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In CAPM, required return is derived from the covariance of a firm's stock with a broad-market index. In an ideal world, this would be based on fundamental relationships between the company and the overall economy. In other words: a company that performs well in a recession would likely see its fundamentals improve when the fundamentals of the entire market are declining; therefore its stock would tend to move inversely with broad-market indices, and it would be valued using a low required rate of return. The opposite would be true for a company that performs poorly during recessions.

Now, think about it as an executive of the company in question. If your required rate of return is "too low", you will likely start investing in many projects. If you keep on increasing investment in real assets, you will need more and more financing. This will cause your company to hold a greater share of broad-market indices (simply due to the fact that you demand more capital, while your per-share value is staying constant). This will inevitably increase your correlation with broad-market indices, which will increase your required rate of return until you reach some equilibrium point. So it's a negative feedback loop. Granted, it is circular, but it does tend towards a fixed point.

 

Correct.

Variances and risk premia are not created equal. Variance needs to be differentiated between bad times and good times. Investors are willing to pay more for assets that do well in bad times. Hence, they require a lower rate of return and thus expected returns of those assets are lower. Safe haven assets like Treasuries even have negative required returns. Vice versa for assets that tank in bad times. 

Buying lottery tickets vs selling lottery tickets. For every investor that requires a low rate of return (buying lottery tickets), there's another investor across the table that requires a high rate of return (selling lottery tickets). Selling lottery tickets generates a steady income and high rates of return in good times, and without a black swan, the limited sample period masks the true risk and creates an illusion of high expected returns, which crowds in investors into those risky assets (selling lottery tickets) and jacks down the expected return. Only when the black swan hits, do we see the real risk of the risky skewed asset. The archetypical strategy of this asset is equity index volatility selling. GFC wiped out more than a decade's worth of profits. (The lottery ticket seller made a lot of money when no one won the lottery, but when someone actually wins, all his profits can be reasonably wiped out.)

Therefore, not all risk premia is rewarded by the market. (E.g., systematic asset beta risk is rewarded, empirical factor risk premia such as value & momentum risk premia is rewarded, however asset standalone risk is not because they can be diversified away)

I'd say risk premium isn't a 'circular concept' per se, but it is ADAPTIVE - investors feed off each other and adjust utility functions accordingly. The old academic theory of CAPM - of constant expected returns and constant risk premia is very outdated and economists have come up with more nuanced views of risk premia. There is also the theory which I mentioned, that risk premium is sort of a 'zero-sum game' analogous to the zero sum game of active management - the pie is fixed, investors divide the pie.

There's also the pain of estimating expected returns and risk premium ex ante. The economist who estimates expected returns wishes for a few hundred more years of data, while the estimator of risk (premium) wishes for more black swans

A difficult and uncertain game, finance, but it's this uncertainty and art that makes it beautiful

 

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