Links For Further Reading

Select links and excerpts on Idiosyncratic Risk

The Capital Asset Pricing Model: Risk, Reward, and Reasons (Capital Gains)
Some excerpts/teases:
The temptation is to think that if risk and reward are correlated—if you can reach for higher returns by selling your investment-grade bonds and replacing them with stocks, or selling your large-cap US stocks and replacing those with wilder emerging market stocks—that all forms of risk-taking are rewarded with higher returns. But this isn’t true: the expected return of a single stock of average volatility is the same as the expected return of the market, but the volatility of one stock, compared to a diversified portfolio, is much higher. And thanks to the relentless math of “volatility drag,” i.e. the observation that you don’t offset a -50% loss until you’ve made a +100% return, the expected overall outcome from this particular form of risk-taking is negative.And there are other forms of unfavorable risk/reward tradeoffs: paying higher fees for exposure to the same asset class, for example, is a straightforward cut to returns with no attendant reduction in risk. In the general risk/reward tradeoff, there are some extreme cases where things don’t work as planned: the longer-term a bond is, the more it’s a bet on interest rates, and the more it’s excess return is compensation for taking interest rate risk. But 30-year bonds don’t get returns quite commensurate with their risk—because when bond portfolio managers want to make a big bet on rates, that’s what they have to bet on.
How can we square these observations with the fact that many investors have achieved great success through concentrated bets on a handful of positions? One obvious answer is that some of them are lucky; “lottery ticket” is an accurate pejorative term for assets and strategies whose risk isn’t commensurate with reward, but lottery winners do exist.However, there’s a subtler answer…
There are many mediocre tradeoffs between risk and reward, where you can get the same mix of them in different amounts. And there are some bad tradeoffs available, with incremental-reward-free risk. To get a good tradeoff, you need a good reason to expect it: some justified belief that there’s a particular asset that’s mispriced, and a good meta reason to think that nobody else has considered it. In a competitive market, you need not just a theory about the asset in question, but at least some kind of theory of why your competitors haven’t spotted it. Yes, “I’m a better investor than they are” is a theory—but do any of your competitors pick stocks despite consciously thinking they’re bad at it? Especially in an environment where cheap index funds are available, you should assume that the average market participant is about as self-confident as you are. And one fun implication of this is that the best returns accrue to people who think they’re less skilled than the average stock picker, but skilled enough that they shouldn’t leave the whole process up to Standard & Poors.Which is not to say that investing by picking a small set of smallish, high-variance companies, watching them like a hawk, and enjoying long-term outperformance with some painful dips is a bad trade. It can be a very rewarding hobby! But the opportunity cost is defined by the average performance of index investing. So stock picking ends up being like many other hobbies: it takes time and effort, and if you’re very good at it and somewhat lucky, you might break even.
A final example comes from portfolio theory in general.
Portfolio theory shows us that if we have 2 assets that are only loosely or perhaps negatively correlated, a portfolio comprising a mix of both assets can have a better risk/reward than either of the components. In You Don’t See The Whole Picture, I give a simple math example to demonstrate this principle.
This principle has a deep implication — it means you don’t get paid for taking diversifiable risks. If I own a sunglasses company, I am the most “efficient bidder” for an umbrella company because I can diversify my weather risk. If markets are liquid, transparent, and the world transmits information cheaply then I should only expect to get paid for risks that are systematic, not idiosyncratic. Idiosyncratic risks are the types that can be diversified by being held by a party who owns the opposite type of risk (like the sunglasses/umbrella example).
A real-world example of this is the vol premium in oil puts when Pemex conducts its annual “Hacienda” hedge. Pemex, Mexico’s national oil company, hedges its forward production by buying puts and put spreads on oil futures. Typically this increases the value of the puts, enticing risk capital and arbitrageurs to sell the puts at a price that they believe exceeds their replication value.
However, I remember a year when Delta Airlines sold them the puts at a relatively fair price. This was a win for both Pemex and Delta. Delta is happy to sell the puts because they are “natural buyers” of oil via jet fuel (Delta also owns a refinery!)
This is a great example of markets doing their job. A risk that could be diversified was paired off between natural counterparties. However, from another perspective, this is bad news for investors who expected to earn the “sell expensive puts” risk premium. If a risk premium exists but it diversifies another party’s exposure, then that party can afford to pay more for it than the standard speculator. So the efficient frontier for speculators is just the set of investments that contain systemic risks that cannot be hedged.
The most obvious example is the equity risk premium in general — the corporate world is levered to financial growth. Corporations are owned by people in the population. Once all risks are netted, there is no stakeholder remaining who benefits from economic collapse. Therefore the only carrot to entice someone to invest in corporations, effectively doubling down on their reliance on economic growth, is a yield in excess of the risk-free rate. That’s an undiversifiable risk premium.

Select links and excerpts on Diversification


Select links and excerpts on Risk Neutral Probabilities


Select links and excerpts on Bet Sizing

Finally, I wrote a post about risk just before Covid that has the fingerprints of this type of theoretical thinking found in this post all over it.
Can you spot the thinking? I think the risk still persists.