Many estimates of the cost of equity start with a risk-free rate, to which a premium is added purportedly reflecting the riskiness of the equity.
There is no such thing as a risk-free investment and, therefore, no such thing as a risk-free rate.
That may seem like less of a bold claim against the backdrop of sovereign debt haircuts and debt-ceiling debates, but such recent events are not the motivation for this statement.
For something to be risk-free it would have to, in all possible future states of the world, do exactly what you want it to (or, equivalently, its condition would have to be perfectly knowable). At best we can invest at the low end of the risk spectrum but we cannot eliminate it altogether.
Modern portfolio theory (MPT) – which actually isn’t modern – puts forward the idea that risk and standard deviation of returns are synonymous. This is fine in a world that consists only of investable assets and where distributions are known.
That prices move in an unpredictable manner is not, in itself, a risk. If we define risk as the likelihood that you do not get at least what you need, then is clear that MPT only looks at part of what is actually going on.
Insurance companies and pension funds manage their investments in such a way as to minimise the likelihood that they will not be able to pay what they need to pay when they need to pay it. There is no sure-fired way for them to eliminate the likelihood that they will fall short on this goal.
In a similar vein, every investor has some goals or needs – these are more explicit and legally enforced for insurance companies and pension funds but that does not dilute the argument. If something can happen that means the investor may not achieve these goals, then there is risk.
For example, an individual investor who puts money away to finance a future capital purchase, a house for example, does not know how much the desired house will cost at the purchase date. Because forward markets do not exist for every capital (or consumption) good, this risk cannot be hedged.
Investors can, in broad terms, protect their capital against general inflation (as official statistics agencies define it) but there is absolutely no way of protecting against the specific mix of inflation that each investor faces. The risk that inflation erodes and alters purchasing power in unpredictable ways is pervasive and inexorable.
There are factors, other than inflation, that have a similar impact. That these exist and will always exist but in an evolving and unknowable manner, means that we should stop thinking that there is a set of assets that will always do what we want and think instead about how to manage and price the risk accordingly.