Sticky Luck
Essays on Stock Market Patterns and Expected Returns
Mark O'Reilly, FIA, ASA, MAAA
oreilly
10 Market Strategy
Eleven:
Stick Luck Math
If you like math...
Rik = the (weighted) sale price a buyer/seller k expects at some future outcome i at time t (assumes dividend reinvestment)
pik = k’s estimate of the (weighted) probability of Rik
For each i, Ripi= ∑ DikRikpik over k = all buyers/sellers
Where Dk = weighting of k’s transaction to total transactions
Po= ∑ Ripiv^t for all i, where v=1/(1+I) and I = the risk-free rate of return
In an efficient market, E(Ri1) = Ri0 , and E(pi1) = pi0 for times t=0,1
Therefore, expected return =E([P1-P0]/P0) = I
But also, pi1 = pi0 ∑qj uij for all j, where
uij = the change factor for pi resulting from news item j
qj = the probability of news item j
So E(∑qj uij)= 1 for all i (“fair game”)
In an efficient market, expected and actual uij for large qjmust be close to 1. In the case of small qj, both expected and actual uij can vary greatly
For certain piT, uijT can be highly correlated over T for high qj, especially when p is small (e.g. an emerging market phenomenon)
Mark O'Reilly, FIA, ASA, MAAA
oreilly
