Wednesday, July 20, 2011

Will the Real Capital Asset Pricing Model Please Stand Up? – Part One

Part of the Treasury and Finance role is to help our companies come up with its cost of capital, which is a technical term for “how much do you want to make on your investments?” This of course needs have major caveat added: “within reason”.
I would love to make 100% on my investments, but that is not a very likely outcome for some investments, and merely impossible for others. So while I might like to make that much, it is not a realistic number to target.
The Capital Asset Pricing Model (CAPM) is one of the classic methods to determine cost of capital, and it enjoys wide-spread academic and corporate application. There are those who say it is wrong and not applicable, and they are probably right, but we use the tools we have, and this is one of the better ones.
The first step is to determine your cost of equity through the following equation:
                       re = Be x rp + rf
Where,
           re  = the cost of equity capital, what we are solving for,
           Be = Beta of the equity, which is how much equity risk is shared by the market, or how much
                   risk is caused by the market,
           rp = the risk premium investors expect to receive over the risk free rate to take on equity
                  market risk,
           rf = the risk free rate, what you can earn in the market if you invest in something 100% safe.
There is a whole host of possibilities for calculating beta, which is the amount of risk equity shares with the market. First question is: what is the market? From the purely theoretical, the market is supposed to contain the entire universe of potential investment alternatives.
However, there are a lot of categories of investment that are not readily measurable in terms of periodic returns: private equity, venture capital, a lot of real estate, some bonds, commodities, etc. Usually a US based stock index considered broad enough to constitute “the market” is used as a proxy for this total universe of investment alternatives, but even there a choice has to be made.
For the sake of simplicity, let’s say there are three to choose from, some version of the S&P, the NYSE, or the Russell. This is the first choice involved.
The second choice has to do with the calculation method. Beta is measured by using linear regression (you can get fancier here if you want, but we won’t in this blog) of the equity’s returns vs. the market. Which return do we use? Daily, weekly, or monthly? And over what time period do we perform this regression? One year, Two years, Five years?
We have so far covered one factor in this equation, and we already have 27 potential combinations (three indices  times three return periods times three time horizons), assuming that we restrict ourselves to the choices mentioned (of course, in real life we do not have to do that so there are even more than 27  combinations, but this is a blog and we need to end this in a reasonable amount of time).
The second factor is the risk premium, the amount investors expect to receive from an equity investment vs. a risk-free one. The key word here is “expect”. This is really not measurable. Even if you surveyed investors about this you probably wouldn’t get a true answer – what we actually expect vs. what we say we want will vary. Because it involves expectation, there is also a probability distribution involved – if we get $1 for heads and nothing for tails, we “expect” $0.50, but behavioral finance tells us that we humans have flawed perceptions of gain vs. loss. In a situation such as this one, where equity is not as simple as a coin flip, where all outcomes are not known vs. known, are we confident that investor expectations attribute the correct probability of a 75% market decline, or a 75% market increase?
One approach to solving this puzzle is to assume that what investor’s have gotten in the past is what they will expect in the future. However, we have already discussed how outcomes are not necessarily a good determinant of the decision we face.
Another approach is to use something that exists as a proxy. This “something” can be lots of different things, investment analyst’s growth forecasts, cubic spline analysis of yield curve steepness, volatility-smile analysis of option prices.
For the sake of simplicity in our example, we will assume the two extremes – historical experience vs. market proxy. So our 27 alternatives now grows to 54.
The final term in the above – risk-free rate – is also not entirely free from debate. What investment is truly risk-free? None. The closest people agree on is US Treasuries (though we will see if that is still the case come August 2nd or thereabouts!). Even if we agree on US Treasuries, should we look at short-term (90 days, 1 year) or long-term (10-year +) as the appropriate measure. There are arguments both ways.
Again, simplifying matters to a choice of the two extremes (short-term vs. long-term) for the risk-free rate, our 54 scenarios has now grown to 108.
Unfortunately, we are not done yet. Look for a future blog to cover where we go from here.
I would love to hear your thoughts about this view of cost of capital or your stories on this topic if you have them.
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