Cost of equity question

So let me state my understanding and you guys can tell me where I'm wrong. Cost of equity is used to calculate the cost of bearing systematic risk - the implicit assumption is the rational investor will have diversified away all idiosyncratic risk. Systematic risk can take numerous forms (aka factors), but most practitioners keep it simple and use market risk via the CAPM as the sole measure of systematic risk (let's ignore F-F and other multi factor models for now). Let's imagine a company that manufactures cardboard boxes. The performance of this company is likely highly correlated with performance of the overall market, and thus we can assume has a beta of circa 1. Assume risk free rate of 2%, market risk premium of 7%, and you can estimate a cost of equity of 9%.

Now, imagine a company that is working on developing a new drug. There is a 50% chance the drug works, and the company is valuable, and a 50% chance the drug fails and the company is worthless. The outcome of the drug's success is entirely independent of the performance of the broader equity markets, and therefore I'd think the beta should be somewhere between 0 and 1 (theoretically should be zero as there shouldn't be any covariance with the broader market, but think in practice it would be probably around 0.5 or so just given real world dynamics). Let's just say it's 0.5 for sake of argument. So cost of equity using CAPM would be 5.5%.

Now in theory I guess this makes sense - companies with lower systematic risk should have lower cost of capital. But in practice I think ventures with binary outcomes not correlated with broader markets would typically attract much more expensive capital (e.g., VC) vs. mature companies that rise and fall with the broader market. So how do you explain this? Is it that the ability to actually diversify away the idiosyncratic risk falls down in practice?


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Comments (16)

Feb 4, 2020 - 1:13pm

Wait - aren't you getting the beta and implied Ke from the comps? Which in this case would be a set of single-drug candidate pharma companies? You'll probably find that the beta is >1, because the volatility in securities with binary outcomes is usually very high, much higher than that of the broad market.

Feb 4, 2020 - 1:28pm

I think that's where I disagree with you. Take a step back and think more theoretically/academically than real world. In this example, the risk that the company fails to produce a successful drug is entirely idiosyncratic. It can be (in theory) entirely diversified away by holding a large portfolio of similar assets with the exact same risk profile (so instead of holding one company with value of 100 if drug successful, 0 if drug fails, you hold a basket of companies with same expected value (50) but with 100% probability of achieving that value (i.e., you have diversified away all the idiosyncratic risk). The beta should therefore, in theory, be zero and reflective of absolutely no covariance with the market (although I understand there are technical dynamics in real world that couldmake binary outcome pharma stocks higher beta). Note that if you actually look at beta of historical venture capital indexes, they're lower than 1 (and that makes intuitive sense - why would there be a strong correlation of VC outcomes with broader equity market performance?).

I think the reason, in practice, that high idiosyncratic risk opportunities command high costs of capital, is because most investors are not actually able to diversify away that idiosyncratic risk as easily as the academic example suggests. Thoughts?

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Feb 5, 2020 - 1:48pm

I think the reason, in practice, that high idiosyncratic risk opportunities command high costs of capital, is because most investors are not actually able to diversify away that idiosyncratic risk as easily as the academic example suggests. Thoughts?

Agreed. I would point to two assumptions:

1) When we talk about being able to totally diversify away any idiosyncratic risk, we assume that there's a perfect supply of other non-correlated opportunities with which to diversify.

I can put $100 on black at the roulette table a thousand times. Each individual bet has a binary outcome, but after 1000 bets its very unlikely that I'll skew too far from the theoretical expected value. But can we really assume, in practice, that I have a 1000 opportunities to invest in different companies with no correlation to the market or each other? In practice investment opportunities are finite, so we cannot assume infinite opportunity to diversify every idiosyncrasy.

2) We assume investors are rational. They aren't.

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Feb 4, 2020 - 1:53pm

I'm probably not following you, or understanding what you're valuing and why. But Beta only tells you how much the equity (or comparable equities) swing(s) relative to the broad market. The fact that your security is totally non-correlated to the market doesn't make it stable, i.e. a beta of zero.
Again I'm probably missing something, but if you told a prospective investor in a single-candidate biotech stock that its theoretical beta is zero because market movements are irrelevant to the share price, you'd be right on the second count but wrong on the first, and someone would probably point out to you that the historical (not theoretical) betas of comparable companies are significantly >1.

