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## Tuesday, April 22, 2014

### risk premium -- clarified

risk premium (rp) is defined as the Expected (excess) return. A RP value is an “expected next-period excess return” (ENPER) number calculated from current data, using specific factors. A RP model specifies those factors and related parameters.

Many people call these factors "risk factors". The idea is, any "factor" that generates excess return must entail a risk. If any investor earns that excess return, then she must be (knowingly/unknowingly) assuming that risk. The Fama/French value factor and size factor are best examples.

Given a time series of historical returns, some people simply take the average as the Expected. But I now feel the context must include an evaluation date i.e. date of observation. Any data known prior to that moment can be used to estimate an Expected return over the following period (like12M). Different people use different models to derive that forward estimate i.e. a prediction. The various estimates create a supply/demand curve for the security. When all the estimates hit a market place, price discovery takes place.

Some simple models (like CAPM) assumes a time-invariant, steady-state/equilibrium expected return. It basically assumes that each year, there's a big noisegen that influences the return of each security. This single noisegen generates the return of the broad "market", and every security is "correlated" with it, measured by its beta. Each individual security's return also has uncertainty in it, so a beta of 0.6 doesn't imply the stock return will be exactly 60% of the market return. Given a historical time series on any security, CAPM simply takes the average return as the unconditional, time-invariant steady-state/equilibrium estimate of the steady-state/equilibrium long-term return.

How do we benchmark 2 steady-state factor models? See other blog posts.

Many models (including the dividend-yield model) produce dynamic estimates, using a recent history of some market data to estimate the next-period return. So how do I use this dynamic estimate to guide my investment decisions? See other posts.

Before I invest, my estimate of that return needs to be quite a bit higher than the riskfree return, and this excess return i.e. the "Risk premium" need to be high enough to compensate for the risk I perceive in this security. Before investing, every investor must feel the extra return is adequate to cover the risk she sees in the security. The only security without "risk premium" is the riskfree bond.