Alternatives to CAPM

At one superday I attended, I was asked this question:
"If we can't calculate CAPM, how can we calculate cost of equity?"
Though it has been almost a year, it lingered on my mind and kept asking myself if I answered it correctly.

So, what are the alternatives to CAPM? The book called Valuation by Mckinsey shows a couple different methods. But in order to understand these methods, you first have to understand that CAPM is really a one-variable prediction model. It basically looks like
y= a+ bx
where
y = cost of equity
a = risk-free rate
b = beta
x = market risk premium

By market risk premium, what we really mean is the historical market excess return with regards to the risk-free rate, which usually is 10-year US Treasury yield.
What this model tells us is that by plugging in the historical excess return, we can estimate cost of equity. Flip it around, it means that cost of equity can be predicted by the historical excess return of the equity market (It's excess because it's calculated as market return - risk-free rate).

What other model points out is that historical return alone can't be the only contributor (or variable) to predicting cost of equity. The question, then, becomes: what other variables are there?

First, you have Fama-French model. It basically takes account into a company size (smaller ones outperform bigger ones) and a P/BV ratio (lower ratios outperform high ratios.)
How do you calculate the variables and coefficients? I decided not to spend too much time on this because 1) you can get these numbers from professional data providers, and 2) it's still not considered a perfect model.

Second, you have Arbitrage Pricing Theory. All that it means is that you basically add all possible variables that affects cost of equity. It's perfect in theory, but the practical issue is 'how do you determine all those variables and how do you measure them?'

Now, I think there can be another way to calculate cost of equity, but it would work best for banks. The bottom line is that you take the average of ROE for the industry. The underlying assumption is same as Dividend Discount Model, where the company pays out all excess earnings as dividends.

Money Market

One thing that had never been clear to me was how Fed's control over the interest rate actually works.  I have always wondered which interest rate they were talking about, and how they actually execute a change in the interest rate.

First of all, "interest rate" here refers to Fed Funds Market interest rate. It is basically an interbank interest rate within Fed, where financial institutions are required to deposit a reserve. It is similar to LIBOR, but the major difference is that Fed Funds Rate is targeted by a government entity Fed (specifically Federal Open Market Committee), whereas LIBOR is determined by the free market of supply-demand.

Why is this rate important? To begin with, there are several ways a bank can borrow money from the government; fed funds market and treasury bills, which account for "government loans to banks" with the duration of less than one year. While this treasury bills are sold through an auction (some through non-competitive bids, but mostly competitive bids), their demand and its corresponding yield will be influenced, or determined, by fed funds rate. Subsequently, as the treasury bills rate changes, the yield for treasury notes and bonds changes accordingly, based on the yield curve.

How is this yield curve determined? I remember learning this in an Econ class, but I have to revisit and fully understand the mechanics of it. One thing to note is that this would probably have an indirect impact on a bank's own yield curve model, and therefore Net Interest Margin and earnings.