Whereas, lower SPS interprets that the value of R-squared is lower, which reflects more idiosyncratic return volatility and less market wide information (Morck et al., 2000).
Wei and Zhang (2006) explain the possible causes for increased idiosyncratic return volatility overtime in the U.S.
Firms should consider active strategies that seek to protect downside risk and focus on idiosyncratic return
streams within client portfolios, Mercer suggests.
To estimate idiosyncratic volatility, we first estimate a stock's day d idiosyncratic return:
where [D.sub.t-1] is the number of trading days in month t - 1 and [[??].sup.2.sub.d] is the square of our estimate of the day d idiosyncratic return estimated in Equations (1) and (2).
where [r.sub.i,t] is the return on stock i at time t, E([r.sub.i]) is the expected return of stock i unconditioned on time, [M.sub.t] is the value of the market factor that affects all securities at time t, [[beta].sub.i] is the sensitivity of stock i to that factor and [[epsilon].sub.i,t] is the idiosyncratic return of stock i at time t.
where [M.sub.t] is the market factor at time t, [[gamma].sub.i] is the specific firm-level fundamental that exists but cannot be measured under the structure of the return of stock [r.sub.i,t] and [[omega].sub.i] represents the idiosyncratic return under the hypothesis that the model proposed in 6 is the unrestricted model.
In addition, as in Waller, Verdier, and Gardner (2002), these firms receive an idiosyncratic return [epsilon] on investment, which is distributed uniformly over the unit interval, that is, [epsilon] ~ U[0,1].
A firm enters the official market if the payoff in the formal sector is greater than the expected payoff from operating in the shadow economy, that is, if V + [epsilon] - [b.sub.1] - [b.sub.2] [greater than or equal to] [(1 - m) V + [(1 - [alpha]) V] or, if its idiosyncratic return to locating in the formal sector satisfies
Pontiff, 2009, "Idiosyncratic Return
Volatility, Cash Flows, and Product Market Competition," Review of Financial Studies 22, 1149-1177.
The idiosyncratic returns
of each fund are measured using prior year monthly returns and a four-factor model.
PCA factors Equity common -0.026 0 (0.632) (0.0%) Equity 0.004 30 idiosyncratic (0.954) (15.5%) CDS common -0.279 173 (0.000) (89.6%) CDS -0.009 19 idiosyncratic (0.922) (9.8%) Lagged Equity Returns Idiosyncratic Returns
Coefficient Count Signif.