Why do we use CAPM for cost of equity?

Beta measures the systematic risk of a company, but when we are acquiring a company, would we not also be taking on the firms unsystematic risk? If so, would this not prove the CAPM to be useless? Relatively new to learning all this so just trying to piece everything together.

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You take into account unsystematic risk by adjusting your cash flow projections for the company. Roughly speaking a company is the sum of its expected cashflow discounted, hence in the numerator (expected cashflow) you adjust for idiosyncratic events or unsystematic risk, for example a company has a 50% chance of giving 100, and 50% chance of going bust and giving 0, hence in your model free cash flow for this year will be 50, and in the denominator (discount rate) you take into systematic risk, typically using CAPM methodology

 

This answer is technically so wrong that I’m just amazed someone could even write this. The numerator of a DCF is an expected cashflow, but that doesn’t reflect “unsystematic risk”. If your expected cashlow is $50, the numerator is $50, and it’s the same $50 irrespective of probability distribution of that cashflow. In other words, you still use $50 irrespective of whether it’s 50% probability of $60 and 50% probability of $40, or 10% probability of $500 and 90% probability of $0.

 
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Yes, CAPM assumes company-specific risks are diversified away. Therefore, in the CAPM, the investor is only compensated for systematic risk. There are other models that address systematic and unsystematic risk - Fama and French Three Factor Model is one of them.

 
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Forgot to mention the “MD” model where they just tell you to change the discount rate to whatever number they think will achieve the desired EV on the football field

 

This is the right answer.

More generally speaking, the return on assets in excess of a risk-free rate is a compensation for bearing risks. If a risk can be diversified away (i.e. it’s idiosyncratic), then an investor won’t get compensation for it.

So let me give you an example. Imagine there’s a company A that you want to buy the stock, and the stock is very volatile. Let’s just say the company is a casino, and the volatility is because of the risk that someone gets the jackpot. So I’m making it very idiosyncratic as you can see. So you think “price should be low so my return is high and I get compensated for the risk”.

Now, imagine that there are entire other 100 companies, all of them identical (and uncorrelated) to company A. So other Casinos.

Someone could buy 1/100 of each Casino and have no idiosyncratic risk. So that investor would be willing to pay more than what you would be willing to pay if you are buying 100%. So you’d get priced out. And more generally, any rational investor would bid the prices so there’s no arbitrage opportunities.

On equilibrium, prices are such that returns only reflect those risks you can’t diversify away.

That’s all theory, and assumes asset returns are normally distributed (so only mean and variance matters).

In practice, CAPM fails miserably to explain asset prices, and that’s why there are more “factors” that people use empirically and that frankly have little to no justification (e.g. size, value, country risk, etc.) other than the fact that there’s some statistical correlation with returns and that there’s some story we can tell ourselves around why those factors are non-diversifiable.

But the principle of not getting compensated for idiosyncratic risk still applies. Even in an M&A context - there are plenty of PE firms with highly diversified portfolios, etc etc etc.

 

An investor not getting compensation for idiosyncratic risk does not mean such events do not still impact the valuation, they do. E.g. coinflip with 50% chance of success (100 payoff), other one with 20% chance of success. In both case the discount rate is 0% (outcome has 0 correlation with market returns), assume only one period

The valuation of the first coin is 50, the second is 20, in both cases the expected return for the investor is 0, yet the valuation is different. This difference is purely driven by idiosyncratic risk, and we adjusted for it in the "numerator"

If you do not agree/do not understand the above I am happy to do some coin flipping with you and arbitrage your bank account away...

 

Because CAPM assumes that you are not compensated for unsystematic risk. Assume that you actually were compensated for unsystematic risk. To make it very simple, let's say that companies with a high unsystematic risk give a return of 15% and companies with no unsystematic risk give a return of 10%. In that case, you could just buy many companies with high unsystematic risk and thereby diversify away the risk. As a result, you receive a return of 15% with minimal risk given that you diversified it away. If this was possible, no one would want to own the companies with a return of 10%, right? 

 

Good question. You're correct that intuitively it doesn't make sense. Beta indeed accounts for systematic risk, but understand that it's a sort of "one size fits all" variable, which due to math elegancy and simplification allows you to apply a standardised discounting profile to similar assets within a class/industry so that you can assess risk premia easier. Idiosyncratic risk is purely firm/special situation specific - material lawsuit, CxO/Founder quitting amidst a crisis, fraud/misrep, insolvency (to a much lesser extent, as one could argue it is somewhat industry-driven and a derivative of default probability, which in itself is formulaic) etc. None of these can be elegantly measured in a "one size fits all" variable. Thus, a reasonable way to account for this risk type is to leave yourself a "margin of safety" as coined by Seth Klarman - paying x% off fair value (however you define / arrive at your estimate of it). However, clearly this implies that YOU as an investor are not compensated for it, i.e. you have to leave yourself room to be wrong AND if you ARE wrong, it’s solely on you, i.e. don’t have a false expectation that the CAPM risk premia “fully” decribes your outcome set (incl. idiosyncratic risk).

 

Will add that CAPM can be held up in a court of law if and when the target sues - I’m sure there are better ways to calculate CoE but CAPM is the most defensible.

 

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