risk, however, remains. Systematic risk is risk that affects the whole economy. In this example, if the island fell back into the ocean, that would be bad for both companies – bad for the whole system.  Systematic risk is not diversifiable.

In the next level of this hypothetical analysis, economists will assume that there are additional investment opportunities in this island economy, or perhaps assume that the island economy is one of several less than perfectly correlated investable island economies around the world.

The next step is to deduce that there are enough investment opportunities that the portfolio of all market participants in aggregate (or more appropriately, the marginal investor) is diversified.  In other words, from this perspective, there is no unsystematic risk in portfolios. Thus, if an investor adds the resort hotel company to his already diversified portfolio, he isn’t worried about the risk of bad weather on this particular island (because he might already own the umbrella manufacturer, or a bunch of other resort hotels on other islands with less than perfectly correlated weather patterns). This marginal investor, therefore, will pay up for the resort hotel company as if there were no firm‐specific risk.

This leads to the uncomfortable and counterintuitive conclusion that people should not care about risks that are specific to a particular firm. Theoretically, according to some (most?) academics, the only risks we should care about are systematic risks. And we should only be concerned with how sensitive an individual stock is to “the market”. In other words, the only thing we should care about is beta – and that is all that matters when determining the risk of a security.

Hence the initial rise in popularity of the Capital Asset Pricing Model, or CAPM.[2] 

In future pieces, we will address whether or not there actually is (or can be) idiosyncratic risk in individual securities, and how concentrated a portfolio might need to be to exploit them.   Meanwhile, however, another somewhat counterintuitive conclusion we can consider is that portfolios may be more “risky” if we look at them more often. This may be even more interesting, and relevant whether you believe alpha exists or not.

Island Economies 2.png

Back in the simple island economy example, let’s assume that it rains half the time and is sunny half the time. Over the short run, it is very possible that either company drastically outperforms the other. It is not impossible, for example, to have four sunny periods in a row (a 6.25% chance). However, over the long run, whether we buy only the resort hotel company, only the umbrella manufacturer, or a portfolio of both – our returns will be exactly the same. The ex-post mathematics of portfolio theory will say that we took more risk if we only held one of the securities – but did we? 

Again, this of course gets us back to the “is risk volatility vs. a benchmark,” or is risk “the potential loss of capital” debate – but as hopefully is becoming clearer, the answer might become moot over a time horizon with long enough periodicity.

And the answer might not matter as much as we think, because when we throw in the whole loss-aversion phenomenon of Kahneman and Tversky, the importance of semantics dwindles.  When the pain from intermittent drawdowns can exceed the pleasure of intermittent gains, even if those gains are greater than the losses cumulatively, it hurts.  It hurts whether you are suffering the move that “creates higher expected returns” and it hurts if your vol increases vs. a benchmark, and no matter where things end up, that journey – emotionally – feels (and maybe is) more important than the destination.   

So, based on this, there is at least one conclusion we’re happy to draw: It probably isn’t a great idea to keep staring at your portfolio.

[1] To keep the example uncomplicated, we have to make a few assumptions here. These include the inability to maintain inventories of umbrellas, the ability of either company to grow in perpetuity, and a few others.

[2] There have of course been many arguments against the single factor CAPM of Sharpe (1964), Lintner (1965), and Black (1972). Most notably Fama French (1993) – in which they show that the addition of a value factor (HML) and a size factor (SMB) to the market factor in a multivariate regression render the explanatory power of the market beta worthless (“Beta is Dead”). There is, however, conflicting evidence (and theory) regarding the relative “riskiness” of small stocks or of value stocks. In other words, we haven’t found terribly strong evidence that HML or SMB (or many of the other factors in the zoo) are certainly state variables of a hedging concern in the spirit of Merton’s (1973) Intertemporal CAPM.



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