Static Risk Premiums in Equity

Expected vs Realized Excess Returns:

• Expected risk premiums ($E[r_t] - r_f$) differ from average realized excess returns ($\bar{r_t} - r_f$) and studies show that the latter is a poor predictor of the former.
• Reason: expected returns are time-varying and realized excess returns are strongly affected by unexpected price movements.

Does CAPM explain expected returns?

• CAPM fails to explain why low beta stocks outperform high beta stocks
• Historical data produce inaccurate estimates of forward-looking betas. When using option data to extract CAPM betas, the Buss and Vilkov (2012, RFS) find a positive relationship between average excess returns and beta.
• Recent research also finds that using high-frequency data to calculate CAPM betas leads to a positive Security Market Line and drives out the significance of Fama-French's value and size factor.

Extracting Expected (Static) Equity Premium via Valuation Methods

The Gordon growth model is described as follows:

$$ E[r_i] -r_f = \frac{D^i}{P^i} + g^i $$

where $g^i$ is the expected dividend growth, $D^i$ is the dividend, and $P^i$ is the price of the stock.

So, if asset $i$ has currently a dividend yield ($\dfrac{D^i}{P^i}$) of 5% and an expected dividend growth rate of 2%, the model implied equity risk premium would be 7%.

Static Bond Premium

• The bond risk premium in the government bond market is also called the term premium.
• It is the difference between the return of long-duration (long-maturity) bonds and that of short-duration (short-maturity) bonds.
• The slope of the yield curve (Bond Yields vs Bond Maturities) is a noisy signal for the bond premium, because it consists of two parts: (i) the change in the expected path of future short-term interest rates and (ii) the actual bond premium.

Static Credit Premium