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Feb 4, 2020 - 10:24pm

Why would the company's performance have a positive covariance with the performance of the broader equity markets? Don't think about this so practically (again I understand, in reality, it would have a beta of greater than zero and very possibly greater than 1) but in theory, beta is a proxy for systematic risk, of which this theoretical company has none (the drug's development and future sales has nothing to do with broader economy, for argument's sake). Appreciate your thoughtful responses btw

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Feb 4, 2020 - 11:48pm

I don't think I follow either. In general (at least from what I've seen), the larger, stable, mature companies have a beta between 0 - 1, while riskier companies have a beta of greater than 1 (both of these ideas are also intuitive, as the greater your beta, the higher the discount rate and therefore the riskier the investment). Why would a drug company, which is extremely dependent on the success of this one drug as you say (which is a lot of risk) be considered less risky (on a cost of equity basis) than the market?

Feb 5, 2020 - 7:32am

Beta is just a factor load that when applied to a factor is an attempt to measure systematic risk. More specifically, in the CAPM, beta measures the covariance of an asset's returns with the returns of the broader market. This is, in essence, a shortcut to approximating systematic risk.

The asset I outlined does not have any systematic risk. It has only idiosyncratic risk, which as I explained above, can be entirely diversified away. Investors are not compensated for idiosyncratic risk - only systematic risk.

I am glad you point out the biotech sector beta is 1.4 - that is getting to my exact point and question. Because it seems to me, despite academic theory telling us this company should have low/no systematic risk and therefore low/zero beta, this is not the case in the real world. And I think the reason for that is the assumption that investors can effectively diversify away idiosyncratic risk exists only in textbook-land, but it is in practice almost never easy to accomplish.

Feb 6, 2020 - 12:24pm

So where you are wrong is your assumption that biotech companies have no systematic risk. Your argument is that a biotech company's potential drug outcome is not correlated with the the performance of the broader equity market. I don't disagree with that -- it's the same as asking what the beta of a lottery ticket is. But that's not the only factor that determines a biotech company's systematic risk. In fact, the systematic risk in biotech companies is quite high because their viability is largely dependent on access to favorable capital markets. For example, a biotech business has a huge reliance on financing to fund its large R&D expense by accessing the capital markets, acquiring R&D through external M&A, etc. These activities are 100% correlated to the broader market, because they are easier to do when the economy is doing well. These are all examples of systematic risks -- not idiosyncratic risks -- that an investor can't diversify away. This is why I originally said that I don't think that you understand what beta is -- based on your response, I think you understand definitionally what beta is, but don't fully understand what systematic risk is.

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Feb 5, 2020 - 8:25am

For some reason it seems like no one here other than you (person who posted this thread) has an actual understanding of what Beta is, so you aren't getting any satisfactory answers. I think Beta is frankly relatively meaningless in binary cases like you've mentioned, and I'd put more weight into probability-weighted expected value.

Feb 5, 2020 - 9:05am

Thanks - felt like I was taking crazy pills in this thread for a minute

So do you agree my conclusion that in practice the assumption that investors can diversify away all idiosyncratic risk falls apart, because it's probably impossible to do so in most cases? Which probably leads to distortion in the beta vs. what you might expect, in theory?

Feb 5, 2020 - 2:05pm

Theoretically, I may buy into your first argument, that the overall systematic risk is lower.

However, the market risk premium is a premium for holding a well-diversified portfolio of stocks, which your one binary biotech stock portfolio isn't, hence the CAPM is insufficient in calculating your true cost of equity due to high unsystematic risk.

In practice there are very few 0 beta stocks, if any. Just because your outcome is binary, does not mean that your stock is. Outflow of liquidity from the market will affect your biotech stock as well, but for the sake of the argument we can keep that out.

I don't know... Yeah. Almost definitely yes.

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